A percentage is literally any number divided by 100.
You can calculate the 90% of 200 as 20090/100 or 2000.9
However, I don't see the improvemnent. Dividing or multiplying by 100 (or any power of ten for the matter) is the easiest operation besides doing it by 1.
ChenChow · 11 points · Posted at 14:30:06 on February 14, 2016 · (Permalink)
In California we only pay 8.5% in sales tax but on the flip side we also have to okay $2400+9.3% tax on all income above $50k. (There are actually even higher brackets going up to 13.3% above $1M)
[deleted] · 1 points · Posted at 21:38:46 on February 16, 2016 · (Permalink)
[deleted]
ScottLux · 1 points · Posted at 17:06:10 on February 17, 2016 · (Permalink)*
That number was just California. I pay close to 50% marginal tax rates while making about ~60% more than the median income in my county. 13.6% payroll taxes (half paid by your employer, though arguably should still be counted as a lot of people are self employed and it's money that would otherwise go in your pocket), 9.4% state income tax, 28% federal income tax
I used the numbers I had lying around (from the halving and doubling). 1.625 is the last number of the halving / doubling steps, and .065 is the first (6.5, shifted 2 places).
Which is 26% of 6,5. Which is 52% of 3,25. Which is 104% of 1,625.
I was computing 104% of 1.625, so I took 1.625 as 100% of 1.625, and 6.5 as 400% of 1.625 (that was two halving steps earlier, so it was 400%). Shift that to the right 2 places and it becomes .065 (4% of 1.625).
Are you fucking kidding me? This is why I love Maths. All these years learning and learning and something so simple and useful escapes me.
Smaktat · 7 points · Posted at 14:45:20 on February 14, 2016 · (Permalink)
Gotta figure stuff like this out yourself. If you feel as if you're capable at that, then you're probably capable of much more advanced math depending on how fast you can find the patterns.
But Reddit was created by and is based out of America. It was "born" here, you might say, which means it's "American".
db0255 · 1 points · Posted at 04:53:43 on February 15, 2016 · (Permalink)
DAGNABBIT. The Internets were founded in America, by Americans, for Americans, and it's well known the center of if it is somewhere off the coast of Kansas. It's the most Americanest thing there is up there with moms, apple pie, hot dogs, blue jeans, and Budweiser beer!!!!
The weirdest part is that we say "mathematics" (plural) when referring to the field as a whole, but only ever use "math" (singular) when referring to a given class or branch of said field. Go figure.
Get it? Go "figure" when talking about math(s)! I'll begoingnow...
w675 · 2 points · Posted at 15:20:55 on February 14, 2016 · (Permalink)
This isn't really a good way to think about it.
If you consider the term Mathematics as plural, it should be implied that there is a singular version of the same word - Mathematic. Have you ever heard anyone say the word Mathematic?
That's my point entirely :/ The term "maths" (i.e. mathematics) is more correct, but nonetheless rarely used in America despite being so.
Reading comprehension. It's a good thing ;)
w675 · 3 points · Posted at 15:32:51 on February 14, 2016 · (Permalink)
No, you're thinking in terms of plural and singular which is incorrect in this situation. Think of my above comment as a proof by contradiction, if you will.
The word math is a shorter form of the word mathematics. The word mathematics is not a plural word, so why on earth would you carry the s to the shortened version? It's nonsensical.
Reading comprehension is definitely a great... um, thing. You should give it a shot.
Wrong again. The term "mathematic(s)" refers to several fields/branches/disciplines that involve numbers and other quantitative values. It's not a singular practice or branch of study. As such, it's quite appropriate to use the plural form even in an abbreviated form, which is why so many people do so.
w675 · 5 points · Posted at 15:53:37 on February 14, 2016 · (Permalink)
I'll just let /u/Davis660's comment from this thread take over from here.
Speaking as a brit who says Maths, math is the correct way. "Mathematics" isn't actually a plural word, it comes from the Greek "Mathematica", in Greek an 'a' at the end of a word sometimes denotes a plural much like an 's' does in English. In this case it didn't but it was carried over between languages and so we have "Mathematics"
So "Math" is correct, but I will always say "Maths" because it's so ingrained in me.
Speaking as a brit who says Maths, math is the correct way. "Mathematics" isn't actually a plural word, it comes from the Greek "Mathematica", in Greek an 'a' at the end of a word sometimes denotes a plural much like an 's' does in English. In this case it didn't but it was carried over between languages and so we have "Mathematics"
So "Math" is correct, but I will always say "Maths" because it's so ingrained in me.
However, the internationally agreed on spelling and pronunciation of that metal that Americans say wrong is actually "Aluminium". So you win some you lose some.
You can also multiply the price and percentage and divide by 100 like this:
2x50/100 = 1
I find it easier to use for calculating tip. For example, if your bill rounds up to 30$ and you want to give 15% tip, for either 15% of 30$ or 30% of 15$ you will need a moment to calculate it in your head but
(30x15)/100
or
(3x15)/10
is pretty easy to do.
You can also try with 12% of 70$, 6% of 25$, 62% of 5$ or even 13% of 13$.
pomlife · 9 points · Posted at 17:20:49 on February 14, 2016 · (Permalink)
If I needed to find 15% of $30, I'd just find 10% ($3.00), then half that ($1.50) and add them together ($4.50).
The easiest way is often that if we have ab% of x (where ab is a 2 digit number and a is the multiple ten and b is the unit) then we have a×(x/10) + b×(x/100). Since 0 <= a,b < 10 this is not hard.
At a restaurant my group got a 20% discount for late food.
They gave us the group check with 20% off.
We kindly asked for separate checks...
Writer said management couldn't allow that because it was a larger discount...
mvp725 · 26 points · Posted at 13:21:16 on February 14, 2016 · (Permalink)
Haha I've been the waiter in this situation where the customers think they're getting one over on us. "We've got a 10% off coupon, can you split our checks so we get 20%"
Oh OK, so we're agreeing. Not sure why I thought the post was saying that management was RIGHT in thinking that splitting checks was a greater discount.
Oh yea haha no they were incredibly dim on the subject. We argued until it wasn't worth it and accepted our new 10% discounts for our individual checks.
Sorry I was just showing that even if the checks were drastically different the discount is the same as oppose to if they were split evenly.
This is bullshit! I have a minor in math. This doesn't mean I'm an expert, but I'm better at math than most people I know. And I've never heard of this simple, perfect fact. That is a crime.
w675 · 3 points · Posted at 15:28:39 on February 14, 2016 · (Permalink)
If you've heard about the commutative property when dealing with multiplication, then you've heard of this fact.
While this is a nice fact, and surely makes it sometimes easier... unfortunately try 7% of 193. :) but hey - 50% of 2 is indeed easier than 2% of 50!
Edit: For the people which think that this won't work on 7% of 193 (ofcourse it will!)... do it from your head without the assistance of calculators in any form or shape.
nukem2k5 · 10 points · Posted at 13:18:04 on February 14, 2016 · (Permalink)
Well it's fairly easy either way, unless you need an exact number. 193% ~= 200%, so 2x7=14, but you know the number is actually a little less (by 7% of 7, which is a little less than 0.7 (i.e. 10% of 7). So roughly 13.5?
This isnt as helpful as it sounds. Calculating those easy examples can also be done without this trick and much effort in the traditional way. When it comes to something like 13% of 77, that formula would make you calculate 77% of 13. Not very useful.
zazu2006 · -5 points · Posted at 13:14:15 on February 14, 2016 · (Permalink)
If by cool you mean like one of the most basic properties of math...
If you have a rope long enough to wrap exactly around the equator of the Earth, you only need to add 6.3 meters of rope for for it to be able to hover 1 meter off the ground.
Scientific notation is usually used in situations like that to make sure the ready can quickly identify the magnitude of the number, and so it can be more easily rounded later on.
makes sense. like when you deal with numbers in the 107 range and addition of 1 will make very insignificant change to the actual calculations of that number compared to the number
If it were an unbreakable unbendable solid then it would, then you could give it an infinite amount of momentum in a direction and have it decapitate everyone on earth! it's flawlesss!!!
NSGDX1 · 1 points · Posted at 08:20:46 on February 14, 2016 · (Permalink)
If it were an unbreakable unbendable solid
You won't be able to add the 6.3m piece in the end then. If it were a normal rope then some X part of the rop will not be in contact and it will travel like a wave forever, even without infinite momentum.
Also, you won't be able to give the ring that much momentum so it moves. And since gravity isn't same everywhere it would bend(or start vibrating at least).
Pretty much every assumption about this scenario is physically impossible, but this is all irrelevant. None of the issues you're raising contribute to or detract from the concept that appears confusing.
NSGDX1 · 1 points · Posted at 08:43:11 on February 14, 2016 · (Permalink)
Kogasa pls
t-- · 1 points · Posted at 10:45:23 on February 14, 2016 · (Permalink)
[deleted] · 1 points · Posted at 21:15:34 on February 14, 2016 · (Permalink)*
Derp. Can't believe no one else noticed that yet. I was sitting there trying to remember chain rule and I thought if c=pi r2 then dc would = 2 pi r dr and couldn't figure out why that wasn't lining up..that's because that's the formula for area haha..I was tired and drunk when I wrote that.
t-- · 1 points · Posted at 10:43:50 on February 14, 2016 · (Permalink)
I think he means the magic of how its going to hover 1 meter off the ground.
I'm assuming it has something to do with gravity waves.
The ratio of Diameter to Circumference is a fixed ratio of 1 : pi. So to increase the diameter by 2 meters (1 meter off each side) you need to increase the circumference by 2pi.
Yea the relatively small amount of length added to add 1 meter around the whole earth seems surprising. Of course to add 1 meter more radius around a tennis ball or the sun you'd add 6.3 metres of rope. Or if you could rope the whole milky way just add 6.3 more metres to give a metre more space around the whole thing.. . Etcetc
...I wanna get a lot of rope and see this in action.
Fuck you Saturn, we made out OWN ring!
kbtrpm · 2 points · Posted at 13:59:46 on February 14, 2016 · (Permalink)
Likewise, if you have a rope long enough to wrap exactly around a tennis ball, you only need to add 6.3 meters of rope to be able to hover 1 meter off the surface of the tennis ball.
[deleted] · 1 points · Posted at 08:08:25 on February 14, 2016 · (Permalink)
A circle of radius 1m has a circumference of 2pi metres. 2pi is approximately equal to 6.3. If the radius is increased by 1m, the circumference is increased by about 6.3m.
Folamh3 · 1 points · Posted at 11:43:32 on February 14, 2016 · (Permalink)
I'm sure this makes sense, but I'm having a hard time believing it.
Basically the idea here is that adding circumference to anything is a LINEAR task that only cares about the percentage of the curve you're wrapping around and how much bigger you want to go. It could be around a beach ball or a curve down interstate 70.
How is the Dyson sphere not more stable than a ring? Wouldn't gravity be a nonfactor in the sphere? In the case of a ring, if it was only slightly off center the ring would come crashing down. But if the Dyson sphere were off center it wouldn't start accelerating towards the planet.
It would, but at a slightly lesser rate because the average distance changes less(iirc the acceleration would be 2/3 that of a ringworld). Rigid Dyson spheres have unstable orbits, but if there were some sort of mesh that countered for collisions it could be stable
Can someone math this? I really wanna know how this all works out now. I'm now invested in know how this all works for sure. I thought I knew but now I'm just learning more new things.
Both the shell theorem and equivalently Gauss' law prove that no acceleration due to gravity would be present inside a Dyson shell due to the shell itself.
It's the same reason the electric field inside a conducting ball is zero.
You're very right about Gauss' law, but it's only true for a point mass/sphere in the center, no? Earth is an oblate spherical but the sun is almost perfectly spherical, so this matters more for ringworld than Dyson spheres. In any case, even if it isn't unstable it also isn't stable. Imagine a meteor crashing into it or solar pressure gradually pushing it. Gravity will have a net zero effect on it so it won't correct and will still crash. Good catch though
You're very right about Gauss' law, but it's only true for a point mass/sphere in the center, no?
Nope! That's the neat thing about it. For a spherical shell, the potential is constant inside. Therefore there is zero gradient of the field, and consequently there is zero force due to gravity (or electrical charge) inside from the shell no matter where you are.
Now there may be other things inside the shell, such as other people, or a star, or whatever, and you will have gravitational attraction to those things, but not to the shell itself.
Fantastic question! Yes, it only applies to inverse square laws like gravity and electrostatics.
verifiy · 1623 points · Posted at 21:40:32 on February 13, 2016 · (Permalink)
You know the quadratic formula? Well there is also one for 3rd order polynomials and another on for 4th order polynomials. however, there isn't one for any higher order polynomials, and there can't be.
Nettius2 · 1310 points · Posted at 02:34:47 on February 14, 2016 · (Permalink)
And those formulas are DISGUSTING.
pikaras · 1177 points · Posted at 05:08:56 on February 14, 2016 · (Permalink)*
For those who didn't know, the equasions 3rd order polynomials ax3 + bx2 + cx + d = x =
I wonder if there's some alternative conception for it, that presents it in an extremely simple way.
bliow · 11 points · Posted at 06:52:27 on February 14, 2016 · (Permalink)
There are patterns to it. You define some intermediate quantities based on a, b, c, d, and e, and use them to make the overall formula simpler to express. You'll see this at https://en.wikipedia.org/wiki/Quartic_function#General_formula_for_roots - there is an initial formula for the four roots x1, x2, x3, x4 that is not too much worse than the quadratic formula. But then you notice it's not defined just in terms of a through e, there are this weird S and p and q you don't remember seeing. And the definitions of S, p, and q end up having more complexity... but there are these recurring patterns that they label as Delta_0 (delta is the triangle on that page) and Delta_1 and Q.
That's also the trick used by /u/pikaras above to write the cubic in less space.
The direct formulas are bad, not only due to their length, but also because you'd have to recompute certain quantities over and over. If you break them down, things get better.
It gets better if you precompute quantities like
2b3 - 9abc + 27c2 + 27a2 d - 72bd, which appears 12 times per equation.
Call it s and the value within most of the roots simplify to
-4(b2 - 3ac + 12d)3 + s2 ; if that's negative, there are no r values.
There are only 3 places where the 4 "r" formulas are different, and these are different signs. The next step is to compute the still somewhat big terms which are the same, and finally to piece them together using the different signs. If you do that, g is the part starting with 1/2 and about one third of the formula, h is about the middle third, and j is the rightmost 1/4 of the formula, and the final step is:
r1 = -a/4 - g - 1/2 sqrt(h-j),
r2 = -a/4 - g + 1/2 sqrt(h-j),
r3 = -a/4 + g - 1/2 sqrt(h+j),
r4 = -a/4 + g + 1/2 sqrt(h+j).
Also, you check if h<j, because r1 and r2 don't exist if it is.
ok how the HELL does someone come up with that? There are variables in the solution that aren't in the equation it solves. I've always loved math, or at least the idea of it. It's beautiful. But I can't understand a damned thing and it drives me crazy. I feel like there's a key and if I were to just find it, it would all make sense.
bliow · 5 points · Posted at 07:40:07 on February 14, 2016 · (Permalink)
There are variables in the solution that aren't in the equation it solves.
which? r1, r2, r3, and r4 are just names for the 4 different solutions.
not just one key. infinitely many. each key unlocks a different door. behind this door are other doors and the reward for opening a door is that you see more locked doors before you. (you are in a maze of twisty little passages, all alike?)
[deleted] · 1 points · Posted at 09:52:58 on February 14, 2016 · (Permalink)
r1, r2, r3, and r4 are just names for the 4 different solutions.
Indeed. You can call them x1, x2, x3 and x4 if you prefer.
If there are fewer solutions, you'll end up with roots of negative numbers, so some of the r's won't compute, or possibly with some roots = 0, so in the edge cases, some r's will come out equal.
Believe it or not, my high school was out in the middle of nowhere, pretty much. Literally, looking around in a 360° angle, all you see is corn.. it was awful.
I stared at this image on my phone for a solid minute thinking "this isn't all that bad" before realizing my phone screen was only showing like the first fifth of it.
RAFCRA · 1 points · Posted at 10:26:37 on February 14, 2016 · (Permalink)
can i just ask why does this stuff matter? like what does it get used for?
bliow · 1 points · Posted at 10:10:26 on February 15, 2016 · (Permalink)
Mostly it just gets waved around like "look how awful this is". And usually it is served up as a side dish to the main mindfuck, which is "oh by the way, the higher order polynomials, starting with quintics x5, are LITERALLY IMPOSSIBLE to write down formulas for" not because the formulas would be too big to be practical, but because they can't exist at all, which is a complete mindfuck and requires a fair bit of study to really understand.
It is used for several things according to wikipedia, but giving a laundry list of how it's used is sort of answering the question wrong. The real answer is more like, lots of things result in polynomials (like the quadratic or the quartic), and so solving these equations where the highest term is x4 tells us things about how polynomials work in general (and those are really everywhere).
Also there are powerful ways of calculating the answers to within many decimal places without touching that god-awful formula.
I tried using that formula in a graphics assignment to draw a torus. (a doughnut like shape).
It was viewable from one side and didn't have a shadow... I checked it even like 5 times. Needless to say, I learned that they are horrible pieces of work.
Colopty · 1 points · Posted at 12:38:26 on February 14, 2016 · (Permalink)
Close: you've got it confused with The distance equation/pythagorean theorem: a2 + b2 = c2. That one is nice, and can keep going forever (into time travel or extra spacial dimensions or whatever (read Flatland if you want that to make sense; it's just 100 pages and very accessible)). You just add a variable: a2 + b2 + c2 ...= z2 where a through y are how far you went in directions a through y, and z is the total distance.
These fuckers are to find a curve's roots (zeros, places where the curve touches/crosses the x axis). The one everyone learned is if x is squared plus some shit, the next if its cubed, errand you can't do it if it's x5.
Source: am math major, want to get rid of shit online math homework
[deleted] · 1 points · Posted at 06:37:21 on February 14, 2016 · (Permalink)
as an engineer, that looks delightful. no wronskians, laplace transforms, or other bullshit. just a simple formula that can be programmed by most any programming language in a few minutes.
jwaldo · 7 points · Posted at 06:52:28 on February 14, 2016 · (Permalink)
When I was young, I was horrified by math. When I was in high school, my teachers taught me to appreciate and respect it. Now though I realize I was right to fear math, that the fear comes from the innate knowledge that equations like this lurk all around us...
rawling · 7 points · Posted at 08:18:29 on February 14, 2016 · (Permalink)
[deleted] · 1 points · Posted at 10:10:02 on February 14, 2016 · (Permalink)
Did someone prove these just to show that they can or is there any advantage to using these rather than solving higher order polynomials numerically (like a normal person)?
pikaras · 1 points · Posted at 19:22:45 on February 14, 2016 · (Permalink)
There used to be math competitions and one of the challenges would would be to factor fourth order polynomials without rational roots. In the 16th century, someone figured it out but kept it secret so he could keep winning. (At least that's the story my math teacher told us)
[deleted] · 1 points · Posted at 19:51:03 on February 14, 2016 · (Permalink)
Haha brilliant. Thanks for that
[deleted] · 1 points · Posted at 10:11:00 on February 14, 2016 · (Permalink)
Mathematician here. Cannot confirm, I've never felt the need to use it. Besides, there's no fucking way I'm going to check that.
Ahn complex polynom formulas. At college I'd always try what is my favorite curiosity to reduce them.
If the sum of the coeficients are equal to 0 the number 1 is a roots. Like
X2+2x-3=0
1+2-3=0 1 is a root
Find the root of a big polynom and divide it to make a smaller one.
Gotta miss my diferencial equations classes, soo many math tricks to resolve integers and shit
Ps: Sorry if there is any math-word wrong not a native speaker
I'm just sitting over here going, "Negative Beeeeeeeeeeee Negative Beeeeeeeeeeeeeeeee.... plus-or-minus the squareroot, plus-or-minus the squareroot..."
The one that relates the sum of products of the roots of the polynomial to its coefficients. In quadratics (ax2 + bx + c) that is
b = -(x1+x2)/a
c = x1*x2/a
[deleted] · 97 points · Posted at 06:33:18 on February 14, 2016 · (Permalink)*
Understanding why is the final result of a year-long graduate-level mathematics course I am currently trying to slog through. It has to do with miniature algebra-things called Galois Groups, and whether they are what's called "solvable". In assuming that there could be a generalized solution to the quintic, you can likely generate a contradiction.
Ph0X · 15 points · Posted at 22:05:18 on February 15, 2016 · (Permalink)
Fun factoid (you might've been told by your teacher).
Galois, who basically started that whole sub branch of mathematics, died at the age of 20 in a duel for a girls love.
He developed a whole branch of math before the age of 20... can you imagine what kind of things he would've achieved if he had lived to 40-50?
[deleted] · 14 points · Posted at 23:10:58 on February 15, 2016 · (Permalink)
Not only that, but he had it mostly in his head and stayed up all night before the duel, scribbling it out for posterity's sake. May have contributed to being slow on the draw.
Joined in attempts at revolution, died for "love", solidified an entire branch of mathematics, and still didn't live out his potential. Here I am at 25 and I can't not masturbate.
Bobius · 43 points · Posted at 08:23:47 on February 14, 2016 · (Permalink)
Or an 8 week course at Cambridge!
At week 4 our lecturer said something along the lines of "and this is where I'd stop if this were any other university."
Why is this downvoted? Cambridge undergrad maths includes Galois Theory. This is part of postgrad maths elsewhere. Frankly I say good on them for having the highest standards, but also it might fry my brain if I attempted it.
Log2 · 4 points · Posted at 23:15:50 on February 14, 2016 · (Permalink)
Mostly because it is not as uncommon as he makes it sound. Personally, I've never met anyone that graduated in pure math that didn't study Galois theory.
Log2 · 3 points · Posted at 23:14:27 on February 14, 2016 · (Permalink)
I had Galois theory as a part of an algebra course, and this was in Brazil. I'm pretty sure that Galois theory is a standard undergrad subject to cover in any math undergrad course in any decent university.
Well, yeah and maybe at Oxford too. Obviously at a top uni for maths (like Warwick) it's not unexpected, I didn't say "elsewhere" to mean "everywhere else".
[deleted] · 3 points · Posted at 18:17:35 on February 14, 2016 · (Permalink)
The year-long course at my university is the full elementary abstract algebra sequence: One quarter each of groups, rings, and fields. It culminates at the end of the year with Galois theory. If you want to assert that students are raised in eight weeks' time from group axioms to the proof of the general non-solvability of the quintic, then I would be very impressed.
Bobius · 1 points · Posted at 18:19:38 on February 14, 2016 · (Permalink)
Groups was an 8 week 1st year course for us, GRM (groups, Rings and Modules) was 8 weeks of 2nd year, Galois Theory was 8 weeks of 3rd year.
[deleted] · 3 points · Posted at 18:29:00 on February 14, 2016 · (Permalink)
Then our algebra sequences are identical up to isomorphism.
[deleted] · 1 points · Posted at 20:04:31 on February 14, 2016 · (Permalink)
Or one term of a frosh course at Caltech!
Those poor frosh, polynomials suck. Algebra used to seem cool, but it's got nothing on topology and logic
There are no freshman courses at Caltech that include Galois theory.
Galois theory is covered in the third term of Ma 5, which is a sophomore course for math majors (and anything from sophomore to senior for people who are not math majors who want to take introductory abstract algebra for fun).
Ma 5 has no prerequisites so intheory one might be able to take it as a freshman, but in practice that would be very hard to arrange because freshman at Caltech have a full schedule of required core courses. It would be hard to get one's advisor to approve taking Ma 5 as a freshman. Furthermore, since freshman are not expected to be in Ma 5 there is no attempt to schedule it to avoid conflicting with required freshman courses, further reducing the chances that one could convince one's advisor to allow one to take it.
[deleted] · 1 points · Posted at 21:07:48 on February 14, 2016 · (Permalink)*
Most people I know in Ma5 are frosh. Every math major I can think of that I know, besides those that switched into math after frosh year, took Ma5 as a frosh. Take that for what you will, it's possible my sample is weirdly skewed, but I don't think so.
But independent of my sample, it's absolutely not hard to get an adviser to let you do that
The proof of this fact is very involved, but essentially it ties the solutions of polynomials to the ability to decompose a certain group into a chain of groups whose factors are all abelian.
It's very complicated. In general, roots of polynomials are exchangeable. If one has the polynomial x2 - 2 = 0, it is has two solutions, sqrt(2) and -sqrt(2). If one would would swap sqrt(2) and -sqrt(2), nobody would notice this, because the only connection to the numbers that you already had, is through the polynomial x2 - 2 = 0. Since x is squared in the polynomial,
the sign disappears.
As a general rule, you can see from the way in which solutions can be exchanged, what is the polynomial that defines them.
If you have a general 5-th degree polynomial, then its solutions are exchangeable by all permutations of 5 numbers. If you want a closed form for these solutions, you need to show that they can also be obtained through a sequence of simple roots, which are polynomials of a restricted form xp - c = 0. It has been shown that, using only such polynomials, one can never get the full permutation group of five objects. Essentially, the solutions of a polynomial xp - c can be exchanged only in a circular way.
Note that I simplified quite a lot. The general theory is called 'Galois Theory'.
Kered13 · 4 points · Posted at 14:31:32 on February 14, 2016 · (Permalink)
While it's by no means a complete proof, that's a remarkably simple and intuitive (for the nature of the problem) sketch! I spent several hours reading the Wikipedia article on Galois theory a couple weeks ago trying to get the vaguest grasp of how the proof went and got nowhere.
Is there any significance as to WHY 5th order polynomials aren't solvable? As in, why can 4th order polynomials be solved when 5th order can't? What changes in mathematics that this suddenly doesn't work anymore? From my very basic understanding I had assumed that most mathematics "just scale". As in "if it's possible to do something in previous instances, with more thought, it should be possible to do in other instances".
Also I'm a bit confused: Has it been proven that 5th order polynomials are impossible to solve generally? Or has it been proven that you can't generally solve quintic functions but some are solvable?
Is this the kind of thing where there's a hard limit to the maths or is this the kind of point in time where we would need another (yet unthought of) conceptualisation of mathematics and numbers in order to solve the problem? Like how we needed irrational numbers to explain sqrt(2) or imaginary numbers to have negative roots?
Sorry for the long text but these questions have been in my uneducated mind for quite some time.
The general 5th order polynomial is unsolvabe: There is no closed formula, using only radicals, that solves Ax5 + Bx4 + Cx3 + Dx2 + Ex + F = 0.
Some concrete 5th order polynomials are unsolvable, e.g. x5 - 6x + 3 = 0.
Others have trivial solutions, e.g. (x-3)(x+2)(x-1)(x+8)(x+5) = 0.
The roots of a 4-th degree polynomial can be permuted in 24 ways. It is a smaller group, and it is still simple enough to be composable into a sequence of cyclic groups. The reasons are a bit technical, but it is still possible.
It is clear that all polynomials have solutions in the complex plane, it is just that some of these solutions cannot be expressed using clean radicals.
That's just a matter of mathematical elegance. Radicals are kind of nice because they represent the solutions of the simplest possible polynomials. Of course in applications, one can always solve the equation numerically.
I really need to revisit that proof. When I took abstract algebra it was the last thing we covered, and I think I understood it like 75%, but now I'm back to being baffled.
[deleted] · 13 points · Posted at 02:50:57 on February 14, 2016 · (Permalink)
Check out the book Fearless Symmetry by Ash and Gross. It's the only book I've ever read that clearly explains Galois theory (and a pretty good outline of the proof of Fermat's Last Theorem) in a way that doesn't require graduate-level abstract algebra.
[deleted] · 15 points · Posted at 02:56:49 on February 14, 2016 · (Permalink)
It's funny that in my country we learn the quadratic formula as the Bhaskara formula (after its discoverer), but that doesn't seem to be the case in the US.
Waniou · 13 points · Posted at 05:59:06 on February 14, 2016 · (Permalink)
My maths teacher taught it to me as "big grunter" because he thought it was big and grunty.
No, that's sounds normal for a math teacher. My geometry teacher always referred to circles as hellagons.
Waniou · 1 points · Posted at 01:27:04 on February 15, 2016 · (Permalink)
He also made several bad jokes, some of which, I legitimately don't know how he never got fired for. These included "Did you hear about the two bad apples? Too bad!" and "If ice gives you icicles, what do tests give you?"
I just started watching this documentary on Netflix, called Maths. One of the things they talk about is there are indications that this universal truth of "a2 + b2 = C2" had been discovered, or at least brush up against by several people/cultures over time, because they are fundamental laws, regardless of counting systems, etc.
They also mentioned that Pythagoras believed reality was directly made of whole numbers and ratios. When Hippasus pointed out that the number which represents the length of a hypotenuse in a right triangle whose sides have length of 1 basically breaks this idea (the square root of 2 is an irrational number), the follower was killed.
db0255 · 2 points · Posted at 10:48:35 on February 14, 2016 · (Permalink)
The pythagorean theorem comes up a lot in the Ancient world before Pythagoras. There were civilizations that understood and used it. The PROOF of the general equation, however, didnt come about until Pythagoras.
[deleted] · 2 points · Posted at 06:41:44 on February 14, 2016 · (Permalink)
This may not be why, but there is a respectably large movement in US math to allot what are considered "useful" names to concepts, rather than naming them after the mathematicians or anything else colorful. I get it in some cases, but there's a few folks who don't even want to call things "pathological" because it's supposedly biasing.
OMG this. I love Galois Theory. Also I really like mathematical results--how would I put it--that before being versed in the field may seem rather arbitrary. Like this, there are linear, quadratic, cubic, and quartic formulas, but no other power. Why? We develop a theory that can reduce certain field theory to group theory problems. The properties of symetry groups can then be used to prove that there is no higher power formula. I'm glossing a little bit, but I really enjoy these sorts of results.
Does this not prove that P =/= NP? You're saying there is no algorithm for finding the roots of a 5th order polynomial, so it is not in P, however given the roots it is trivial to check that they are correct, so it is in NP.
This result shows that you can't in general describe the solution for polynomial equation in a way that is significantly better than decimal expansion.
If roots are given as (potentially infinite) decimal expansion, then it takes an infinite amount of time to check that the answer fits.
Not sure can't is the right word. Using a series of approximation formulae and expansions, we can get a 5th order equation + o(.) where o(.) just denotes a negligible component.
[deleted] · 1 points · Posted at 04:30:07 on February 15, 2016 · (Permalink)
Almost only counts in horseshoes and compact spaces!
Do you know why there are no such formula for the 5th order? I've not been able find a good initiative explanation of why. It seems a bit like saying there's no solution to x2 = -1, but its turned out to be pretty useful just define i := √-1
Furthermore Galois discovered this and the formulas for quartics and solveable quintics the night before he died. He stayed up all night writing down everything he was working on and things that just occurred to him into a letter which he posted to a friend and then went straight off to fight a duel at dawn. He lost the duel and was killed.
ggeoff · 1 points · Posted at 21:59:52 on February 14, 2016 · (Permalink)
Is there an eli5 proof for why there can't be?
ectish · 1 points · Posted at 02:42:20 on February 15, 2016 · (Permalink)
The quadratic formula can be sung to the tune of Gilligan's Island and also to Pop Goes the Weasel.
There's a lot more digits so it's not really accurate, just accurate enough. In my first year of college we had to use 3.1415 or the professor would mark it.
Whether it's "accurate enough" depends entirely on what you plan on doing with the results.
High school math: accurate enough.
Wood working: probably accurate enough.
Fine machining: probably accurate enough.
Astrophysics: not even close to close enough.
Archack · 3 points · Posted at 15:49:09 on February 14, 2016 · (Permalink)
Pi is approximately 22/7, just like it's approximately 3.14. If the diameter of a circle is rational, then the circumference must be irrational, and vice versa. Or they both could be irrational. Cool stuff!
I suppose, when I was first taught it when I was 12, the teacher didn't want to complicate matters.
The funny thing is that I've now taken maths up to second year university, using pi many many times in many many calculations but have never had the occasion to question that original piece of misinformation.
Pi can be calculated by doing the following series.
Pi can be calculated by doing the following infinite series.
(4/1) - (4/3)+(4/5)-(4/7)+(4/9)...
You keep doing that indefinitely, it doesn't mean you cant express it as a ratio of integers, it's that there is no pattern of integers than can difine the number in a finite solution
gratz · 110 points · Posted at 01:05:55 on February 14, 2016 · (Permalink)
Somebody please explain this to me
[deleted] · 398 points · Posted at 01:17:39 on February 14, 2016 · (Permalink)*
irrational = cannot be a whole number ratio - that is, cannot represented as a fraction of two integers, like 1/2 or 53/26. You can't write pi as a fraction* because a circle with a whole-number radius doesn't have a rational circumference.
* a fraction of two rational numbers, anyway. Technically, pi can be written as a continued fraction, or something like
π/1 like /u/Autumn_Thunder pointed out.
Edit: Apparently I have no fucking idea what I'm doing. Just scroll down for a better analysis.
[deleted] · 264 points · Posted at 05:22:38 on February 14, 2016 · (Permalink)
Irrational = cannot be ratio of whole numbers.
Pi = ratio of circumference to diameter.
Ratio of circumference to diameter = cannot be ratio of whole numbers.
Therefore, Pi is irrational.
But this is circular. Your definition implies that a rational number is a number that can be expressed as a fraction with two rational numbers, and you can't use a word to define itself in this way.
However all rational numbers can be expressed as fractions with two integers, which renders this step unnecessary
I mostly agree, but you (and very many other people) make it sound like it's always bad to use a word in its definition. Sometimes a recursive definition is the only way to define something.
A list is an element and a list, where the smallest list is the empty list. A tree is a node and a list of trees (the roots of its children). An addition expression is a pair of smaller addition expressions that we will later add.
Well, I'm not sure if these really support your point. A list isn't what you're describing - a list is just an ordered collection of elements. What you're describing is how we actually implement a linked list, which can still be thought of iteratively (a collection of nodes, each of which points to the next). A tree can be defined mathematically as a minimally connected graph, etc. But I see what you're saying. Recursive definitions can be very useful.
I wasn't trying to define the mathematical notion of either tree or list, because minimally connected graph isn't exactly a good definition either ;) I was defining and naming the recursive structure in one go. Like you said, though, the goal was to provide an intuition about the concept.
A tree is a directed acyclic graph where each node has exactly one parent. This is why it is useful to think of trees as recursive structures. A minimally connected graph can form an X shape where to sources point to a convergence node, which jumps out to 2 sinks, and so you may not be able apply the exact same algorithm across each node.
Hmm, I see. I would consider that more of a specific type of tree, I guess a rooted tree. I remember learning DAGs as a different structure. But I'm not sure.
All this means is that at most one of the circumference or diameter is a natural number.
Edit: As splergel pointed out, integer is more correct than natural number, when defining rational numbers.
Edit 2: As klod42 pointed out, radius and circumference are both non-negative, so I feel smart for changing it back to how it was originally.
[deleted] · 29 points · Posted at 01:56:31 on February 14, 2016 · (Permalink)
What it actually means is that the definition posted above is wrong. An irrational number is one that cannot be written as a ratio between two integers. And if the radius (or circumference) of a circle is an integer, it follows from the definition of pi that the other one isn't. So there's no contradiction.
What it actually means is that the definition posted above is wrong. An irrational number is one that cannot be written as a ratio between two integers.
More generally it means an irrational number is one that cannot be written as the ratio of 2 numbers where neither is irrational since you can always turn a rational number into an integer.
I think I see what you're saying, that even if the circumference was an integer, the ratio would still be 2 irrational numbers.
Unfortunately that's not what defines an irrational number. Just because 1 ratio is only irrational numbers does not mean there is no ratio which includes only integers (and integers all have the same rational value [integer]/1)
minimim · 2 points · Posted at 04:29:10 on February 14, 2016 · (Permalink)
How do you get negative measurements?
klod42 · 2 points · Posted at 10:56:04 on February 14, 2016 · (Permalink)
How is integer more correct? Circumference and diameter have to be positive. If anything, natural number is more precise.
You are right. The way I phrased it initially, I said a non-natural number, where non-integer would have been more correct.
I was staring directly at the definition of rational number, and the way I was looking at it, considered any negative fraction as not a rational number, which was wrong.
We just don't have to worry about it negative numbers for this case.
What he said is slightly wrong. Irrational means 'cannot be a ratio of two integers'. You cannot possibly find a circle whose diameter and circumference are perfectly integer values (not that is makes sense for natural measurements to have such precise values, but anyway..)
kohbo · 9 points · Posted at 01:16:25 on February 14, 2016 · (Permalink)
I'm no mathematician, but the pi normally used is rounded for simplicity. The constant pi is never ending and can't be expressed as a ratio of two whole numbers.
The answer on stack exchange gives a good way to think about it. Since pi is a never ending number how would you ever express pi in terms of 314159265.../1000000000.... (you can't!)
The other answers have it actually, though I think you learned something by doing some research here. A rational number means a ratio of two numbers, but specifically the ratio of two integers (where the denominator is not zero). Pi is geometrically defined as the ratio of the circumference and diameter of the circle, but both of these cannot simultaneously be integers.
Slightly OT: not only is pi irrational, but it is also transcendental, meaning it can never be a zero for a polynomial with rational coefficients. Proving this finally resolved the "squaring the circle" problem of antiquity.
Correct. Squaring the circle means that you would need to construct a line of length proportional to pi, using just straight edge and compass, which is impossible if pi can never be the result of an algebraic equation.
seantme · 1 points · Posted at 07:22:26 on February 14, 2016 · (Permalink)
Being pedantic (although when isn't maths pedantic), 1/3 is a never ending number. It can't be expressed by xyz.../100... yet it is definitely rational. It's a stronger thing to say that it has to be a decimal that doesn't repeat to infinity. Whether it is a never ending number is not really useful either, and even 1/10 could be written as a repeating decimal, although it would be a trivial one.
Ltbsd · 1 points · Posted at 09:11:15 on February 14, 2016 · (Permalink)
1 and 3 are both integers already, so "1/3" is a ratio of integers --> rational number
Anything you can write as a fraction is a rational number. EDIT: using integers
A fraction is essentially a ratio.
Rational numbers "end" (terminate and result in endless zeroes, like 1/8 is 0.12500000...), or they repeat (like 1/3 is 0.3333333...). Even numbers like 1/97 repeat eventually (it's a 96 digit sequence).
Numbers which cannot be expressed as a fraction are irrational numbers. Things like pi, e, sqrt(2), the golden ratio, and so on. You can make up fractions that are really CLOSE to the right value (22/7 famously for pi, etc) but you can't make a fraction that's exactly right.
jimmery · 2 points · Posted at 05:34:30 on February 14, 2016 · (Permalink)
It's not, because it's incorrect (mainly the first line). You can write irrational numbers as fractions, if you use other irrational numbers. An obvious example would be sqrt(2) = 2/sqrt(2). Or Pi=Pi/1.
One actual definition of rational numbers is "any number that can be written as a fraction of two integers".
But if the diameter of a circle is a rational number, then the circumference will be irrational because you are multiplying a rational number by an irrational one, so pi is not a ratio of two rational numbers
mkap26 · 1 points · Posted at 05:05:08 on February 14, 2016 · (Permalink)
But those are variables, not constants. Pi cannot be expressed as the ratio of any 2 constant values.
As in "cannot be the ratio of two rational numbers" for example, with a radius of 2 you have a circumference of 4 Pi an irrational number. A rational number could be defined as "can be described as the ratio of two other rational numbers"
More specifically it means it cannot be expressed as the ratio of two whole numbers.
Simpae · 1 points · Posted at 07:59:41 on February 14, 2016 · (Permalink)
Is this not because the Formula is using the assumtion that the in the ratio the circle is split into multiple ever smaller triangles with a base that approaching 0?
But we've used circular mathematics for so long that we define the circumference in terms of pi and the diameter.
Se314en · 1 points · Posted at 10:09:12 on February 14, 2016 · (Permalink)
The point is, in a true circle, either the diameter, or the circumference (or possibly both) must be irrational numbers. So whilst pi is given by circumference/diameter, this 'ratio' cannot be written as one rational number divided by another.
Bruntaz · 1 points · Posted at 10:23:53 on February 14, 2016 · (Permalink)
But either the diameter or circumference (or both) must be irrational so the ratio isn't between 2 integers
g5pw · 1 points · Posted at 10:28:09 on February 14, 2016 · (Permalink)
Ratio between integers. In this case, either the circumference or diameter must be irrational.
zeekar · 1 points · Posted at 10:54:40 on February 14, 2016 · (Permalink)
A rational number is a ratio of integers. So the fact that pi is irrational means that no matter what length unit you pick, the circumference and diameter can never both be whole numbers of that unit.
zwat · 1 points · Posted at 11:24:14 on February 14, 2016 · (Permalink)
More precisely, an irrational number can't be expressed as a ratio of integers. Therefore pi can't be rational, because both the diameter and the circumference can't be integers at the same time.
ktikp · 1 points · Posted at 11:40:53 on February 14, 2016 · (Permalink)
A rational number, more precisely, is a number which can be expressed as the a ratio of two INTEGERS (where of course, the denominator is not 0).
Because the definition of rational number is a number that can be expressed as p/q where both p and q are integers. Given any circle you'll never have both the diameter and the circumference to be integers.
Pi is not only irrational, but also transcendental. That means it cannot be expressed with any (finite) combination of algebraic operations done on algebraic numbers. Or alternatively, you cannot reduce it to zero using algebraic operations.
For example, something like square root of two is irrational, but it's not transcendent because you can represent it algebraically (√2, or 2½) and it's simple to reduce it to zero ( (√2)2 - 2 = 0 ).
Transcendental numbers - or at least some of the known ones like pi, e, or the golden ratio - can be expressed with infinite series, but not much else.
Ackmar · 1 points · Posted at 22:38:31 on February 14, 2016 · (Permalink)
On my phone, so I can't see other replies. But this means that if the diameter is rational then the circumference is irrational and visa versa. Pi still can't be represented as a ratio of whole numbers.
But the diameter and circumference cannot both be rational also. So while it is true pi can be expressed as the ratio of circumference and diameter, the ratio consists of irrational numbers, meaning itself is also irrational.
The diameter and circumference of a circle cannot both be rational numbers. A ratio of an irrational number to a rational number is still irrational in this case.
Not how ratio is defined. There is no fraction for Pi.
[deleted] · 10 points · Posted at 02:35:29 on February 14, 2016 · (Permalink)
Which is also why numbers that are ratios of integers are called the rational numbers. The symbol that represents this set of numbers is Q, which stands for "quotient"; the result you get when you take the ratio of two integers.
[deleted] · 15 points · Posted at 01:54:01 on February 14, 2016 · (Permalink)
The actual definition is "cannot be written as a ratio between two integers".
The discovery of irrational numbers was actually one of the most monumental steps forward in human thinking. You could very well argue that it gave birth to philosophy as we know it.
You see, before its discovery, numbers were thought to be rational. Meaning from reason, numbers were thought to be a construct that we came up with to describe the state of the world. That is to mean, we came up with numbers in order to make sense of world.
So then what are fractions? Well again, they were numbers that describes something in the world. For example, 1/3 of an apple, despite being 0.3333 recurring, accurately describes the state of an apple that was cut into a third. The important thing here is that these fractions, no matter how complex, are simple ratios. A massive ratio like 12345/98765, might describe the amount of mass coming off a mountain in a land slide. For the ancients, all ratios were rational - they were things that we made up to describe something with rationality and reason.
So what does this mean? Well, a fraction that was not a ratio couldn't exist. Such things did not exist in the world, and such a number would literally make no sense.
And so, the discovery of the irrational number was a massive paradigm shift. Not only did it change everything we knew about mathematics, but it also changed the way we thought about the universe and the fundamental questions of existence.
The existence of an irrational number (a fraction that is not a ratio, that is to say, you could never get to it by dividing a bigger number by a smaller number) meant that numbers could not have been a human construct. An irrational number does not describe anything in the world, it simply is! If there is nothing in the world that corresponds with the number (in the sense that 1/3 corresponds with an apple that was cut into a third), why then would we think up such a number? It would make no sense, it's existence was irrational, and hence the name.
The impact of this discovery opened up our eyes to the abstracts of the universe. From this, we knew that there were numbers that were removed from human rationality, they were the very fabric of existence. For example, the number pi is the keystone to a circle/sphere/cylinder/cone etc. Without it, we could not make calculations of these shapes. We could approximate it, but without the discovery of it, we could never approach the essence of it. These numbers could not be invented by the human mind, they could only be discovered, because they have always existed as part of the universe.
This opened up a door to a plane of existence that we have never known before - the plane of the abstract. It showed us that there existed things that had no physical manifestation. it is with this key progress in human thinking that Plato would come up with his concept of Forms. It is why there came about cults that worshipped these numbers as if they were God. The entire philosophical field of ontology (the study of being and existence) was birthed, and it allowed the millennia of human thinking of the abstract that followed to get us to where we are today.
All of this was because of the discovery of the irrational number.
mungd · 1 points · Posted at 07:56:05 on February 14, 2016 · (Permalink)
sqrt(2) is irrational but sqrt(2)/1 is a ratio. to be precise, it cannot be a ratio of integers.
Gee_Eem · 2 points · Posted at 02:00:47 on February 14, 2016 · (Permalink)
"Ratio" is "reason" in Latin, so irrational numbers are unreasonable numbers.
[deleted] · 7 points · Posted at 02:34:26 on February 14, 2016 · (Permalink)
Reverse causality; "ratio-" in latin more means to account for or judge. Our usage of the world "irrational" as in "can't be argued with" stems from the analogy of argument as a "weighing of sides" to determine a balance. So if someone can't be reasoned or argued with, they are irrational.
Related is the fact that "argue" is sometimes used to denote putting a number somewhere into a ratio.
[deleted] · 1 points · Posted at 04:02:42 on February 14, 2016 · (Permalink)
That's a very useful etymological snippet. Why do they not teach that? I always felt like mathematicians were accusing the numbers of being thoughtless and unreliable, a bunch of hippie-numbers that refuse to behave logically.
drac07 · 1 points · Posted at 12:39:02 on February 14, 2016 · (Permalink)
In fact, "irrational" has the meaning it does in common usage because of how irrational numbers were thought to be illogical - and not the other way round.
This introduced me to the world of math and science (I was 13 at the time, only reading science fiction before then) and it is one of my favorite books. I've purchased it multiple time for myself and others. It was the first book in a series of hundreds of books about math and physics that I've purchased since then.
I cannot recommend this book enough if you have even the slightest interest in math and how the modern world as we know it has been shaped because of it.
This is a copy/paste of the list I gave to another. Enjoy!
Math:
The Nothing That Is, by Robert Kaplan - Another book about zero and its history throughout the ages.
Infinity, by Brian Clegg - What's the opposite of zero? This is written much in the same vein as Zero, being a math history book of sorts that's trying to reach a broad audience with a dense subject matter.
The Golden Ratio, by Mario Livio - We've done nothing and everything, but what's in between? This book, again, is a layman's journey through the history of a specific number: Phi. Where we discovered it, how we apply it, and why it's constantly popping up in nature, manufactured or otherwise.
Prime Obsession, by John Derbyshire - This book title explains exactly what happened to me shortly after being introduced to Zero. I have an embarrassing amount of books written on the subject, but this is one of the best to approach the subject in a broad manner. For a more math heavy version, look no further than...
The Music of the Primes, by Marcus du Sautoy - Have some pencil and paper ready, just in case ;)
The Man Who Loved Only Numbers, by Paul Hoffman - Tired of numbers? Let's learn of a man who never would have considered that a possibility. This book revolves around the life and accomplishments of the mathematician Paul Erdos. He was an interesting character, to say the least.
Physics:
The Elegant Universe, by Brian Greene - Jumping to the physics side of things, this serves as an excellent introduction to both relative and quantum theory. While the book is of considerable length, it is, to me, on par with anything Stephen Hawking has written (side recommendation: read anything Hawking has written).
God's Equation, by Amir Aczel - This book is about Einstein and his "greatest blunder", the cosmological constant. It is part math, part astronomy, part history. I also started this section with this book because almost anything written by Amir Aczel is a joy to read. Such as...
Entanglement, by Amir Aczel - If you're unfamiliar with the term, it's a phenomenon that occurs when two particles are "entangled" and thus behave together at the same time. The real fun part about this is that these two particles will enter the same quantum state, regardless of distance (I'm also painting with an extremely, laughably large brush here. Any person reading this who is halfway knowledgeable in the realm of quantum mechanics must surely be furiously typing up a response at tachyon speeds).
Introducing: Time - This is actually a part of a series called "Introducing", which covers a large swath of topics, from physics to philosophy. This one in particular tackles "time" as we know it and what it means to, well, everything. Does time still tick by if a universe is in a completely static state? This, and other paradoxical questions are covered in this book. It's also illustrated, for dummies like me.
A Short History of Nearly Everything, by Bill Bryson - This is a fun romp through the ages of man, from when he flicked his first flint for fire, to when he placed the first foot of extraterrestrial soil. It covers math, science, and all things in between, but never bogging down in any one particular category. He is another author I'd recommend you could pick up anything with his name on it and enjoy.
Sorry for the late response, but here's some of my favorites (tried to do a good split between math and physics):
Math:
The Nothing That Is, by Robert Kaplan - Another book about zero and its history throughout the ages.
Infinity, by Brian Clegg - What's the opposite of zero? This is written much in the same vein as Zero, being a math history book of sorts that's trying to reach a broad audience with a dense subject matter.
The Golden Ratio, by Mario Livio - We've done nothing and everything, but what's in between? This book, again, is a layman's journey through the history of a specific number: Phi. Where we discovered it, how we apply it, and why it's constantly popping up in nature, manufactured or otherwise.
Prime Obsession, by John Derbyshire - This book title explains exactly what happened to me shortly after being introduced to Zero. I have an embarrassing amount of books written on the subject, but this is one of the best to approach the subject in a broad manner. For a more math heavy version, look no further than...
The Music of the Primes, by Marcus du Sautoy - Have some pencil and paper ready, just in case ;)
The Man Who Loved Only Numbers, by Paul Hoffman - Tired of numbers? Let's learn of a man who never would have considered that a possibility. This book revolves around the life and accomplishments of the mathematician Paul Erdos. He was an interesting character, to say the least.
Physics:
The Elegant Universe, by Brian Greene - Jumping to the physics side of things, this serves as an excellent introduction to both relative and quantum theory. While the book is of considerable length, it is, to me, on par with anything Stephen Hawking has written (side recommendation: read anything Hawking has written).
God's Equation, by Amir Aczel - This book is about Einstein and his "greatest blunder", the cosmological constant. It is part math, part astronomy, part history. I also started this section with this book because almost anything written by Amir Aczel is a joy to read. Such as...
Entanglement, by Amir Aczel - If you're unfamiliar with the term, it's a phenomenon that occurs when two particles are "entangled" and thus behave together at the same time. The real fun part about this is that these two particles will enter the same quantum state, regardless of distance (I'm also painting with an extremely, laughably large brush here. Any person reading this who is halfway knowledgeable in the realm of quantum mechanics must surely be furiously typing up a response at tachyon speeds).
Introducing: Time - This is actually a part of a series called "Introducing", which covers a large swath of topics, from physics to philosophy. This one in particular tackles "time" as we know it and what it means to, well, everything. Does time still tick by if a universe is in a completely static state? This, and other paradoxical questions are covered in this book. It's also illustrated, for dummies like me.
A Short History of Nearly Everything, by Bill Bryson - This is a fun romp through the ages of man, from when he flicked his first flint for fire, to when he placed the first foot of extraterrestrial soil. It covers math, science, and all things in between, but never bogging down in any one particular category. He is another author I'd recommend you could pick up anything with his name on it and enjoy.
Ok, well hopefully this is something to get you started. I don't expect you to enjoy all of them (or any of them, really), but if you found Zero even passably interesting, then one of the above is bound to tickle your curiosity in one way or another. Have fun!
I have read The Man who Loves only Numbers, LOVED IT, read it many times, Paul Erdos is my hero.
I have read Infinity and Nothing that is.
Some of these books are hard to find digitally for free, but libgen has been serving me well :)
Thank you for you sharing, I look forward to read most of these !
Yes! I actually have 2 books on Erdos, but this one was more enjoyable.
Yes, I'm not sure how easy it will be to find these, but I definitely think some are worth the entry price of $10-$15. I have an entire wall of books ready to turn into a fire hazard at a moment's notice, haha.
I found all but one online and now they are resting peacefully with 30,000 others on my iPad. I had thousands of books but slowly trading them in for cash as I build and hoard a bigger digital library :)
Yeah, I've been slowly converting my library to digital as a just in case. Anything new I've bought in the last 5 years has been digital, but some old things are just hard to find in digital or just flat out do not exist.
971365 · 1 points · Posted at 13:43:21 on February 14, 2016 · (Permalink)
+1
Would love to get some recommendations
Philoso4 · 11 points · Posted at 03:28:38 on February 14, 2016 · (Permalink)
I remember taking a philosophy class where the teacher was talking about the mathematical concept of limits, or something like that. He was trying to blow our minds, so I asked the question, "was zero an accepted concept at the time?" Because I happened to have just read that book. He responded that the question was getting in over my head. It was the most annoying cop out I've ever experienced, you can't blow a mind that has already been blown.
By Pareto principle alone Reddit is more than 80% complete and utter fucktards. By in large it's a freebooting site for entertainment and porn. I don't think I've ever met anyone here with more than two brain cells.
That was a neat article, but what did that have to do with the man's murder? It didn't tie the irrationality of the square root of 2 back to the guy who was thrown overboard
ngwoo · 36 points · Posted at 00:20:10 on February 14, 2016 · (Permalink)
People didn't like hearing that something as simple as the diagonal of a square couldn't be represented by a whole number because it challenged their view that the universe was orderly and perfectly crafted.
The first guy proved mathematically, that irrational numbers exist, and the people that wanted a world of only rational numbers were so upset, they responded by throwing him into the sea and letting him drown.
Dubaku · 19 points · Posted at 02:02:10 on February 14, 2016 · (Permalink)
This is almost certainly a made up story. The square root of two wasn't even the first known irrational. The Pythagoreans knew that the ratio of lengths between near corners and far corners of a pentagram was irrational before they knew sqrt(2) was irrational. The myth persists because the method is an easy way to introduce young math students to proofs, and because of the "told ya so" nature of the story.
Do you have a source? Not disagreeing, I just find the pythagoreans fascinating (most people forget that they were seriously a cult and secret society, with practices like banning the eating of beans or celebrating music for its mathematical nature) so I'd like to read more about it.
There's not a direct source for the tale being untrue but there is no reason to trust it given the evidence cited above. Ancient philosophical biographers didn't treat historical fact with the same reverence that we do today and happily invented all sorts of events in the lives of their subjects in order to emphasise their philosophical theories in a literary manner. Once a good illustrative story gets made up it then gets passed around the other biographers without real concern for whether it is literally true. Another good example is the claim in the biographies that Heraclitus died after burying himself in horseshit because he thought the warmth would drive out his cold. This is an attempt to illustrate his theory that fire is the principle of everything rather than the sort of historical report we can trust. More obviously ahistorical are the reports that Plato was visited by Apollo in the form of a 'bee epiphany' when bees landed on Plato's lips as a baby, indicating his future ability to write 'honeyed words'.
[deleted] · 3 points · Posted at 02:07:42 on February 14, 2016 · (Permalink)
After spending the longest time considering whether or not to publish his proof, he realized it was only a rational risk to take, and decided to do so.
[deleted] · -1 points · Posted at 00:54:09 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 11 points · Posted at 01:02:28 on February 14, 2016 · (Permalink)
No it's not.
[deleted] · -4 points · Posted at 01:37:13 on February 14, 2016 · (Permalink)
[deleted] · 1 points · Posted at 03:07:01 on February 14, 2016 · (Permalink)
Sincerely hope you're joking. "Imaginary" numbers are anything but (It's an awful name) and have some profound and stirringly beautiful properties. I chose one as my response to this thread.
I like how that article just throws out a proof by contradiction that took me like 4 hours to figure out when I was taking analysis. Good to know it had already been done 2600 years ago, hah.
drew442 · 1 points · Posted at 01:52:06 on February 14, 2016 · (Permalink)
Reddit hug on the Google cache version too? Any other mirrors?
Dubaku · 1 points · Posted at 02:08:49 on February 14, 2016 · (Permalink)
The plot thickens. I was told this story in high school. Before I realized it was about a bunch of Greek people I was imagining a noir film or something.
He was killed because he revealed a secret of a secret society. in 500BC this was cutting edge information stuff. Kind of like revealing the plans on how to build a nuclear bomb. It's a great story, but it also helps to put it into context so people can understand why he was killed.
The article doesn't seem to be working on my android's Google Chrome. It turned from math to philosophy.
"How is it possible to prove that there is no ratio making [Math Processing Error]?
The logic is a little fiddly, but not too heavy.
Let's imagine that it is possible to come up with such a ratio to produce [Math Processing Error].
Let's call it [Math Processing Error]."
[deleted] · 1 points · Posted at 08:06:01 on February 14, 2016 · (Permalink)
Here's another tidbit I really like about irrational numbers.
There aren't as many of them as you might think. You can take all the irrational number (including all the rational numbers) and sort them in a specific order and then assign the number one to the first one, 2 to the second and so on. So, in a sense there are just as many irrational numbers as there are whole numbers.
BUT, it isn't so with the set of Real numbers. There are incredibly many more real numbers than there are irrational numbers. Check out cantor's diagonal argument
If you ask me they are misnomers, the irrationals are real and the reals are true imposters.
If my understanding is correct there aren't any questions whose answer is a single specific Real number that is neither rational or irrational. So all those incredibly numerous Real numbers that makes the set of Reals so much bigger than the irrationals? We can't even identify a single one of them.
So you tell me, are the Reals really real?
[deleted] · 1 points · Posted at 10:04:34 on February 14, 2016 · (Permalink)
Learned this on The History of Maths recently. Its worth watching. Good read. Thanks!
So I went to the story page.. saw a bunch of numbers, letters, squiggle lines all bunched together had an anxiety attack and noped the fuck out of that page...so Ive figured out my fear.. its definitely math.. I mean look at this shit... nope..
\frac {top2}{bottom2} = 2
Next multiply both sides by bottom2 , ending up with
top2 = 2 \times bottom2
Edit: Yes I did go back to the page for this.. it was hard.
[deleted] · 1 points · Posted at 11:40:08 on February 14, 2016 · (Permalink)
Well I didn't understand any of that and regretfully have no motivation to. Not trying to disrespect the post, more being critical of myself.
FUZxxl · 4 points · Posted at 13:15:25 on February 14, 2016 · (Permalink)
The generating function of a sequence is a function such that the coefficients of its power series (Taylor expansion) are the terms of the sequence. For example,
what he meant was that it's okay to ask "wut?" even though it seems to be explained in detail already, but given his qualifications of someone who is supposed to be on a deeper understanding of mathematics, he already forgotten about the basics which is fraction series, and so it's okay to ask "wut?" and not feel stupid about it
you people have to not be so mean to others...
[deleted] · -32 points · Posted at 03:37:15 on February 14, 2016 · (Permalink)*
Well, in order to be a programmer you (in most cases) need to have a strong foundation in mathematics. OP probably means that he once understood what the above comments were talking about (i.e. when his maths education was still fresh in his mind), but he doesn't anymore.
Edit: Some people appear to be confused about this. While Computer Science is by definition a theoretical and mathematical field (primarily relating to discrete math, combinatorics, graph theory, etc), This problem is relating to real analysis, something most Computer Science students would not take in college.
Argue all you want, 99.99999999% of day-job programmers will NEVER need to look at or think about anything in this problem domain. Hence the reason the guy forgot the math in the first place. Learned the absolute basics of sequences/series in college, then forgot because it's not relevant to programming.
[deleted] · 2 points · Posted at 07:13:57 on February 14, 2016 · (Permalink)
Almost all programming is an application of rudimentary logic and discrete math, if that. This is more along the lines of calc 3 or real analysis, which shares no resemblance to anything almost any programmer does.
Hi, computer science major here! Calculus and a couple of higher level maths were core requirements for my degree. I went with differential equations and linear algebra. I took some combinatorics for fun, and while it covered a lot of stuff that would fall under discrete math, it also dealt with generating functions.
Yeah. Calculus , diffeq, and linear algebra are standard but discrete math and combinatorics are pretty unique in application to computer science and engineering students.
Furthermore, the question at hand isn't relating to anything remotely covered under the domain of computer science and programming. If anything I'd say this fits under something like real analysis, which most computer science students would not even consider taking.
Discrete math and combinatorics is not strictly in application to cs and engineering...
Most discrete math courses are a good introduction to proofs for math majors or people who will be taking more proofy courses.
Combinatorics is good for lots more applications than just cs and engineering.
Yeah I agree, but at most colleges, look at the majors that require discrete math. It will usually be someting like computer science, computer engineering, cognitive science, etc. Obviously I'm not saying those are the ONLY fields relevent to those topics, but they are the classic ones.
Numerical analysis is a thing for programmers. Who's gonna program the physics simulations (e.g. video games, money)?
There are many applications for programming, so there are many people who won't need SOME knowledge that they teach. For example, some programmers will never need databases, while others probably can't imagine not having them as a key part of the curriculum.
In fact, I'd say that real analysis is more useful for actual programmers than academia. My impression is, academics are more into graph theory, combinatorics, and logic, while analysis is more applicable and less abstract.
Yeah you're totally right, it absolutely depends on where you're going into. It also is massively important in the finance industry. Hell, they are hiring a lot of EE's now just for the firm grasp on analysis.
But at that point, we are arguing about specializations, rather than computer science and programming itself. I think you'd agree that the mathematical lingua franca of programmers does not contain or deal with analysis, and that's reflected in the core cirriculum of most CS degrees.
I'm a programmer and while I might have once known what they are talking about, I don't anymore.
The poster probably learned about series in the process of learning programming, and might have had the impression that it was standard for programming students to take calculus. Calculus is where you first learn about series, not full-blown analysis. My school, for one, required calculus for CS majors.
Just a series? Granted that's a series representing a polynomial, but computers don't "just know" how transcendental functions like sin/cos/log/etc work. We still need series so that computers can approximate them. Someone had to write those math libraries in the first place!
Binomial expansions! You can write any expression of the form (1 + f(x))n, where n is any real number and f(x) is any function of x, in the form:
1 + nf(x) + (n(n-1)/2!)*f(x)² + (n(n-1)(n-2)/3!)*f(x)3 + ... and so on.
So that's what's being done with the expression above. It only works if -1 < f(x) < 1 though.
In fact you can write most functions as a series of powers of x, so a + bx + cx² + dx3 etc., except some will work for all x, some for -1<x<1 and some for other constraints. It's just that binomial expansions have an easy to remember formula, and the others require differentiation to get the power series.
OK, since nobody's actually answered you yet, I'll give it a shot. Although it's hard to explain Calc II like you're 5.
So almost any given expression with a variable can be written as a sum of numbers with patterns. An example is cos(x), which equals equal to sum (((-1)n x2n )/(2n!)) from n = 1 to infinity. So set n = 1, n = 2, n = 3, ... and add up everything. That gets you 1 - x2 /2 + x4 /24 - x6 /720 + ... This equals cos(x) for any value of x.
A more common series representation is 1/(1-x), which is simply sum(xn ) from n = 0 to infinity. Again plug in n = 1, 2, 3, ... and add it all up. The answer is 1 + x + x2 + x3 + x4 + ... Again, this equals 1/(1-x) for any value of x.
Now, the series for 1/(1 - x - x2 ) is a little complicated, but when expanded, it equals 1 x0 + 1 x1 + 2 x2 + 3 x3 + 5 x4 + 8 x5 + 13 x6 + ... You'll notice that the coefficients are numbers in the Fibonacci sequence.
Now, plug in x = 0.1. The original expression becomes 1/(1 - 0.1 - 0.12 ) = 1/(1 - 0.1 - 0.01) = 1/0.89, which, if you multiply top and bottom by 100, equals 100/89.
Finally, plug in 0.1 into the expansion (which is easy because the powers of 0.1 are simply 0.1, 0.01, 0.001, ...). The result is 1 + 0.1 + 0.02 + 0.003 + 0.0005 + ... and this equals 100/89. The top comment describes 1/89, so if you divide each term by 100, you get 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 ...
Hope that was clear. Sorry for any formatting errors (I typed this up on mobile), but the math is all correct.
[deleted] · 5 points · Posted at 05:04:50 on February 14, 2016 · (Permalink)
It's more about differential equations and real analysis tbh.
Define a recurring sequence as a(n+1) = a(n) + a(n-1) for all n greater than or equal to 2. a(0) is 0 and a(1) is 1.
Now, claim that a(n) = xn. Hence, xn+1 - xn - xn-1 = 0 from a(n+1) = a(n) + a(n-1).
xn+1 - xn - xn-1 = xn-1 [x2 - x - 1]. Hence, finding the roots of [x2 - x - 1], namely r(1) and r(2), would produce a recurring pattern such that a(n) = xn and a(n+1) = a(n) + a(n-1).
The roots of x2 - x - 1 are: r(1) = (1+sqrt(5))/2 and r(2) = (1-sqrt(5))/2.
From now on, it's easy to see that c(1)r(1)n+1 + c(2)r(2)n+1 = a(n+1) satisfies a(n+1) = a(n) + a(n-1) for all n greater than 2.
We're left with determining the values of c(1) and c(2).
So a(n) = (1/sqrt(5)) [(1/2)(1+sqrt(5))]n - (1/sqrt(5)) [(1/2)(1-sqrt(5))]n
i.e.: a(3) = 2
And that's why x2 - x - 1 is a generating function for the Fibonacci sequence, namely because its roots along with the proper coefficients can generate any Fibonacci number.
You're absolutely right, but what you just did was essentially derive the series representation of 1/(1 - x - x2 ) (since (1/sqrt(5)) [(1/2)(1+sqrt(5))]n - (1/sqrt(5)) [(1/2)(1-sqrt(5))]n is simply the series form of 1/(1 - x - x2 )). I tried to intentionally avoid that to keep with the spirit of ELI5, because I thought it would get too complex.
I mean, I have a math minor, so I get it, but I doubt others who have less exposure to differential equations will.
[deleted] · 2 points · Posted at 06:11:43 on February 14, 2016 · (Permalink)
I'm doing a major in maths, so I tend to forget how most things that seem very simple to us (like the one I described above) tend to be quite complex for non-math people.
For me the problem has always been 'i dont know what direction to take to solve this math problem' so when someone spouts a giant list of statements and at the end says 'tadaa' i'm just wondering 'why did you do x'. Like for example 'plug in 0.1'. Why 0.1? What's the rationale behind it, how is 0.1 relevant?
Or 'define a generating function like such: <func>'. Why? What thinking went before this?
So it's all just a bunch of random statements which make no sense so me and look like gibberish.. very offputting.
[deleted] · 1 points · Posted at 09:40:18 on February 14, 2016 · (Permalink)
It's not meant to be easily understood by anyone and everyone. That doesn't mean it's all random gibberish tho =/
But I get where you're coming from. I too sometime struggle to understand math concepts sometimes, especially when they aren't explained properly.
ck2839 · 1 points · Posted at 07:10:34 on February 14, 2016 · (Permalink)*
There's a simple proof of all of this. I've already posted it here in the comments.
The Fibonacci sequence is defined by the sequence a_0 = 1, a_1 = 1 with a_n = a_{n-1} + a_{n-2} for all n∈ℤ, n≥2.
Let G(x) = a_0 + x·a_1 + x2·a_2 + ··· This is called a generating function.
That's not the usual way of deriving a generating function, though, is it? The derivations I've seen have just been a relatively simple manipulation of sums to get it. The tricky part is getting a formula for the coefficients, but you don't need that to get the generating function.
Edit: The derivations I've seen have gone something like this
[deleted] · 1 points · Posted at 15:59:29 on February 14, 2016 · (Permalink)
You and I are basically doing the same thing, hence why we're both ending with x2 -x - 1 as the core of our generating function. It's just that I wanted and actual formula for a(n) rather than the generating function itself. By treating a(n+1) - a(n) - a(n-1) as an homogeneous differential equation (kinda), I set "x" to be equal to the sum of some coefficients times the roots of "x".
That's the usual way to get a precise formula for such recuring patterns, namely a(n) = c(1)r(1)n + c(2)r(2)n . That enables you to evaluate the upper and/or lower limit of a(n), as well as its convergence or lack thereof. Merely deriving the generating function sadly doesn't let us do such things, hence what I did.
Tl;dr : yours is the standard way to get the generating function's characteristic polynomial, mine is the standard way to get a formula for a(n).
Did you forget to mention, that this is only true for any value of x with 0<x<1 (or something like that)? Because the series doesn't converge for x>=1, does it?
It's not that I can't, but it's pretty obvious that someone who doesn't understand "1/(1-x-x2) is a generating function for the Fibonacci sequence" couldn't.
The number 1 is finite and can be written as an infinite sum of numbers:
1 = 1/2 + 1/4 + 1/8 + 1/16 ... = sum (1/2)n
This can be similarly done for 'finite' expressions such as 1/(1-x):
1/(1-x) = 1 + x + x2 + x3 ... = sum xn
Similar with the fib generating function case:
1/(1-x-x2 ) = 1 + 1x + 2x2 + 3x3 + 5x4 + 8x5 ...
It is miraculous that an expression could return something like the fib sequence, when expanded to it's infinite series version. It has to do with the denominator of the expression, by including both x and x2 in the denom we are able to select the previous two terms to be added to the current term. Similarly to how the natural numbers (1,2,3,4...) only need information about the previous one number, thus in the denom of 1/(1-x) there is only x.
When I first learned this I was amazed as well, but it actually just is that 'coincidental' that it could work out. If you are interested as well, you should do more research from here on.
I learned generating functions in combinatorics, which is a 300 level math class at my school. Basically if you study discrete math you'll come across it. Probability generating functions are also useful, so it should come up in probability classes as well.
It roughly means that it's meant to be taken in the 3rd year of college/university. Of course, you can take whatever class you want if you meet the prerequisites, so that's not strict - I took combinatorics in the first semester of my 2nd year without issue. But it's sort of in the third "tier" of math classes, however the faculty at my particular school decided to define that. Other schools might have similar classes at different levels, but you would expect a 200 level combinatorics to be less rigorous, for example.
He actually gave the explanation that was the easiest to comprehend, in just 2 lines of basic maths. You only have yourself to blame if you fail to get it.
but Bens mom dies giving birth to him??
Oh wait he was being sarcastic wasn't he.
Fuck I'm an idiot.
Tezmata · 72 points · Posted at 06:26:34 on February 14, 2016 · (Permalink)
Not even sarcastic, since Jack didn't know that about him. He just straight up lied all the time whenever he felt like it. It was a very nice one-off line with a lot of context behind it.
Exactly. Ben did this constantly. At one point he mentions he's a Pisces, but he can't be because he was born in December.
ipslne · 10 points · Posted at 10:51:17 on February 14, 2016 · (Permalink)
If you like shows where you are given everything about the characters and nothing about the plot, check out Evangelion!
[deleted] · 9 points · Posted at 10:54:57 on February 14, 2016 · (Permalink)
Also check this out if you like to be mind fucked and torn into emotional shreds and need a week to decipher what the fuck you just watched. Evangelion is fantastic though, but you will feel very conflicted after everything is said and done.
"Oh, my best friend is unconscious in a hospital bed, let's fap and come all over her."
ipslne · 1 points · Posted at 11:43:44 on February 14, 2016 · (Permalink)
best friend
I take it you didn't watch it then?
That scene has quite a lot of meaning behind it. Part character development, part realism and part immersion. It was a fucked up thing, he knew it was fucked up, and the viewer now feels fucked up. Now everyone's in Shinji's shoes.
There's also a bit of social commentary going on here with regards to the sexualization of characters that is rampant in anime.
[deleted] · 2 points · Posted at 21:58:47 on February 14, 2016 · (Permalink)
a bit of social commentary
I would go as far to say that's the major reason for the scene's existence. Anno hated otaku culture, and was basically pointing at them saying, "HEY, THIS IS YOU, YOU'RE ALL FUCKED UP".
NGE is really more of a "coming of age" story in anime clothing than a mecha show.
[deleted] · 1 points · Posted at 11:52:47 on February 14, 2016 · (Permalink)
That was the weirdest scene I've ever seen. It actually kind of seemed out of character for Shinji because of how risky doing something like that is. Shinji is a scared kid so just whippin out his dick and jackin off to an unconscious chick when anyone could walk in...bold strategy cotton, especially when a bathroom is right there.
m00fire · 2 points · Posted at 13:29:18 on February 14, 2016 · (Permalink)
Also be sure to watch End of Evangelion (not the dub though as it's fucking horrible) since the actual ending is horse shit and makes no sense at all
[deleted] · 1 points · Posted at 18:57:11 on February 14, 2016 · (Permalink)
Whattt? The ending makes complete sense, what didn't you understand?
[deleted] · 2 points · Posted at 08:23:33 on February 14, 2016 · (Permalink)
Technically, your proof requires proving generating functions are unique. But yes, you're right.
Also, subscripts can be done via star underscore WORDS underscore star.
ck2839 · 1 points · Posted at 08:28:05 on February 14, 2016 · (Permalink)
Thanks, edited the underscores.
Kered13 · 1 points · Posted at 13:43:36 on February 14, 2016 · (Permalink)
Generating functions are fucking magic. Unfortunately they're one of the two subjects I didn't manage to quite grasp out of my freshman discrete math for CS lass (not the actual name of the class).
Also what I found out is that when you convert the fib sequence into bass 6 then write out just the number in the ones digit, the numbers are recurring and form a pattern.
I'll post numbers and a better explanation when I get home. Here are steps if you get confused :
Convert number to base 6
Take the base 6 number and just write down the number in the 1's digit
EX : Base 10 : 8 converts to Base 6 : 10. Then just write down the number 0.
Kubby · 2 points · Posted at 04:49:20 on February 14, 2016 · (Permalink)
That actually is a thing for every single number base.
For base 6, the cycle is 24 digits long, for base 10 it's 60 digits.
No finite number of terms will equal 1. But that's not a finite number of terms. It's exactly 1 if you have infinite terms. The left side is just a number - numbers don't move. They can't approach anything.
If you were talking about 1 + 1/2 + 1/4 + 1/8 + ... + 1/2n, then you could say that as n goes to infinity, that series approaches 1. But in the case I gave above, nothing changes, so nothing can be approaching anything.
I don't see why that's the case. A number that approaches an infinitely small number is could fall under either a hyperreal number or a limit. Though I haven't done any formal math training any time recently.
No, they really don't. I don't have time to provide a better source right now, but on the Wikipedia page for hyperreals there are three mentions of the word "limit". One is not about hyperreals but the general idea of infinitesimals being used in limits, one is about hyperreals being abandoned in favor of limits, and one is talking about the set-theoretic construction of the hyperreals.
Limits are specifically defined using ε,δ ∈ ℝ. .999... is not 1 minus an infinitesimal even in the hyperreals.
An infinite series can converge to a finite, rational number. Converging means that, as the number of terms in the series approaches infinity, the sum approaches a certain number. Sometimes that number is a finite number and sometimes it's rational, too! :)
MadTux · 2 points · Posted at 07:14:19 on February 14, 2016 · (Permalink)
Yes, it just doesn't look that way at first ..
Something like 0.5 + 0.25 + 0.125 etc is a lot easier to see, somehow.
Atmosck · 1 points · Posted at 05:18:09 on February 14, 2016 · (Permalink)
What makes you think that?
heap42 · 1 points · Posted at 23:26:58 on February 13, 2016 · (Permalink)
purely the fact that the number we are talking about is 1/89 says its a rational number, since a rational number is defined by each number that can be represented unsing one natural number(nominator) and one integer(numerator) which 1/89 is.
Just to split hairs here, the sequence is not encoded in the number because there is no way to get that sequence from the number. You can get 1/89 from the Fibonacci sequence by turning the sequence into that series by writing out the zeroes, but I can't see a way to get the sequence from the number 1/89.
Klashus · 1 points · Posted at 03:16:39 on February 14, 2016 · (Permalink)
Fibonacci patters that occur in nature are some amazing things.
Kz_Rob · 1 points · Posted at 05:41:04 on February 14, 2016 · (Permalink)
Yes I was going to say this as well, but I was going to add a little.
Isn't the fibbinaci sequence the one that accounts for a lot of things in nature? Like the way a shell swirls or a galaxy from afar? Awesome.
89 = 1 + 1 +2 + 3 + 5 + 8 + 13 + 21 + 34 + 55, and is one of the natural fibonacci numbers.
89 decimal is 1000100010.0010001001... in base golden ratio according to wolframalpha, but I think that's been rounded off from 1000100010.00100010001...
The sequence was first explored by chinese mathmen thousands of years earlier. The geographic divide between east and west necessarily required the west to discover for itself math principals well known and in common use in the east.
No it is not:
1/89=0.01123595505617977528089887640449438202247191011235955056179775280898876404494382022471910112359550562...
Edit: Yes it is, sorry... (After seeing http://www.mathpages.com/home/kmath108.htm)
And the Fibonacci sequence can be used to easily convert miles to kilometers or vice versa.
18BPL · 2751 points · Posted at 23:15:15 on February 13, 2016 · (Permalink)*
Gabriel's Horn, a cone formed by revolving the curve y=1/x where x is greater than or equal to 1. It has an infinite surface area, but a finite volume. In other words, it can be filled with paint, but it can't be painted
Edit: Okay, maybe it can be painted, I don't fucking know, I'm just a lowly HS Calc student. I'm sorry my quick and dirty analogy has offended some of you.
MrMoby · 548 points · Posted at 04:27:37 on February 14, 2016 · (Permalink)
To help with grokking that fact, consider the area under the normal distribution - it's equal to 1 (a finite number). However, the length of the boundary of that area is infinite.
grok (verb): understand (something) intuitively or by empathy.
Huh, TIL!
Gaff3r · 149 points · Posted at 07:29:51 on February 14, 2016 · (Permalink)
“But the Martian language is so much more complex than is English [that] I’m not certain that it will ever be possible for us to think in Martian…. [T]ake this one word: ‘grok.’ Its literal meaning, one which I suspect goes back to the origin of the Martian race as thinking, speaking creatures… is quite easy. ‘Grok’ means ‘to drink’….
[But it could also mean] a hundred other English words, words which represent what we think of as different concepts, even pairs of antithetical concepts. And ‘grok’ means all of these, depending on how you use it. It means ‘fear,’ it means ‘love,’ it means ‘hate’–proper hate, [as] you cannot possibly hate anything unless you grok it completely, understand it so thoroughly that you merge with it and it merges with you–then and only then can you hate it. By hating yourself….
The Martians seem to know instinctively what we learned painfully from modern physics, that the observer interacts with the observed simply through the process of observation. ‘Grok’ means to understand so thoroughly that the observer becomes a part of the process being observed–to merge, to blend, to intermarry, to lose personal identity in group experience. It means almost everything we mean by religion, philosophy, and science–and it means as little to us as color means to a blind man.” – Robert A. Heinlein, from "Stranger in a Strange Land."
It's pretty much the same thing as the concept of samadhi from yogic philosophy... Heinlein was a brilliant and original thinker, but he did make that concept up entirely out of the blue.
[deleted] · 5 points · Posted at 08:19:33 on February 14, 2016 · (Permalink)
Give a man water, and he is quenched for a day. Teach a man to stop breathing underwater, and he groks.
wraneus · 4 points · Posted at 14:13:36 on February 14, 2016 · (Permalink)
lets be water brothers!
[deleted] · 4 points · Posted at 13:57:08 on February 14, 2016 · (Permalink)
[But it could also mean] a hundred other English words, words which represent what we think of as different concepts, even pairs of antithetical concepts.
That's no longer true. It's now simply synonymous with "understand", because so many pompous people have used it to sound intelligent without bothering to learn its meaning.
Shouldn't PSA's be accurate? The word became common slang in the 1960s amongst hippies and sci fi buffs, neither of which were exactly micro cultures. And they still use it today.
Stranger In A Strange Land was hugely popular and — unlike most sci-fi published before it — was a mainstream success and vastly influential. Likewise "grok" became a mainstream (or "counter-culture lite") word amongst the younger generation, and is still used in mainstream books and films.
But go with your feelings if you choose; the irony won't be lost on me.
I have done research, namely having conversations with people. Nobody that I have ever met in real life uses the term. I have seen a few people online use it, but it is not at all common. I conclude that it is rarely in use and that it sounds like you are offended by your or your friends being classified as ubergeeks. Wear the badge with pride my friend.
It was more of a fad word for most people back then.
Of course, it was started by geeks and hippies being hipsters.
When the words fifteen minutes was up, it was the geeks and hippies who kept it alive.
Funny, I belong to a Bowie group, two members in the last half hour were using "grok." Neither are geeks or hippies, though they are Gen X musicians.
Like I say, believe what you want. I'm no hippie or geek, I can tell you that. And I haven't touched Heinlein since high school — where SIASL was required reading for AP English.
'Grok' was coined by Robert Heinlein in his novel, Stranger in a Strange Land (1961)
[deleted] · 1 points · Posted at 15:57:03 on February 14, 2016 · (Permalink)
From "Stranger in a Strange Land". Great book.
TMinAK · 1 points · Posted at 17:14:26 on February 14, 2016 · (Permalink)
It's a Heinlein word.
Habtra · 1 points · Posted at 19:13:01 on February 14, 2016 · (Permalink)
Is it from "A history of nearly everithing"? I read it in French and the verb was gnoquer, but it reminded me of it immediately and has the same definition.
EnkoNeko · -2 points · Posted at 09:59:46 on February 14, 2016 · (Permalink)
It's pretty mind-boggling, but infinite surface area enclosing finite volume makes sense. A better way to visualize would be to consider an infinitely large, elastic sheet being plucked up off its mounting surface. This would now enclose a finite volume, although the sheet would be too large to make/paint/whatever.
An infinite number of mathematicians walk into a bar. The first one orders a beer, the second one wants to show he's more temperate than the first, but still willing to unwind, so he orders a half a beer. The game of one upsmanship is afoot. The third says I'll take half of that and orders a quarter of a beer. The next orders an eighth.the mathematicians go on and on, halving the previous one's order.
After a while, the bartender gets fed up and hands them 2 beers, shakes his head and says, "You mathematicians just don't know your limits."
The joke would demonstrate Gabriel's Horn if the bartender said, "I have enough beer, but there aren't enough mugs."
That's actually a really clever way of making it make sense.
[deleted] · 5 points · Posted at 08:44:19 on February 14, 2016 · (Permalink)
Here's a great VSauce video about supertasks and Gabriel's Horn. The video starts with Michael explaining /u/imgonnabutteryobread's analogy.
n-ion · 1 points · Posted at 14:30:12 on February 14, 2016 · (Permalink)
I will use this in life in general
[deleted] · -14 points · Posted at 08:17:31 on February 14, 2016 · (Permalink)
You will confuse the students like me who know that you can't divide a cake beyond atoms and still frost them. Ergo you can't frost it at all when the frosting no longer sticks due to lack of friction, and therefore a finite amount of cake is absolute and an infinite amount of frosting covering that cake is only possible by frosting the frosting and just sprinkling in the cake as you go. You are finitely caking the infinite frosting at that point, and after an infinite amount of time the ratio of cake to frosting is so small that you essentially just have an infinite amount of frosting, which you should then sell to fat people and 3.) Profit
Maybe I'm just stupid but I found this really funny :D it makes sense at first, then becomes chaotic and ends in nonsense. Reminds me of a dad joke somehow. Well, I hope you feel better to know that you made at least one person laugh :)
[deleted] · 41 points · Posted at 07:18:14 on February 14, 2016 · (Permalink)*
In Zeno's Paradox you take the hypothetical distance between you and another person standing in front of you, and you close half of that distance (by stepping half the distance between you and that person). After walking half the distance between you and said person, take half of your current distance, and walk towards the person again. Proceed to keep walking half the distance of the previous space, and you will find that you will never reach the other person. This new analogy with the cake just adds another mind-blowingly cool dimension to an already awesome paradox. Thanks /u/GrammatonYHWH for sharing
The important part to realize is that the paradox is illustrating a flaw in your logic. In this case the fault is the assumption that all infinite sum are infinite when this is not the case.
You're absolutely right, and it wasn't until I read his cake analogy that I realized it. That's the mind-blowing "dimension" I hadn't considered until the end of my post. It's almost like a paradox inside another paradox!
Except the flat sides of the cake will remain a constant size (the radius of the cake times the height), and all infinite sums of a constant (that's not 0) will infinite
And to get an infinite amount of frosting you could just make the frosting into a solid, then cut that an infinite amount of times. Then bam! Infinite frosting. Right?
In philosophy, there's a debate in which one side argues that math is best understood as a construct while the other argues that it is best understood as a discovery. I think you just convinced me that both are wrong. Math isn't invented, nor is it observed. It's not passive in either way! It's a proactive thing that's here only to mess with us. :P
you can keep cutting the rightmost half an infinite amount of time.
Citation needed. The physical universe has physical properties that prevent this. Eventually you will be splitting atoms, then smaller and smaller particles, but how do you cut a probability function of the tiniest piece of cake in half?
You only need finitely many frostings because the original cake (which needs the same frosting as the cut up cake!) needs only finitely many frostings.
In that same line of thinking, why could you not just do the same to the frosting. In theory, keep dividing a finite amount of frosting up by half - an infinite amount of times?
Then some smart arse comes along and says that you can only cut the cake slivers to approximately atom width. So there are a finite number of slices.
Jopomo · 1 points · Posted at 14:46:54 on February 14, 2016 · (Permalink)
Ultimately though it's all theoretical. You can't cut a cake that way in reality, a cake has probably never been cut perfectly in half. There is no infinite elastic sheet, there is no curve of y=1/x because the material to make up that curve is never going to be perfect.
Just like the notion of a perfect circle or square, it's an interesting and occasionally useful concept in mathematics, it's theoretically a shape, but it isn't real. If it seems difficult to get your mind around, just know that it's probably because it can't actually exist. That's the way of thinking I prefer.
You have a finite amount of cake which requires an infinite amount of frosting to cover.
How does this explain anything? You jumped straight from the example to what it's supposed to show without giving any explanation in-between...If you're cutting a cake into slices, each slice still has a finite surface area, right?
blippyz · 1 points · Posted at 19:59:49 on February 16, 2016 · (Permalink)
I understood it before reading your cake analogy but now it just made it more confusing. So you've taken something finite (amount of frosting needed) and somehow transformed it into something infinite. You've also taken 100% (amount of frosting covering the cake) and transformed it into less than 100% (same amount of frosting no longer covers all the infinite slices) without taking any of it away. I feel like this is just word play now and doesn't actually show anything.
This kind of maths works because mathematical objects are infinitely divisible. Since real objects are made from finitely many smaller indivisiable objects, atoms, chemicals whatever, you can't actually perform these operations on them. That's not even mentioning that it would take an infinite amount of time to do so, even if you could.
I don't really like these real world analogies. People can understand cutting up a chodelike cylinder, and covering it in some kind of theoretical paint.
The idea is you can keep making the surface area bigger and bigger and bigger as long as you want by slicing more cake, but the starting amount of cake remains the same.
This doesn't have to be too large to paint, it's more that it's too small at the one end to create on even an atomic scale let alone paint. I'm not so certain the surface area can be infinite, you'd hit a theoretical microscopic limit. If you keep dividing by x you never get to zero. Is that really infinite?
Gabriel's horn (GH) has infinite area. Let's construct a smaller horn which is still infinite:
The first length unit of GH has more surface area than a simple tube of length 1, diameter 1/2; Proof: its minimum diameter is 1/2, so its surface area must be greater.
The 2nd length unit of GH has more surface area than a simple tube of length 1, diameter 1/3; proof is the same with 1/3. Etc, etc.
Adding these, you get a surface of 1/2 + 1/3 + 1/4 + 1/5 +..., a sum of infinitely many fractions, and you know that GH has more surface area than pi times that sum. That reduces our question to the following:
"Does the sum 1/2 + 1/3 + 1/4 + 1/5 +... grow towards infinity?"
It does. Let's make this sum smaller and prove that it's still infinite:
(We're putting larger numbers in the denominators, the smallest power of two that's >= the old denominator. The individual fractions didn't increase, so the >= relation holds.)
Ah thanks I understand it now. I was thinking of reductions in size, which leads to misunderstanding but you can see a problem there. How are you gonna paint the very tip of the horn? Pretty hard considering you can't see where it ends. You could grab some spray paint and say it lies within an area but that's about it.
The "tip" is infinitely far away, so when it comes to practical issues, you can't even get to the tip.
The underlying mathematical problem is even worse because of the finite area. (Although a clever mathematician could say "give me a transparent horn and I'll paint its inside by filling it and then I'll let the paint dry", there would still be one issue: the layer of paint would be extremely thin at most places.)
There is the practical issue of the tip getting past atom thin very quickly. There's a whole other theoretical issue that none of the atoms are where we think they are and they're moving at all times. We could get pretty close by bringing it to near absolute zero and using carbon atoms. We can't 3D print carbon atoms anyway it's a tricky scenario. Then what do you do when you get past that? We don't even understand how the quantum world works, let alone how to control or make it work with physics in our current understanding.
If we knew the entirety of what there was to know about physics, who knows. Maybe it would still be a mind bending problem pushing the limits of our minds and philosophy.
singham · 1 points · Posted at 14:08:29 on February 14, 2016 · (Permalink)
It is not as obvious as you make out to be. The integrals are where the magic happens. If you slightly increase the exponents, the volume too becomes infinite.
shabinka · -2 points · Posted at 06:02:30 on February 14, 2016 · (Permalink)
I'm not sure why its mind boggling, as you get towards large x the value is practically 0, but it still exists so you have surface area but no contribution to volume. Its kind of like looking at a step function.
But why. Something seems like a flag line. Acts like a flat line, and you're surprised. Its like having a step function that goes to zero at say 5, goes on to infinity. This has a finite volume but has infinite surface area.
[deleted] · 1 points · Posted at 06:40:33 on February 14, 2016 · (Permalink)
That is literally the words that I wrote..............
FolkSong · -1 points · Posted at 07:01:44 on February 14, 2016 · (Permalink)
It's mind boggling because if you imagine a container filled with paint, the idea that you couldn't paint the surface makes no sense.
But the answer is that the container becomes so shallow as you move away from the center that the depth is less than the thickness of a coat of paint, and eventually less than the thickness of an atom.
shabinka · -2 points · Posted at 07:49:20 on February 14, 2016 · (Permalink)
Before you downvote me like an idiot. Look at surf area. Surface area depends on length.
I just had a flashback to Calc II in community college. Thanks!
rock217 · 20 points · Posted at 05:56:57 on February 14, 2016 · (Permalink)
the whole argument falls away when we bring the horn into the realm of physical space
So, what, we're just screwing around then?
[deleted] · 14 points · Posted at 06:20:48 on February 14, 2016 · (Permalink)
Lots of math looks this way from the outside. Take imaginary numbers as a simple example.
Say you have an apple. With the apple, you can cut it into pieces (rational numbers), or owe two apples to me (so you have -1 apples total, giving us negative numbers), or have no apples (sad day). But, can you have i apples? (i being the square root of negative one) Of course not! i is imaginary! So why mess with i? It doesn't apply to my apples! To your apples, complex numbers are nothing more than a mathematical concept that just doesn't apply, but they are huge in electrical engineering.
So, yes. Gabriel's Horn (and other discoveries in math) might make many people say, "why does this matter?", but maybe it is like the complex numbers to electrical numbers: just a concept looking for its apples. (:
[deleted] · 13 points · Posted at 06:59:41 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 2 points · Posted at 08:00:09 on February 14, 2016 · (Permalink)*
How can two circles not intersect but intersect at the same time at imaginary points? Where are those imaginary points? Before you answer you should know I study engineering ( and I've taken the electrical systems class already ) so I know what complex numbers are and all that but I can't understand this and it is also driving me nuts. Where are the imaginary points of intersection of two circles that don't intersect???? My mental picture right now is two circles seen from the sides ( so you only see two lines ), not intersecting ( the lines don't touch each other) and also a point above or under the circles which you can a point at which they intersect. Is that what complex numbers mean? If yes then this doesn't make any fucking sense. If yes, then I would suggest not calling them point at which the circles intersect because they don't intersect. I would just call it a solution to a problem.
I think the previous comment is imagining two circles flat on a 2 dimensional plane rather than circles rotated at some angle to that plane. The description of intersection would seem to correspond to the solution of some quadratic equation, yes.
No, they do not physically intersect. Maybe they intersect in the complex plane?
I suppose another solution would be that the circles intersect at all points, but that probably brings the question of whether or not they can be distinguished as separate objects, to which I would expect the answer would be that mathematically they cannot.
I might have some of this stuff wrong, so anyone is free to correct me if I do.
Maybe not. As far as my understanding of the size of the universe goes, I'd say it's a place with an infinite surface area that contains only a finite volume.
[deleted] · 2 points · Posted at 07:45:14 on February 14, 2016 · (Permalink)
You don't seem bad at math, you seem "bad" at not knowing what ... means but you wouldn't consider yourself bad at English for not knowing what anfractuous means right? :)
I'll admit I was under the influence last night so I may have missed the "...". I just read where he stated the equation and then said " you end up with 2" and it didn't compute in my drunken head.
I am pretty bad with math though but I'm slowly getting better at it. I'm 28 so long past school days, but I could never grasp it in school.
[deleted] · 0 points · Posted at 06:04:48 on February 14, 2016 · (Permalink)*
That sounds stupid: You can just take two cups ( and even one ) to pour out the total volume. You can take any series of infinite numbers and say "you need infinite cups to pour out the infinite volumes". It's a redundancy. Why are you surprised that you need infinite cups to pour out infinite volumes?
I'm not a native English speaker so maybe I'm not getting an implied meaning in the pour out /fill the order analogy but I think I got it.
He's referring to a joke. A group of n mathematicians walk into a bar. "What'll you have?", asks the bartender. The first mathematician says "A beer please." The second one approaches the bar, but orders a half pint instead. Before he can fetch their orders, the third requests a quarter pint and a fourth demands an eighth. The annoyed bartender grumbles, pours out two pints, and says "that should serve all of you."
[deleted] · 1 points · Posted at 07:53:40 on February 14, 2016 · (Permalink)
Thanks! I'm gonna put it a different way:
If the cone can be filled with paint, it can be painted because the paint filling the cone paints the walls therefore painting the cone.
One could divide the cone into infinite pieces and try to paint them all, but saying those infinite pieces can't be painted is not true ( explanation above ).
If I remember correctly, it takes pi amount of something to fill, or something like that. Maybe it's not pi but another irrational number. It's a finite number but cannot be represented exactly in the real world (well Gabriel's horn can't exist in the real world).
Gabriel's horn fucked with my head until I realized that.
Now... Assume that the horn is very very very thin. So thin that the inner surface area is almost the same as the outer. Now the amount of paint required to paint the outside then is no more than twice the amount of paint required to fill (and paint) the inside.
This seems to make sense but there's something probably wrong... Anyone who knows?
Or, worded slightly differently, if Gabriel's horn is made of paper, and I fill it with paint, would the paint not bleed through and thus coat the exterior?
This is why I don't do applied math. Reality is always getting in the way and fucking shit up.
[deleted] · 1 points · Posted at 16:25:36 on February 14, 2016 · (Permalink)
eventually the tube of paper is so tight that paint can't get through
n1c0_ds · 1 points · Posted at 06:12:22 on February 14, 2016 · (Permalink)
Welcome to engineering
[deleted] · 2 points · Posted at 14:54:21 on February 14, 2016 · (Permalink)
What would happen if I were to fully submerge it in a bucket of paint?
18BPL · 2 points · Posted at 19:29:44 on February 14, 2016 · (Permalink)
You would need an infinitely deep bucket of paint
[deleted] · 3 points · Posted at 19:31:57 on February 14, 2016 · (Permalink)
2deep4me
MuttyMo · 2 points · Posted at 17:58:32 on February 14, 2016 · (Permalink)*
How dare you make a clever analogy that helps explain a wildly abstract concept but is also subject to distinction when you take the analogy way too fucking literally? How dare you?
For real good analogy. I'm a 40 year old lawyer who needs an online conversion tool to calculate percentages, and this made sense to me!
I wish I could upvote a Wikipedia article. That thing was concise, informative, fun to read, and not overly technical.
[deleted] · 1 points · Posted at 07:50:16 on February 14, 2016 · (Permalink)
I'm sorry but if it can be filled with paint, it can be painted because the paint filling the cone paints the walls therefore painting the cone.
chato94 · 1 points · Posted at 07:53:34 on February 14, 2016 · (Permalink)
Michael Stevens from vsauce recently made a video that explains this more intuitively (can't link on mobile right now). Basically, another way to understand this is to imagine a cube, and then slice that cube vertically into equal parts, and then stack those parts on top of one another on their smallest face.
By cutting those initial slices as thin as you want, you can have as many squares as you want (which means that your delicate stack of faces can get as tall as you want). The surface area tends toward infinity as slices get infinitesimally thin, but when you get each block glue it back together (you're gonna need quite a lot of glue), you get the original cube with a finite volume.
Well since we're obviously allowing idealized infinite objects and paints in this thought experiment, it could be painted because a finite volume of paint could cover an infinite area.
Ah the first day of Calc I, that was a fun class honestly.
tburn1 · 1 points · Posted at 08:28:32 on February 14, 2016 · (Permalink)
This approach made it understandable for me:
"A perhaps more convincing approach is to treat the horn as a stack of disks with diminishing radii. As their shape is identical, one is tempted to calculate just the sum of radii, which produces the harmonic series that goes to infinity. A more careful consideration shows that one should calculate the sum of their squares. Every disk has a radius r=1/x and an area π·r2 or π/x2. The series 1/x diverges but 1/x2 converges. In general, for any real ε>0, 1/x1+ε converges."
[deleted] · 1 points · Posted at 09:45:49 on February 14, 2016 · (Permalink)
i hate it when mathematicians do this.
physical constraints mean that in fact it can also be painted. paint is not some concept that is infinitely thin, and a horn like that will at one point be too thin to allow paint in between, meaning that at that point it WILL be painted.
in other words, the only reason the surface area is "infinite", is due to sloppy boundary conditions picked by someone who would probably paint themselves into a corner in real life.
Hey, I just saw this in calculus 2. You are actually wrong. This is called a false paradox because it seems that an infinite surface area can't be painted by a finite amount of paint, but it can. However this is purely theoretical. You can paint an infinite surface with every finite amount of paint as long as the layer of paint will be small enough. But yeah I guess you can also argue that the layer would actually almost equal zero in thickness, but this would only keep you from saying the surface is painted in practice, not theoretically.
I'm sorry for my mathematical English, it's hard you know...
[deleted] · 1 points · Posted at 10:11:48 on February 14, 2016 · (Permalink)
Isn't that a contradiction, filling with paint/painting are similar functions. To fill with paint is to paint it?
I had an assignment question to explain this topic just recently, I was mind boggled because the more I tried to explain, the more paradoxical it seemed, in the end my teacher didn't mark it at all because shit looks like a thesis paper on paint without limit of how small its size can be
Maybe I'm incorrect but I assisted a calc class last semester, more or less did the job of a TA without the grading or the grad student status. And this was a challenge problem on a project they had. But the professor at the time explained it to me like "Imagine you used thinner and thinner coats of paint." In essence, since volume is in units cubed and surface area in units squared, there is no proper way to compare them like that. You could technically paint it with a finite volume of paint if you spread it to infinitely thin coats. At least that was my understanding at the time. I wouldn't even begin to know how to show this rigorously.
Maybe you can help me with this because I've always questioned that notion. So obviously this is all hypothetical. Take a Gabriel's horn of max radius two, fill it with paint, put a Gabriel's horn of max radius 1 inside the other horn which is filled with paint, wouldn't the smaller horn be coated on its exterior?
kbtrpm · 1 points · Posted at 13:54:46 on February 14, 2016 · (Permalink)
This is not as contradictory as it seems. The volume is finite, but you cannot fill it. Suppose the horn is pointing up and you are pouring in the paint in the center. As the horn fills up, it will take longer and longer for the paint to flow towards the edges. You will have quickly emptied your can with the right amount of paint, but it would take infinitely long for the paint to even out. In fact, the horn is so shallow at the top, that filling the last bit amounts to painting it.
for anyone that will look, area is a squared measure and volume is cubic. so you find the edge case of when the volume, being cubed gets smaller fast enough compared to area. since n3 > n2 when numbers are bigger than 1, its opposite when numbers are smaller than 1. so the smaller the numbers, the volume gets EVEN smaller. thus you can get the sum of volume bits to converge while the sum of area bits to not converge. the horn is just one of the examples of functions at this edge case.
exactly with that reasoning you can deduce that since perimeter is linear (power 1) and area is squared (power 2) you can get infinite perimeter and finite area at some edge case. one example is the Koch Curve.
It took me a while, but after some reading I realized you can explain this as being very like a cone with an infinitely long tip at the narrow end.
You could approximate it visually as a cone with a line joined to the tip if that helps, then just smooth it out in your imagination and keep in mind that the "line" is actually an ever thinning cone reaching off asymptotically towards the horizon (the x-axis).
The final thing to realize is that the volume inside the cone converges to a finite quantity because as you progress downwards into it, its getting smaller so much faster than it is getting farther away from the part of the cone that has the bulk of the real holding capacity.
this is also one of my favorite mathematical paradoxes. You could fill it with paint, which would cover the full surface area on the inside, but painting the surface area would take an infinite amount of paint.
Broan13 · 1 points · Posted at 05:33:31 on February 14, 2016 · (Permalink)
I remember randomly noticing something like this when teaching Calc 3 at our high school.
"Oh look! It is an infinite shape with a specific middle location...that's odd."
[deleted] · -1 points · Posted at 05:55:23 on February 14, 2016 · (Permalink)
It can be painted: there's a value of x at which the circumference is so small that you can't even see it therefore you stop painting there. But you could use machines... There's a value of x at which the circumference is smaller than the smallest form of paint used and you would have to stop there. Yes, I am an engineering student :)
ClemDev · 0 points · Posted at 06:08:21 on February 14, 2016 · (Permalink)
it can be filled with paint, but it can't be painted
Well duh, It's an imaginary shape. You could just say, all shapes that are impossible to create, are impossible to paint.
Exaskryz · 720 points · Posted at 02:22:03 on February 14, 2016 · (Permalink)
Learned this most recently from Matt Parker:
3435 is the only number (besides 1) where if you split each digit up, raise each digit to that digit's power, and sum all of those products, you get the same number back.
Exaskryz · 48 points · Posted at 05:28:05 on February 14, 2016 · (Permalink)*
Nope.
I don't know what the proof is, but a topic I would explore is the rate at which a number grows compared to its maximum value by adding digits. 99 is n digits long. You could only add up to 99 by adding another digit 9 onto the candidate number. So if the candidate number is already so much larger than a string of n 9's, the value of the candidate number grows faster than the sum of the products of each digit raised to itself.
With some numbers, it's impossible for 999,999,999,999 to sum up to itself because 12 * 99 = 4,649,045,868 -- oh so much smaller. Adding another 9 digit onto that number (adding a value of 9 trillion) to that parent number isn't going to make the child number even come close to the parent number.
99 is 387,420,489, so some upper bound is probably only 10 digits long. At that point, you'd get a maximum sum from 9,999,999,999 which is 3,874,204,890.
(There is a quirk with a nine digit number where if you allow for 00=0, the property works. But 00=1, so that number loses the property.)
No, it is defined based on the function it is an undefined point of. For any function which has an undefined value, it is assigned a value in a useful way if the value is equal to the limit of the function when approaching that point. Xx does not have a defined limit on the complex numbers when approaching that point, because it depends on direction. It does on the reals. 0x does, and x0 does, and they are different.
If you assign it a value, it depends entirely on what the function is defined as near 0.
You only seem to be considering it from an analytic approach, though. How many functions are there from the empty set to the empty set? There are 00 = 1. How many ways can you choose 0 things when you have 0 things to choose from? 1 = 00 . In analysis, 00 should be left undefined, but in other areas defining 00 = 1 makes perfect sense.
Because even in those contexts, the reason you're choosing it is part of analysis.
The number of functions from a set of size n to itself is nn, restricted to n real, so as n goes to 0, its limit is 1.
Choosing 0 from 0 is either choosing n from n, or choosing 0 from n, which is n0 or nn again restricted to reals.
In the majority of cases where 00 is going to be 0, the equivalents in set theory are trivial and uninteresting, being trivially empty over the entire domain, but it is not remotely true in any field to claim that it is sensible to just assume 00 is 1. There are ALWAYS situations where it is just wrong.
narbris · 21 points · Posted at 05:57:33 on February 14, 2016 · (Permalink)
Yep, short answer 2,999,999,999 is the last number where the powers are larger than the number itself, so you can stop looking after that. Side note: this is only special in base 10. Any other base might have their own special numbers like this.
Of course lim y-> 0 gives 1 so xy is indeterminate at (0,0). In certain cases like set theory it is convenient to define it as 1 (think - how many permutations of the empty set are there? There's still one permutation even if the set itself is empty). It's far more common for these cases to be given as examples, hence why people tend to think 00 = 1 (rather than that it's indeterminate). In the case were talking about (PDDI numbers), I assume it's more convenient to take 00 to be defined as 0, although I'm certainly no expert in PDDI numbers (I imagine it's a very niche topic), so I can't say for certain what the experts in this field think about 00.
Kindof similar to narcissistic numbers like 8208. If you raise each number to the power of 4 (number of digits in the number) and add them up you get 8208.
opceryu · 2 points · Posted at 14:38:36 on February 14, 2016 · (Permalink)
I used to do windsurfing and in any sailing sport you need to have a sail number in order to other people (other racers, referees, spectators etc.) to indentify you in the sea since it is hard the see the person's face from such a distance. İnterestingly enough it was my sail number 3435 and also the numbers of most important cities to me.
It's not difficult to proof that there are finitely many of these kinds of numbers in any given base. There are only four PDDIs in the base 10 decimal system, two of them are trivial: 0 and 1.
I didn't see in that link, if there were, if there are infinitely many Canouchi numbers (besides 0 and 1) due to an infinite number of bases. Any idea if there might be?
The theorem I know states that for any given base there is a finite number of PDDIs. There may be very many in some bases, but usually it's just a handful. Let's collect each PDDI for each base and make it a set, so there is a set for the four base 10 PDDIs, a set for the base 2 PDDIs, for base 3 PDDIs, etc.
As you said, there is a base for every natural number, so there are countably infinite bases. We now have a countably infinite collection of non-empty, finite sets. The union of a countably infinite number of sets all with order >1 must have a countably infinite order.
We can prove this with some more rigor by considering the set of all these sets, let's call it S. So S = {s1, s2, s3, ... , sn} where sn is the set of PDDIs of base n. Create a bijection from each element in S to an element in the natural numbers. This is clearly a bijection because a set of PDDIs exists for every natural number (i.e. every base). Therefore, S is countably infinite (it can be put in a one to one correspondence with the natural numbers). Lastly, each element s in S is a set with finite and positive order because it's the collection of all the PDDIs for a base. In counting the number of individual PDDIs, we make a new set, let's call it P and it is necessarily true that |P| >= |S| because every s in S contains an element p in Pand by definition every p in P is also in some s in S. That last part is really just getting rid of the extra parenthesis/brackets that exist in S when you compare it to P (i.e. S and P are almost the same set, but the elements of S are are sets, the elements of P are numbers; realistically S just has some brackets that organize the PDDIs to correspond with their base, the last bit shows that omitting those brackets cannot make the set smaller).
Ergo, there are at least a countably infinite number of PDDIs if we consider any and all possible bases.
Edit: My post was created prior to seeing your post about bijections. I have not taken high enough maths to understand that part. Maybe after my law exam I'll try to wrestle with understanding it.
I'm getting lost in this. I can understand the countably infinite following a countably infinite argument. But I don't know where we can say that's applicable here.
I got lost in this because bases 2, 5, and 8 on the Wiki only have one PDDI. This is what I'm questioning - is 2, 5, and 8 the norm, or the exception, or just part of a pattern where every third base only has one PDDI. What I'm interested in is the count of bases with PDDIs besides (0 and) 1.
I guess another perspective to this question is how many numbers are there (infinitely many, or finitely) that can be represented in at least one base as a PDDI? The Wiki lists in base 10 that both 28 and 29 are PDDIs (in base 9 and base 4, respectively). But there seem to be inconsistent gaps between them.
I would also consider the possibility that a number can be a PDDI in multiple bases, and perhaps there are a finite quantity of PDDIs that appear in multiple bases to have the property. Unlikely based on the first nine bases, but I wouldn't rule them out.
This is all coming from being out of a maths class for many years, so I could be overthinking it or going in a totally wrong direction.
Ah. Well... if we discount the trivial case, the question becomes much more complex, and we'd have to query a number theorist. Same goes for asking if there are patterns to how many PDDIs a given base has. But if we are counting trivial PDDIS...
I think you are overthinking and I am over explaining.
Basically, there is a base for every number, and there will be a PDDI (or many) for every base, and since natural numbers are countably infinite, there cannot be fewer PDDI's than there are numbers. But each of these PDDI's is distinct in it's own base. 1 is a trivial PDDI for every base, so for example an infinite set of PDDIs could be {1, 1, 1, 1, 1, ...}, where each 1 is the trivial PDDI for a different base.
If we are not counting trivial PDDIs, or we are turning them into base 10 numbers to rid ourselves of overlap before we count, then... hmm. Well, if I had a proof that there is a finite number of bases with only trivial PDDI's, then we could confidently say there are infinitely many non-trivial PDDIs, but I don't know if such proof exists concerning the number of bases with trivial (or non-trivial) PDDIs...
I would hazard a guess that yes, there are an infinite number of bases with non-trivial PDDIs and thus an infinite number of non-trivial PDDIs, and that it can be proven, but I don't have the time (nor perhaps the knowledge) to prove that, and hazarding a guess is not math :-(
This sounds like some random stat of Lebron James just trying to make him sound better.
db0255 · 2 points · Posted at 04:59:15 on February 15, 2016 · (Permalink)
LeBron is the greatest of all time because he has the most assists in the third quarter in games where their team was losing by a prime number for a majority of the game and in which they eventually won on a Tuesday night before a full moon.
So he has that going for him.
martixy · 1 points · Posted at 13:54:37 on February 14, 2016 · (Permalink)
I bet there's other numbers, just not in base10.
Notsoace · 3923 points · Posted at 20:49:04 on February 13, 2016 · (Permalink)
It's impossible to comb all the hairs on a tennis ball in the same direction without creating a cowlick.
GotHamm · 2 points · Posted at 04:55:28 on February 14, 2016 · (Permalink)
In 5th grade I had a teacher with the last name Ball and I wondered if her brothers name was Harry. We also had a Ms.Butts (she went by Ms.B) and Ms.Cockman
Heh, I went to Greenfield Jr. High in El Cajon, CA in the late 80's. Our PE coaches were Harry Balls and John Hiscock plus Mrs. Tucker. Apparently after Hiscock retired they hired a guy named Longerbone but that was after my time.
I assume this was recently added to the page by one of the more charismatic members of Reddit, but when checking out Harry Baal's Wikipedia page you can find this beauty:
Everyone in Indiana is proud of their Harry Baals, and wants everyone to know about Harry Baals.
[deleted] · 2 points · Posted at 02:56:07 on February 14, 2016 · (Permalink)
From the wiki (seriously):
Everyone in Indiana is proud of their Harry Baals, and wants everyone to know about Harry Baals.
Harry Baals's descendants have since taken to pronouncing their name so that it became a homophone of "Bales.
[deleted] · 2 points · Posted at 03:31:18 on February 14, 2016 · (Permalink)
The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one p such that f(p) = 0.
I wasnt expecting to be so utterly lost when reading about something called "hairy ball theorem".
zarraha · 266 points · Posted at 23:34:22 on February 13, 2016 · (Permalink)
I don't think it applies, because wind speed is of variable strength. You could, theoretically, have all wind on the planet cease for just an instant. Also, you could have winds spinning in a circle at 1 mph, which barely counts as a "cyclone"
One scenario, in which there is absolutely no wind (air movement), corresponds to a field of zero-vectors. This scenario is uninteresting from the point of view of this theorem, and physically unrealistic (there will always be wind).
zarraha · -7 points · Posted at 00:08:13 on February 14, 2016 · (Permalink)
It's unrealistic that everywhere would be zero. But the theorem assumes that it is zero nowhere, that is, there is some wind on every single spot on the planet at all times, which is also unrealistic.
Well, how would we define wind? It's moving air particles. Air would only not be moving at absolute zero, and It's even more unrealistic to assume anywhere would reach absolute zero except for labs, which 1) use carbon, which isn't really an air particle, and 2) tests absolute zero in closed systems that would not affect the wind.
I wouldn't consider individual air particles wind. Wind is bulk movement (convection, not diffusion).
zarraha · 1 points · Posted at 01:48:17 on February 14, 2016 · (Permalink)
Well, if we're zooming into the microscopic level then I suppose 10 air molecules circling each other counts under this definition of "cyclone" so the statement is almost trivially true.
ScLi432 · 101 points · Posted at 23:51:04 on February 13, 2016 · (Permalink)
Cyclone meaning some swirling air, not a hurricane
I think there is a bit of a confusion here. In Oceania (Australia, NZ and the Pacific Islands) Hurricane/Typhoon type of storms are called Tropical Cyclones. Cyclones without the word tropical appended to it means just that, a coil of air mass at any speed rotating around a central point as the original poster above has stated. (Though in the Australian media a lot of people just drop the word tropical due to everyone usually being aware of what they're talking about)
No that's Asia. In Australia they're called Cyclones. Same thing as an American Hurricane.
ScLi432 · 5 points · Posted at 06:30:29 on February 14, 2016 · (Permalink)
I understand that. What I meant was you're interpreting the meaning of the word "cyclone" to mean in a large tropical storm, while in this context the word is being used to describe swirling air.
goerila · 9 points · Posted at 01:42:46 on February 14, 2016 · (Permalink)*
The theorem is working with continuous vector fields. A vector field can have variable "Strength" aka magnitude of the vectors and still be continuous. Clearly the zero wind case is unrealistic because there is always wind somewhere.
For your wind in a circle, wind is continuous, so if you mean a circle as in a circle from our perspective on the ground, then you would have problems with continuity of the velocity of air. Now if you mean a great circle (a circle around the globe) the problem is that as you approach a pole you are going to be having a higher and higher angular velocity in order to keep that 1 mph limit. This will give you a cyclone at the north and south poles.
Edit: Furthermore, you may wonder if the 3 dimensions fuck this up. They don't you could take the average velocity at every height on the globe (a continuous operation) then project that 3 dimensional vector down to two dimensions (another continuous operation). And now you have a perfectly good continuous vector field on the sphere.
No you couldn't, wind is caused by convection or the heating of air by the sun, it's about energy and so for as long as the sun exists there will be wind.
It doesn't apply. The theorem supplies the existence of singular points. So you could have the wind moving south to north everywhere in the world all the time and just canceling out at the poles (two zero points)
xigdit · 13 points · Posted at 06:56:06 on February 14, 2016 · (Permalink)
This is true but it kind of means the opposite of what you would think it means. It doesn't mean, there's always going to be a storm, it means, there's always going to be an "eye," a place of complete calm. (And the article further elaborates that this only pertains to a given 2-D layer of atmosphere, so in reality there's no assurance that we'd have a canonical cyclone anywhere that goes from sea level up to the clouds)
Really? I thought the theorem was that Sn S2 is non trivializable parallelizable. This refers to vector fields or the tangent bundle so necessarily to the Cinfty (or Ck) structure of the sphere, right? Or can you define a tangent bundle on topological manifolds so that the theorem is also true?
Edit: S2 is non parallelizable, TS2 is non trivializable
Quoting from the article, "it follows that for any compact regular 2-manifold with non-zero Euler characteristic, any continuous tangent vector field has at least one zero", so it's the topological properties of the sphere that are important, as far as I can see.
Well yes, but then what does the theorem mean about (only) topological spheres? It's like saying "a paracompact smooth manifold admits partitions of unity"; what does this mean about paracompact topological spaces? In cases like the Gauss-Bonet theorem it turns out that some differentiable definitions (integration) can actually be restated for topological manifolds. But is that the case? Is the hairy ball theorem about positive Euler characteristic topological manifolds? Or just about smooth manifolds whose underlying topological manifold has positive Euler characteristic? These are genuine questions, I honestly don't know. But I ask them because the Earth can be quite pointy!
[deleted] · 7 points · Posted at 23:32:35 on February 13, 2016 · (Permalink)
This is extremely misleading because the magnitude of the 'cyclone' according to the hairy ball theorem can be of any magnitude; this would most often be of extremely small magnitude; not nearly enough to be considered an actual cyclone.
Does this explain the great spots on Jupiter and neptune, along with the hex vortex on Saturn?
moom · 1 points · Posted at 00:42:18 on February 15, 2016 · (Permalink)*
No. As with many things scientific and mathematical, it didn't really survive the attempted translation into human language. It's not really saying anything about storms, nor about large storms, nor about long-lasting storms. It's just saying something like "At any given moment, there is some spot on the face of the earth that, at that moment, has no wind."
Somehow this means that the same science that causes my bad hair days is also relevant to the weather (which is also relevant to my bad hair days).
singham · 1 points · Posted at 14:14:15 on February 14, 2016 · (Permalink)
It's not a cyclone if it is small.
[deleted] · 1 points · Posted at 01:23:12 on February 14, 2016 · (Permalink)
Even more: there will always be at least two.
tellisk · 1 points · Posted at 03:35:05 on February 14, 2016 · (Permalink)
Not necessarily. This explains how 1 would be possible.
[deleted] · 1 points · Posted at 14:41:49 on February 14, 2016 · (Permalink)
Ah, of course, they can be infinitely close (a.k.a. the same point). Thanks for pointing that out.
tellisk · 1 points · Posted at 15:49:51 on February 14, 2016 · (Permalink)
No problem. I kind of fell down the rabbit hole of looking for information about when this started being called the "hairy ball theorem" (like, was it named that at a time when kids and redditors wouldn't think it's hilarious?). And read almost the entire Talk page looking for that info just before seeing your comment. I think the third image on the Wikipedia page also illustrates what it looks like (and there's an animated version if you click it).
[deleted] · 0 points · Posted at 00:05:15 on February 14, 2016 · (Permalink)
I'm not sure if you meant the mathematical topology or the dirty topology, but the earth is a sphere where that theorem is concerned. Unless there's a core bore I'm not aware of? Donut earth?
No, its actually not since the theorem really needs the object to be homeomorphic to a sphere. Since genus is a topological invariant this is equivalent to the earth having genus zero, but it doesn't! If you think about a tunnel through a mountain (which there are loads of) this gives the earth a strictly positive genus! There are also some funky rock formations which give the earth bigger holes, so unfortunately the theorem doesn't actually apply :(
Except that the atmosphere is not of constant pressure, so wind blowing into an area doesn't necessitate wind blowing out of that area. Not immediately, anyway.
Weird, here in texas atleast a cow lick is where you have some hair sticking up
F-0X · 284 points · Posted at 21:50:08 on February 13, 2016 · (Permalink)
No it's not. A tennis ball is not totally covered in hair. You need a hair at every point for this to be true; if there's even one single hairless spot, a flat-combing will be possible.
This is precisely because a sphere with one point removed is homeomorphic to a disc.
0876 · 853 points · Posted at 23:00:17 on February 13, 2016 · (Permalink)
Is it homeomorphic to a disc because that point turns into the edge of the disc, and the point opposite to the one that was removed becomes the center?
F-0X · 1 points · Posted at 10:13:57 on February 14, 2016 · (Permalink)
That doesn't make practical sense, though, because "a point" is a completely relativistic term; it can be as small as you want it to be. Nothing ever covers all points in a 3 dimensional reality, such as we experience. So for the purposes of that theorem, it's totally kosher.
F-0X · 1 points · Posted at 10:22:50 on February 14, 2016 · (Permalink)
A point is not relativistic at all in a topological sense. The theorem he's referring to states there is no non-vanishing section of the tangent bundle on a sphere. The tangent bundle is defined at all points, thus a section is defined at all points, so to talk about sections requires us to talk about all points.
I even gave an example of where ignoring just one point yields a case in which the claim is obviously false, too.
Depends on what qualifies as a cyclone. Even if you put the epicenter on a line, there would still be a cyclonic pattern around that point in the hairs.
I'd like to imagine some mathematically inclined ATP tour pro sitting in the locker room with a comb and a tube of fresh-smelling wilson brand balls doing calculations and totally forgetting to go outside and play their match.
Note that you have to be trying to comb it flat, i.e. tangent to the sphere, otherwise the normal vector at each point is an example of a smooth non-vanishing vector field.
[deleted] · 1 points · Posted at 00:57:06 on February 14, 2016 · (Permalink)
Wouldnt there be two cowlicks?
[deleted] · 1 points · Posted at 01:58:13 on February 14, 2016 · (Permalink)
No, imagine starting at an arbitrary point (let's call it the south pole). Now come every hair individual directly away from the south pole. Eventually, the issue of the cowlick arises at the north pole, but only there.
Can this explain why the universe cannot be homogenous? I.e. As soon after the big bang as there was space (i.e. a volume in which everything exists) at least one place was remarkable? As the universe expanded and cooled perhaps the at least 1 remarkable place became more diverse and more numerous. (Contrary to popular belief I'm stone cold sober right now)
[deleted] · 1 points · Posted at 02:08:08 on February 14, 2016 · (Permalink)
This sounds like folk wisdom, like you can't make an omelette without cracking some eggs.
"You know what Pa always says, you can't comb all the hairs on a hairy ball the same direction without a cowlick."
As a corollary, since you can comb all the hairs on a cat flat, a cat cannot be continuously deformed into a ball. By the classification theorem for closed surfaces, it follows that the cat must have (at least one) hole. This is the "cat's asshole theorem."
This also works for any 2n-sphere embedded in R2n+1 (e.g a 5 dimensional sphere)
sueca · 1 points · Posted at 04:57:55 on February 14, 2016 · (Permalink)
I had to look on wikipedia what a cowlick was (non-native English speaker) and then it became weirdly obvious when it was something as simple as "looks like whatever hair looks like after being licked by a cow"
There is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. You can comb the tennis ball because it has those ridges which are vanishing portions of the 'hairs as vector fields' interpretation.
Trying to work this one through hurts by brain. The "always" you've thrown in there makes it so much more complicated as it means the whole sentence could be a fallacy also, not just the answer of no haha.
If you answer no to the question, it doesn't mean your answer to the implied question has to be "Yes". It can be literally anything but "No", and the answers will not have been the same.
Fuck no, nah, negative, go away, not in a million years, etc...
It would be most effective with binary yes/no answers, a smart girl should quickly realise that "maybe" or "perhaps" ambiguities can break the logical sequence.
[deleted] · 1 points · Posted at 04:53:33 on February 14, 2016 · (Permalink)
"I cannot honestly answer your question since you've constructed it in a manner that requires me to answer one of the two questions dishonestly. Also, I find you unattractive."
amlybon · 1 points · Posted at 04:56:28 on February 14, 2016 · (Permalink)
No. Then when you ask me to go home with you I tell you to fuck off.
But seriously you're committing the fallacy of begging the question (this means you are giving a premise in the form of a question, without allowing them to disagree with the premise), so it wouldn't work on all those sexy logic majors you're targeting with logic based pick up lines.
sqqueen · 1 points · Posted at 05:34:09 on February 14, 2016 · (Permalink)
"If I asked you to go home with me would" is the first question. However, I don't see a second question. There is an inference of a second question, but it doesn't exist. Right?
[deleted] · 1 points · Posted at 10:02:18 on February 14, 2016 · (Permalink)
"No."
"So, do you want to go home with me? You can't say no..."
"Not a chance."
You can solve this problem by initially asking: "Yes or no: If I asked you 'Yes or no: do you want to go home with me?', would your answer to that question be the same as your answer to this question?"
I don't wanna go home with you, and you have no power to dictate my possible answers.
[deleted] · 1 points · Posted at 11:18:50 on February 14, 2016 · (Permalink)
"Umm, you're weird leave me alone."
[deleted] · 1 points · Posted at 12:32:42 on February 14, 2016 · (Permalink)
You did not specify that they had to answer Yes or no to the second question. So they could simply say no and then answer go away to the second question.
"Your conditions on the answers do not sufficiently encompass all the possible answers to the question you asked. You might as well ask 'Purple or Flint, Michigan: If I asked you to go home with me, would your answer to that question be the same as your answer to this question?'. Therefore I reject the conditions you impose. If you find this unacceptable that is your problem. In any case I will positively assert to you that I will not go home with you. Also, you're ugly and stupid."
[deleted] · 1 points · Posted at 17:48:50 on February 14, 2016 · (Permalink)
She then throws you off by telling you to "eat a dick".
wjwwjw · 1 points · Posted at 15:10:13 on July 19, 2016 · (Permalink)
The issue is that you act as if "yes or no" is one single question on its own. Followed by the stuff regarding to coming home. So actually if this would be a pick up line it would not make any sense.
This seems really superfluous because they start the whole proof by using the derivative of 1 to prove it. Can we not all just accept that if you have 1 thing and 1 more thing, there are now 2 things? I just don't understand how they complicate such a simple concept so much.
[deleted] · 4 points · Posted at 06:45:39 on February 14, 2016 · (Permalink)
I think the point is proving something mathematically without using math... Like if I say 1 + 1 = 2 in my system, what's to stop someone from saying how do I know your system is even right?
And you stop that person by proving 1 + 1 = 2 without adding 1 and 1
At that point, they don't actually show it, they just say that "From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2" which is on page 379 of volume 1. They don't actually finish the proof until page 86 of Volume 2, which is where you find the footnot
I'm pretty sure that's an axiom. You can't "prove" it.
Kered13 · 1 points · Posted at 13:49:15 on February 14, 2016 · (Permalink)
You can start there, but why when you can start with much simpler axioms? Modern mathematics usually starts with ZFC set theory, and constructs the natural numbers from sets. Then you can define addition over natural numbers and show that 1+1=2.
[deleted] · 1 points · Posted at 12:35:54 on February 14, 2016 · (Permalink)
Safe to assume you are talking about PM?
XenoD · 1 points · Posted at 16:57:19 on February 14, 2016 · (Permalink)
Except it isn't a theorem but rather the definition of the number two.
All math starts as axioms, which are statements we accept as being true. You can say 1+1=2 by definition, but you can start with different axioms too. A common way of getting to 1+1=2 is to start with Peano's axioms, which include:
0 is a natural number
succ(a) is the successor function, and yields the next natural number
Then we define addition
a + 0 = 0 the additive identity is 0
a + succ(b) = succ(a+b)
So with the definition 1= succ(0), and 2 = succ(succ(0))....
x = 1 + 1
x = succ(0) + succ(0)
x = succ(succ(0)+0)
x = succ(succ(0))
Substitute the first line for x, and our definition of 2, and we get 1+1=2.
Russle and Whitehead took so many pages to prove 1+1=2 because they wanted to construct modern mathematics from even simpler axioms than Peanos.
XenoD · 2 points · Posted at 17:27:13 on February 14, 2016 · (Permalink)
I think you hit the nail on the head.
BiggerJ · 0 points · Posted at 07:11:02 on February 14, 2016 · (Permalink)
Like when a child, in the fashion of Mindy from the Mindy and Buttons cartoons in Animaniacs, asked, "Hello, Mister Man/Lady! Why? Why? Why? Why? Okay love you buh bye."
EDIT: Just to clarify, it was not to nitpick. It's fucking Principia, one of the most important books written in history. It's not just about how '1+1=2'.
[deleted] · 322 points · Posted at 23:54:01 on February 13, 2016 · (Permalink)*
Probably, but the idea that 1+1=2 seems super simple but when you really start to think about it proving 1+1=2 already depends on quite a lot. You have the notion of equality with =, the notion of an operation with +, and these funny symbols that surround them. 1+1=2 seems pretty simple when you think about it in terms of I have one apple and I get another apple so now I have 2 apples, but that is kind of putting the cart before the horse in a mathematical sense. Math might help describe the physical world, but it doesn't depend on it. Math should be true regardless, and once you start thinking in those terms 1+1=2 is actually a really complicated idea.
af0929 · 3 points · Posted at 05:54:31 on February 14, 2016 · (Permalink)
The subtitle is: The entire project was futile anyway.
[deleted] · 6 points · Posted at 02:29:19 on February 14, 2016 · (Permalink)
Nonsense, the book was very influential and had very little to do with proving 1+1=2 in particular. Popular accounts like that Hofstadter book focus on Gödel and set theory etc. but ignore Russell's and Principia's influence on the most important philosopher since Kant, namely Wittgenstein.
I would contest the claim that Wittgenstein was the most important philosopher since Kant. I'd put Heidegger up there myself, or perhaps, though I hate to admit it, Peter Singer. Wittgenstein is almost a swear word in my philosophy faculty, if there is anybody who likes him, they're too ashamed to admit it.
As for the influence on others, it still doesn't change the fact that Whitehead and Russel had a stated goal, which has been shown to be impossible. I'm probably one of about 5 people in this thread who has actually read PM, rather than stuff like the Hofstadter.
db0255 · 1 points · Posted at 11:33:27 on February 14, 2016 · (Permalink)
Let's be real here. GEB wasn't a walk in the park either.
serfis · 1 points · Posted at 13:29:30 on February 14, 2016 · (Permalink)
Where would Frege fit in, importance wise? Logic classes were my favorite philosophy classes, and it seemed to me that he was very important in that particular area.
[deleted] · 2 points · Posted at 15:56:27 on February 14, 2016 · (Permalink)
[deleted]
serfis · 1 points · Posted at 16:45:38 on February 14, 2016 · (Permalink)
That's absolutely not the cool part.
The cool part is that this proof, got proven wrong/incomplete (in this case incomplete) (Kurt Godel)
zilpe · 659 points · Posted at 20:12:21 on February 13, 2016 · (Permalink)
It's not that the proof is wrong, it's that what they were attempting to do was shown to be impossible. They weren't trying to prove 1+1=2, they were trying to provide a rigorous frame work from which you could derive ALL of mathematics. Obviously 1+1=2 should be derivable in this framework which is why the "proof" is so long, most of it is simply setting up the framework.
What Godel showed isn't that their proof is wrong, but rather no matter how they create this framework there will be mathematically true statements about arithmetic which are unprovable.
But you're still wrong. Russel and Whitehead's proof that 1+1=2 is neither incomplete nor wrong.
What Gödel showed was that their more general attempt was futile: no matter how comprehensive your axiom system, there will always be some statements that can't be proven or disproven.
bg93 · 6 points · Posted at 00:35:00 on February 14, 2016 · (Permalink)
Could you explain a little more how it is that no axiom system can prove all true systems in arithmetic?
It is more or less that no (sufficiently strong) consistent system (being able to prove no contradictions) is complete (being able to prove all true statements).
What Gödel did was to construct a mathematical statement that states, "I am not provable." If the system can prove it, then there is a contradiction. If the system can't prove it, then it is incomplete (because it is true).
[deleted] · 1 points · Posted at 20:30:56 on February 14, 2016 · (Permalink)
How do we know that Mathematica statement to be true? If it were false then the system won't have to prove it.
At the behest of others, I have decided to do a brief (well, that's the plan, we will see) write-up of the key points of Godel's proof.
First, we start with formal logic.
You don't just start with axioms. You need a language. A language consists of the functions, relations, and constants1 that, in conjunction with logical symbols and variables, your statements will be made from.
The language of Peano Arithmetic has 1 unary function: S. S stands for successor, and its standard interpretation is "+1". PA has no relations, and 1 constant, 0. The standard interpretation of 0 is 0, shockingly.
With this are a small number of axioms that basically explain how S should behave, as well as Induction. Also, we can define the functions + and * and the relation < using PA. It's a very concise system that does arithmetic.
So, you have a language, so you can make formulae. There is a nice, concrete definition for something called a "well-formed formula" but the basic idea is that the formula "makes sense". Like it's not just a random combination of symbols. Formulae may contain any number of variables, and we refer to formulae with no free variables as "sentences". That means that a formula may have variables, but each must be associated with a quantifier (for example, in "for all x, x =2*y" the variable y is free, but x is bound).
A proof, then, is a finite sequence of formulae such that each formula is either an axiom, or follows from 1 or more previous formulae in the sequence using a rule of inference. So if you have "P" and "P implies Q" then you can put "Q".
Now, very cleverly, Godel found a way to take any symbol, formula, or even an entire proof and encode it to a unique natural number (that is, two symbols, formula, or proofs have the same Godel Number if and only if they are the same). So for a formula P, we denote the Godel Number of P as #P. The exact encoding doesn't matter too much, but basically you just "number" the symbols of the language (this goes to infinity, because there is no limit on the number of variable symbols you can use) and then encode the formula using primes. If P is the formula "x=0" and #x is 17, #= is 1 and #0 is 2, then #P is 217 * 31 * 52.
The bulk of his work is in the next part. Godel showed that there is a formula that takes a single variable x, and is true when there is a proof of the statement whose Godel Number is x. This is amazing. I would argue this is the meat of the proof, because it must have been a nightmare. Let's call this formula Prov(x).
Some consequences of the above. If PA can prove P, then PA can prove Prov(#P), since if PA can prove P, there's a proof of P, so Prov(#P) is true in all models, so Prov(#P) is provable. And we notice now that, in particular, "not Prov(#P)" is a formula with one free variable.
Then we have The Diagonal Lemma. The Diagonal Lemma says that in certain axiom systems of arithmetic, for any formula F in the language, that has one free variable, there is some sentence P such that the axioms prove "P if and only if F(#P)". And what do you know? PA happens to be just strong enough to be one of those axiom systems!
So, that means if I take a formula with one free variable, oh, say "not Prov(#P)" then we see that there is some formula P such that PA proves "P if and only if not Prov(#P)" (*). What does this mean?
Well, we pretty much know PA is consistent. So what can we say about P? If P is provable then we concluded above that PA proves Prov(#P). But (*) tells us PA proves not Prov(#P). That would mean PA is inconsistent. So we conclude P is not provable.
And if P is not provable, then PA proves not Prov(#P). In this case, (*) tells us P.
So PA is an axiom system, and it cannot prove the true statement P.
So that gives us that at least PA can't prove all true statements in arithmetic. What if we take some other axiom system that's strong enough to do arithmetic? Well, we aren't considering inconsistent axiom systems, because of course they are complete, and the axiom system is strong enough to do arithmetic, so it satisfies all the parts of this proof that PA was necessary for, so this proof applies, and we see any axiom system fails to prove all true statements.
-1 : technically, these are function symbols, relation symbols, and constant symbols. They have no meaning in the language alone.
If you have any questions about specifics here, I would be glad to help if I can.
"How" is just "because it has been proven." I wish there was a more fulfilling answer, but there isn't. Maybe looking at it in a different light will explain it better.
There are some very important details that tend to be glossed over when people reiterate Gödel's theorems. Perhaps most importantly, it's not just any type of axiom system that fails to be sufficient. It's recursively enumerable axiom systems, which means one can find a Turing machine that uniquely defines the set of axioms in some way.
Otherwise, we could simply take the set "all true statements" to be our axiom system, and then it would be complete.
So in this sense, Gödel's theorem kind of says "there does not exist a Turing machine capable of deciding all true statements".
His proof is very complicated. There are just too many points that would amount to "and then Godel proved X" that I may as well just say "Godel proved the whole theorem".
I mean, if you really want, I could break it down, but I just don't think it offers a ton more insight.
I'm not the one who needs the explanation. But there are ways to explain his incompleteness to laymen without getting extremely technical. You miss some of the finer details but the proof is still intact.
I always liked Turing's version of it, the only issue being that people often take it to mean "Oh well computers will never be as smart as people anyway, we already knew that".
kaibee · 3 points · Posted at 07:51:43 on February 14, 2016 · (Permalink)
You may be joking, but you are actually sort of correct!
The proofs of each have a lot of similarities, and there is a weaker form of Incompleteness that is a direct consequence of the undecidability of the halting problem.
kaibee · 1 points · Posted at 18:31:23 on February 14, 2016 · (Permalink)
Huh, maybe I've learned something from all of these CS classes :v
LE4d · 1 points · Posted at 07:40:38 on February 14, 2016 · (Permalink)
heap42 · 1 points · Posted at 23:29:31 on February 13, 2016 · (Permalink)
at least in Peano Arithmetic.
Shaxys · 5 points · Posted at 00:50:15 on February 14, 2016 · (Permalink)
If this refers to how some statements can't be proven or disproven; no. No matter what axiomatic system you have there's always two possibilities: 1) there's some statements that can't be proven/disproven or 2) the system is inconsistent and unreliable (not interesting).
heap42 · 5 points · Posted at 00:57:34 on February 14, 2016 · (Permalink)
I am fairly sure that Predicate logic(First order logic is complete) Same holds for Pressburger Arithmatic... sure you dont have everything but still... Also, Gödels Completeness itself is has some restrictions... something about beeing a set of axioms strong enought to do arithmetic etc...
nilcit · 3 points · Posted at 04:01:39 on February 14, 2016 · (Permalink)
yeah, first order logic can be show to be both consistent and complete
[deleted] · 264 points · Posted at 20:16:52 on February 13, 2016 · (Permalink)*
It's not that the proof for 1+1=2 was proven wrong exactly, rather Gödel showed there are some true statements of number theory (or any system capable of representing itself) that you cannot prove are true. He showed that Principia Mathematica was necessarily incomplete.
Edit: I like how the parent comment to this was quietly edited to include my incompleteness remark and now I'm getting downvotes.
To be fair, Godel's incompleteness theorem was probably a joykill for just about everyone.
[deleted] · 1 points · Posted at 02:16:50 on February 14, 2016 · (Permalink)
No, we get erections in the logic class just mentioning it. Last year's prof said it was "almost poetic".
heap42 · 1 points · Posted at 23:31:40 on February 13, 2016 · (Permalink)
No. The proof is correct. Also, proof cannot be complete(i think) completeness is the property of an algorithm/calculus. also 1+1=2 this is a true and proven statement. However the original paper, tried to prove that everything can be proven in peano arithmetic, AKA Completeness, but Gödel proved that this is not the case.
[deleted] · 6 points · Posted at 19:21:17 on February 13, 2016 · (Permalink)
The proof is given on page 379 of principia mathematica: volume I. Actually it is still to be finalized, that is done somewhere in volume II, but I can't find the right page right now.
Do you know a resource I could use to learn more about this stuff? I've had an interest in philosophy for a while, but particularly in stuff like this, where you take basic statements and just use the four basic laws of logic to deduce stuff.
[deleted] · 3 points · Posted at 02:25:16 on February 14, 2016 · (Permalink)
"The simplest thought, like the concept of the number 1, is a complex logical underpinning..."
[deleted] · 2 points · Posted at 00:09:45 on February 14, 2016 · (Permalink)
There's also one about zero (by coincidence titled Zero) which describes the concept of zero. Apparently the mathematical concept wasn't derived in the west until ~1200 c.e. I never read the book but I remember hearing that the author somehow proved that Winston Churchill was a carrot (or something).
What exactly is this whole 1+1=2 not being true thing? I'm good with basic math and geometry but never branched out into even knowing any n and n+ or ! Stuff.
How is adding one of something and another of the same something hard to prove that it equals two of that thing?
It's very easy to prove, depending on what sort of proof you want or what foundations you are working from. What they were really doing was trying to create a firm foundation for all of mathematics, and to check it was working they showed 1+1=2, because if they couldn't prove that then their foundation wasn't very good.
Principia mathematica--written to prove everything in math but then the authors gave up and after that somebody proved that it's impossible to do that.
No there isn't. If you're thinking of Principia Mathematica it attempts to prove all of math (later shown impossible by Gödel). It's not necessary to prove all of math to prove 1+1=2 since it's trivially derived from whatever axioms your formalism of mathematics espouses, so what Principia Mathematica attempted to do is not reducible to proving 1+1=2.
Can someone explain how a proof like this is even possible without being self referential?
As a layman, it seems to me that all of mathematics is based on extrapolation of a handful of fundamental givens and that we assign labels to these things. For example, that integers are incremented by adding 1 to each. The labels we give these groups of things are just shorthand.. like the symbol "6" really just means 1+1+1+1+1+1.
I don't know.. it's just weird to me because it seems like it would boil down to a pointless semantic argument about the definition of words. The entire concept of 2 is that it is 1+1. Apparently, I am wrong, but it seems to me like Alfred Nobel having to prove the dynamite he invented was, in fact, dynamite.
at 18 minutes 55 seconds. it doesn't actually mean 1+1 equals one. it means that it is mathematically possible for one object to double itself without adding anything else. its pretty cool. you should watch the whole video. it also does a good job explaining how huge infinity is. for example, if you subtract any finite number it would still equal infinity. Infinity-1=Infinity
No, I'm not making that up either. This is not the fallacious proof where 0 = 1, but rather that the domain of answers is limited to 0 and 1 (or true and false..... but you can use numeric conventions as they are also used in computing). The "+" symbol in this case is a synonym for the "or" operator in Boolean algebra. The other cases similar to addition work out just fine though:
But when engineering 1+1 = 3 for sufficiently large values of 1.
HW90 · 1 points · Posted at 10:58:25 on February 14, 2016 · (Permalink)
Until you do boolean algebra where 1+1=1
[deleted] · 1 points · Posted at 11:47:13 on February 14, 2016 · (Permalink)
I remember having to do some maths papers in engineering intermediate. When the lecturer devoted a whole lecture to proving 1+1=2 I decided I was glad I was going to be in engineering school the following year, and away from the mathematicians.
Consider some prime number (let's say 5) and consider a number that isn't a multiple of it (say, 9). What we're interested in is the remainder when 9 is divided by 5 (4, in this case), and the pattern that develops if we look at the powers of 9.
The powers of 9 go 1, 9, 81, 729... and the remainders go 1, 4, 1, 4... These two values repeat forever, and we say that 9 has order 2 modulo 5. It turns out that, when you write a fraction in a specific base system (decimal, binary, etc), the length of the repeating "decimal" (or repeating digits in whatever base) depends on the order of the base you're working in modulo the denominator of the fraction.
This is why fractions with 9 on the bottom produce easy, single-digit repetition, because 10 has order 1 modulo 9. Same with 3: 10 has order 1 modulo 3. It's worse with numbers like 11, because 10 has order 2 modulo 11 (so you can get decimals like .090909090909...). But the worst of them all, for small numbers, is 7.
The order of a number mod 7 (or mod any number) cannot possibly be bigger than the number itself minus 1 (in the case of mod 7, the order is at most 6). A number that reaches this maximum is called a primitive root, and unfortunately for math students everywhere, 10 is a primitive root mod 7 - that is, 10 has order 6 mod 7. As a result, fractions over 7, when written in decimal, have repeating segments 6 digits long.
Interestingly, if we choose a "nicer" base, this problem vanishes. In base 8, for example, fractions with 7 on the bottom have only a one-digit repeating part, just like fractions over 9 in decimal.
Endur · 13 points · Posted at 11:10:51 on February 14, 2016 · (Permalink)
574N13Y · 1 points · Posted at 10:21:14 on February 15, 2016 · (Permalink)
effort
[deleted] · 3 points · Posted at 14:52:39 on February 14, 2016 · (Permalink)
There is no shame in being good enough to make a living in something but not revolutionize the field. In fact, thats what the majority of people are at in terms of skill level.
Too lazy to find the source, but I've heard that with respect to intellect if you can grasp algebra all higher math simply requires time and dedication to learn.
Lack of interest is completely understandable, but you are in no way incapable of learning it reading the right books and practice.
There are plenty of people who're better than math than me, too. I have a Master's in it, but I don't really intend to study it too much further than that. There are folks who spend PhD and an entire career studying the behavior of things like primitive roots (in fact, there's a very celebrated theorem about them that has more known proofs than almost any other).
Depends on the kind of math. Combinatorists often do comp sci, analysis experts often develop engineering approximations and theorems, topologists and algebraists tend to be into physics.
3 and 7 are the only remainders of primitive roots mod 10. If you're thinking of 3 and 7 as symbols for equivalence classes then they're the only ones (but in that case, "bigger" makes no sense because the equivalence classes aren't ordered), but not if you're thinking of them as symbols for the natural numbers one usually writes 3 and 7. In fact, any number of the form 10n+3 or 10n+7 is a primitive root mod 10.
Do you mean the smallest primitive root mod 7 bigger than 10? Uh, well, there are 2 basic prim roots mod 7 (there's a function for this that's pretty easy to evaluate in your head for small numbers): 3 and 5. So 10 (which is 1*7 + 3) would be followed by 12 (which is 1*7 + 5).
[deleted] · 2 points · Posted at 10:58:31 on February 14, 2016 · (Permalink)*
I like the part about "nicer" base. Really, if we were base 8 everything would be nicer. We could half 1000 until reaching 1; computers wouldn't need binary kilo / mega (1024 vs 1000) and so on.
We could even count to 24 (30) easily on our hands.
And I can literally think of millions of reasons why binary is better. (I only need 64 :P)
aaeme · 6 points · Posted at 11:21:55 on February 14, 2016 · (Permalink)
The base of the number only has any meaning when writing it or naming it. As counting on our hands doesn't involve writing, I can only assume you want to rename the numbers something like this:
one, two, three, four, five, six, seven, octy, octy-one, octy-two, octy-three, ..., octy-seven, biocty, biocty-one, biocty-two, ..., triocty, ..., etc.
I think that's a great idea but I doubt most people would.
Each finger represents an order of 2 and you can encode 1024 numbers on your hands based on which fingers you have up or down.
i.e. if you have your hands out palms away from from you;
00000 00100 which is 4 would be represented by putting your middle finger up on you right hand.
00001 10000 which is 48 would be represented by putting both your thumbs up.
I don't think it's viable because some numbers are ridicolously hard to hold, such as any even number because holding my ring finger up without my pinky finger is painful.
I much prefer the base six version where you use the left hand to count how many times you've reached six and restart the count on your right hand again, this allows simple counting to 35 (who even needs to count to 1023) with no hand strain and little more complexity than normal hand counting.
It should be one, two, three, four, five, six, seven, ten, eleven..., seventeen, twenty, twenty-one,..., twenty-seven, thirty,..., seventy-seven, one hundred, etc.
Interestingly, if we choose a "nicer" base, this problem vanishes. In base 8, for example, fractions with 7 on the bottom have only a one-digit repeating part, just like fractions over 9 in decimal.
Is there a nicest base?
I'd imagine base 6 is nicest for this as all primes (par 2 & 3) are 6n ± 1.
A "nice" base for this purpose would be a minimum of lambda(n)/n, where lambda is the Carmichael function. 6 is one such minimum, since lambda(6) = 2 and 2/6 = 1/3, which is lower than any smaller number. You can do better, though: if you choose base 30, for example, you get lambda(30) = 4 and 4/30 = 2/15 is much less than 1/3.
Fmorris · 2 points · Posted at 11:32:28 on February 14, 2016 · (Permalink)
Then how do we get the digits that we get?
The multiplicative group modulo 7 (of which 10 is a generator) is:
{3, 6, 2, 5, 1, 4, 0}
But the decimal digits we get are:
{1, 4, 2, 8, 5, 7}
What is the link between the two?
zilti · 1 points · Posted at 12:14:17 on February 14, 2016 · (Permalink)
Those are my favourite math facts. Sometimes you suddenly notice something, and find out it's because of something else you thought is completely unrelated.
[deleted] · 1675 points · Posted at 02:15:43 on February 14, 2016 · (Permalink)
No, it just means that a certain number divided by a certain number equals a number. We just make the patterns significant.
[deleted] · 417 points · Posted at 02:33:04 on February 14, 2016 · (Permalink)
Actual it's more a description of a certain part of reality. If it was just a number that only had significance because we gave significance that then it probably wouldn't also be a naturally occurring phenomenon but it is.
[deleted] · 784 points · Posted at 03:17:45 on February 14, 2016 · (Permalink)*
[deleted]
TikiTDO · 528 points · Posted at 04:22:56 on February 14, 2016 · (Permalink)*
Except this also happens in say, base 12... In that case the decimal component is a repeating variation on ...186a35...
In fact this patter repeats itself in some way for any integral base, though not for an fractional/irrational base due to how decimals are represented in those cases.
Just because numbers are an abstraction, does not mean that the concepts that are being abstracted do not exhibit interesting patterns. I could argue that in fact these abstractions, and the patterns encoded there in are more "real" than anything in the physical world.
Edit: Since this comment got some popularity, I'd figure I'd paste my math rant from below.
A lot of time certain patterns do depend on other conditions. For instance, 1/7 in base 7 is simply 0.1, while 1/7 in base e is a non-repeating decimal. In fact the very idea of a "number" is deceptively much more complex than most people believe.
In general, math is better understood as a sort of language than some sort of immutable idea. It allows people to strictly define information in such a way that anyone else that understand that language can figure out exactly what is encoded. The beauty of math is that it allows people to define (nearly) any type of information, and to ensure that it can be understood in the exact same way by anyone else that understand the principles used to encode that information (mathematical axioms).
This is in contrast to a natural language, which may allow the exact same statement to be interpreted in different ways based on any number of contextual factors (say the mood of the reader).
Unfortunately, most schools do not present math that way until way into upper level university math courses, and by that point most people will never see the material, and will never realize how dreadfully they were cheated by our utterly horrible education system. The worst part is, once you learn to see math that way all of those strange rules and patterns that you had to memorize for school level classes become extraordinarily obvious. So much so that you could probably condense all 12 years of school math education down into a semester or two.
We do this all under the guise of it being "easier to understand," which is really just code for "we don't want to put in the work to figure out how to teach it correctly so even kids can get it, so we just teach it like we've always done."
[deleted] · 165 points · Posted at 05:10:08 on February 14, 2016 · (Permalink)
This comment chain is like a math nerd rap battle. Each comment I read I hear BOOM! or OOOOOOOH!
Broan13 · 108 points · Posted at 05:31:39 on February 14, 2016 · (Permalink)
It is a common fight between two major camps that typically are variations on "Platonism" (the idea that math exists in some abstract way and we only discover it) and "Nominalism" (the idea that we make definitions and put names on things, and therefore construct mathematics).
I am not treating the field of the philosophy of math with anything more than the broadest of brushes though. A good text I have read is on Aristotilean Realism which offers a 3rd idea that is a bit of a combination, but more of a real world version of platonism.
It's clearly a combination of both. Natural patterns exist with or without humanity, we simply happen to have discovered the patterns. We made sense of those natural patterns by assigning logical definitions to describe them. Obviously "mathematics" doesn't exist without us because it's a word we came up with and assigned a definition to, just like every other thing we've ever described. But nature doesn't care what we call it because it's already there doing its thing.
It really isn't that clear. Very clever people have spent their lives debating both extremes. Whilst obviously the names for things is a human construct, the idea that the "real numbers" actually exist or are some useful abstract tool we invented is very much up for debate.
Besides the numeral statues here on campus, "numbers" don't exist. We've never caught a glimpse of wayward digits floating through space, that's an idiotic idea. But the fact is that if there are several ducks standing by a pond, there is a certain number of them no matter what you call it. Objects in the universe are numerous and patterns exist. Numbers are things that we came up with to describe those objects and patterns.
I'm of the opinion that in some cases scientists and philosophers think way too hard about stuff that really is common sense.
Of course when you talk about number of ducks it seems obvious, but then start talking about how electrons only have spins of ±h/4π, and how the wave function describes quantum systems so unreasonably well (a wave function that has absolutely no physical interpretation until you take its modulus squared). You only need to look at the Higg's mechanism to see how a purely mathematical solution manages to predict the existence of whole new particles.
This reminds me of the descriptivist vs prescriptivist argument of linguistics
TikiTDO · 1 points · Posted at 20:02:20 on February 14, 2016 · (Permalink)
I never really understood that argument. It's an impossible distinction, at least within the context of our Universe. What would it mean for math to "exist" in some way? For us it means that the idea is somehow realized within the Universe we inhabit. If the idea does not exist in that way, then for all intents and purposes it does not exist for us.
Whether the idea "exists" in some abstract way or not is meaningless to people, since we would at least need to define what it means for an idea to "abstractly exist." What more, as you mentioned there are other perspectives. What if we define what it means to "abstractly exist" and find that only some of math is "discovered" from this abstract existence, while other math is a purely original construct. There are a near infinite number of way to mix these ideas.
In fact, you can draw benefit from viewing math as a superposition of both concepts, and applying just the right mix to whatever problem you have at hand. That I feel is the only proper answer.
Broan13 · 1 points · Posted at 20:10:08 on February 14, 2016 · (Permalink)
I don't have any answers for you, nor can I contribute much as I am not a philosopher, much less a philosopher of math.
To some extent I think the relationships exist in nature already, and that we discover them. To another extent I think we provide specific definition and define structures and discover the relationships inherent in that structure.
[deleted] · 1 points · Posted at 16:49:58 on February 19, 2016 · (Permalink)
I agree with your conclusion. The thing for me about all this is, and maybe it's because I'm not half as smart or educated on this topic as everyone else here, I can't see how someone might think that an idea doesn't actually exist. Of course it exists. It exists like any other phenomenon. It's synapses in a brain. Just because it's abstract and not tangible like a rock doesn't take it out of reality somehow. We accept other small electrical signals to exist, why if the context is in a human brain does it come in to question? Because it requires another human brain and language to decode it? That happens with other types of electrical signals we use every day. The content of an idea doesn't have to be logically true or false for that idea to just exist.
What do blondes and spaghetti have in common? They both wiggle when you eat them.
[deleted] · 13 points · Posted at 04:29:51 on February 14, 2016 · (Permalink)*
[deleted]
TikiTDO · 43 points · Posted at 04:34:59 on February 14, 2016 · (Permalink)*
In base 12 the pattern is 186a35. Or say, in base 19 the pattern is 2:13:10:16:5:8
In fact there are three rules about how this number is represented.
If the base is divisible by 7 then any number that is itself not a multiple of 7 divided by 7 is a non-repeating decimal point.
If the base + 1 or base - 1 is divisible by 7, then any number that is itself not a multiple of 7 divided by 7 will be a short sequence of repeated numbers, multiplied by the actual number. So for instance 1/7 in base 15 is 0.2222... while in base 22 it's 0.3333...
For all other integer bases, any number that is itself not a multiple of 7 divided by 7 will be the exact same sequence of repeating numbers.
It's not exactly an unexpected pattern, in fact it shows up across all sorts numbers in all sorts of bases. The number 7 just illustrates that property quite well in base 10. The number 5 exhibits the exact same property in base 7 for example.
It is simply an artifact of how the division operation works. So in this case it's not really a property of any specific number, but a property of the operation of division itself. It's still a cool fact about math that most people might never think about, but it has nothing to do with the number 7. You don't need to understand all that much math to see how it arises. Just do the division by hand and it will quickly become obvious.
[deleted] · 3 points · Posted at 05:29:14 on February 14, 2016 · (Permalink)
[deleted]
TikiTDO · 16 points · Posted at 06:01:50 on February 14, 2016 · (Permalink)*
That's actually not always true. A lot of time certain patterns do depend on other conditions. For instance, 1/7 in base 7 is simply 0.1, while 1/7 in base e is a non-repeating decimal. In fact the very idea of a "number" is deceptively much more complex than most people believe.
In general, math is better understood as a sort of language than some sort of immutable idea. It allows people to strictly define information in such a way that anyone else that understand that language can figure out exactly what is encoded. The beauty of math is that it allows people to define (nearly) any type of information, and to ensure that it can be understood in the exact same way by anyone else that understand the principles used to encode that information (mathematical axioms).
This is in contrast to a natural language, which may allow the exact same statement to be interpreted in different ways based on any number of contextual factors (say the mood of the reader).
Unfortunately, most schools do not present math that way until way into upper level university math courses, and by that point most people will never see the material, and will never realize how dreadfully they were cheated by our utterly horrible education system. The worst part is, once you learn to see math that way all of those strange rules and patterns that you had to memorize for school level classes become extraordinarily obvious. So much so that you could probably condense all 12 years of school math education down into a semester or two.
We do this all under the guise of it being "easier to understand," which is really just code for "we don't want to put in the work to figure out how to teach it correctly so even kids can get it, so we just teach it like we've always done."
Anyway, that's a bit of a sore point. Sorry for the rant.
In any base fractions of that base will be as you described. It does depend on the Base system, but 7 is interesting because it has the cycling repeating decimal in any Base that's not a multiple of 7 or +/-1
I came here expecting to discover new words I could write in my calculator like BOOBS, but now I'm struggling to reconcile my perceptions of mathematical abstractions and the universe.
Sure, but this doesn't mean "there is order in the universe." There are patterns in a rigidly constructed logical language, but the universe is not made of numbers. It's made of energy and mass, and time and space, and probability wave functions.
Does math have an existence separate from the universe? Separate even from all universes?
TikiTDO · 2 points · Posted at 19:46:00 on February 14, 2016 · (Permalink)
Math is a set of ideas, which are themselves ordered structures. It doesn't really make sense to ask whether ideas exist separate from a Universe or not, unless you can exhaustively/mathematically define what it means for an idea to be "separate" from a realized, physical object or in this case a set of objects.
The idea that there is order in the Universe arises out of the fact that the Universe can be described by such ordered ideas, both in part and likely in whole. What more, not just described, but described often in a concise and simple form as opposed to a myriad of exceptions and special rules that would have to account for countless random phenomenon. In other words the logical relation is "there is order in the Universe" because "the Universe can be clearly described by math."
I love how bitchy you guys just got with each other.
[deleted] · 43 points · Posted at 04:15:38 on February 14, 2016 · (Permalink)
Couldn't you use that logic to claim that basically any natural phenomenon isn't actually a natural phenomenon? Just because that phenomenon would look different when seen with different tools doesn't mean it's not there.
[deleted] · 58 points · Posted at 04:23:39 on February 14, 2016 · (Permalink)*
[deleted]
SlickMaw · 21 points · Posted at 04:48:52 on February 14, 2016 · (Permalink)
Isn't this a contested viewpoint between mathematicians and scientists?
[deleted] · 39 points · Posted at 04:55:46 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 9 points · Posted at 05:12:34 on February 14, 2016 · (Permalink)
Reality is that which still exists when you stop believing in it.
If you give two people the same set of mathematical rules they can derive the same proofs and verify them. Two computers running the same computer program will return the same results. If I work out a computer program by hand, I'll get the same result as a computer.
All of those things seem to indicate that math has a reality outside of any particular physical manifestation of it. None of those things need to have any relationship with the real world at all.
[deleted] · 13 points · Posted at 05:22:56 on February 14, 2016 · (Permalink)*
I agree that numbers are abstractions but patterns like Pi do occur in nature. It's the ratio of the circumference of a circle to it's diameter. While numbers themselves are abstractions they are used to describe reality. No matter the units or base number system you use your Pi will be equivalent to my Pi just expressed differently.
And an electron certainly "knows" precisely how much it's charge is because it "knows" how to behave as if it had that precise amount of charge. While the numerical representation of that is an abstraction it is equivalent to any other abstraction that represents the electron's charge.
As I've expressed elsewhere already, the question then becomes, are all abstractions real? You've admitted that Pi is an abstraction based on other observations/properties, "circle", "circumference", "diameter", and "ratio".
There is no debate on whether or not abstractions can pertain to real objects, the question is, does that make the abstractions themselves "real"?
Also, "natural". Is "natural" anything that happens in the universe, in which case abstractions, and the patterns that emerge out of abstractions are certainly "natural", or does "natural" only refer to non-human constructs?
I once had a metaphysics class, taught by a philosopher of language, who saved the last bit of reading for a piece about how all metaphysical arguments were actually problems of language. Was a neat way to cap the course.
It depends on what you mean by "real". Abstractions are absolutely real at least to some degree. If we take "real" to mean something I can hold in my hand or touch then your consciousness doesn't qualify as "real" but I think you might disagree and say that you do in fact have a consciousness and I believe you. I'd say that means that specific definition of "real" is only useful for discussing if something is a physical object. In that case of course numbers aren't "real" but it seems dishonest to imply that mathematicians think numbers are "real" physical objects you can hold. To demand to see a "two" and then say that because I can't show you one that you can touch that proves that numbers aren't "real" is juvenile and no more correct than saying your consciousness doesn't exist because you can't "show" it to me.
If we take google's definition
actually existing as a thing or occurring in fact; not imagined or supposed.
Okay so if it occurs in fact then it's real. Well I'd say integers occur in fact; there is no base number system in which one plus one does not equal two. The way you express "one" and "two" is expressed differently in binary but the math comes out exactly the same no matter which base system you use. So integers exist.
Let's address the original topic; 1/7 does not equal 0.142857142857. You can't express 1/7 exactly as a decimal just like you can't express 1/3 exactly as a decimal. As you correctly pointed out the interesting behavior of 1/7 disappears in other base systems however other such interesting behaviors from inexact decimal expressions of fractions emerge in other base systems. This means that all base number systems have the "real" property of being unable to express all of it's fractions as exact decimals. Except base one I guess.
TL;DR
Ultimately we are talking about emergent properties of systems and we are asking ourselves if those properties are "real". Your consciousness is just an emergent property of matter so I think the answer to "do abstractions exist?" is the same as asking "do I exist?" Since that is the only thing I can be truly certain of I'd answer with a resounding yes; yes, abstractions do exist.
I can certainly work with the google definition provided, for now at least.
So let's look at the second part:
not imagined or supposed.
Then let's take the definition of axiom (the foundation of mathematics) from WolframMathworld
An axiom is a proposition regarded as self-evidently true without proof.
Axioms, and thus the foundations of mathematics itself is stated as a pre-supposition, from which all other patterns and emergent properties derive.
Given that, it would seem that mathematics is not "real" in google's definition of the term.
I will agree, there is a hell of a grey area when asking about the reality of abstractions. I mean, I have abstractions, I experience them, as do countless other people, but they are obviously not of the same "stuff" as physical objects or forces.
You're pretending that mathematics is based on baseless assumptions that we could all discover to be incorrect next week but that isn't the case. It is axiomatic that there is no integer between one and two; not because it is an assumption but that is literally how we are defining one and two. The axioms of math don't dictate the truths of math but are instead derived from math using proofs not guesses.
Any axioms that are used that are assumptions are essentially meaningless ones meaning that if you make different assumptions then you are using a different system of math but one that will produce equivalent answers to the math we use now.
You're conflating the types of axioms to make it sound like mathematical axioms are made up truths like they sometimes are used in philosophical discussion to narrow the scope of the argument.
7+5=5+7 is not an assumption.
As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. As modern mathematics admits multiple, equally "true" systems of logic, precisely the same thing must be said for logical axioms - they both define and are specific to the particular system of logic that is being invoked. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.
takua108 · 4 points · Posted at 05:52:03 on February 14, 2016 · (Permalink)*
When do perfect circles occur in nature?
EDIT: According to the first result on Google, never. I'll admit to being not entirely sober right now but the fact that a perfect circle itself is an abstraction created by humans, and all that that implies, is blowing my mind right now.
I'm pretty sure the event horizon of a black hole is a perfect sphere which is made of an infinite number of perfect circles.
Edit: I'll add that photons orbit black holes at their event horizon and would also produce perfect circles in a slowly rotating black hole with no in-falling matter.
Well yeah, that's all that you can perceive with your human eyes. It's probably also surrounded by an infinite number of fourth-dimensional metaspheres, and so on to infinity
I was actually half-joking, but before your edit, I was thinking about gravity. I know nothing about physics beyond a handful of successful Mun landings (emphasis on "landings") in Kerbal Space Program, but: is it possible to build an artificial object and put it into orbit around a celestial body at as close of an approximation to a perfect circle as possible? Would there be any way to "prove" it was "perfect"? At that point, you'd be using mathematics to create an artificial thing, in order to prove that the artificial concept of a perfect circle was, indeed, a naturally-occurring thing, given the right circumstances... then my head hurt and I stopped, and now I'm reading about black holes. Fun stuff!
The fact that the object being orbited is not a perfect sphere would mean the gravitational forces would not be perfectly spherical either. The only thing I could think that would exhibit a perfectly spherical field of gravity would be a single particle, but that's way outside my layman's knowledge of particle physics.
If it wasn't a perfect sphere that would shift its' center of gravity. In that case the gravity would be equal at any equidistant point from the center of gravity which would just be shifted a teeny tiny amount from the center.
I don't think that's true though. Yes the center of mass would move, but the gravity wouldn't be the same from every point equidistant from the center of gravity. We can look at this example of the gravity of a massive cube-shaped object and see that any deviation from a perfect sphere would create a distortion in the gravitational field.
[deleted] · 2 points · Posted at 06:03:30 on February 14, 2016 · (Permalink)
Because the geometric object, a circle, exists completely independently of humans, and Pi is merely the term we use to explain the relationship between the circumference of a circle and it's radius. That is true regardless of human existence and names, and would be true in any universe with the same geometry.
Yes, I am not arguing that real properties don't exist. What I am arguing is that the systems we use to describe those properties, such as mathematics are nothing more than abstractions, and not existent things in and of themselves.
[deleted] · -4 points · Posted at 06:27:53 on February 14, 2016 · (Permalink)
Except numerous people were arguing with me and others even directly cited where and how this is actually a pretty contentious debate among scientists and mathematicians.
Don't get me wrong, I'm glad you agree with me, though I am now greatly concerned about your reading comprehension level.
[deleted] · -1 points · Posted at 07:08:15 on February 14, 2016 · (Permalink)
And what was the context in which I kept repeating the obvious? Could it be that others kept disregarding the obvious, thus necessitating a restatement of it?
[deleted] · 1 points · Posted at 12:58:17 on February 14, 2016 · (Permalink)
Sure, it's simply what we name a ratio that exists with or without us.
[deleted] · 1 points · Posted at 06:00:10 on February 14, 2016 · (Permalink)
As long as circles still exist the concept of pi would still exist. It wouldn't equal 3.14 but the nature of a circle wouldn't cease to exist just because a person never thought to come up with the use of radians to describe a circle.
Yes, but the use of "radians" to describe it, is an abstraction of the circle. The description of the circle is not the same thing as the circle itself. The mathematical description of an object, is not the same as the really existing object.
Then the question becomes, if there were no humans, super computers, or any sentient beings with which to derive the proofs or run the programs, would the concept of pi still exist?
If a tree falls in a forest but nobody is around to hear it, does it still make a sound?
Yes, it does. The physical phenomenon that we have dubbed a "sound wave" would still occur throughout a portion of spacetime, regardless of whether or not a sentient being is there to perceive or classify it.
What we're asking now is a question of whether or not we want to call abstractions "real" or not which is a very problematic area.
It's only problematic if we are overly-focused on semantics. Abstractions in and of themselves are not "real" except in the mind of the abstractor, but that which is being abstracted upon exists independently of the "abstraction".
Did "yes" and "no" exist before meaningful communication of any sort?
Continuing down the line of thinking summarized above, "yes" and "no" are abstractions of duality and non-duality (i.e., something either exists in spacetime independently of other things throughout spacetime, or it does not). So, before meaningful communication existed, the abstraction of "yes" and "no" did not (technically) exist, but that which "yes" and "no" abstract upon (duality and non-duality) still existed.
That is my take on the topic, anyway--I don't claim to have all the answers, as this is one of the most fundamental questions in all of philosophy, but to me personally this line of thinking makes the most sense.
And to me, personally, it seems that the tacit concession is that while mathematics can certainly correspond to and describe a physical object in supreme detail, that does not make the description of that object as real as the object itself, thus mathematics aren't "real" in the sense we think of as every day physical objects being "real".
Well said--although I think some people may define "mathematics" as being (or, perhaps, as including) the subject of the abstraction, rather than only the abstraction itself.
Very true. There's no rule that says you can't abstract based on an abstraction. If anything, I would call mathematics an extremely high-level abstraction, which also partially explains it broad usefulness. Its near-total detachment from any specific corresponding physical phenomena means its generality can be applied to countless phenomena regardless of their apparent difference.
saremei · 1 points · Posted at 12:35:45 on February 14, 2016 · (Permalink)
Oh but the mathematics are real. If we came across a sentient alien race, you would likely discover that while they use different numeric systems and different units of measure, their mathematical equations would most certainly be identical for things we have completely right. Units are arbitrary, equations are not.
Well, that's where the power of abstraction comes in. From a massive set of imperfect circles, we can abstract what a perfect circle would be and from that perfect circle we can then abstract the value of pi.
Marthman · -1 points · Posted at 06:13:50 on February 14, 2016 · (Permalink)*
Have you read the "platonism in metaphysics" SEP page?
No miracles argument?
indispensability argument?
Singular term argument?
Ontic Structural Realism, which is kin to (if not, just) mathematical realism, is quickly becoming the accepted position in theoretical physics. Have you read the SEP on that?
And you do realize that sets and other non number entities/structures count as mathematical objects, right?
The way you've just laid down your position so... assuredly, without noting that it's your opinion (and technically not even the majority one, according to philpapers) for the less educated to lap up with zero context doesn't sit well with me. I was going to be a little bit more critical with you, but I see from your history that you post in /r/philosophy and know who Heidegger is (not that that's any standard metric- but most non-philosophy-oriented people have no idea who that is), so I'll leave it at: I wish you had been a little more objective, less opinionated, and perhaps more willing to explain both sides for people to make their own decision.
And if you don't understand the other side, or can't post both sides of the argument because of that lacking, then you're completely unjustified in posting you opinion as if it were fact so that the stemlord hivemind just accepts it without batting an eyelash.
Knowledge is power. You seem to have it. Don't abuse it.
As for myself and my opinion... well, Plato was wrong about abstracta. Aristotle is where it's at.
There are plenty of others who are rather articulately arguing for the other side of the issue. That's how a debate works. I'm not here to educate others on the various positions wrapped up in the discussion of whether or not contemporary forms of platonism are correct, I am solely here to argue my position on the issue.
Do you mean "believe" as take as fact, or "believe" as in may use a theory or a concept that isn't empirically demonstratable in my daily life?
No to the first, and even then I bite the problem of induction, hard. Half-yes to the second, because even then I only use things that experientially help me, but I know that my experience doesn't constitute an infallible data set.
is there any proposition you hold as true that isn't empirically demonstrable?
Or are you just a nihilist in numerous senses (ethical, mereological, etc.)?
How do you empirically prove that what your senses tell you is true?
Do you believe the scientific method (in its various iterations) is a reliable source of knowledge? Do you believe you have a mind? That others aren't p-zombies?
Do you think infallibility is necessary to believe something?
I'm saying that what is evaluated as truth, both in broader social context and on an individual subjective is mediated by context and relationships. To frame it in the Phil 101 way, I don't believe in any capital "T" Truths, but countless, little "t" truths.
To go with your dinosaur example, given the context of knowledge of the process of how bone fossilizes, and given the context of the existence of dinosaurs (both of which are predicated on an innumerable number of given contexts) at this juncture, I would argue that dinosaurs once did in fact exist. Absent the necessary context for that evaluation, and the contexts that underlie those contexts, I cannot make any meaningful statement on the matter.
So arguments begin and end with what given contexts are agreed upon.
I'm saying that what is evaluated as truth, both in broader social context and on an individual subjective is mediated by context and relationships. To frame it in the Phil 101 way, I don't believe in any capital "T" Truths, but countless, little "t" truths.
So you believe that there is a difference between these two types of truth? What empirical methods did you utilize to come to this belief?
History of science mostly, of which I will freely admit that I learned primarily from second-hand sources. Theories and concepts in the sciences are predicated on the theories and knowledge that came before, as well as through empirical tests, and those empirical tests expose relationships between entities in the world, whose truth would not exist absent those relationships.
History of science mostly, of which I will freely admit that I learned primarily from second-hand sources.
Perhaps I am misunderstanding, but how would history of science be able to empirically evince anything vis a vis abstract categorization per se?
It seems like you can't empirically evince it because you're abstractly categorizing types of truth.
The propositional attitude you hold in regard to the proposition, (a) "there are different types of truth," is one of assent. You believe (a) is true. But I don't see what empirical process you engaged in to arrive at this propositional attitude.
The entirety of my life experience? Reading about how old truths were overturned as new knowledge came to light? The fact that different observers can have different experiences of a given phenomena?
You're trying really hard to go Socratic on my argument and not doing that good of a job of it. So let me help.
If, what I say is true, and there are no capital "T" truths, only little "t" truths that are relative to given context, what is the purpose or use of making a distinction between these two kinds of truth, seeing as given the proper context any little "t" truth, will appear to be a capital "T" truth?
And for that question, I have no answer and I am still struggling with it.
But empiricism relies on sense experience, which, in principle, precludes abstract reasoning about the concept of truth.
(a) is not a posteriori knowledge, which is what empiricism yields.
You're trying really hard to go Socratic on my argument
I was actually curious about whatever it is you seem to know that I don't about empirical knowledge. I took a charitable, dialectical tack rather than an accusatory argumentative one.
and not doing that good of a job of it.
What do you believe that "good" means?
So let me help.
Towards what end?
In any case, it seems like you don't believe all bachelors are unmarried men, and that triangles have three sides. Why not?
Lastly, do you not believe that you're not a brain in a vat?
Yes, I have derived my perception and definition of truth based off of my life experiences, that is the order that it went in.
Throwing out philosophical terms and arguments from the history of philosophy is not dialectics.
For the objective of showing a fault or flaw in my argument, you were doing a poor job of attain that objective. In that given context, that is what "good meant"
Given the context of the definition of the word "bachelor" in English, yes all bachelor's are unmarried men, because that's the context of the definition of bachelor. Same thing for triangles.
I am intensely skeptical of being a brain in a vat, but I cannot discount it as a possibility.
Except you can't perceive truth with empirical methods, no?
and definition of truth based off of my life experiences, that is the order that it went in.
your life experiences might inform your judgements about what truth ought to be considered but I don't see how they constitute the basis for a priori knowledge about the concept of truth itself.
Throwing out philosophical terms and arguments from the history of philosophy is not dialectics.
I agree with your position for one simple but also highly complex reason: how is mathematics privileged enough that it gets to be real while other abstract concepts are not so privileged.
Isn't it ironic to provide a diatribe against a comment and then, like a seven mile rapper, to just slam some Aristotle down on the stage?
Or was that your intention all along?
Marthman · 2 points · Posted at 17:42:55 on February 14, 2016 · (Permalink)*
The way you've just laid down your position so... assuredly, without noting that it's your opinion
As for myself and my opinion...
well, Plato was wrong about abstracta. Aristotle is where it's at.
So no, it's not ironic when the entire point of my post was to indicate that he should have surveyed the other side of the argument if he wasn't going to indicate that what he was saying was just his opinion (which, by the way, was terribly reasoned, as I expected from someone who just acts as if nominalism is fact).
I indicated that this was unacceptable because what he was saying is not a fact at all, despite his implying it.
And if you don't believe me, reread his posts. He claims to not believe anything that isn't empirically demonstrable, then in the same breath, espouses nominalism. No empirical endeavor evinces nominalism.
This is misleading to people who don't know anything about the topic, and thus, intellectually irresponsible. Then I proceeded to demonstrate that his reasoning processes are incoherent, and his beliefs untenable- which I knew would be the case when he cocksuredly indicated that platonism was false despite having no way of demonstrating this due to his epistemological commitments.
So again, when I "slam Aristotle down on the stage," as you so put it, I do so under the banner of opinion, thus setting the example for how to appropriately proceed with this conversation.
Question: Isn't that like saying two people who know how to spell a word the same way will spell the word the same why when asked how to spell it correctly?
The two people are using the same rules, so why would they not arrive at the same answer? The same goes for the computer. It was programmed by "us" with a set of rules.
But if you change or update the program, then the methods and results become the new reality. Which seems to be what people are, as organic computers. And in all fairness, I'm not sure if i'm agreeing with you, disagreeing, or just attempting to add to the conversation.
Whether or not you call the distance between objects by a specific unit, their distance is still existent. The concept of mathematics exists merely as a way to rationalize real "values" that simply don't have naturally assigned units. Just because an electron doesn't know that it has a charge of 1.60217662 × 10-19 coulombs doesn't mean that the properties that those abstractions describe are non-real. Whether or not you decide to assign the name or concept of the coulomb to this electron, it is still has real properties that such a unit describes. Irregardless of the existence of the base of our systems of measurement, their are values that are real, and are quantitative, and while our specific measurements of those things are non-real and abstract, they serve as a comprehensible means to understand very real things. For example, the Fibonacci sequence is a real, set ratio. It exists naturally in the universe, and can be observed throughout everything in existence. No matter what unit system you are using, no matter how abstract to us, if it is a comprehensible reflection of reality, the ratio between units will still be the same. Due to the fact that any system capable of measuring such phenomenon will require parallels to aspects of reality to be useful in understanding aspects of the universe, like the definite charge of electrons, any unit of measure will result in the same understanding of these real things. The units and math merely describe real things that will be observed and understood through any abstract rationalization of the phenomenon observed, if the rationalization is to be, well, rational. We may choose abstract ways to communicate these ideas, the concepts involved are still real. I don't know if we could change each others minds, but I do believe that we are describing real things with our mathematics, and that as such, math is an inevitable component in any rational universe.
Yes, real things are real. I am not arguing that. The debate is whether or not mathematical values are real, or are merely descriptions of those real objects.
Is the mathematical description of the charge of an electron as real as the physical property that is the charge on an electron os is it merely a description of that property?
drew4232 · 2 points · Posted at 05:58:47 on February 14, 2016 · (Permalink)*
I don't think that's where the debate goes, because of course those numbers are made up. They are not inherent in the universe. The names and units are of course made up. I think the debate is more on whether or not the mathematics exist as an inherent part of the universe or not, and while I am not arguing whether real things are real or not, I can see how I gave that impression. I more mean to say that because any rationalization of phenomenon in this universe would have inevitable parallels, to the point that any unit created would share ratios that describe natural phenomenon, that math exists in the universe. IE: No matter what unit you use to describe the Fibonacci sequence, the ratio between spacing of the units will be identical, and that as such, math exists naturally and we are merely describing it.
No one thinks that 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0; or the relations between those numbers, existed before we created them, and the debate is whether or not they are parallels to things that existed before the descriptors, or if they have no bearing in reality.
So you're describing mathematical applications to real world phenomena. What about mathematical abstractions that have no real life, physical analogues. Pure math, as it were? Is that "real" in the same way an electron will always have the same charge, or is it "real" only by way of the agreed upon axioms of mathematics, which are human abstractions?
[deleted] · 1 points · Posted at 05:57:16 on February 14, 2016 · (Permalink)
Now that I've read further into this I think we're making the same argument from different angles. What I was trying to say is that the math, in this case the fractions of 7 in a base ten system, isn't in itself a "naturally occurring phenomenon", but it is describing something that can be described in any number of ways. Mathematical constants, things like pi, don't only occur in base 10. They translate into something real and tangible.
I disagree on "real and tangible", but that similar or identical patterns will emerge, regardless of the base system used, is not something I am contesting.
[deleted] · 1 points · Posted at 06:14:56 on February 14, 2016 · (Permalink)
A circle having a diameter and circumference is just as real as an electron having a charge, is it not?
Is the description of that circumference, and the description of that diameter the same thing as the circumference of the diameter themselves, or are they nothing more than descriptions made by humans of the properties of that object?
AgAero · 1 points · Posted at 08:47:09 on February 14, 2016 · (Permalink)
Well shit man, you got your stuff all sorted out. Math just doesn't exist in the real world because we created it. I'll be honest that seems a little screwy. I feel like I lean towards math being intrinsically a part of the universe but I guess you would refute that by saying what you just did. But the guy ain't wrong either about the base 12 also having a reoccurring phenomena. Same result in a different situation.
But I guess that's why it's a philosophical point of moot. Weird that this is actually a debated topic. Figured everybody was like, "yes there is a order to the world and its our job to discover it."
But the fact that there is this completely incidental order to an abstract description tells us something about the thing we're describing.
Its representation in the language we use might be arbitrary, but there is something about it that's different from the other things.
Yes, but why all the 'it must be this, so it can't be this', when enumeration is just the lens we apply to math to work with, in this case, material behaviour within the universe?
Because that's the topic of the discussion. The fundamental question is whether or not math is real in the same way physical objects are real, or is mathematics a system of description.
I have been arguing that "math is just the lense we apply to work with." This entire time.
Consider, 1/10 is 0.1 in base 10.
Convert that to base 2 (binary) and you have 0.0001100110011.....
Where the 0011 keeps repeating forever. In this example we have taken a rational number and turned it into a number requiring infinite precision in base 2. But this is a repeating decimal, and thus not irrational.
A true irrational number will have no repeating pattern in any number base.
If we convert pi (3.14159265...) to binary
11.00100100 00111111 01101010 10001000 10000101...
(Which I was too lazy to do myself, so I got that here Binary Pi )
It does not repeat.
[deleted] · 1 points · Posted at 05:53:06 on February 14, 2016 · (Permalink)
To put it more simply, irrational numbers will be irrational in any rational base, and if you use an irrational base that number and it's multiples will be the only whole numbers.
(We could create a base pi system. It just turns out it's completely useless)
I would doubt it, considering changing the base system doesn't change the value the number has. Like if I hold out all my fingers on one hand, in base ten, we would represent that as "5", while in base five we would represent that as "10", but I'm still holding the same number of fingers up.
So, in anything other than base pi, pi would still be an irrational number.
(Please for the love of God no one start advocating for use of base pi.)
That's my take too, and I'm honestly kind of stunned I have to be defending it so vigorously. It seemed so patently obvious to me, but I apparently severely underestimated just how contentious a debate it actually is.
"Theories thus become instruments, not answers to enigmas, in which we can rest. We don't lie back upon them, we move forward, and, on occasion, make nature over again by their aid." - William James
I think it's because a lot of people see maths as a kind of physic : "something that explain world" instead of a tool used by physic to describe nature, because they often learned math directly with a physic application. That's basically what you were (very well) explaining in this thread.
I know fuck-all about math and Mathematical-antirealiwhatsit, but if we can use math to shoot a satellite into space and travel BILLIONS of miles with the unfathomable accuracy needed to reach Pluto at juuuuust the right time and place and with the proper speed for it to successfully enter the planetoid's orbit, and we can achieve countless other similar feats rather predictably using contemporary mathematical objects and descriptions to guide us, well then what difference does it make if those descriptions are "intrinsic to the universe" or not?
To me it's like asking if a photograph, or a series of photographs of a cow is the same thing as a cow. While the photographs, the "description" of the cow, might tell us a hell of a lot about the cow, they are still merely descriptions, however elegant and precise they may be.
He said we cannot verify these things as intrinsic to the universe so he assumes they are not intrinsic, though obviously that cannot be verified either. So you assume that the methodology that delivers tangible results over and over and over again is not intrinsic while tacitly admitting that there is no evidence you'd find acceptable to change your stance. Empirically, people want results. As for you, you sound like a denialist.
For things like that, I really prefer the term, emergent. Prime numbers will always emerge given the agreed upon axioms of arithmetic. However, those axioms are human conceptualizations and not inherent properties of the universe.
Because then we run into nasty philosophical problems such as, as I brought up earlier, the existence of unicorns. I can certainly conceptualize a unicorn and I can even describe a unicorn. If I ever got to utterly indescribable levels of boredom, I may even mathematically describe a unicorn. Does that make unicorns an inherent property of the universe?
Then again, by that logic unicorns are inherent properties of the universe. They exist as describable concepts, they can be conceptualized and described, that doesn't make them real.
The concept and description of unicorns are inherent properties of the universe because they exist. Actual unicorns are not inherent properties of the universe because they don't exist. Different things
which can be perfectly described using the values of math - an abstraction which, for example, the electron embodies. When math describes the embodiment of nature, its abstraction is redundant.
I'm already seeing where this thread is going and I'm very excited to read the rest of it. This is amazing.
([5])
AgAero · 1 points · Posted at 08:53:37 on February 14, 2016 · (Permalink)
Just because that phenomenon would look different when seen with different tools doesn't mean it's not there.
This concept exists in physics. Tensor quantities have this property of invariance with respect to coordinate system. e.g. a velocity vector is the same geometric thing no matter if you try to describe it in cartesian, cylindrical, or (fuck it!) even hyperbolic coordinates.
Actually, this idea of invariance is one of the grand unifying notions of physics. Conservation of momentum can be derived from invariance of the properties of a system with respect to changes in position. Conservation of energy can be derived from invariance with respect to time.
This pattern is simply the resonance of 7 against 10: the pattern created by dividing by 7 in base 10. Dividing by 5 in base 9 yields a different pattern. But since king olaf was remarking on the fact that there was such an extensive pattern at all, rather than the details of the pattern itself, the fact remains cool in any context.
While I agree with everything you said, I arrive at a different conclusion about numbers and nature.
Numbers are an arbitrary construct the same way language is. There is nothing inherent that says grass is "green" and not "blue" other than the way our language developed. But that doesn't take away from its utility. The fact remains that photon particles bouncing off grass making it green are similar to the ones reflected off of grasshoppers making them green. Just like the Pythagorean theorem would remain true for a number system of any base and the golden ratio would still be found in nature.
[deleted] · 11 points · Posted at 03:21:22 on February 14, 2016 · (Permalink)
Thats not really true. There are more than just base 10 number systems. Just because we have described most things in a base 10 system doesn't really impact that its a naturally occurring phenomenon. Sumerian's used a base 60 number system.
They actually used base 12, ten fingers and toes plus a null or cypher digit. A finger was used as an indicator as to which group of ten you were dealing with, say the thumb meant 1-10 (the first decimal), then you count nomally as we do today, then end by "not" counting the thumb, to indicate that decimal is complete. You do this 10 times, once for each finger and you have 120. From there you get sexagesimal.
I think you mean "it may be uncommon in other bases". This is definitely a natural occurring phenomenon. We may have made the representation, but the pattern is not man made.
Legion3 · 2 points · Posted at 04:13:53 on February 14, 2016 · (Permalink)
It's just pure random chance. In all the possible occurrences, there have to be patterns eventually. Doesn't mean it's important or that it's made at all. It just is.
Not random chance at all. The patterns are identifiable because the universe operates under it's own laws. While the universe goes through varied and often catastrophic change, all the evidence is, is that those laws don't change. Laws, such as the conservation of energy, suggest our universe has always been here in one form or another, going though its changes, according to the laws which govern it.
Legion3 · 1 points · Posted at 00:07:11 on February 15, 2016 · (Permalink)
This isn't about laws. This is numbers. I understand what you mean with the conservation of energy/mass etc and other scientific laws. But this is no such law.
This is just a cool mathematical image that we see because we have specified what the division means (what 1/7 actually means, to explain it better, the way we defined divide is what allows us to view the pattern), and as others have said better than I have, that it only occurs in base 10 numerical systems, not base n.
Imagine having a full grid of numbers, with 1-10 on the X&Y with 1-10 going diagonal down the middle. This will produce this pattern (replicated on the axis around the diagonal integers) and the pattern, is legitimately, viewable. This, however does not mean this is a scientific law, nor anything worth while. It may lead us to discover new laws, ideas etc. But as of yet, it's merely a cool sequence that means diddly squat.
To refer to the original post then, the universe is the coolest mathematical fact I know of. Of the enumeration we've done, which proves this universe, the laws are the most significant.
Right? You'd think that would be the end of the argument.
[deleted] · 1 points · Posted at 04:33:19 on February 14, 2016 · (Permalink)
fibonacci numbers in nature https://www.youtube.com/watch?v=ahXIMUkSXX0
there are patterns in nature that follow a certain mathematical order regardless of numbering system.
I never at any point argued there weren't. Those objects are real, certainly. The mathematics we use to describe and define them are man made abstractions based off of physical objects.
Even the words used to describe those things are all abstractions, despite pointing at 'real' or 'imagined' animals. You're totally accurate in your argument.
That pulls us back to the question of the reality or naturalness of all abstractions then. Obviously, math still works regardless of the base system we use for it, but base 10 math certainly didn't exist before human cognition. So, are all abstract cognitions as "real" or "natural" as base ten. See my unicorn example.
teefour · 1 points · Posted at 06:11:26 on February 14, 2016 · (Permalink)
I'm too drunk tired to do the math now, but wouldn't a similar pattern emerge in base 12?
Sound reasoning but a slippery slope. Are you speaking from somewhere outside of nature? Is base 10 arbitrary or conventional and why? Does it speak to human nature and would that be less fascinating?
Considering computers may relay the information to humans in base 10, but perform the calculations themselves in binary, yes base 10 is an arbitrary system, as any base system yields the same results.
In my opinion, human nature is a tricky term, and it would not be less fascinating.
It's a pattern in mathematics and numerical systems. Whether or not mathematics and numerical systems count as "part of the natural world" is kind of the entirety of the debate.
[deleted] · 1 points · Posted at 07:19:36 on February 14, 2016 · (Permalink)*
You're stating that there is no order or mathematical nature to the Universe because numbers are arbitrary? Mathematics are present in the natural world, and it's elucidations have nothing to do with numerical systems. The framework of the Universe is defined by quantitative functions/relationships, not by numbers themselves. Functions don't give a shit whether you define the world in base 10 or base 256, they still maintain their consistency. The fabric of space time has been defined to a high precision by mathematics to present an accurate image of the reality of gravitational distortion of space. The relative shape of the framework doesn't change based on the number system used.
If, however, you are just saying that numbers themselves, and not mathematical relationships, are arbitrary...then yeah, no poop. Numbers are referential, that doesn't change the fact that concrete relationships exist when we look at the world in a quantitative fashion, regardless of what type of discreet system is used. Marginalizing mathematics because to put forth a philosophical fap argument about how numbers "aren't real" is a waste of time. It doesn't change the fact that mathematics is the structural language of physical reality. It doesn't change the fact that things like the precision of GPS or the functioning of integrated circuits would not be possible without these mathematical relationships.
To make this a little bit clearer, the part of mathematics that are consistently present are the operators. Multiplication, equalities, exponents, division, addition, subtraction. The number systems can change, but the relationships as defined by the operators will remain regardless.
The fabric of space and time has been define to a high precision by mathematics to present an accurate image of the reality of the gravitational distortions of space.
My entire argument is that the distortions of space were already there. They were not "defined" by mathematics, mathematics makes a very good description of the already existent physical property. The universe didn't write itself in math. Math merely provides a very powerful abstractive tool to help us understand and describe these physical phenomena.
In other words, the universe has no structural language of its own. We as thinking sentient beings use the structural language of mathematics to describe what we observe.
To go along with recent discoveries, there were still gravitational waves before the mathematical models for them were created. There were gravitational waves before there were entities capable of conceptualizing mathematics at all. The universe does not care about our models and systems, it merely is.
[deleted] · 1 points · Posted at 16:30:21 on February 14, 2016 · (Permalink)*
There were gravitational waves before there were entities capable of conceptualizing mathematics at all.
You're making an unprovable argument here. It seems 'obvious', but without entities being around to see the existence of something, there's no way to know it exists at all. Something has to be observed to exist.
The universe didn't write itself in math. Math merely provides a very powerful abstractive tool to help us understand and describe these physical phenomena.
In other words, the universe has no structural language of its own.
There is absolutely no proof for this. For all we know we could be in a highly advanced species' simulation which has been programmed completely using mathematical systems. The fact that mathematics perfectly describes a multitude of phenomena with high precision indicates that it's very possible that the Universe is built upon mathematics. It's also possible that these properties are arbitrary and emergent.
It's not a matter of a caring Universe, and I'm not sure what that notion has to do with this discussion. It's a matter of mathematical definitions of reality being far more true than talking about it in a system of words. When we sit here and use words to argue that mathematics are an abstraction of reality, we are further abstracting our own perception of reality via the English language. At least with mathematics, once you know the framework, you have an intuitive understanding of reality that makes the abstractions drop away. Opposingly, arguments like this are engaging a word game that detracts from the real world. So, why is this important enough for you to argue this earnestly? What useful knowledge about the Universe does someone get through arguing the semantics of mathematics philosophy? It's all wretch and no vomit, it never gets anywhere. It's a circle of words that just drives a person to further abstract away from reality, moreso than if you were learning mathematics, yet you are passionately trying to use this symbolic language to undermine the significance of mathematics. What I'm curious about is why...what's the motivation here? What's the end game for this philosophical circuit?
There is absolutely no proof for this. For all we know we could be in a highly advanced species' simulation which has been programmed completely using mathematical systems. The fact that mathematics perfectly describes a multitude of phenomena with high precision indicates that it's very possible that the Universe is built upon mathematics.
That's called an argument from ignorance and it's a logical fallacy. At that point I can claim that literally anything could be an inherent property of the universe and because you can't conclusively prove that it isn't, I am therefore right? No that's not how it works. Considering the Universe was here before we developed mathematics, I see no logical reason to assume that the universe is written in math.
...yet you are passionately trying to use this symbolic language to undermine the significance of mathematics.
If you read through the rest of my arguments, you will see that I at no point argue that mathematics isn't useful. In fact, at more than one point, I argue that its high level of abstraction gives it its generality that allows it to describe so many phenomena so well. I'm not "undermining the significance" of mathematics. The other side of this debate is arguing for a significance we have no evidence for, and I'm the unreasonable one for arguing we shouldn't believe something without evidence to support it?
No one is arguing that math isn't pretty neat. It is. The entire argument is whether or not math is an inherent property of the universe or a man-made series of abstractions developed to help describe that universe. Neither answer says that math isn't important or not useful, it's just asking the basic question of what math actually is.
rasto_x · 1 points · Posted at 07:26:47 on February 14, 2016 · (Permalink)
Even though it's not a muscle, your brain does kind of behave like one. You know you're actually getting a good workout when you're feeling the burn, and you know you're pushing the boundaries of what your knowledge at present is capable of when your brain starts to hurt.
[deleted] · 1 points · Posted at 07:34:39 on February 14, 2016 · (Permalink)*
If I'm getting your jist correctly, are you suggesting things like the pattern described by the function of say, relativity, is one that is only observed due to our number system?
Observed mathematical patterns in the Universe are made practical with numbers, but the relationships themselves are not impacted by the number system used. Patterns in the Universe have operational relationships, that is, defined by multiplication, addition, equality, exponents, integrals, and derivatives. The relationships do not change when the number system used to quantify them changes.
If you're just talking about the arbitrariness of numbers, sure...but what a pointless argument.
That's not what I'm saying, at all. You have horrifically misconstrued my point, and I have argued rather consistently that real phenomena are, in fact, real.
What I am arguing is that descriptions of phenomena are not the same thing as phenomena themselves. As I said earlier, a picture of a cow is not the same thing as a cow. Following from that, the mathematical description of a gravitational wave is not the same thing as a gravitational wave.
In this sense mathematics is not "real" in the same way we think of everyday objects of our experience being "real".
If I need to open a physics textbook, you need to brush up on your reading comprehension.
wouldn't numbers/ratios like Pi, Euler's number, and the Fibonacci sequence be noticeable regardless? and why do they show up in nature if they are arbitrary?
It's all fake and made up if you think about it. Someone wanted an outcome and one point in time and made something up to give them that outcome. It became gospel and the rest is history
Except as has been pointed out elsewhere, base 7 +- 1. So the emergence of this particular pattern is dependent on the choice of base system, which is an arbitrary decision.
Because, that means any pattern that does emerge, is a result of the initial framing which is arbitrary and is not some inherent property of mathematics, much less reality.
But different patterns appear in every number base. They are inherent properties of mathematics. Just because one pattern shows up in one number base, doesn't make it any less significant.
I get what you are saying, but I fail to see how it makes any difference significance wise
The initial statement I responded to claimed the emergence of those patterns as a "naturally occurring phenomena" which is what my argument was against. Since the emergence of any given pattern is dependent on the arbitrary framing used, it is not a naturally occurring phenomena.
In that case, I agree with you. It is not natural. But the patterns are inherent in mathematics.
RainaDPP · -1 points · Posted at 03:40:55 on February 14, 2016 · (Permalink)
Here's a weird question to think about. Why is our natural number system base 10, when there's technically 11 states to our fingers? No fingers up is a valid state.
(The answer is probably that 0 wasn't really a thing until the Babylonians or whoever invented it. I'm sure nothing was a concept, but zero wasn't a number that could be counted.)
Here is where I'm pulling my information from. It looks like it was originally conceptualized by Sumerians, then the Babylonians got it from them. The Mayans came up with the concept independently about 700 years later.
The first place that zero as a number was used seems to be in India, which made its way over to Baghdad and got adopted into the Arabic number system.
Porrick · 1 points · Posted at 04:50:13 on February 14, 2016 · (Permalink)
10, not being prime, is a more useful number than 11. Of course, 12 would be more useful still (having even more factors), and there's something nice about powers of 2 like 16.
Here are some other base systems people use - none of them quite as popular as 10, of course.
I'd argue that numbers aren't really a naturally occurring phenomena. If there are five apples on the ground, there isn't actually a "5" in existence; those are all completely distinct and unique objects that are just existing. It's the human mind that groups and enumerate them because it's useful for us.
Numbers and math are no more real than ideas, and math has order because of its logical basis.
Number systems aren't naturally occurring but math IS!
If there are 5 apples on the ground then regardless of number system, there are still 5 apples on the ground. If you divide the circumference of a circle by its diameter you will always get the same result, even if your number system doesn't call it 3.14, that will always be pi mathematically.
Quick edit: the deviding by 7 thing is a product of our number system though haha.
It does take a mind to label the quantity, but if all of humanity disappeared, there would still be five apples beneath this tree. Numbers are an abstract which exist wholly apart from human acknowledgement. Much like gravity would remain if all humanity disappeared. The thing is that even if all physical matter burned up, there would still exist the possibility of real number sets.
Well gravity is completely separate as it isn't abstract. But in what way do abstract things exist apart from a mind? If all minds capable of understanding abstract concepts like numbers suddenly disappeared from the universe, in what exact capacity would those concepts exist?
in what exact capacity would those concepts exist?
Varying forms of chaos, I suspect. e.g. We only achieve a limited range of perception from our senses, relative to the energy spectrum that exists. My one use of lysergic acid showed me how mundane the daily level of our sense operation is in that regard. And, in that regard, the universe is itself a math abstract.
They would continue to exist by their very nature. If all minds capable of understanding the abstract concept of numbers ceased to exist, the five apples under the tree remain. They do not cease to exist nor does their quantity change. The concept of their being five of something is still just as logical and coherent in a hypothetical world without conscious beings.
There would be no description, but the quantity of apples has not changeded. Numbers are not created by the mind, they are discovered. Prior to humans describing the concept of five, five apples could indeed exist.
It seems like 5 apples could exist without a human to see them and call them five - but the problem with this scenario is that you are using logic to reach back to a point in time that completely lacks that logical framework. Saying that there were "five apples" before humans existed to witness them is to describe a completely fictional scenario in our common terms. Those apples weren't "five," those apples weren't even discrete nam-able (and countable) objects; it's humans who press math onto nature, not the other way around.
Interesting. There are no apples unless the universe observes there to be those things, in time. "..quantum Zeno effect, in which a quantum state would decay if left alone, but does not decay because of its continuous observation."
In this case, the term observation refers to the inclusion of regions of energy pertaining to matter operating under universal law. What causes the universe to cease 'observing' or 'including' things?
Time. Where time ceases to exist, things aren't observed by the universe. So, there's no point in time where apples exist separately from a form of abstraction.
The abstraction of numbers is created to describe said apples. In fact, the word 'apples' and the letters and the sounds are also all fabricated abstractions as well.
Forget enumeration for a minute. The universe is itself a mathematical abstraction (operates under mathematical laws. We know this because we've discovered them). So, as I've posted elsewhere here, the universe does the math, and we do the enumeration to understand the math. Look at what the universe fabricates with its math.
No. We use mathematical abstractions to attempt to understand the world around us.
The crux of this whole discussion and argument is that what you are claiming, i.e. "the universe does math" is false.
You are pointing to the universe and saying that it exists "because math". That is literally no different than pointing to the universe and all creation and saying it exists "because God".
The fact that math is useful does not prove it is real or exists in and of itself.
If it offends you that the universe does the math, take it up with the universe. I'm just reporting what science has already discovered. If you want to extrapolate unhappily, that's your business.
Well I was saying that the concept of a number is abstract. There is no object "two". There can be two of something, but the integer itself is abstract. This remains true if there are only physical agents at play without consciousness.
[deleted] · 1 points · Posted at 05:03:14 on February 14, 2016 · (Permalink)
You're just being pedantic. It's not that the concept is abstract, it's an abstract concept. The concept of rain water, or gummy bears, or jump ropes are all concepts of tangible things. These are not conceptually abstract in the way a number is.
Durty_ · 1 points · Posted at 09:30:04 on February 14, 2016 · (Permalink)
Lines exist in relativity, and we live in a relative universe. They may not be a property of circles and elipses, but how we describe their circumference.
Thanks for the link, and for pointing out the lack in my ripples argument.
Well, if you divide a real circumference by a real diameter, you're going to get different values more or less close to pi. Only a mathematical abstraction will get you pi. In fact, you cannot get a precise value of pi by measurement, only by calculation.
The irony is that ideas are real. They are one and the same with the state of some physical system. This conversation, for example, is real; to argue otherwise is to argue against the physical reality of the electrons and whatnot that it comprises.
Pluto, the planetlet, is an idea; you have never seen it with your naked eye, nor can you see it without a pretty hefty piece of hardware.
Pluto exists independently of your mind, has for a long time, willl continue long after.
Its existence was postulated in the 1800's and was confirmed in 1930. Using ideas. Ideas that turn out to be universally applicablle. Literally in this case.
A mind is irrelevent. The planetlets will continue to spin.
So, by virtue of the fact that you agree that Pluto exists and, you cannot verify the existence of Pluto with any means available to you, and because of the prior Pluto is only an idea, it must be the case that things exist without your mind, ergo things exist without your mind.
Things not existing without your mind was your premise. A thing that exists without your mind has been shown.
Things not existing without your mind was your premise
You're misunderstanding my premise entirely. I'm saying that invented concepts like math, not discovered objects like a planet, cannot exist without your mind.
Let me put it this way - Math is like language. Language is useful for humans because it lets us express and reason about our environment. But language would not exist if beings were not there to use it.
We distinguish a difference between mental energy and physical matter. Both are real. Both can or do exist, to an extent, independently of eachother.
So, the product from identifying, categorizing and enumeration become real, because we conceive them.
[deleted] · -17 points · Posted at 03:02:20 on February 14, 2016 · (Permalink)
[deleted] · -9 points · Posted at 03:06:52 on February 14, 2016 · (Permalink)
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[deleted] · 4 points · Posted at 03:15:33 on February 14, 2016 · (Permalink)
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Kaliedo · 3 points · Posted at 03:17:21 on February 14, 2016 · (Permalink)
Why are you insulting him for this? He's right, and makes an important point we often forget; math is not the language of the universe, it's not something intrinsic to the world. It's a system of logical rules and statements that, combined, happen to allow us to explain some of the phenomena that happen around us. Math is something wholly man-made. The fact that it works does not change that.
[deleted] · -2 points · Posted at 03:21:48 on February 14, 2016 · (Permalink)
I was stating a fact that gave credence to the argument that numbers and math are not real "things." Whether or not that's true, it's a view that the person I replied to did not have, and so in my mind was worth addressing.
But it seems like you're getting off on not being able to see the forest for the trees, so I'll let you get back to that, "fam."
the hell do you mean a "naturally occurring phenomenon"? What's "natural" about it? And how is it a phenomenon? That's like saying that the rules of chess are a "naturally occurring phenomenon".
trey82 · 1 points · Posted at 08:54:47 on February 14, 2016 · (Permalink)
Actual it's more a description of a certain part of reality.
No, it's just math that forms a pattern. Only out minds give it any significance.
If it was just a number that only had significance because we gave significance that then it probably wouldn't also be a naturally occurring phenomenon
That claim is so cringe worthy, but I have to ask anyway. What "naturally occurring phenomenon"??
but it is.
No its NOT. It's just a sequence of numbers. It has NO significance to reality.
[deleted] · 2 points · Posted at 05:23:51 on February 14, 2016 · (Permalink)
We're talking about two completely different things, but I appreciate your concern.
[deleted] · 1 points · Posted at 03:04:22 on February 14, 2016 · (Permalink)
Actually I have no idea why I'm posting but I felt like everybody needed to hear my opinion
[deleted] · 8 points · Posted at 02:32:22 on February 14, 2016 · (Permalink)
Patterns are intrinsically meaningless, yes. They do have constructed meanings, or contextual meanings, but it is fair to say that patterns have no meaning in and of themselves.
[deleted] · 1 points · Posted at 04:14:34 on February 14, 2016 · (Permalink)
Which is not the same as nihilism, and still not what I'm arguing.
Meaning has to be meaningful for something, there's isn't a magical "meaning" hardwired into the universe and if there were, there would be no disagreements about what constitutes something as meaningful.
[deleted] · 1 points · Posted at 04:55:31 on February 14, 2016 · (Permalink)
In that scenario you described, you're missing a couple of steps. The first is that you immediately recognize it as human writing, which is already an assumption of meaning. If a cow were to walk by the same wall, it wouldn't distinguish the writing on the wall as anything meaningful. It only has meaning for you, because of the context of you being human, and being able to recognize writing. The squiggles on the wall have no intrinsic meaning beyond that context.
[deleted] · 1 points · Posted at 05:05:03 on February 14, 2016 · (Permalink)
Okay what's the use of saying meaning is an intrinsic property of the universe, while simultaneously negating the intrinsic value of any specific meaning?
[deleted] · 1 points · Posted at 04:31:25 on February 14, 2016 · (Permalink)
Personally, I think of a pattern as essentially the definition of intrinsic meaning.
How do you figure a pattern is the definition of intrinsic meaning? The essence of all meaning is patterns?
Exactly. Humans are the ones who designed base 10 mathematics. The fact that we arbitrarily decided that we would use these 10 symbols, and then start over with multiple next to each other just so happened to work out into a pattern with a specific prime number.
Humans are great at finding patterns. Figuring out why they exist takes a while, and that's if there even is an answer.
To correct you its not the division of a certain number it's the division of any number in regards the the recurring decimal patterns.
[deleted] · 5 points · Posted at 03:52:40 on February 14, 2016 · (Permalink)
Pfft only in the base-10 counting system. Show me another cool fraction of 7 in another base.
Grokent · 1 points · Posted at 05:37:58 on February 14, 2016 · (Permalink)
In base 12 it's 186a35 someone above said. I'm on my phone however so I'm too lazy to check. Pop 2/7 in base 12 into wolfram alpha and see what you get.
Hey you know this logical mathematical framework that we constructed? If you look closely and break it down, there's some neat patterns that almost seem as if they result directly from that logic.
Where and how? If I make up an imaginary object and tell no one about it, does that object retain its essential objectness after I die? Did it exist before me? The concept of a circle, for example, is useful for humans but does not exist (perfectly) in nature.
Whothrow · -1 points · Posted at 07:14:36 on February 14, 2016 · (Permalink)
The circle argument, which you cannot prove btw, is why I used A triangle. The concept of a (perfect) triangle does exist in nature. Water, for instance, is neither imaginary, nor will cease to exist, with or without you. It will, often enough, be in a platonic ideal state, arranged in sufficently trangular position, to retain its triangleness, regardless of wether or nor you were able to see it.
I'm not the person you originally replied to, but I think Plato would have changed his mind if he had known anything about quantum mechanics. This "triangular" water you speak of is a human construct as well. (I assume you're referring to the "bent" shape we say that water molecules have). This shape doesn't really exist...only the relative positions of the electrons wave functions around the hydrogen remain "bent" relative to the oxygen or an arbitrarily selected plane.
So, while all water molecules share the same properties, individual water molecules have emergent properties.
I mean, does an atom that decays radioactively have some platonic form before it decays but not after? I don't know Plato that well, but would he have said that it's part of uraniumness to eventually become lead? I highly doubt it.
No, math has nothing to do with the universe. It just the philosophy of number, and humans have made a philosophy with certain patterns (and still some gaps).
[deleted] · 0 points · Posted at 05:25:54 on February 14, 2016 · (Permalink)
Order yes, purpose no. Order can come from chaos and randomness as long as there are solid and unchanging rules for what can happen and what can't happen. You can argue about whether or not your God created those rules in the first place, but you can't argue that order comes from chaos. It happens all around us all the time and it isn't disputed by anyone except those who haven't bothered to learn about it.
I know a house had a builder because I have NEVER seen houses spring up out of the ground on their own. I have also built houses personally, so I know what is required to build one. I've also built a radio before and I understand the principles and mathematics behind electromagnetism. There's absolutely nothing magical about building radios. Humans do these kinds of things and we can repeat them and show other humans how to do them. There is no mystery in your examples...yet you're ascribing a sense of mysticism to them...why?
You're talking about making inferences. Yes, we do that all the time. It's one way we get clues about the past...and making inferences about evidence we find is the only way to make inferences about the past before humans began recording history in writing.
Thing is, there's a huge difference between making inferences about the past based on physical evidence and reasoning and doing what you're doing, which is reasoning from a predetermined conclusion (that the universe has purpose and design). How do you make the leap from physical evidence to "God did it"?
[deleted] · 1 points · Posted at 03:28:28 on February 16, 2016 · (Permalink)
how do you think something as complex as the human brain which we know absolutely nothing about happen by chance? Just look at the endless variety of life, you can't say that any of that just happened by chance!
No, it didn't happen by chance. Evolution is not random. This is a common misconception that people have about evolution. Organisms evolve based on their interaction with their environment. The human brain is simply a more highly adapted and more complex version of every other brain and nerve bundle we see in nearly every multicellular organism on earth. Humans survive and reproduce more successfully because of our intelligence...it's beneficial to us in our environment so it exists.
If you believe god created the universe with the big bang (as your link suggests) and then let it go, that's not a claim I can really say anything about. However, if you believe god creates miracles and intervenes in the daily lives of humans, then that sort of thing is disputable.
We have physical writings from the past that is inspired by god.
You have no evidence that those writings were inspired by God. You just have writings written by humans. Beyond that you have no proof because what you're saying is by definition supernatural.
Same with wind for example, you cant see wind, but you can feel it when it hits your hand or a leaf is floating through the sky.
Again, I don't know why this is reason to believe anything religious. We can't see atoms or electrons either, but we understand them through our use of mathematics, scientific tools, reasoning, experiment, etc. We can't see wind, but we can understand that it is caused by changes in air pressure and that we can feel the force applied by the elements and molecules that make up our atmosphere.
There are MANY unscientific claims in the bible including the claim of a virgin birth, changing of water to wine, walking on water, resurrection...all of these are unscientific claims.
Anyway we don't need to discuss all that. Let's just say for the sake of the discussion I grant you that there aren't any unscientific claims in the bible I'm not sure why that makes the bible worthy of particular special consideration. There are many books which lack unscientific claims...
Its hard to accept there being someone that is of a higher power than us because we can't comprehend it. But thats why the bible exists. Also the principles that we can apply in our lives today are invaluable. These principles are the foundation of human law. Every single person living in the United States of America are covered by those same exact principles written in the bible.
I don't know what you're talking about here. I mean, I know you're telling me what you believe, but I don't understand how you started down this path of thought from what we were talking about.
Even more primal. This universe could have been a different universe instead. These mathematical truths could never have been anything else. They would exist in the empty void.
Toodlez · 1 points · Posted at 06:49:14 on February 14, 2016 · (Permalink)
And as we all know, order begins somewhere between 1 and Graham's Number.
[deleted] · 1 points · Posted at 10:42:44 on February 14, 2016 · (Permalink)
The abstract concept of mathematics is the mind-blowing part. Once you accept its self-evidence, its curiosities are trivial, and speak no more about 'order to the universe' than the fact that 1 + 1 = 2.
No it just means we've organized our perception of the universe into a foreseeable predictable pattern
[deleted] · 1 points · Posted at 14:26:25 on February 14, 2016 · (Permalink)
No it doesn't. Math is a tool of the human brain; an invention. We find models that are descriptive to the natural world, but that natural world is noisy and therefore our models have imperfections. We can only quantify the deviations from our model using statistics.
We created math. It has no connection to the universe. Based on the system we created, it might have some coincidences, but it could've been done differently. Why does everyone jump to universal grand claims over things like math that are totally just ideas made up by us?
ophello · 0 points · Posted at 08:57:58 on February 14, 2016 · (Permalink)
No, it means we use a decimal system. The relationship between 10 and 7 yields this result.
The pattern is a product of the number base, not magic or even math really.
You'll get different results in binary, octal, and base64. A really carefully chosen base system would either have none of these, or use them to highlight meaningful things.
Math can be done in any number base, arithmetic has to pick one.
[deleted] · 2 points · Posted at 07:49:38 on February 14, 2016 · (Permalink)
If you had "six hundred, sixty six" oranges. It would be equally true to substitute one of those 'numbers' to tell someone how many oranges you had. The arabic numeral system is just an arbitrary choice of ten symbols.
An easy exercise is, count from 0 to 9, then call the next 'number' A and continue down the alphabet. That would be base 36. Where 10 represents "thirty six". Because it's a one in the 36es place, and a 0 in the 'ones' place.
If you don't understand it, you haven't "learned" it ... you've merely learned of its existence. That said, it's often true that the more you learn, the more you discover that there's even more to be learned. Perhaps that's what you really meant?
It's obviously not a "trick" question. Perhaps rephrasing would help? A declarative statement of the issue would say that a person of average intelligence does NOT "understand" certain things in the same way that a person of high intelligence does.
Not all of maths is logical. E.g, adding up all the numbers from 1 to infinity gives you -1/12. Sometimes maths makes no sense at all. The maths itself works. But thinking about it logically completely contradicts it. How can you add up infinite positive numbers and get a negative answer?
Idk if an ELI5 is possible but the proof hurts my brain
Talono · 3 points · Posted at 04:28:23 on February 14, 2016 · (Permalink)*
There's a difference between "intuitive" and "logical." The sum of all positive integers is counter-intuitive, not illogical. It only seems illogical because people often forget that infinity is a man-made concept to make understanding things easier, not something that exists in nature. Same goes for zero, imaginary numbers, etc. (It really applies to all numbers, but that's harder for people to see :P)
Math is inherently a pattern seeking discipline. Its like saying, "oooh, i lined up these tiles in order from smallest to largest, and a pattern emerged! The tiles go from smallest to largest!!! Omgsocoolapattern!"
But yea, i know what you mean, and i get that same feeling as you. :)
Remember, a lot of the patterns that we see may simply be a result of using a base 10 number system. Other number systems would have different patterns, which means the patterns come from our ability to recognize them, not necessarily the numbers or operations themselves.
Just because you can't understand it doesn't mean god did it. I've seen Penn and Teller catch bullets in their teeth, but I would never think they actually caught a bullet just because I can't figure out how they really did it.
Similar to this, numbers divided by 5 in base 12 are repeating series of 2497. When you divide by 10 instead you get one other digit, and then a series of 2497. For anyone who doesn't know, base 12 works with 12 different digits as opposed to 10. Here's a quick summary:
Base 10
Base 12
1
1
2
2
5
5
9
9
10
A
11
B
12
10
13
11
99
83
100
84
101
85
142
BA
143
BB
144
100
Now, fractions feel weird when you make them, because you get stuff like this:
Base 10
Base 12
.5
.6
.333...
.4
.25
.3
.0833
.1
Now when we start getting into some the 5 and 10 fractions, we will get that 2497 I mentioned:
cayal3 · 11 points · Posted at 02:48:51 on February 14, 2016 · (Permalink)
Do you watch Arrow?
One of the characters - Felicity Smoak - has kind of taken over the show (blame tumblr) and they are keen on telling us how she is a great, strong & powerful woman as she deals with being in a wheelchair.
Atlas001 · 3 points · Posted at 03:02:31 on February 14, 2016 · (Permalink)*
I only watched half the 1st season
Also, what's with the overwatch and calculators joke? seems to be related
Awela · 4 points · Posted at 03:03:45 on February 14, 2016 · (Permalink)
Spoilers ahead:
Her nickname is Overwatch and her father nickname is Calculator.
cayal3 · 2 points · Posted at 03:12:50 on February 14, 2016 · (Permalink)
Overwatch is her hero name and Calculator was a bad guy who turned out to be her dad. But I haven't heard any jokes regarding that.
jrkirby · 1 points · Posted at 05:04:25 on February 14, 2016 · (Permalink)
You know, calculator actually used to be a profession. But it's unlikely that his father did that unless he's very old. So it's more likely his grandfather. Or great-grandfather. Or, since there were more female calculators, grandmother.
[deleted] · -1 points · Posted at 23:57:55 on February 13, 2016 · (Permalink)
I really like how the number represented by the highest digit in a base has that property like nine, where you sum the digits to test for divisibility. If the digits of a hex number sum to 5, 10, or 15, it's divisible by 5.
Extremely cool. But I find it surprising that you'd say "fractions feel weird" in base 12. I always felt like we might be a little better off as a base 12 society, specifically because so many of those "common" fractions would be so much less unwieldy than they are in base 10.
I thought we were a base 12 society no? Our global time-keeping system orientates itself around base 12 for the exact reasons you've given.
We use 60 seconds to denote 1 minute. Where each minute is divided into 12 five second slices.
We use 60 minutes to denote 1 hour. Where each hour is divided into 12 five minute slices.
We use 24 hours in 1 day.
We use 12 months in a year.
The only weird one is weeks. Why the fuck do we use 7 day weeks? lol.
Everything else we count in as a society is in base 10 purely because of the unilateral ease of the concept (as the norm is to have ten fingers/toes, so the public at large find it easier to visualise/grasp when interacting with others).
Literally all of our other math is done in base 10 though. Also I'm fairly sure that the way we divide time is based off a base 60 system.
s_s · 5 points · Posted at 03:43:37 on February 14, 2016 · (Permalink)
Yep.
Take your right thumb and touch it to each of your finger tips on your right hand. Then, do it again using the next pad on each finger. Then do it again using the last pad on each finger. Congratulations, you counted to 12 like a Sumerian.
Now extend your fingers out on you left hand to indicate a complete cycle. Do that whole thing 5 times (one for each finger on your left hand) and you're counting in base 60.
Yeah all our maths is in base 10 but I think that is from ease of use conceptually more than anything else.
After a quick google it seems our time system is a mix of base 12 and base 60, though more swiging towards the base 60. Seems to be a mish-mash of many past civilisations own particular systems! Never realised how interested I was in all this until this thread.
An intellectually stimulating askreddit, I like it!
There isn't that much difference between bases conceptually, at least not when starting out. It's just much easier to count and show ten on our fingers than anything else.
Makes sense. Especially back in the day before most people were literate/had an education. Much easier to be able to show what you mean than try and explain it.
Though I would argue our timing system is the basis of our technological society (however, depending on the argument I could say the same of so many other things which are in base 10, like money).
Brings a new meaning to the saying "time = money" haha, maybe not after all lol.
I have to disagree on that. Our society in general rests pretty squarely on base ten, what with money, the majority of math and science, our natural counting, and just about everything else we do on a daily basis consisting of base ten. Even with time, we use base ten units. For it to be proper base 12, we would say that 9:00 is followed by A:00, then B:00, then 10:00 (which is what we would think of as 12:00).
Other bases are really only used for specialized applications, such as base twelve and base sixty being used for time, base two being used for computers, and base sixteen being used for colors.
Don't worry I don't really believe we are a base 12 society, I was more saying it for the sake of the discussion. It is very evident that we use base 10 in the majority of situations and in where it really matters. Everything that doesn't is the exception.
However, where you have changed my view is on time being in base 10 as opposed to base 12. We still use 10 digits in our timing system so you're right in that it is base 10. Pretty obvious once I think about it, thanks for that, I have thought for a while it is in base 12, not sure why, probably some rubbish I read somewhere on the interwebs which agreed with my world view, damn confirmation bias!
Also what I meant by time is the basis of our technological society is that without the precise measurement and understanding of how to describe time we wouldn't be able to have all the satellites, the internet or even a train timetable. Ie. without an agreed upon timing system, we wouldn't be able to live in the computational/technologically advanced civilisation in which we live today. Hence why I thought it reasonable to say our society is a base 12 society as we rely on our ability to describe time accurately. However I was wrong in that time is base 12 so the statement isn't correct. Thanks for enlightening me :).
saremei · 1 points · Posted at 13:18:56 on February 14, 2016 · (Permalink)
Weeks are based on the moon. Each phase is a week.
So now I have to ask... is there a general relation between bases and repeating fractions, and if so, what is it?
Change of base transformations have always fascinated me.
lukfugl · 9 points · Posted at 01:39:35 on February 14, 2016 · (Permalink)
I'm not 100% on this, so I won't be surprised to be corrected, and you should confirm before repeating it as fact (or maybe I'll confirm and edit), but...
I believe it has to do with relative primality of the base and the prime factors of the divisor (though not the divisor itself). E.g. 10 is not relatively prime with multiples of 2 or 5, fractions with only 2s and 5s in the factorization of the divisor will have finite decimal representations. But if the divisor includes a 3 or 7 (or larger prime) in the factorization, it will have a repeating decimal representation.
In base 12, 3 is not relatively prime to the base, so e.g. 2/3 has a finite doudecimal (aka dozenal) representation. But 5 and 12 are relatively prime, so 1/5 has a repeating representation.
I have a suspicion that the product of the distinct relatively prime factors plays into the period of the repetition, but it's not direct (see 1/3 in decimal, who's period is 1 not 3).
So is this why 1/3 in base ten gives a recurring decimal, but 1/5 in base ten is finite? It's just to do with the number of digits used in the numeral system you are dealing with, in our case, ten digits.
If so you just blew my mind, that is really cool way of explaining positional notation. Just explain it in terms of relative 'primeness' to the base used and it makes SO much more sense to me. Holy fuck thank you!
I was looking for a problem that I could write Python code for that would push my beginner programming skills, and also require that I learn something new, since it's easy enough to put into code something you already know well, but much harder when you just learned it. So I made a code that would switch base 10 to base 12, then modified it to switch between any two bases.
makes a lot of sense now why Greeks preferred a base 6 system. Although there's things we can do that they couldn't. I wonder if a base 12 system would have both worlds?
Xcodist · 1 points · Posted at 03:18:47 on February 14, 2016 · (Permalink)
For anyone that may be a little confused: I found this
Is there a perfect base numbering system? I think I understand the gravity of such a question.
For general things base ten doesn't break down. But for larger or smaller things it's sort of 'unfocused'? Or inaccurate, like .333x3.
Is base twelve producing a clearer description of reality? Does it matter if we go higher or lower in base systems? Is there a base system that would be clearer than ever needed?
In simple terms I guess I'm asking if reality is 1080p, base ten is 480p and base twelve is 720p. Does this increase linearly, or logarithmicly by each base? And what base would produce 1200p clarity but would be too accurate for reality?
Is this the wrong way to think of base numbering systems? Also slightly confused on how prime numbers would effect any of this.
Dimpl3s · 1 points · Posted at 05:02:35 on February 14, 2016 · (Permalink)
Just wanna say, the division aspect us why there are 12 inches in a foot instead of 10. It makes the fractions easier
What I get from this is that base 12 is even more beautiful than I'd previously thought because not only do most common fractions fit into it elegantly, the fractions that base 10 has an advantage on still have a predictable, attractive appearance when interpreted in base 12.
One day this planet will be taken over by an alien race that uses base 12. I genuinely feel we're at a disadvantage, mathematically.
[deleted] · 1 points · Posted at 09:02:47 on February 14, 2016 · (Permalink)
Try using long division with something like 1/7, and it would give different remainders that carry over for every new digit (10/7 gives 3, 30/7 gives 2, 20/7 gives 6...). But the only nonzero remainders that you can have when dividing by 7 are 1, 2, 3, 4, 5 and 6, and these are all cycled through and then continually repeated. Therefore something like 2/7 simply starts off at a different point in the sequence (you would begin with 20/7 instead of 10/7).
A number like 1/3, however, only observes one possible remainder (1 from doing 10/3) when using long division, and doesn't have all the possible nonzero remainders when dividing by 3 occur (1 and 2). This is why 1/3 and 2/3 don't show similar behaviour.
For more information or an alternate explanation this site may be useful.
Edit: As for applications, I don't actually know of any other than being a nice trick for being accurate to as many decimal places as you like if you don't have a calculator but have the digits memorised. Wikipedia does tell me it has use in cryptography, though...no idea how true that is.
Remainder 1 is where we started from, so the whole sequence repeats.
Now some things about this...
Since the denominator is 7, you can only have 7 possible remainders -- 0, 1, 2, 3, 4, 5, and 6. If remainder is 0, you end up with repeating zeros. So in order to have a repeating sequence, the remainders must either stay the same (like 1/9 yields 0.11111111) or bounce around the other remainders in a sequence. 7 is neat because it manages to hit all possible non-zero remainders, creating the longest possible sequence at that point, a 6-number sequence that repeats. It has a period of 6.
Other neato fractions that have a period one less than the denominator include 1/17, 1/19, 1/23, 1/29, 1/47, 1/59, 1/61, 1/97, and so on.
It was clever of you to notice that the denominators of these beasties are all primes!
Now, since 1/7 hits all the possible remainders, that means 2/7, 3/7, 4/7, 5/7, and 6/7 are all going to generate those same remainders which will be divided by 7, so they in effect have the same sequence, just starting at a different point in the sequence.
This same effect holds true for all those other fractions I mentioned, but the sequences are longer. 1/97 generates the sequence "010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567" and 2/97, 3/97, and so on all enter the sequence at different points.
So these magic numbers are related to cyclic numbers, which connects to a bunch of math that fancy pants mathemeticians like Euler have been exploring since the 1700's at least.
heap42 · 2 points · Posted at 23:21:17 on February 13, 2016 · (Permalink)
It is 'because' of the Modulo operator... \Forall x x mod 7 is only a small set of numbers(by definition of mod it is 1-6). Anyways each of the numbers 1-6 have these numbers 28.... in their first digits. so you get that.
Yes! Fermat (yes, that Fermat) noticed and proved a remarkable pattern - if you raise a number to the power of a bigger prime, then divide the result by that prime, the remainder will always be the original number.
This is now called Fermat's Theorem (not to be confused with the more famous Fermat's Last Theorem)
This means if you write down successive powers if a number a, and take the remainder on division by p, the remainders start to repeat after p-1. They might repeat earlier, but if do, the number if different remainders will always be a factor of p-1.
When you work out the decimal expansion of 1/p, you are basically working out different powers of 10 and their remainders when you divide by p. The trendiness get coded into the decimal digits.
So, 1/7 has digits .142857, repeating every 6, because the powers of 10 have remainders 1, 3, 2, 6, 4, 5; reiterating every 6.
Every possible remainder is there, and when you work out 2/7, you just start the pattern in a different place.
1/11 must repeat every 10 digits, but in fact repeats every 2.
1/13 must repeat every 12 digits, but in fact repeats every 6. Some of 2/13, 3/13, and so on will share the same six digits that 1/13 has, the rest will share between them a different set of six digits.
And so on with other prime fractions: 1/17, 1/19, 1/23, etc. They each have a repeating decimal that repeats after some factor of 16,18, 22, etc places.
As for practical applications:
Fermat's Theorem forms the basis of RSA cryptography, so it's immensely useful. I won't go into the details here, instead I'll site you how it can be used as a way to test a number to see if it's prime.
Suppose we're wondering if 21 is prime. We could start looking for factors, and that works very well for 21. It might not work very well for a number with ten thousand digits, so here's another way.
We could work out the decimal expansion of 1/21. If 21 is prime, that must repeat after 20 digits (or done factor if 20, maybe 10 or 5 or 4 or 2 or 1). Instead, it repeats after 6 digits: 1/21 is 0.047619047619... This proves that 21 isn't prime, because the remainder of 1021 when you divide by 21 isn't 10.
skratch · 1 points · Posted at 05:48:04 on February 14, 2016 · (Permalink)
One application that my dad taught me was that if you want to get a quick approximation of pi , you can just use 22/7, which comes out to 3 +
1/7 = 0.142857142857...
Easy 3.14 if you're doing rough estimates. Had no idea about the repeating pattern though, neat.
In some parts or the world the sewerage system cannot handle toilet paper so there is a bin in the toilet. Also in most places the sewerage system cannot handle tampons and pads.
Also some memes are so dank and smelly you wouldn't want to put them in the bin in the kitchen.
We still call it a bathroom, or a restroom if you're feeling fancy or prudish.
[deleted] · 0 points · Posted at 11:30:09 on February 14, 2016 · (Permalink)
Wrong. It's a bathroom if there's a bath or shower in it. It's a restroom otherwise
Stickit · 1 points · Posted at 13:57:00 on February 14, 2016 · (Permalink)
Well, yes, but people still call it a bathroom. Signs in restaurants say "Restroom" and people still say "I'm going to go to the bathroom" at least some of the time.
[deleted] · 1 points · Posted at 13:58:53 on February 14, 2016 · (Permalink)
Yes and colloquially speaking that's OK.
But to say that the difference between the terms is about being fancy or prudish is silly
No, they call the whole toilet room the toilet. The room with a bath is the bathroom. A room with a bath and a toilet is a bathroom, but they can use the toilet without needing a bath, or vice versa, or both.
When saying "they call the whole bathroom" I was using American lingo, and a room with a toilet and no bath is called a bathroom here. If you want to be technical, it's a "half-bath," that's what you'll see in real estate listings, but literally no one calls it that. A bathroom without a bath is still a bathroom... we're totally divorced from the origins of the word.
It's cool to know the British difference though. So if you just need to pee, but you're going to a room that has a bath in it, you still say I'm going to the bathroom?
Also in some parts of the world the bathroom is called the toilet, and a bun is a garbage can. I feel like it's normal to have a garbage can in your bathroom. Goodnight.
In some parts or the world the sewerage system cannot handle toilet paper so there is a bin in the toilet. Also in most places the sewerage system cannot handle tampons and pads.
gnorty · 3 points · Posted at 22:44:52 on February 13, 2016 · (Permalink)
my toilet system in the UK cannot handle toilet paper tubes, toothepaste boxes, disposable razors etc. That in itself is not a problem, but my wife cannot handle loads of shit on the floor of the bathroom, so we have a bin
Why do you not? What do you do with used razors or empty shampoo bottles? Walk them out to the kitchen? Fuck that. Throw them in the trash in the bathroom.
[deleted] · 1 points · Posted at 23:50:05 on February 13, 2016 · (Permalink)
Read the comment again, he only has a bin in the toilet that's out on the patio.
2T2T · -6 points · Posted at 20:55:55 on February 13, 2016 · (Permalink)
You'll find out if you ever grow up, move out of your parents basement and get a human (non Anime ) girlfriend.
Shmeeku · 1 points · Posted at 06:39:57 on February 14, 2016 · (Permalink)
I know this is a joke, but there is actually such a thing as a "perfect number." The first few are 6, 28, and 496, so 5/7 isn't perfect in the mathematical sense.
[deleted] · 3 points · Posted at 07:13:43 on February 14, 2016 · (Permalink)
I figured this out while taking a test, I ended up failing the test cause I sat there trying all the fractions of 7.
[deleted] · 5 points · Posted at 22:55:46 on February 13, 2016 · (Permalink)*
I cant be bothered to check but do other prime numbers behave similarly?
EDIT: I checked and nope
smc5230 · 1 points · Posted at 01:27:27 on February 14, 2016 · (Permalink)
Not sure if its a typo or not but 5/6 begins with .71 and according to looking at the numbers in the previous one 6/6 should begin with .42 but begins with the .85.
I discovered that exact pattern years ago. And this works for any number that isn't a factor or multiple of 7. For example, 1256 divided by 7 is 179.42857... (The whole number increases regularly but there's always the same pattern at some point.)I checked with my mathematician granddad and he says it isn't a new discovery but it's still interesting.
So what's between the 14 and the 57? Infinity? But it seems like it repeats, right? Infinite numbers can't repeat. Right?
I mean the first series seems to be 14 and then anything after has 14 preceded by 57. So would 14 be the 'first' and then 57 for everything after is the end of the loop?
Yes! I only noticed this late last year when I realised that the only fractions I didn't know decimal for between 1/2s and 1/12s was 1/7s, so to improve my mental math game I went to memorise 1/7 through 6/7 and realised this pattern.
goat18 · 1 points · Posted at 04:02:41 on February 14, 2016 · (Permalink)
I discovered this on my own. The numbers in the decimals are also the multiples of seven.
1/7 = 0.14 28 57 142857...
14 = 2*7
28 = 4*7
56 = 8*7
112 = 16*7 (the 1 is added to the 56 making it 57, and the 2 has 2 added to it from the next iteration)
etc.
I tried to play around with other numbers for a little while to see if I can get something useful out of it but didn't get very far. I basically ended up deriving a formula for 1/7.
1Rab · 1 points · Posted at 04:09:18 on February 14, 2016 · (Permalink)
This turned me on.
MrMi10s · 1 points · Posted at 04:17:03 on February 14, 2016 · (Permalink)
Coming from an idiot to facepalmingly figuring this out... remember that the symbol for times is x and also * and sometimes just a tiny dot. next look at the law/rule/formula stating that n! = n*(n-1) * (n-2) * (n-3) So in this case starting from 10! and not n! the math goes 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 which = 3,628,800 = 6 weeks in seconds.
looking closer into this equation There is no 9 but there are three 3's. with 3 * 3 = 9 we can take two of the 3's out in this equation and represent it as 9.
Left part of equation is converting to seconds. Next part is breaking up some of the numbers into smaller factors (24=8*3). Next part is rearranging in (somewhat) order.
Exaskryz · 10 points · Posted at 02:25:09 on February 14, 2016 · (Permalink)
That second to last part isn't really putting in order, but combining factors into what was missing. We had three threes but no nines, so it just took two threes and wrote it as a nine.
I think most people who have had to endure a university math course solution manual would laugh at the post before yours considered as "the most concise explanation possible".
How is that an explanation to anyone who doesn't know what factorial means, and anyone who does doesn't need an explanation
peon2 · -5 points · Posted at 23:11:03 on February 13, 2016 · (Permalink)
6 weeks in 10 seconds= 10!
More concise, just shows less work
[deleted] · 6 points · Posted at 01:17:18 on February 14, 2016 · (Permalink)
Rephrasing a theorem doesn't prove it.
Example:
eπi = -1
Oh, want proof?
eπi -1 = 0
Checkmate.
(This doesn't proof anything)
The aim of a proof is to communicate an understanding why a theorem is true by deriving it from other proven mathematical rules, axioms or by proving that if it isn't true, these proven rules or axioms would be broken.
A proper proof of eπi = -1 (which is called Euler's identity, and is one of the coolest facts I know) can be made by proving Euler's formula:
exi = (cos x + i sin x)
For when x = π, sin π = 0 and cos π = -1
A really elegant proof of Euler's formula can be found here, along with some others. If you understand the proof, it now should make sense to you that eπi = -1
Edit: Not necessarily meant directly to your reply, /u/peon2, I just had to insert it somewhere in the comment chain.
peon2 · 5 points · Posted at 01:30:16 on February 14, 2016 · (Permalink)
Edit: Not necessarily meant directly to your reply, /u/peon2, I just had to insert it somewhere in the comment chain.
Ok glad to know you didn't waste any time typing that out for my silly joke. I've had to write out eulers proofs for several classes in the past and appreciate it's wonder. Was just making a dumb joke.
raddaya · 0 points · Posted at 02:11:36 on February 14, 2016 · (Permalink)
Nah, here's the best and most concise proof available.
6 weeks = 10! seconds. The proof is trivial and left to the reader.
[deleted] · 1 points · Posted at 02:17:43 on February 14, 2016 · (Permalink)
There should be a name for this... "proof by audience"?
[deleted] · 0 points · Posted at 04:00:23 on February 14, 2016 · (Permalink)
I think this is:
10 weeks in seconds = 6×7×24×60×60 = 3628800 = 10!
There really is no reason to the through the factorization. This is just a coincidence and it isn't too surprising imo
really? even more than (10x9x8x7x6x5x4x3x2x1)/6/7/24/60/60.... uh im quickly realizing I dont' know how to write math anymore
ebbomega · -4 points · Posted at 23:32:30 on February 13, 2016 · (Permalink)
Proof, not explanation.
[deleted] · 2 points · Posted at 01:52:18 on February 14, 2016 · (Permalink)
Both in this case. It should be easy to figure out what each number represents, as they're neatly ordered: 6 weeks, 7 days per week, 24 hours per day, 60 minutes per hour, 60 seconds per minute.
deusset · 16 points · Posted at 01:52:00 on February 14, 2016 · (Permalink)
I'll be honest, the elegance of the proof is more exciting than the fact itself
[deleted] · 9 points · Posted at 06:56:58 on February 14, 2016 · (Permalink)
This is why physics teachers fail people who don't use units.
Argh, I spent so long trying to figure out how to split up the factorization in a way that showed each time unit that you multiply. Now I see that the 9 could not be included in the factorization and had to be split into two 3's. Good on you for figuring it out :)
Oh god, this reminds me of the new Common Core standards.
[deleted] · 1 points · Posted at 02:00:02 on February 14, 2016 · (Permalink)
That's cool as f**k
[deleted] · 1 points · Posted at 02:36:27 on February 14, 2016 · (Permalink)
I don't know enough about the alphabet to dispute this statement.
CalebDK · 0 points · Posted at 04:30:07 on February 14, 2016 · (Permalink)
I'm so confused
[deleted] · 5835 points · Posted at 22:20:56 on February 13, 2016 · (Permalink)
[deleted]
Qqaim · 1876 points · Posted at 22:32:53 on February 13, 2016 · (Permalink)
In case you want to know, n! (pronounced n factorial) means n*(n-1)*(n-2)*(n-3)*....*2*1. So 10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800.
[deleted] · 1259 points · Posted at 01:01:58 on February 14, 2016 · (Permalink)
Also, really clever people leave out the *1 because it doesn't do anything. When we point this out to other people, we feel super clever and are happy for days!
Edit: Wow, reddit is really representing itself well tonight. Really, really good stuff. Thanks to each of you.
[deleted] · 110 points · Posted at 02:04:05 on February 14, 2016 · (Permalink)
Ok, step by step (read this more slowly if you think I'm going too fast):
0! = 1
This is a definition. You can read n! as: "How many different orderings can I pick from n objects"
So say you have 3 colored pieces of paper; at first you can choose any of the three, then there are only two left to choose from and the last one you have to take any way, so there are 3 * 2 * 1 ways to choose orderings from 3 pieces of paper.
That's basically what factorial does.
We define 0! as 1, i.e. if you have no pieces of paper, there is only one ordering: an empty ordering.
That covers 0! = 1
0! = 1!
There is only one ordering of one piece of paper:
1! = 1
but also: 0! = 1
therefore:
0! = 1! (which both equal 1)
In programming, "!=" often means "not equals" (think of this symbol: ≠) and it is used to check the values of variables and such:
Consider this piece of made-up code:
x = 4
if (x != 3) then print "x is not equal to 3"
It prints "x is not equal to 3", you can read it as a task list. First we give x the value of 4, then we raise the condition: "if x does not equal 3, then we print some text on screen".
A condition that holds in programming, evaluates to true (which is a special word in a program to identify conditions that hold).
The joke is that 0! = 1 holds, but in programming, 0 != 1 also holds since 0 is not equal to 1, so it evaluates to this true :)
Scizors · 12 points · Posted at 01:57:54 on February 14, 2016 · (Permalink)
In some programming languages "!=" is used as a "not equal" operator. So if you put the statement "0 != 1" it would return true since 0 is not equal to 1.
And I just assumed it was for mathematical convenience so that Taylor series and Maclaurin series (and others) worked out in a nice, little, easily written summation.
Think of a factorial more like "how many ways can I arrange these certain number of things?" So if you have 4 things, you can make 4! (24) different combinations of them.
How many ways can you group 0 things together? There's only one way: a big pile of nothing.
An analogy which I think will help you understand better why 0! =1 is looking at each element as a card and thinking of factorial as "the number of different shuffles I can do to those cards".
For example, we have 2 different elements, let's look at them as 2 cards stacked on top of each other. The different shuffles we can do are:
1: don't shuffle
2: switch the two cards
No other option other than that.
For 1 element, how many ways are there to shuffle? Only one, which is:
1: don't shuffle
No matter what you try to do with that card, you cannot shuffle a single card.
For 0 elements it's a similar situation. No matter what you do, you can't shuffle 0 cards. Therefore the only shuffle is:
Sweet, I like that analogy.
So is n(n-1)(n-2) etc not completely true as a definition for factorials, but instead gives us an easy way to calculate them?
Or is 0! More of a exception?
you have two cards, how many ways are there to shuffle them?
the answer is 2, which is also 2!.
now if we add a 3rd card, how many ways are there to shuffle them?
you can go and count each and every one of the possibilities, but that's boring. instead let us look at all of the different positions the 3rd card can be at.
it can be on top of the other two cards
it can be in between them
it can be at the bottom
for each one of the positions of the 3rd card, the other two cards can be shuffled between them (we won't know which order they're in).
so we have 3 positions for the 3rd card and for each such position we have 2 possibilities for the other cards (the number of ways you can shuffle 2 cards). so all in all we get that the total number of possibilities is the number of possibilities for the 3rd card times the number of ways to shuffle 2 cards, which is 3*2, or more accurately 3*2! which is 3!
this can be broadened for an arbitrary number n.
you have n cards, how many ways are there to shuffle them?
n possibilities for the top card times the number of ways to shuffle a deck of (n-1) cards, meaning n*(n-1) which is n!
This used to piss me off in high school and my teacher couldn't give me a good explanation as to why.. other than that it would break perms/combs otherwise.
[deleted] · 1 points · Posted at 09:30:16 on February 14, 2016 · (Permalink)*
But it's still a relevant note for the thread. It's an interesting mathematic fact.
Siarles · 1 points · Posted at 16:11:55 on February 14, 2016 · (Permalink)
It's because n! is actually the number of ways you can arrange a series of n items. There's only one way to arrange zero items, because there are no items to arrange.
14flash · 4 points · Posted at 02:21:26 on February 14, 2016 · (Permalink)
When you "expand" 0! you'll find that there are no terms in the sequence because you start with a number less than 1. This is what's known as an "empty product" which equals 1 (because this is the multiplicative identity). This is the same reason why doing a0 also equals 1 (when a =/= 0).
And factorials are also defined for zero (0! = 1), so it should be:
10! = 10*9*8*7*6*5*4*3*2*1*1
[deleted] · -4 points · Posted at 01:56:35 on February 14, 2016 · (Permalink)
1! = 1
But also:
1! = 1 * 1 * 1 * 1
You don't break anything by adding * 1 to a formula, and if you have other constants, you can even leave it out. (3 * 1 = 3)
It will break the pattern, yes, but it's not invalid. And it saves you some time writing down the sequence (especially if you have slow handwriting or are low on ballpoint ink)
if you have other constants, you can even leave it out.
That wasn't my point. I understand the multiplicative identity property. My purpose was that if you're trying to use a formula that works for ℤ+ you need to include the *1.
[deleted] · -2 points · Posted at 02:28:59 on February 14, 2016 · (Permalink)
I don't follow. There is absolutely no reason to include the *1 when you have other constants, other than that it looks pretty (for n > 1. Obviously you have 0!=1 and 1!=1).
[deleted] · 1 points · Posted at 02:31:28 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · -1 points · Posted at 02:53:19 on February 14, 2016 · (Permalink)
You were talking about *1 in all your comments; as in "multiplied by one". That can always be left out.
1! = 1 does not include a "*1", so there's nothing to leave out.
I don't know if you're honestly just missing his point or if you're being facetious, but this one (link because I don't know how to latex within reddit's reply box). Removing the *1 (i.e, making it i = 2 on the bottom instead of i = 1) would make that formula only work for > 1, instead of >= 1.
[deleted] · 1 points · Posted at 14:45:29 on February 14, 2016 · (Permalink)
I'm guessing you're all just misreading my comments on purpose...
Indeed this requires n > 1 (I pointed this out multiple times), but your link is just one of the many definitions of a factorial. I wasn't stating it can be left out in the definition; it can be left out in the sequence of integers I replied to. By the points on that comment, most people seem to agree.
The context of you pretending that you didn't know what formula he was talking about repeatedly while he agreed that you could leave it out in the sequence of integers (also repeatedly)? If you wish to be a jackass, feel free to reply and feel like you've "won". I've better things to do with life then waste it on morons such as yourself. I'm out.
[deleted] · 1 points · Posted at 13:15:25 on February 15, 2016 · (Permalink)
lol wat..?
I'm not here to win anything, I was genuinely confused about why he thought you have to multiply by one. So I attempted to explain it several times that it's just a pattern in the sequence. You don't break anything by leaving it out.
If you really think I'm just trying to be an asshole, suit yourself. Just know that I only tried to help..
[deleted] · 4 points · Posted at 01:32:12 on February 14, 2016 · (Permalink)
Now. What about negative numbers factorial? -10! for example? Is it = (-11)*(-12) etc? Or can you not do negative factorials?
nrufl · 9 points · Posted at 01:27:01 on February 14, 2016 · (Permalink)
0! is defined to be 1. The most natural way of extending the factorial to other numbers (negative numbers, fractions, imaginary numbers, etc.) is the gamma function, but it has singularities at the negative integers (like 1/x does at zero).
Qonic · 4 points · Posted at 01:25:05 on February 14, 2016 · (Permalink)
The Gamma Function can extend the factorial function to most complex numbers.
tom808 · 1 points · Posted at 01:39:00 on February 14, 2016 · (Permalink)
What about if you had a negative number (-n!) you would need the 1 to get the correct answer then? Also shouldn't it always be included for completeness?
Non mathematical person here so those may just have been totally stupid questions.
[deleted] · 1 points · Posted at 01:51:35 on February 14, 2016 · (Permalink)
I'm not a mathematician either, computer science though, so not that far off.
Factorial only applies to non-negative integers. We call these: "Natural numbers", because you can count natural things with it, like 4 sheep or 10 coins.
We define 0! equal to 1
n! can be defined as n * (n-1)!
This is called recursion. For 3! we get
3! = 3 * (3-1)! = 3 * 2!, so we look at 2!
2! = 2 * (2-1)! = 2 * 1!, so we look at 1!
1! = 1 * (1-1)! = 1 * 0!, so we look at 0!
0! = 1 (defined above)
we can complete the rest now:
1! = 1 * 1
2! = 2 * (1 * 1)
3! = 3 * (2 * (1 * 1))
3! = 3 * 2 * 1
... or:
3! = 3 * 2 = 6
If you want to explain factorial to someone, you'd probably include the * 1, but if you're doing a lot of homework or writing down a sequence like that multiple times, you will probably just leave it be. It's similar to leaving out 1*x when writing x. You still mean "one times the value of x" where 2x means "two times the value of x".
If you are doing a lot of homework it would be done on a calculator. If you are in a class where they want you to write it down and you skip 1! and get full credit, you have a terrible instructor.
There is a way of extending the factorial to allow things like (1/2)! called the Gamma function, but it has singularities at all of the negative integers so (-n)! isn't something you can really consider. The factorial is strictly only defined for non-negative integers, and the definition of the gamma function has nothing to do with a product representation, it's just that if you evaluate the gamma function at positive integers it agrees with the factorial.
I don't know why you'd call that clever, leaving something out. The definition of factorial includes it (I believe), so leaving it out is probably doing a disservice, even if it happens to not matter in this example. I'm not a mathematician (and probably the furthest thing form it, so I could be wrong) but I have to imagine there comes a case where the *1 actually matters and so it's good to not ignore it.
[deleted] · 2 points · Posted at 14:26:36 on February 14, 2016 · (Permalink)
It's called the multiplicative identity:
There exist an integer 1 such that 1n = n
Combine that with the definition of factorial:
The product of a non-negative integer and all non-negative integers below it
And you get the factorial sequence excluding 1.
Knever · 1 points · Posted at 07:23:34 on February 14, 2016 · (Permalink)
I was just about to say that when I read that last *1.
It makes the sequence look neat. That's not "nothing".
klod42 · 1 points · Posted at 10:36:41 on February 14, 2016 · (Permalink)
When you learn maths to a little bit more advanced level, you get even more cleverer and you understand that 0! also belongs there, so you might want to actually write n * (n-1) * ... * 2 * 1 * 0!
REALLY clever people point out that the traditional definition of factorial is really just so that small children can understand a tiny piece of it, and you've actually got to do calculus on complex numbers to properly define it and do things like (1/2)! = (-1/2)! = sqrt(pi)
[deleted] · 2 points · Posted at 14:47:40 on February 14, 2016 · (Permalink)
Nah, we're just working with natural numbers here, since we're discussing the number of seconds in 6 weeks. You aren't the first to point out that there are multiple variations of factorial, by the way. :)
I just taught this to a student yesterday. She preferred the other name of factorial, which is "bang". You get to say things like "10 BANG over 2 BANG = x", which is delightful when you're 13.
[deleted] · 1 points · Posted at 22:51:23 on February 13, 2016 · (Permalink)
A better definition is 0!=1, n!=n.(n-1)! This extends the above to zero and makes the gamma function just a little easier to intuit.
I guess they don't teach you about sequences in US highschool...
which isn't true.
[deleted] · 0 points · Posted at 01:09:36 on February 14, 2016 · (Permalink)
I guess that can be read in a negative way, I've got experience with 3 different systems and they are all different enough in regards to what subjects are taught... I added that bit in after a few downvotes.
That doesn't mean it explains how to do it. Let's say I didn't know what "10!" meant (which is the situation here).
So I ask you how to do it. If you tell me "well 0!=1 and n!=n.(n-1)!" or whatever, that wouldn't tell me how to solve the problem at all
It tells you exactly how to solve the problem. It is a recursive function. You just have to apply it repeatedly.
You want to find out what 10! is. OK, let's apply the definition. n is not 0, so n! is not 1 (because, remember, from the definition, 0! =1). Therefore, let's go with n! = n*(n-1)!. So, 10! = 10*(10-1)! = 10*9!. Now, you need 9!. Apply the same definition again. 9! = 9*(9-1)! = 9*8!. So, 10! = 10*9! = 10*9*8!. Keep applying the definition recursively, and you'll reach:
Nope, you do not have to be exactly math-literate to understand factorials and the factorial notation/definition! :-) That's the beauty of a recursive definition: you don't really overthink it - just keep applying the definition over and over until you reach a terminating condition. In this case, the terminating condition is: 0! = 1. You don't go further down to think about -1!, -2! etc.
Recursive functions are atypical in that they are used in their own definitions, so it could be a little tricky to wrap your head around them initially.
[deleted] · -4 points · Posted at 00:00:52 on February 14, 2016 · (Permalink)*
In the UK educational system (which IMO is very inefficient) you learn in year 10 how to work out sequences:
You learn that "n"= whatever value you assign to it.
So if 10=n, "well 0!=1 and n!=n.(n-1)!" becomes: "well 0!=1 and 10!=10*(10-1)!"
Well, I guess they don't teach you that in the US, but this is coming from someone who doesn't know how to turn a fraction into a decimal (which is year 8 stuff) and has trouble with simple division...
Somehow I could never grasp this when my teacher explained it in math class, but now I understand it and can not believe how simple it is. Thanks for the succinct explanation, it's great to understand it even when I don't think I'll ever actually have a need to use it.
boldra · 1 points · Posted at 06:59:13 on February 14, 2016 · (Permalink)
Is n!! = n! * (n-1)! * (n-2)! * ... ?
Qqaim · 2 points · Posted at 09:23:55 on February 14, 2016 · (Permalink)
It's not, no. n!! (read n double factorial) = n*(n-2)*(n-4)*...*(2). Depending on n is odd or even, the multiplication either ends with 2 or 1. Similarly, n!!! = n*(n-3)*(n-6)*...*3. Again, the last number can change depending on what you started with.
Fexmeif · 1 points · Posted at 22:17:49 on February 15, 2016 · (Permalink)
Late for the party, but when I was in sixth grade I read a book called "Number's devil" (I think? Unsure of English title) that called factorial the "boom" numbers, because they so easily "exploded " into big numbers.
I really enjoyed that book and to this day I often call factorial "boom" in my head.
It was premature commenting. My thought process was to contribute not going past zero, staying solely in the natural numbers.
You are right 1 reads better.
[deleted] · 1 points · Posted at 01:48:14 on February 14, 2016 · (Permalink)
As an adult I can confirm I'm enthusiastic for about ten seconds every six weeks.
quasive · 1 points · Posted at 01:48:24 on February 14, 2016 · (Permalink)
In my school textbook, in the section on factorials, it read something like:
“5 factorial is 5 * 4 * 3 * 2 * 1, and can be represented by writing 5!”
They treated the exclamation point as punctuation, which I think is the wrong thing to do, because I spent a frustrating while wondering how 5 differs from 5, and why the book was so damned excited about it.
except every 100 seconds, except every 400 seconds.
diMario · 12 points · Posted at 08:08:48 on February 14, 2016 · (Permalink)
This only is true for metric leap seconds.
Imperial leap seconds come about every twelfth full revolution of the minute hand, unless it is divisible by a baker's dozen dozens (13*12), with the exception that every third or fifth time this happens (third time for the second half of the century, fifth for the first half) gets skipped. If you are in the Southern Hemisphere, swap the third and fifth times around unless you are in New Zealand, where they shift the year a count of 24 into the future before applying the rule as if in Northern Hemisphere.
Of course, that means the ratio of the number to the number after it converges on (φ-1).
The fibonnaci sequence shows up in nature all over the place, which means approximations of the golden ratio show up all over the place.
The golden ratio is also in logarithmic spirals, which are also found everywhere, like the arms of the milky way, hurricanes, most animals with spiral shells, etc.
Some people have noticed that the golden ratio shows up in all sorts of other places... some almost certainly by chance, but the argument is that we humans tend to find that ratio aesthetically pleasing. The number of female honey bees to male honey bees in a hive is generally φ. The number of kilometers per mile is ~φ. 1920x1200 monitors have a ratio of ~φ. Our eyes appear about φ times wider than they are tall. 3x5 notecards are ~φ. Some measurements in the mona lisa approximate φ. The Vitruvian Man is supposed to have φ in it. The Parthenon in Greece is φ times wider than it is tall. And so on...
The leap seconds thing happening to happen every 1.6 years or so on average since the early 70s... Pure chance, but I thought it was funny.
A math teacher should totally write this on the board for extra credit. "Jimmy asks, 'How many seconds are there in 6 weeks?' Sally replies, '10!'" Is Sally right or wrong?
blh1003 · 3 points · Posted at 02:32:47 on February 14, 2016 · (Permalink)
And there's 52! unique ways to shift a standard deck of cards, which is a number so big, that if you shifted one deck of cards every second since the Big Bang, you still wouldn't have made much progress in all the unique ways it can be shifted.
In general, a↑↑↑...↑ (n arrows) = a↑nb = a↑n-1a↑n-1a...↑n-1a (b times)
To put this in context, 3↑3 = 33 = 27.
3↑↑3 = 333 = 7625597484987. This is over 50 times the distance to the sun in m
3↑↑↑3 = 3↑↑3↑↑3 = 3↑↑7625597484987 = 3333...3 (7625597484987 times). If we wanted to write this out in full, with each 3 taking up 1 cm of paper, this would take us about halfway to the sun. And actually expanding it down would be a HUGELY insane number. Which hasn't even scratched the surface of Graham's number yet.
3↑↑↑↑3 = 3↑↑↑3↑↑↑3 = 3↑↑3↑↑3↑↑3...↑↑3, the number of times being that HUGE number which takes us halfway to the sun just to write down the power stack. Wolfram alpha can't handle this number. There are no analogies I can think of to help comprehend this number. This number is called g1. We're getting closer to Graham’s number, but we're still a long way off.
What is g2? It's 3↑↑↑↑...↑3, but how many arrows are there? There are g1 of them. When only using 4 arrows, we got an insanely huge incomprehensible number. Now we're using that many arrows. This number is HUGE.
And g3 is just 3↑g23. Which is WAY bigger than g1 and g2.
In general, g(n) = 3 ↑g(n-1) 3.
And, finally, Graham's number = g64. If you wanted to write this down, and you could write every digit in one Planck volume (the smallest possible volume in the universe, equal to 4.22×10-105 m3, you wouldn't have enough space to write it all down. In fact, if you replaced every planck volume with another universe, and used every planck volume in THOSE universes to write down Graham's number, you STILL wouldn't have enough space.
In fact, the ONLY thing bigger than Graham's number is the weight of your mum.
[deleted] · 13 points · Posted at 23:31:17 on February 14, 2016 · (Permalink)
Take a look at TREE(3), or SCG(13). In comparison Graham's number looks almost as small as your penis
You can write any repeating decimal, like 0.789789789... as a fraction with the repeating part over the same number of 9's: 789/999. That also implies that 0.9999 repeated is 9/9 = 1.
The multiples of 999 are basically multiples of (1000-1), so their magic is to chop the 1000s digit off, and reinsert it as the units digit. After 3 iterations, the old result reappears, so we know that the digits obtained so far will repeat forever.
Good. Now we know that 789/999 equals .789789789... But what about other numbers?
They will scroll through just like 789 did, so we can draw the same conclusion:
0.(3-digit number repeated ad inf.) = (3-digit number) / 999.
For other period lengths, just take
0.(n-digit number repeated ad inf.) = (n-digit number) / (10n - 1).
It'll take a different number of iterations to scroll the period through, but otherwise, it'll work the same.
The Banach–Tarski paradox: Given a solid ball, there exists a decomposition of the ball into a finite number of disjoint subsets, which can be put back together in a different way to yield two identical copies of the original ball.
chocapix · 3510 points · Posted at 21:07:24 on February 13, 2016 · (Permalink)
What's an anagram of Banach-Tarski?
Banach-Tarski Banach-Tarski.
Schohns · 1532 points · Posted at 22:04:22 on February 13, 2016 · (Permalink)
Hah I like that one! Reminds me of this:
What does the B. in Benoît B. Mandelbrot stand for?
Benoît B. Mandelbrot.
Sipczi · 741 points · Posted at 00:50:53 on February 14, 2016 · (Permalink)
That makes more sense. I was thinking along the lines that when you are posting something it generates your unique comment ID and he found it in the source code and pasted it in his link... But that works too =)
-WPD- · 3 points · Posted at 06:42:57 on February 14, 2016 · (Permalink)
I thought he was some kind of reddit wizard.
Sipczi · 3 points · Posted at 08:42:30 on February 14, 2016 · (Permalink)
Correct, it took me a few seconds, but I believe it's a 2 minutes window.
Backronym, actually. It was originally "Personal Homepage Tools". It started as a small set of perl scripts to let Lerdorf make his homepage be a little more dynamic. After people started asking for copies of the 'program', and started expanding it / asking Lerdorf to add features, it became a preprocessor language supporting a name change. These days it's closer to a general purpose programming language than a preprocessor, so I would suggest they update the acronym again.
There's a type of Jewish biscotti called "mandelbroit". I had a box of some the other day and asked my wife if they were made out of other mandelbroits and does that mean it's a mandelbroit set. She just gave me this strange look while I spent five minutes laughing at myself.
Same look my dad gave me earlier tonight when we drove past Dijsktra St. and I mentioned how it's easy to find the shortest way to get here.
[deleted] · 1 points · Posted at 05:37:48 on February 14, 2016 · (Permalink)
In college when people used to use "slash" as a conjunction, someone asked my friend what it meant. She said, "I always thought it stood for the slash in between and/or."
jmezfm · 3 points · Posted at 07:02:42 on February 14, 2016 · (Permalink)
One of my favorite math professors told us this joke after explaining the Banach-Tarski paradox to us. I remember a solid 10 seconds of silence before the class burst out laughing. Thanks for the reminder on that one, happy memory.
[deleted] · 2 points · Posted at 04:18:23 on February 14, 2016 · (Permalink)
I was lost at the Diagonal part. Why does he say that it is different from any other number on the list. Why couldn't it have been randomly generated in the original list?
Well, it can't be the first number, since it's different in the first decimal place.
It can't be the second number, because it's different in the second decimal place.
Indeed, it can't be the nth number on the list for any n, because by the nature of its construction, it differs from the nth number of the list in the nth decimal place.
I had the same question, so thanks for your simple explanation. This is one of the things that makes me realize I could never even begin to fathom infinity.
[deleted] · 2 points · Posted at 04:01:45 on February 14, 2016 · (Permalink)
I still don't get it... ohhhhh wait. I just realized, ok. There's just another infinity you've got to throw in.
So I was gonna say, how don't you know it wasn't randomly generated like guy said. But you are literally going through the infinite list that was generated and changing the numbers.
I know he says we shouldn't consider infinity weird or strange, but goddamned if it isn't weird and strange.
Some of the weirder points of infinity are explained well by the full version of the Hilbert Hotel.
First you can fit a new guest in the hotel. Then you find rooms for a bus containing an infinite number of guests. Then an aircraft carrier with an infinite number of buses, each with an infinite number of guests. And finally, an algorithm that allows you to move hotel guests around to make room for an infinite number of aircraft carriers, each with an infinite number of buses, each with an infinite number of passengers.
And then the hotel is full, but can still make room for uncountably infinitely more people.
Why couldn't the first number reappear on the list with a different number in the first digit? Sure, the odds against it are near infinite, but still non-zero. When we're talking about an infinite list, isn't that basically one?
We're not making a number where the first digit is different from the first number and then making a second number where the second digit is different from the second number. We're making one number where the first place is different than the first number, the second place is different than the second number, the third place is different than the third number, and then continuing until we reach the "last" number and the "last" place. Therefore, our new number is one which each place has an original number which doesn't match, and vice verse.
In your situation, if you consider that the 250,000,000,000,000th number is identical to the first number, except that its first decimal place is one more than the first number, the new number's 250,000,000,000,000th decimal place will be different.
But the list is infinite, so aren't you really just describing a way to generate another number? It seems like the only way a number "couldn't" be in the list is if it couldn't be generated by that algorithm
It is a way of generating another number, and that number can't be on the list because it's not the same as any of the numbers on the list.
Remember, the point is that it doesn't make sense. It's a reductio ad absurdum argument. The list is impossible, it can't exist, and this number that we can generate explains why - the list is supposed to be complete, and yet we have a number that cannot be on it, so the list must not exist.
Not at all, really. I haven't watched the video, but the point of the theorem is that there are certain types of sets of points in 3-d space where it doesn't make sense to assign them a volume.
The idea is that you start with a ball of volume 1, and you break it up into five or so pieces in this crazy way. If those pieces each have a volume, then when you move each piece around, its volume shouldn't change. But if you move your pieces around in the right way, then you can put them back together and get two balls, each of which is volume 1. So the total volume of your pieces should be 2. But when you started the total volume of your pieces was 1. So 2=1, a contradiction.
You get a contradiction because you assumed you could say those crazy pieces had "volume". The point of the theorem is that it doesn't make any sense to assign a volume to those pieces you broke the original ball into.
So, by rotating the sphere, it magically increases in mass? Just because you apply an arbitrary label to points on the sphere doesn't mean that it exists. Those points would, exist, but there would be nothing there, just a small gap between the other points.
I don't get it. When you "fill in" from infinity, you can't just pull mass out of nowhere, that "infinity" that you are pulling from is not infinite, it is a finite object with defined and limited definitions.
I don't see how that paradox makes sense. It does not seem to be physically valid.
As for the hadron collider creating "more" particles, don't the collisions convert the energy into new mass? I thought that was the entire point of the experiment, to create new particles from the sheer amounts of energy from the collision of the particles.
I haven't watched this video, but it seems like it is more confusing and overwhelming than it needs to be.
The point of the theorem has nothing to do with physically being able to duplicate two balls. That's how people like to try to sell it, because it's shocking and sexy, but that's not at all why mathematicians care about it. Its to show that there are certain types of sets in 3-D space where it doesn't make sense to say they have a "volume."
The idea is that you start with a ball of volume 1, and you break it up into five or so pieces in this crazy way. If those pieces each have a volume, the sum of their volumes should add up to 1. When you move each piece around, its volume shouldn't change. But if you move your pieces around in the right way, then you can put them back together and get two balls, each of which is volume 1. So the sum of the volumes of your pieces should be 2. But when you started the total volume of your pieces was 1. So 2=1, a contradiction.
You get a contradiction because you assumed you could say those crazy pieces had "volume". The point of the theorem is that it doesn't make any sense to assign a volume to those pieces you broke the original ball into.
physchy · 1 points · Posted at 08:05:45 on February 14, 2016 · (Permalink)
Wouldn't that sphere have to be infinitely dense?
Artren · 1 points · Posted at 09:30:46 on February 14, 2016 · (Permalink)
I read that in Kevin's voice from The Office. I've been watching too much of The Office.
I like how he explains that the infinity is rather something size-like than a number, but I don't like the "different sizes of infinity". I personaly prefer to think of infinity as a name, or concept. So yes, inf+1 is still inf, but not bigger nor smaller infinity, just infinity.
"Different sizes of infinity" is an important concept in math, but it might mean something different than you think.
In math, you say that two sets have the same cardinality (i.e., "size") if you can create a one-to-one correspondence between the things in those sets. For example, the set {3, 4 ,5} has the same cardinality as the set {6, 7, 9}, because you can say 3 corresponds to 6, 4 corresponds to 7, and 5 corresponds to 9. The word we use to describe this cardinality is "three". The set {1, 2} has cardinality "two", which isn't as big as three because when you try to create your one-to-one correspondence between {1, 2} and {3, 4, 5}, you'll always have something in {3, 4, 5} left over which doesn't correspond to an element of {1,2}.
You can do this with infinite sets. The even numbers have the same cardinality as all integers because for each integer n, you can assign it to 2n.
The set of real numbers is "bigger" than the set of integers because if you try to create this one-to-one correspondence between the integers and real numbers, then you'll always have a bunch of real numbers left over.
(It doesn't stop there, though. There are sets which are "bigger" than the real numbers in the same way. There are actually infinitely many sizes of infinity...)
Well, it is notable because it is provable in ZFC but not in ZF. So in a sense the weirdness of the result could be an argument against including the axiom of choice.
kaladyr · 1 points · Posted at 03:36:32 on February 14, 2016 · (Permalink)*
Maybe they should write down its measurements on a Post It before breaking it down, then they'll have enough information to know you can only make one ball out of it when they resurrect it.
Rlysrh · 1 points · Posted at 12:37:02 on February 14, 2016 · (Permalink)
Oh my god thank you. I watched that whole video, came out feeling like a dumbass and you've explained the whole thing in a short paragraph.
I think the issue I have with it is that he mentions a countable infinity, which to me seems to go against the definition of an infinity. Not that I would understand a mathematical infinity but expressed with just words an infinity has no end (at least how I see it). Since it has no end it can't have a definite size or volume or anything really, any definite characteristic becomes irrelevant.
In the end all this reminds me of is that story of some Greeks (I think it was Greeks) who argued that time and distance doesn't exist. If I recall correctly the example used was the race between the hare and the turtle and how if you divided time into small enough increments they both traveled at the same speed. I don't remember enough keywords to find it again though.
GuSec · 1 points · Posted at 13:36:50 on February 14, 2016 · (Permalink)
Countable infinite just means that you can enumerate all elements using the natural numbers, not that a counting process where each step takes a finite time will also complete within finite time (which it obviously won't as you say). The real numbers are not countably infinite in number because you can't assign each real a natural number, they are simply too many and the amount of them all is a larger, non-countable, infinity.
Which is a cool mathematical fact in itself.
kaladyr · 1 points · Posted at 18:39:32 on February 14, 2016 · (Permalink)*
Tell me if I'm misunderstanding something, but wouldn't this only work for an object with infinite density? Basically the "paradox" is a fancy way of saying infinity × 2 = infinity.
kaladyr · 1 points · Posted at 18:32:08 on February 14, 2016 · (Permalink)*
.
[deleted] · 1 points · Posted at 00:00:18 on February 16, 2016 · (Permalink)
Yes it's provable within ZFC, where things like "Sphere" and "decompose the ball" do not mean what everyone thinks they mean.
Sadly the Wikipedia article of the paradox doesn't mention the word energy even once. I'm pretty sure this goes against the law of conservation of energy. I can see how the new matter might be created from energy, as we're dealing with subatomic particles anyways, but how do you get the overall energy level before the process to be doubled afterwards (as you now have the original object twice)?
no_nick · 2 points · Posted at 11:05:17 on February 14, 2016 · (Permalink)
The 'ball' in this case is an abstract notion, not a physical object. Physics doesn't factor into this.
kaladyr · 1 points · Posted at 18:27:43 on February 14, 2016 · (Permalink)*
So basically take a solid ball, do magic to it so it exists in another dimension where size doesn't matter, cut it up, then do more magic to bring it back to our dimension and put it back together again, twice. Got it.
kaladyr · 3 points · Posted at 07:46:45 on February 14, 2016 · (Permalink)*
It's not really a paradox, but rather a thing-that-is-pretty-unintuitive-and-seems-like-it-should-be-wrong. Unfortunately, mathematicians got tired of calling it the Banach-Tarski thing-that-is-pretty-unintuitive-and-seems-like-it-should-be-wrong.
[deleted] · 2 points · Posted at 13:17:34 on February 14, 2016 · (Permalink)
As a mathematician studying mathematical logic, I've always been taught that a "paradox" is a statement that is contradictory. The most famous example being the liar's paradox: "This statement is false." If the statement is false, then that statement is true then the statement is false then the statement is true... A more important example is Russel's paradox: "Let R be the set of all sets that are not members of themselves." If R is not a member of itself, then the definition dictates it must contain itself, and so on. Paradoxes are a huge part of mathematical logic and they are pretty rigorously defined (as are most things in mathematical logic).
Now, outside of mathematical logic, then you get into the usage of paradox as an "unintuitive result", which is fine. My problem with the Banach-Tarski paradox is that is a problem INSIDE of mathematical logic (specifically set theory), so it's odd for them to call it a paradox when that term has a rigorous definition inside of mathematical logic.
[deleted] · 1 points · Posted at 15:27:42 on February 15, 2016 · (Permalink)
I only know Zeno's paradox(the one with the tortoise) in calculus and the birthday paradox in stochastics, and both aren't contradictory. I don't know about mathematical logic though.
Zeno's paradox is sort of iffy. The "paradox" there is that you shouldn't be able to reach the end point, but you obviously can. Now, Zeno didn't have the mathematical tools to discuss limits, so it was contradictory to him. To us, not so much.
Birthday paradox is straight up an unintuitive result.
[deleted] · 1 points · Posted at 23:53:14 on February 15, 2016 · (Permalink)
"The sphere can be divided into parts and reassembled into two copies of the original sphere" would be a false statement under elementary geometry, but becomes a true statement given higher level concepts like the axiom of choice.
It's a matter of English interpretation and what fundamental ideas one understands. The statement is false for all practical purposes, using everybody's grade-school definitions of "sphere, divide into parts" etc... So, for most people, it is an oddly true/false statement. i.e. a paradox. For mathematicians it's a matter of definitions and axioms.
I agree that technically it is most likely not a paradox, just a weird result that we don't yet know how to interpret.
What I'm fundamentally getting at is that in mathematical logic, the word "paradox" has a more strict meaning. Yeah, the Banach-Tarski paradox is a "paradox" in the common usage, but it isn't really a "paradox" in the mathematical logic usage and the Banach-Tarski paradox is fundamentally a result in mathematical logic, which is why it is weird.
PS: We know exactly how to interpret it; it's just intuitive. Just like it's easy to interpret the well-ordering principle being equivalent to the axiom of choice, but it is highly unintuitive.
[deleted] · 1 points · Posted at 16:20:27 on February 18, 2016 · (Permalink)
Of course. Though it's interesting to think about, in a philosophical sense, what it means for mathematics if the results are actually not applicable to reality.
Well, mathematics is a language and like any language, it can be used to describe impossible things. A good example is a non-intersecting Klein bottle is impossible in reality, but there are all sorts of mathematics describing such a beast.
In the case of the Banach-Tarski paradox, part of the decomposition relies on non-measurable sets, i.e. sets with an undefined volume, in order to get the two spheres. Things with undefined volume are not a realistic thing. In a sense, this is similar to those proofs that 1=2 that depend on dividing by zero at one step.
[deleted] · -4 points · Posted at 01:47:07 on February 14, 2016 · (Permalink)
Paradoxes make me think math is just a bunch of mumbo-jumbo.
It's not an actual paradox. A lot of times, a mathematical result is called a paradox if it contradicts intuition in a significant way. In the Banach-Tarski paradox, it seems that just doing rotations and translations should not affect the volume in the way it does. The flaw in intuition is that the sets one does these rotations and translations on can not have a volume assigned to it, which is a somewhat-surprising result.
[deleted] · 1 points · Posted at 23:57:17 on February 15, 2016 · (Permalink)
"The flaw in intuition is that the sets one does these rotations and translations on can not have a volume assigned to it"
That's less a flaw in intuition and more a flaw in description, would you say? Most people when presented the banach-tarski paradox are not thinking about infinite sets, they're thinking about a ball of play-dough and a knife. This is equivalent to changing the axioms of the system without informing the listener.
It's not mumbo jumbo because in all likelihood it'll turn out to be useful somewhere.
Most people when presented the banach-tarski paradox are not thinking about infinite sets, they're thinking about a ball of play-dough and a knife.
That's just misunderstanding mathematical terminology. A ball, in mathematics, is a particular type of infinite set satisfying some property. I don't believe I've ever heard someone who knows what they're talking about every imply in a serious manner that the Banach-Tarski theorem can apply to reality.
It essentially boils down to the fact that without having an understanding of the terminology and jargon of a field, you're bound to misinterpret what's said.
[deleted] · 1 points · Posted at 16:19:22 on February 18, 2016 · (Permalink)
I feel like I understand it better every time I watch it again. Ive seen the video well over 10 times and I feel as if I have a pretty clear understanding of it.
I guess it's saying if you divide infinity into a finite number of disjoint infinite parts, you can make an exact equal of the original infinity by combining only some of the parts, because infinity. I got lost on how the countability of infinity mattered in any of the steps.
[deleted] · 1 points · Posted at 04:51:03 on February 14, 2016 · (Permalink)
I'm confused as to how this is different from Zeno's arrow paradox.
I haven't watched the video, but from what other people have said, it seems like they might be covering a lot more detail than they need to for you to get the gist of what theorem is saying.
I wrote this for another comment in this thread:
It shows that it doesn't make sense to assign a volume to certain sets.
Suppose you said that every subset of 3-d space could be assigned a volume. Volume should satisfy a couple properites:
If you move a set around (rotate/translate) it should still have the same volume
If a set is broken up into smaller sets, then the volume of the whole set should be the sum of the volumes of the parts.
The theorem shows that this is impossible, because when you start with a ball of volume 1, you break it up into a finite number of parts whose volumes should add up to one. But now when you move those parts around, their volumes shouldn't change, so the total volume should still be 1. But when you put them back together, you now have two balls, whose total volume is 2. So 1=2.
The reason we get a contradiction is that we assumed we could assign a volume to any set we wanted in a consistent way, which turns out to be impossible. The point is that while it makes sense to assign a volume to the balls before they've been dismantled and after they've been put together, it doesn't make sense to assign a volume to the sets you break them up into.
I should add that there are other, easier theorems which also show that there are "nonmeasurable sets" (basically sets to which you can't assign a volume or length), but the Banach-Tarski paradox is especially compelling because you only need finitely many pieces and finitely many rotations/translations of the pieces.
Erekai · 1 points · Posted at 07:44:52 on February 14, 2016 · (Permalink)
Loved that video, but it completely blew my mind. Same with his recent deck of cards one, about 52! So crazy.
I don't think he did a very good job of explaining it to be honest, which I'll just chalk up to the seeming complexity of the subject matter.
u56i67 · 0 points · Posted at 03:10:34 on February 14, 2016 · (Permalink)
Take a line from 0 to 1. It is one unit long. Take a line from 0 to 2. It is 2 units long.
Every single point on the line from 0 to 1 can be mapped to a unique point on the line from 0 to 2. To go from any point on line one (say, 0.514528) simply multiple it by two (to get 1.029056, for example) and 100% of the points in line 1 can be mapped to a unique point on line two. To go from any point on line 2 to a point on line 1, simply divide it by two. Now, if 100% of the points of line 1 can be mapped to a unique point on line 2 and 100% of the points on line 2 can be mapped to a unique point on line 1, it what sense is S1 = {number of points on line 1} different from S2 = {number of points on line 2}?
Despite line 2 being twice the length as line 1, we say that S1 and S2 have the same cardinality. There are an infinite number of points in each and both of those infinities are of the same "size." Or, less formally, this kind of infinity is still that same kind of infinity regardless of whether we multiply or divide by 2. Infinity*2 = infinity/2 = infinity.
You can do the same thing with 3-dimensional objects, you just need a more complicated function to map between the two, which is what that vsauce video took so long to develop. Note that this only works with mathematical objects. Real objects are finite(ish).
[deleted] · 25 points · Posted at 06:31:33 on February 14, 2016 · (Permalink)
You just called someone a shitbag over a discussion of the banach-tarski theorem. Consider getting a good nights' sleep, possibly while listening to some Rachmaninov on youtube
[deleted] · 10 points · Posted at 06:26:24 on February 14, 2016 · (Permalink)
it isn't appliable because we can't really cut infinitely complex objects
Soluz · 1 points · Posted at 13:02:54 on February 14, 2016 · (Permalink)
Just because something isn't applicable in physics doesn't make it useless in mathematics at all.
Yet....well, technically, ever. But, we can cut them infinitely small enough to be able to map the object, in which case, replication is possible. It's impractical as fuck to do it with complex objects, but not impossible. Just need to have the computing capability to map all the points uniquely and tag them and categorise them and, then, replicate it.
Even if balls were made of some abstract, continuous fluid instead of atoms, it would be impossible to physically apply the theorem because it depends on the axiom of choice. It is impossible even to concretely describe which points are in which set.
The point of the theorem is not that you could physically do this, but that there are certain types of sets for which it is impossible to assign a volume in a coherent way. But that doesn't sound as interesting to most people.
I'm glad I read this, because I could never figure out why in the world such an obviously-never-applicable claim about the ball could be at all useful.
Now that I know it doesn't actually have anything to do with the theoretical ability to duplicate theoretical objects, it finally makes sense why anyone would care.
Also: There are some scientists who think this actually happens when smashing subatomic particles together. Sometimes you end up with more particles than you start with, this is one proposed reason as to why.
DISCLAIMER: I know nothing about this, i just watched the Vsauce video posted above.
It splits everything down infinitely, then postulates that because the gaps after the split are infini-small they can be filled without loss of data or without being unmathematical.
It is true, but if you handle things like that you can dublicate anything once you split it down infini-small.
Well it's a little more complex than that and deals with some rather specific definitions, but basically it holds for any manifold I believe. The property of manifolds are what makes it possible, and its quite easy to find counter examples where Banach Tarsky doesn't work
One can interpret Banach-Tarski as a statement about the importance of Measurable Sets; that is, you have to be careful how you cut if you want things to reassemble cleanly.
21stGun · 2 points · Posted at 23:47:40 on February 13, 2016 · (Permalink)
Yeah, but is universe infinite?
[deleted] · -6 points · Posted at 01:51:30 on February 14, 2016 · (Permalink)
The Planck length doesn't technically define the minimum finite distance possible in the universe, if it did we would observe the universe as being pixilated or granulated, which experimentally we have been unable to do, and instead what we see is a universe that is continuous. The Planck length minimum is a side effect of the uncertainty principle which mathematically creates a black hole with a schwarzchild radius of a Planck length when trying to observe anything on that small of a scale, and the more you try to "zoom in" the larger the black hole becomes. So basically a Planck length is the theoretical limit on observation, but not the minimum distance across which action can take place (the propagation of a photon for example).
While they might be solid objects, you would still need an infinitely fine cut and an (uncountable) infinite amount of time to define every point on it's surface.
fknprob · 1 points · Posted at 13:39:48 on February 14, 2016 · (Permalink)
well, it actually is.
that fact is quite important in understanding measure and probability theory. and i assume you know that probability theory is very much applicable.
I would like to add that the process of separating the ball into two is only made by rotations of the subsets. (Otherwise this is just saying something about cardinality)
ngwoo · 13 points · Posted at 00:28:42 on February 14, 2016 · (Permalink)
But if the ball is hairy they'll both have cowlicks
No axiom is "necessarily" true. In a more serious mathematical discussion, your comment would be fine, but I feel like in a thread like this, people will just read your comment and think "oh, so it's not really true" and dismiss it outright.
The important thing to note is that BT follows from choice, and pretty much all analysis is done with choice.
Bollocks. No layman would dispute the Peano axioms. The axiom of choice is only even understandable to hardcore mathematicians, so don't even bother asking a layman if he thinks it's true or not. But more often than not, if you explain the implications (for example, the Banach–Tarski paradox), this will be consider by said layman as evidence against the Axiom of Choice.
people will just read your comment and think "oh, so it's not really true" and dismiss it outright.
Which is appropriate.
The important thing to note is that BT follows from choice, and pretty much all analysis is done with choice.
Bollocks. No layman would dispute the Peano axioms.
If they could be proven true, they wouldn't be axioms. We made them axioms strictly because we are so damn sure of their "truth". That doesn't make them necessarily true, and there are quite a number of mathematicians that reject PMI (an extreme minority, but they do exist).
The axiom of choice is only even understandable to hardcore mathematicians, so don't even bother asking a layman if he thinks it's true or not.
It's not about whether you "think" something is true. Mathematically speaking, it is consistent with the other axioms that pretty much everyone thinks should hold, and we use it to do a lot of math. In particular...
The important thing to note is that BT follows from choice, and pretty much all analysis is done with choice.
That doesn't make it a "fact".
the field of mathematics in which the entire statement of BT is formulated assumed Choice as a default. In this realm, it absolutely is a fact. It's not an opinion, or a hypothesis, or a conjecture. It's a theorem.
You're missing the point. A "mathematical fact" is something that every reasonable person can agree fits with their reality. The Peano axioms do meet that criterion, the axiom of choice does not. If you want to be pedantic about things, nothing is true, but honestly, that's a nihilist view.
Or more precisely, you could say, "Given the Peano axioms (which basically every reasonable person agrees with), the following are mathematical facts.., and if you further accept the axiom of choice (which many academics agree with, but basically no one else), then this clearly absurd ridiculous thing is also true..."
But if you start citing the Peano axioms as the context in which you are replying to this post, people are going to wonder why you bothered because basically no one disputes them. If you do the same for axiom of choice then it will be seen as a useful clarification.
Well for starters, the Peano Axioms are not the ones being discussed. The Zermelo-Frankel axioms of set theory are.
And if you want to define "mathematical facts" to be those things that "every reasonable person agrees with" then you suddenly have bullshit like 0.99... not equal to 1. Fortunately, your definition of fact is not the standard.
A mathematical fact is something that has been proven from mathematical axioms. It is a fact that the Banach-Tarski paradox follows from the axioms of ZFC, which many people (that is, most current mathenaticians) agree with.
Also, you keep using phrasing that suggests the axioms are "debated" in some philosophical sense (which ones are true, which are false). While that certainly does happen in some areas, and while it may be the case that most mathematicians have some sense of which axioms they personally agree with, it is not a mathematical question to ask "is choice 'true'?" All that matters is that it is independent from, and equiconsistent with, ZF. In some areas, Choice is useful or "obvious" and in those areas it is taken as true. In other areas, it isn't.
And in the area of (set-theoretic) geometry, the context in which Banach-Tarksi is stated, Choice is assumed. To say Banach-Tarksi is not a fact is the mathematical equivalent to a straw man: you have changed the terms and assumptions to make your argument true, but you are no longer working in the context as the people you are saying are wrong.
[deleted] · 2 points · Posted at 02:52:48 on February 14, 2016 · (Permalink)
I was thinking of this earlier today, remembering seeing it at least a year ago. Then I saw OPs comment and was weirded out because I had just looked up the comic. And then I saw you post it... it's a weird day.
No, this is something more complicated. This is not just saying that a ball and two balls have the same cardinality as sets. The pieces the ball is cut into are not stretched or distorted in any way when reconstructing the two balls - they are only rotated.
I have read about it before that it's not a paradox in itself since it is a proven fact but I may be wrong. Would you be able to provide an explanation for the layman, preferably with colourful illustration and diagrams?
Edit: Got my explanation in one of the links below.
[deleted] · 1 points · Posted at 02:27:38 on February 14, 2016 · (Permalink)
Vsauce did an interesting video that further explains this paradox.
[deleted] · 1 points · Posted at 03:46:05 on February 14, 2016 · (Permalink)
I always knew there would be something I would learn about that is a mathematic or scientific fact that my brain is just not ready for. Thank you for confirming.
Given a solid ball, there exists a decomposition of the ball into a finite number of disjoint subsets, which can be put back together in a different way to yield two identical copies of the original ball.
Not to be a party pooper, but I think this result should be stated more modestly: there exists a decomposition of the set of points of the unit ball, and rotations+translations of these pieces, that produces the set of points of two disjoint unit balls.
I phrase it this way because I don't believe that there is any definition of a decomposition, that is compatible with any of the usual geometric structure we usually associate with the unit ball (metric, topology, measure, etc.), that is also compatible with Banach-Tarski.
In my opinion, Banach-Tarski, while fascinating, is really a theorem about the bad behavior of the operation take the points, and only the points.
For example, a 2011 paper of Alex Simpson has argued that Banach-Tarski fails when we acknowledge that sets of points come equipped with certain topological information (specifically, they should be treated as something called a sublocale).
What amazes me specifically about the this paradox is that it mathematically proves it is possible, but we cannot mathematically or scientifically prove that it is possible (or that it could happen). It's literally questioning the boundaries of nature. I just learned about it today so it's very cool to see this post!
Some math is just made up to allow for impossibilities to be possible. I could say it's possible for me to become a billionaire without working, by inventing a conceptual imaginary universe in which a billion dollars is not made of money and where work isn't really work but simply an exertion of energy and then thus prove that I can be a billionaire without working. But that shit don't have any bearing on anything real.
[deleted] · 1 points · Posted at 11:11:09 on February 14, 2016 · (Permalink)
Oh I wish I could believe or understand that!
itisike · 1 points · Posted at 12:16:46 on February 14, 2016 · (Permalink)
There is a thing called the Axiom of Choice. It is one of the fundamental "rules" for maths. Some mathematicians do not like this Axiom because they think it is too "powerful". They often point to this paradox as an example!
Good math trick, but I would love to see them try to do it in a machine shop. She conservation of energy might have something to say about that.
aaronod · 1 points · Posted at 01:09:26 on February 14, 2016 · (Permalink)
I am a total maths dunce but would this have anything to do with quantum particles supposedly appearing to be in two places at the same time? Or am I way off?
It's way more than that. It shows that it doesn't make sense to assign a volume to certain sets.
Suppose you said that every subset of 3-d space could be assigned a volume. Volume should satisfy a couple properites:
If you move a set around (rotate/translate) it should still have the same volume
If a set is broken up into smaller sets, then the volume of the total set should be the sum of the volumes of the parts.
The theorem shows that this is impossible, because when you start with a ball of volume 1, you break it up into a finite number of parts whose volumes should add up to one. But now when you move those parts around, their volumes shouldn't change, so the total volume should still be 1. But when you put them back together, you now have two balls, whose total volume is 2. So 1=2.
The reason we get a contradiction is that we assumed we could assign a volume to any set we wanted in a consistent way, which turns out to be impossible. The point is that while it makes sense to assign a volume to the balls before they've been dismantled and after they've been put together, it doesn't make sense to assign a volume to the sets you break them up into.
[deleted] · 0 points · Posted at 12:46:29 on February 14, 2016 · (Permalink)*
I meant finite number of parts. The issue here is not cardinality, which is the idea of sets have the same "number of elements." You can show that by assigning to each element of one set an element in another set. It is relatively trivial to show one ball of points has the same cardinality as two balls of points; you could ask an undergraduate math major to do it for homework.
The idea of the B-T theorem is that you are trying to come up with an idea of "volume" for sets of points in 3-d space. This is supposed to measure not "how many points are there," but "how much space does this set of points take up". This works for some sets, but if you try to do it for all possible sets in 3-d space, then you get a contradiction.
Paradox solved: Any such process would require an infinite amount of energy. An infinite amount of energy would have nowhere to go/be transferred to/produce no work. Therefore there is no possibility of Banahch-Tarski existing in our world.
Awesome!! I came here for Banach Tarski. I recently asked a math professor for the 10 second definition: if a sphere is comprised of 2000 points but is defined by 1000 points, you could theoretically decompose the sphere and rebuild it as two spheres defined by 1000 points.
Munninnu · 1518 points · Posted at 19:36:23 on February 13, 2016 · (Permalink)*
How big is the number of possible permutations when shuffling a 52 cards deck.
Specifically the example to give us the faintest perception of how ridiculously big 52 Factorial is.
EDIT: u/LotharWilhelm reported that this video gives us a visualization of what Scott Czepiel wrote in the original link I gave. It starts at 14:00 though.
EDIT II: In this video posted by another redditor the guy uses a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
If you shuffle a standard 52 card deck, there's a very real chance that nobody in the history of the world has ever created such a combination of cards.
Fun fact #2: computer card games require special, stronger randomization. Most "random numbers" in a computer are one of 232 specific numbers (between 00000000000000000000000000000000 and 11111111111111111111111111111111) that are chosen randomly. This is about 4 billion different ways the cards can be mixed, which means that 99.9999999999999999999999999999999999999999999999999999999999% of all possible card orders will never be seen in a poorly coded card game.
(Gambling websites have figured this out, and they do a good job of randomizing now.)
EDIT: That means that if you could see six cards and know which order they were in, you would have a very, very good chance of being able to figure out the rest of the deck.
There would need to be some extra chaos thrown in for that to be useful. Computers are completely deterministic, and will come up with the same results given the same inputs.
In a bad card shuffling algorithm, the inputs are "one of 232 numbers, selected randomly" and the shuffling algorithm. It doesn't matter if that same random number is used in multiple places in the code, the inputs are the same so the outcome would be the same too.
In contrast, in a good card shuffling algorithm, the inputs are something like "one of 2256 numbers, selected randomly" and the shuffling algorithm.
Why not request entropy from the user in the form of keyboard mashing to shuffle the cards? I remember this kind of entropy is necessary to set up a key ring in arch Linux or something along those lines.
[deleted] · 47 points · Posted at 06:46:48 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 5 points · Posted at 07:12:27 on February 14, 2016 · (Permalink)*
There's a bit of a counterintuitive problem when hashing "good" randomness together with other inputs, especially those provided by an attacker, and even more so if they'll have an opportunity to observe, or make a guess at, the "good" random number when providing their input. Say one random number generator is seeded by the system clock only, and another is seeded by the system clock hashed with a number I provide. To attack the first, I need to guess the exact system time. To attack the second, I can choose my input in a way that attacks a whole range of possible system times. All I have to do is take the range of likely system times, run the hashing algorithm against every number in that range myself using as many various inputs as I have time to try until I find an input that results in low entropy.
Even simpler example. Imagine we need a random number from 1-100, and we have a hashing algorithm which, say, multiplies numbers together, then discards all but the two least significant digits, and adds 1. You have two fair 10-sided dice you can use to get a number from 1-100. You can either use just your dice alone, or you can use your dice and the hashing algorithm with another input that I provide. If I also roll fair dice, the output will look pretty random, but if I'm malicious and just put in 100 every time, the algorithm will cause the "random" number to always be 1. This is obviously a very weak example just for the sake of illustration. The upshot is that allowing an attacker who knows (or can guess at) your hashing algorithm to control any of its inputs lets them erode your entropy, and hashing can not add entropy. Usually hashing destroys entropy, and the more complex your hashing algorithm, the more likely it will throw out a bunch of entropy by accident. This is why many people in the crypto community advocate just reading raw bytes off of /dev/urandom for random numbers. Doing randomness in user space is almost always buggy and is frequently attackable.
tyrico · 12 points · Posted at 09:20:48 on February 14, 2016 · (Permalink)
Pokerstars uses user input AND quantum randomness as entropy sources for their shuffle:
Could you not have a deck and randomly select a number between 1 and 52 from the order of the current deck to form the first card of the new deck then 1-51 for the next card for the 2nd card of the new deck and so on?
The problem is not the shuffling algorithm, it's how you generate the randomness in the first place. If you use many common methods, you can guess the state of the generator with a few values of the output and then no matter what shuffling algorithm you're using it won't help.
Good random numbers generators have a huge amount of different states which makes inferring them from some data too hard (if you need to see 30+ cards, it's probably not very useful) and with no way to predict their initial value.
You haven't answered my question. You've just explained why it's better to have a good randomization algorithm, which is what I'd call a "no shitter"
Why is it better to determine the order of all 52 cards at once, rather than randomly selecting one card from the pool of remaining cards every time a card is revealed?
__kojeve · 28 points · Posted at 05:00:15 on February 14, 2016 · (Permalink)
When he says:
Computers are completely deterministic, and will come up with the same results given the same inputs.
What he means is that there's no such thing as "randomly selecting" to a computer. Selecting them one at a time will never be any more random than computing the entire deck because there's no randomness involved.
My original point was that that would allow any theoretical deck arrangement to exist.
However, if the randomization seed was determined by a nearly random method, such as a very specific measurement of how long an action takes to reach the server, wouldn't that allow true randomization?
dJe781 · 29 points · Posted at 05:14:59 on February 14, 2016 · (Permalink)
wouldn't that allow true randomization?
True randomness cannot be achieved because <what he said>.
That's not true. True randomization can't be programmed as of now. There are such things as hardware random number generator which rely on circuit noise. There's also random.org which uses atmospheric noise, I think. That allows for "true randomness" until someone figures out how to perfectly model both of those phenomena.
18scsc · 1 points · Posted at 21:02:18 on February 19, 2016 · (Permalink)
I'm no physics major, but I think this site gives true random numbers. It measures the timing of radioactive decay and uses that as seed.
So if they determined the seed based on a measurement (in nanoseconds) of how long it took the user to submit an action to the server, there would be some way to predict that? Because there's shit like wind patterns, rainfall, etc. that effect how long that measurement would be.
The amount of time a signal takes is not random either. It may or may not be a good seed, but it doesn't solve the problem of determinism.
Look at it this way, throwing the cards in the air is also deterministic, it's just that the number of inputs are invariably more complicated than any computer such that the pseudo-randomness generated by the individual movement of the cards over a body of air is functionally indistinguishable from true randomness. That doesn't mean that it is truly random, however.
Why is it better to determine the order of all 52 cards at once, rather than randomly selecting one card from the pool of remaining cards every time a card is revealed?
Because if you don't add in any extra source of randomness, these aren't actually different things.
An RNG with only 232 states, by itself, can only produce 232 outcomes, no matter whether it produces the deck all at once or one card at a time.
The seed itself would need to be randomized for each card, ideally through a "true" randomization process like ping times. Then it would be truly random, but have 52! permutations from only 52 seeds.
[deleted] · 0 points · Posted at 23:22:52 on February 14, 2016 · (Permalink)
False assumption that ping times are random. They run off other computer hardware, emitting packets only on some multiple of their clock or the network fabric (ie 100mb).
Just because they have to be a multiple of something does not mean they aren't random. There are too many factors involved to predict what a ping time will be with certainty.
They are mathematically identical. Let's say that the random number is 3134212345 (converted to base 10 to be smaller).
You shuffle the 52 card deck in pattern 3134212345, draw the top card, then shuffle the 51 cards in pattern 3134212345 again, draw the top one, and repeat until you have drawn all 52 cards. Every time that 3134212345 is the random number and you use the re-shuffle algorithm, the draw order will be exactly the same.
Contrast that to shuffling once. You shuffle the 52 card deck in pattern 3134212345, draw the top card, then draw the new top card, and so on. This will be different than the results from the re-shuffle algorithm with 3134212345, but it will be identical to every other one-shuffle that is seeded with 3134212345.
As long as it still uses the same seed, it would be the same outcome every time.
The 52card algorithm with seed 3134212345 would have a certain output. Removing the top card and plugging the new deck into the 51card algorithm with seed 3134212345 would then have its output. same with the 50card and the 49card and so on until the 2card algorithm.
If the inputs are the same, then the outputs are the same. Picking a new seed for each card would be difficult, as most computers don't have true (hardware) random number generators.
Yes. The comment above yours isn't quite right. It's fine to output one 32-bit number at a time - because you're really only picking one of 52 cards, anyway - what matters is the internal state of your random number generator. Your generator's internal state completely determines its output.
If your random number generator only has 32 bits of internal state, then it can only be in 232 possible states - so it will start to repeat itself after only ~4 billion steps, in the best case. Even worse, that series of 4 billion outputs is the only one it can ever produce.
If you have a better pseudorandom number generator with 256 bits of internal state, then it can be in 2256 possible states. log(52!)/log(2) = 225.5810 is less than 256, so this would (potentially) be enough to make a good random shuffle algorithm that could potentially generate any deck.
Consider a random number generator with only one bit of internal state. Its output might look like this:
qevlarr · 5 points · Posted at 09:21:35 on February 14, 2016 · (Permalink)*
Computers use pseudo-random number generators with a truly random seed as input. Care must be taken with how many different possible seeds there are, relative to the number of possibilities you want to pick from using the PRNG. The seed being too short is only one of many pitfalls. Another would be using modulo arithmetic creating a bias to smaller outcomes (under certain conditions).
Ignore the top reply. You're right. At least for texas hold'em poker, and other card games that do not use the entire deck.
With 10 players, there are 25 cards being drawn, for a total of 52!/27! combinations. Very significantly less combinations.
It's still better not to use the naive algorithm, as /u/ulyssessword points out. However, not completely permuting the deck at the start, but selecting one-by-one would improve the naive algorithm.
Note that the order of permutations of a whole deck exceeds 264 (e.g. a 64-bit seed), but for just 25 cards, the number of combinations is significantly smaller than 264. That means that, assuming you refresh your seed sufficiently often, 64 bits is enough for one-card-at-a-time, but not for shuffling the whole deck.
8 bits would actually be enough for one at a time, because the seed for the card is itself random, you only need 52 possible seeds, so 11111111 is enough.
No, unless you want to reseed between individual cards (which doesn't make sense).
Given a seed, e.g. 10011101, the sequence of random number drawn will be identical. So on 10011101, the first card is 8h, then 4c, then Ah, etc. Such a sequence exists for every seed. Since you have 256 sequences, on average, there's about 5 sequences that start with any arbitrary card. And, with two cards, you have almost certainly enough info to deduce the seed.
My whole point was that you would be reseeding between cards. Because each seed will always lead to the same sequence, 52! seeds must be possible to have the same amount of randomness as a shuffled deck of cards. If you have a true random component determine the seed for each card, then only 52 seeds are needed.
The problem is that the only proper seed uses external unpredictable data (e.g. hash of system time, hash of temperature readings, dedicated noise machines etc.) I'm not sure you can find a source of random data that fluctuates sufficiently fast to extract so many unique seeds. If you don't give the clock a chance to change, or the temperature readings a time to update, then the seed remains the same over multiple cards.
If you use, for example, the time in ticks between actions submitted to the server, it's totally random. Not client-side manipulation can account for variance in data reaching a satellite.
Well if you know the randomization software, then you need 52! possible values for the seed for every theoretical arrangement to be possible. Instead, some truly random thing (Geiger counter, times for a ping,etc.) could determine a new seed for each card, so only at least 52 possible values need exist, or 000000-111111. Way less than 52!
I say determine it as each card comes up so you don't have to do this 52 times.
Of course you can encode the values from 0 to 52 in a small amount of bits and rewrite to that memory to change it... But when we talk about bit count we aren't talking about software memory used to run the algo, but the number of total bits to encode the problem size (from a mathematics perspective).
yokhai · 2 points · Posted at 05:01:49 on February 14, 2016 · (Permalink)
He didn't mean to say would, he means to say should. You can't random a new card each time, because they are supposed to represent a physical deck. So you actually have to created 52 "objects" and shuffle them using a randomizer, or else you would create a virtual game that in no way resembles physical poker/blackjack
That's to prevent cheating by the dealer. And technically, the deck was never truly shuffled and never even existed before each card was revealed. Kind of a false equivalency.
yokhai · -1 points · Posted at 05:49:28 on February 14, 2016 · (Permalink)
There are very strict rules in place to make sure the digital games do not operate with behavior that violate the rules of the physical game.
So how would this be addressed if there was never a deck or determined order of cards? Because technically the order of the cards never changed because it never even existed.
yokhai · 0 points · Posted at 05:59:03 on February 14, 2016 · (Permalink)
"Existed" is philosophical construct that shouldn't be used in this conversation. Electrons are real, so the representation of the cards are real. Trying to reduce the problem by saying "but they aren't even real" is rather pointless.
To answer the question you asked, a player would probably never notice, as far as they are concerned, they are getting random cards out of a pool of cards. It would have to be discovered on the shoulders of whatever regulating body performed inspections of the software companies. If they found out the algorithms were doing something "shady" there would be fines, probably.
But that's not the point. If I were running a gambling application, I wouldn't want to add an extra 50 shuffles into each game. That's a lot of computing power, especially having to re-seed each time. You are also diluting the value of your seeds, but I'm sure that point is probably mathematically irrelevant.
I'm not saying that the fact that there are no physical cards is the issue. I'm saying that there was never a deck to reshuffle. In card games, your options are shuffling the deck once or reshuffling. In online card games, there is a third option, which is randomly determining exactly one spot in the arrangement of the theoretical deck, which means that each card is shuffled once, and the order of cards can't be changed because the cards have no order.
What I'm saying is that it is entirely a philosophical debate whether or not this would even be considered reshuffling.
yokhai · 0 points · Posted at 06:15:15 on February 14, 2016 · (Permalink)
I don't think you understand data structures and how digital objects are stored in memory.
You can make a Graph of cards, that contain no explicit order, and randomly assign the order at your choosing, which is what I think you are referring to. Or you can created a List of cards, which have an explicit order, indexed at 0.
These algorithm use graph theory to do the shuffling once, which what another user was talking about when they mentioned "programmers are getting very good at this stuff", and then once the order of the deck is solve, the digital objects are arranged in a list, to be drawn from.
So think of taking a deck of cards, and spreading them all over the table, face down, and "shuffling" them by mixing them all up in pile, that's graph shuffling; difficult and clumsy for humans, very very efficient for computers. Then the pile is pulled together to form the deck. That's exactly what a computer does, but digitally, and its orders of magnitude faster than trying to digitally perform a riffle shuffle.
Neither of these are what I'm talking about. I mean you have a list of cards with an explicit order (organised by suit and the rank) and you remove one of them at random each time a card is revealed. So if you know the first fifty cards that were revealed, you still have no way of predicting which card will be next, even if you knew exactly how the software that determined the card worked. You would need to know both how a seed becomes a card and how that seed is determined, which ideally would also be random and based on something impossible to predict, like a Geiger counter or something.
This also means that the deck is never shuffled. At no point is there even a known order of the cards. There is no virtual order being stored anywhere.
yokhai · 1 points · Posted at 08:08:22 on February 14, 2016 · (Permalink)
Again, that would like pulling a random card from the middle of the deck and using it to play, which is against the rules of the physical game, so there are strict policies in place to insure that the software isn't doing that. They take a list of cards, shuffle that list, and pull one at a time off the top of the list.
The randomness in each game isn't the mathematical problem. I don't care how random the deck is in a single game. It's the randomness across ALL games, which is the point of the original commenter. So running your RNG 50x more than normal would severely dilute your seeds over millions of games, assuming you only have a 4 billion seed count. You'd actually reduce the fidelity of randomness across your games. But that whole point is mute. It doesn't change the game itself, it's only a comment about the uniquiness of the games played.
Oh, so you're running on the assumption that a seed is never used more than once. Well, considering that in this case every possible arrangement of cards can exist, that's more random.
Firehed · 1 points · Posted at 08:36:48 on February 14, 2016 · (Permalink)
Not necessarily, it's just shuffling by selecting one card at (cryptographically secure) random at a time.
Then draw from the deck normally with deck.pop() or similar.
Technically you only need six bits of entropy per card in the deck (26 == 64 > 52) so depleting the system entropy pool is unlikely to be a problem. And it's only O(n), which (skimming SO) seems like it's on par with most shuffle implementations.
Could you do it in a more clever way? Almost certainly. But trying to get it down to O(log(n)) will likely obfuscate what's going on (bad for auditing crypto/security-related code), and you already know n is never going to be more than 52 for a one-deck game so the runtime practically doesn't matter anyway.
Disclaimer: I know enough crypto to know that this shouldn't be totally fucked up, and more importantly know enough about crypto to get work peer reviewed. I don't work for a gambling approval board or anything, so don't assume that example would pass any sort of audit.
rawling · 1 points · Posted at 08:23:05 on February 14, 2016 · (Permalink)
Picking one card at random at a time is the Fisher-Yates shuffle, which is the goto shuffling algorithm.
or else you would create a virtual game that in no way resembles physical ...blackjack
In most modern casinos, that's basically what blackjack is now, actually. They introduced autoshufflers that reshuffle cards back in right away and use high deck counts, in order to eliminate card counting (which revolves around knowing the ratio of high cards in the deck, which increase the likelihood of the dealer busting, and thus the likelihood of the player winning the hand on account of they can stop before 17+ in a hot deck while the dealer can't) and reduce the potential for dealer error/curtail any accusations that the dealer is cheating (but mostly it's a card counting countermeasure; people being aware of dynamically shifting odds in a casino game really pisses them off).
yokhai · 3 points · Posted at 05:42:25 on February 14, 2016 · (Permalink)
They don't reshuffle the deck in the middle of the game. They use high deck counts 8-12 decks shuffled together, then swap the shoe at 30% of the cards remaining.
If you see a casino reshuffling dealt cards back into the shoe, contact your local Games Board, they should be breaking most laws.
joshu · 9 points · Posted at 05:22:58 on February 14, 2016 · (Permalink)
Most "random numbers" in a computer are one of 232 specific numbers
You are talking about stdlib's rand(), which is not "most." Anyone who cares about randomness is using something else. Which is all the crypto on your system, which is almost certainly your majority consumer of randomness.
The standard implementation of a "random number" in a computer is one of 232 numbers, although the large majority of applications dependent on randomness use different standards that are more secure.
joshu · 5 points · Posted at 05:57:49 on February 14, 2016 · (Permalink)
not really. the shuffle problems were deeper than that: they used the current time as a seed (guessable and much, much smaller than 232) and didn't use yates-fisher shuffling.
When I programmed a Black Jack my programm selected a random card then a random slot in the deck and assigned the card to it. It repeated this with with all remaining cards and empty slots until every card was in the deck.
I think that randomization should have allowed for completely random decks. The key wasn't to create a random value high enough to create a deck seed but to eliminate any possibility for a pattern to form by handling every single associaton as random as it is possible within the game's rules.
t014y · 1 points · Posted at 06:00:01 on February 14, 2016 · (Permalink)
What is the weaker method for shuffling cards in a computer? The only way I can think to do an algorithm based shuffle in the computer is to go though each card and randomly place it into a position in the new deck. This method should allow for any possibly because on the last step there will only be 52 positions the card could go into, well within the range of a standard random method.
Ex. Fist card taken will go into the only position avaliable in the new deck. Second card goes on top or on bottom. 3rd goes 1 of 3. And so on until the last card has 1 of 52 spots to go into.
If this is the weaker shuffle can you explain why?
I do understand that random is not really random but it seems your claim is that the weaker shuffle would be unable to configure the deck into most of the configurations. I'm trying to figure out what shuffling method you would use to have this problem, short of a static list of preconfigured decks that are randomly chosen from.
The guy is confused and doesn't realize that the fisher-yates shuffle can give you all of those permutations despite using random numbers between 0 and max_int. One weaker shuffle would be to pick a random number between 1 and 52 for each of the 52 cards, instead of using fisher-yates.
t014y · 1 points · Posted at 07:31:09 on February 14, 2016 · (Permalink)
So going straight to 1 of 52 for fist card then 1 to 52 minus the last value and so on. That sounds harder to program but I still don't see why you wouldn't have the chance of getting every combination.
t014y · 1 points · Posted at 23:10:13 on February 14, 2016 · (Permalink)
That is what I was looking for. Maybe it's just me but, even without the flaws mentioned in the article, the idea of shuffling this way is not intuitive. In general when I program I try and simulate the real life method. But I see the concern now.
You only need a random number between 1 and 52, 52 times to do the fisher-yates shuffle. How do you think a poorly coded game would be coded so that all of those orders wouldn't be possible?
edit: Other than something like simply not shuffling the deck?
Can you explain why is it 232? I understand the digital signal is either 0 or 1 (binary) so thats 2 possibilities but what is 32? There ar 52 cards in a set a cards
Assume you can shuffle the deck of cards once per second. every Billion Years, take one step forward. Every time you complete a lap around the earth, take a drop of water out of the ocean. Every time you drain all the oceans, put a piece of paper on the ground. By the time the stack of paper reaches the sun, you'll have finished less than 1% of all possible shuffles.
Ltbsd · 1 points · Posted at 13:42:43 on February 14, 2016 · (Permalink)
I would just pick a random number between 1 and 52 for the top card, between 1 and 51 for the second card, etc.… then you don't need a special system for it.
Only if you used a single randomly generated number to determine the entire order of the pack. Instead, generate 51 random numbers and use each one to choose what the next card in the pack will be out of the unpicked cards.
(Yes, this assumes access to a source of sufficient randomness.)
Why not pick a random seed 32-bit int, shuffle the deck once. That's one of four billion options. Now pick a new random seed, shuffle again. Now it's ~1.6 x 1019. Keep doing this a few times and you're good. It would help tremendously if the order of the seeds made a difference i.e. if the first seed was 1 and the second seed was 4, you get a different deck than if the first seed was 4 and the second seed was 1. Isn't this basically what people do? We don't just shuffle a deck perfectly in one shuffle, we repeat our actions for a little while to get a good shuffle.
Unless of course the algorithms they use today achieve the same outcome, but are much more efficient.
Decades ago, I learned of a mathematical formula that you could use as a card trick: Take a deck, divide into three piles, face down. Turn over the top cards on the first and third decks; plug the card numbers into the formula and you get the middle card.
Something like that. It's been so long I forget the details, but as a kid I was blown away.
Well since non virtual decks are all arranged in a given fashion when you open the pack, some permutations are more likely.
dj0 · 9 points · Posted at 02:13:09 on February 14, 2016 · (Permalink)
I did the math on this one day and I got ridiculous numbers like if everyone that has ever lived made a deck every second for a billion years that would be like 0.00001% of all combinations
[deleted] · 24 points · Posted at 03:52:40 on February 14, 2016 · (Permalink)
52!/(number of people that ever lived)(number of seconds in a billion years)
8.07x1067/1.07x1011 x 3.15x1016 = 2.39x1040.
That's 27 orders of magnitude smaller than 52!. "0.00001%" is quite a bit off. Either remember to carry your 22 zeros next time or stop making shit up.
Stephen Fry described it as a thousand suns, each with a thousand planets, each with a billion people, shuffling a thousand decks a second since the big bang would just now have started to repeat.
[deleted] · 1 points · Posted at 16:11:19 on February 14, 2016 · (Permalink)
I'm pretty sure too that a solitaire hand can be played in a second. Every card is in order with aces on top and so forth. Kinds at the bottom.
thuktun · 17 points · Posted at 01:51:28 on February 14, 2016 · (Permalink)
I think you mean permutation. Combination is order-independent, IIRC.
Absolutely right, I even typed permutation before posting, but changed my mind because permutation is a pretty scary word to budding mathematicians who are interested in learning cool facts. I guess I should have had a little more faith! If people are interested, check out this simple page from one of the best sites for explaining mathematical concepts.
[deleted] · 1 points · Posted at 02:34:06 on February 14, 2016 · (Permalink)
This is one of those things that is mathematically true but not necessarily practically true.
For instance, a new deck has the cards arranged a certain way that is common to all new decks. So if you give it one standard shuffle, chances are you're not the first person to shuffle a new deck in precisely that way. So if n people have achieved that shuffle, then a subset of n will have also achieved the next shuffle, and so on.
If for instance you shuffle a new deck three standard times and then deal a game of Klondike solitaire, you may not have been the first person to do that. If you and your card-shuffling forbears play that game optimally, even if you don't win the game, you may retrieve the cards in the same fashion. If you do win the game -- and this goes for many solitaire games -- you'll have reorganized the cards into suits and your next few shuffles will also not be unique.
If you have a situation where a professional dealer is shuffling new decks on a regular basis, it is likely that he has created the same arrangements of cards over and over again. I don't know much about how casinos deal with new decks, I imagine there are machines that shuffle in ways that don't produce similar results.
108241 · 6 points · Posted at 03:34:25 on February 14, 2016 · (Permalink)
Odds are even higher of repeating if playing at certain casinos.
[deleted] · 11 points · Posted at 02:17:03 on February 14, 2016 · (Permalink)*
To put this into perspective: 52! (52 factorial - 52 * 51 * 50 * 49...*3 * 2 * 1) = 80658175170943878571660636856403766975289505440883277824000000000000 (8.06*1067)
Let's say that every country in the world sells 750 billion packs of cards every year - with 196 countries, that's 1.47*1014.
Let's say that they do this for 5,000 years, and that every single deck they produce gets shuffled 1,000,000 (1 million) times. That number is 7.35*1023.
If you divide 52! by 7.35*1023, you get 1.097*1044 . Meaning you would need every country in the world to produce 750 billion packs of cards every year for 5000 years and shuffle each deck 1 million times 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times to cover all the possibilities of orders of cards.
This is assuming that every shuffle gets you a completely new order, which probably wouldn't happen, so the number is even higher, but you can't really calculate that I don't think.
[deleted] · 1 points · Posted at 03:42:46 on February 14, 2016 · (Permalink)
If you divide 7.35*1023 by 52!, you get 1.097*1044
I don't see how you did this. Did you mean perhaps dividing the 52! By 7.35*1023?
[deleted] · 3 points · Posted at 04:43:42 on February 14, 2016 · (Permalink)
"Very real chance" is a misleading way of saying it. You're more likely to win a dozen lottery jackpots at the same time than to randomly produce a card order that has previously existed...
Xaxxon · 5 points · Posted at 02:53:51 on February 14, 2016 · (Permalink)
very real chance is an odd way to put it.
It's almost a certainty it's never happened before. It is massively improbable it's happened before.
[deleted] · 1 points · Posted at 23:40:41 on February 14, 2016 · (Permalink)
That's assuming everyone shuffles perfectly randomly and evenly.
Xaxxon · 1 points · Posted at 23:45:40 on February 14, 2016 · (Permalink)
That's really only a problem with a brand new deck..
But if you're not talking about random patterns, then the whole thing is uninteresting. If you pick the order of the cards, then there's really nothing mathematically to say about it.
I call bullshit on that. It depends on how many shuffles you make. It's certainly possible if you only shuffle 1 or 2 times. I think most people learn to cut the deck in a similar way and shuffle the 2 sides together, plus we've seen each other shuffle so we emulate how others do it. I'm not saying it's common or uncommon, but to say that no one has ever shuffled a deck in the exact same sequence as anyone else on the planet, as this is how I often hear it said, is b.s. I think 3-5 shuffles is probably sufficient to meet that criteria though.
I used to be a poker dealer and I've seen some weird shit.... really weird shit. Like the same two people getting KK and AA in a no limit game on back to back hands... and the kings beat the aces both times. I once asked for 222 on the first 3 cards and it came out. I once saw a hand where the only card that could help someone win was the 10 of spades, and another player announced he folded it already, the dealer thought the hand was over and had fouled the cards and had to reshuffle. The next card was the 10 of spades (only 47 to 1 chance, but misdeals in a spot like that are like 10,000 to 1 at least).
However I've yet to see or hear of anyone who has shuffled a deck of cards and had it come out perfectly in order the way it started (or even close).
But cards aren't truly randomly shuffled. And most decks of cards start from a sequence as new, or as the result of a game. So likely a huge portion of "shuffles" are pulling from a smaller subset of possible outcomes and the chances of a collision are exponentially higher.
Yes, there are certain patterns that can occur, but variables such as shuffle type and frequency mean that these patterns become much less predictable as the number of shuffles increases, not to mention changing order of cards in use (e.g. while playing a card game).
What's really interesting is your claim of "true" randomness. It's a very interesting topic.
As a very big TL;DR: A lot of things we consider random aren't random. For everything else, we aren't sure.
But while there ARE a huge number of potential decks combinations that isn't what is going on. That's the difference between probability on paper and in reality.
"true" I only meant as plain English speech to describe the situation. It's not a mathematical paper, it's a Reddit post ;)
Yeah I saw the video. But if you include digital decks of cards along with considering the matching birthday problem it seems like it isn't too outrageous for there to have been a match at some point.
[deleted] · 6 points · Posted at 02:34:26 on February 14, 2016 · (Permalink)*
I was talking about having every single combination of cards completed, I was talking about the probability of a shuffled deck matching any one combination cards previously made.
When you take the large amount of online poker tables and combine it with the matching birthday problem it seems to me that we're getting much closer to a reasonable result rather than the comparable improbability of being able to walk through a solid wall because all the atoms lined up.
dj0 · 3 points · Posted at 02:14:20 on February 14, 2016 · (Permalink)
[deleted] · 7 points · Posted at 22:54:02 on February 13, 2016 · (Permalink)
on my last calculator, the highest factorial product it would display, using scientific notation, was 69! that's 69! 70! and above it would just show an error.
[deleted] · 4 points · Posted at 03:52:53 on February 14, 2016 · (Permalink)
Most calculators have a max value of 10100 - 1
69! ≈ 1.711 * 1098
70! ≈ 1.199 * 10100
IAmScare · 13 points · Posted at 21:01:53 on February 13, 2016 · (Permalink)
Yeah. Also, if you're on a PC, below the video where it says "Share", you can check the box "Start at: ", write the timestamp and it'll give you your marked link.
But right click > "copy video URL at current time" works faster if you want the timestamp to be exactly where it's playing at the moment.
I had read "more possible arrangements of cards than there are atoms on Earth", but still, this is an example I find difficult to visualize.
The example above on the other hand made me think more than once that it couldn't be true.
ngwoo · 2 points · Posted at 00:38:28 on February 14, 2016 · (Permalink)
I find the most relatable way of explaining it is just that every time you shuffle a deck (perfectly), you're statistically seeing a configuration of cards that no human ever has seen or will see again.
That evokes thoughts of there being an absolutely huge number of configurations, and still hugely understates how many there are.
I usually hear it said as, every time you shuffle a deck of cards, the odds are overwhelming that the sequence you end up with has never occurred before.
jtp8736 · 2 points · Posted at 01:18:02 on February 14, 2016 · (Permalink)
But, how do you know it's exactly the same hand without recording it? And how can you achieve something like that, unless you first arrange all cards in the same exact order before shuffling?
I can't. But if we see familiar hands, we just say someone fucked up and shuffle again. Usually by this point we're quite sloshed and wearing only most of our clothes.
In this video posted by another redditor the guys says at the end:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
In this video posted by another redditor the guys says the same with a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
In this video posted by another redditor the guys says the same with a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
It's really haunting the end of that video. The chance of being born and experiencing conciousness is so astronomically rare, and here we are, using our time well.
In this video posted by another redditor the guys says the same with a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
How nuts is that? Think of all the times people have played cards. It's a very small chance any poker game has EVER been played with the same shuffle.
hil2run · 1 points · Posted at 02:14:50 on February 14, 2016 · (Permalink)
Most card games do not rely on the entire deck being drawn. Pragmatically the entire ordering of the deck is irrelevant. Even in long-hand hold'em with 8 players you'll only see 21 cards.
What you're missing here is that a shuffle of a deck of cards doesn't randomize the entire deck. Odds are, a lot of shuffles have been repeated, just a very small subset of them.
The point is not about cards, the point is about Factorial 52, whether you have cards or numbers. Cards are only mentioned because they are 52.
Also what does it mean that shuffles have been repeated? Because that doesn't change the fact that factorial 52 is still a gigantic number, and that was the point.
That I do not believe myself, though it has been said a lot.
Also when a deck is new, the cards are always in the same position, with ordered suits and colors. So since every deck that has been shuffled, has been actually shuffed at least once from the very same starting position, and many dealers may just shuffle decks for 3-4 seconds, we can safely say that some permutations most likely have been obtained more than once.
When people say any newly shuffled deck is probably new, do they take into account the birthday problem? I don't know how relevant that is but I'm curious.
Munninnu · 1 points · Posted at 04:36:44 on February 14, 2016 · (Permalink)*
What's the birthday problem?
EDIT: ah, okay. So maybe here there might be an answer.
Also, as I was saying earlier, when a deck is new, the cards are always in the same position, with ordered suits and colors. So since every deck that has been shuffled, has been actually shuffed at least once from the very same starting position, and many dealers may just shuffle decks for 3-4 seconds, we can safely say that some permutations most likely have appeared more than once.
The point was only that factorial 52 is so huge that precaution must be taken before thinking about it.
Tetration is the iteration that follows exponentiation.
n a = aaaa... with an n number of a's.
Also, it is referred to as "a to the superpower of n"
[deleted] · 391 points · Posted at 01:09:59 on February 14, 2016 · (Permalink)*
You can go on forever, these are hyperoperations (H_0 = increment by one, H_1 = addition, then multiplication, exponentiation...)
I quite like the number 65536. Many programmers will immediately see it as 216 (ie. the number of values of a 2-byte variable) but the cool thing is that since
65536 = 216
16=24
therefore
65536 = 2222 = 4 2
But since 4=2 2
65536 = 22 2
Therefore we now go up to pentation, which I don't have Reddit-notation for (Knuth's arrows would be used)
65536 = pent(2, 3)
Which I just find to be pretty cool
Edit: I've quickly implemented the definition on Wikipedia into a few languages, though only tested the Haskell version. Here. Will probably crash your stack with even small values though, and passing a negative n will cause infinite recursion Edit Edit: See here for a cleaner and quicker Haskell version
Edit 2: Currently have h 5 2 3 running, literally no idea how long it will take, about to try a poor first year CS attempt at determining its asymptotic complexity in terms of n, a, b
[deleted] · 5 points · Posted at 06:09:42 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 2 points · Posted at 12:33:32 on February 14, 2016 · (Permalink)
Good point, I was so set on copying the wikipedia definition exactly I forgot that pattern matching lent itself better here. Do you know why it is that pattern matching performs better? It certainly looks nicer but I thought it would have the same runtime
[deleted] · 3 points · Posted at 01:08:31 on February 15, 2016 · (Permalink)*
On another note, although this isn't as "pure", it's a good idea to explicitly define h for n<=3, since it's easy to do so and will cause fewer stack overflows:
h :: Int -> Integer -> Integer -> Integer
h 0 a b = b + 1 -- incrementation
h 1 a b = a + b -- addition
h 2 a b = a * b -- multiplication
h 3 a b = a ^ b -- exponentiation
h _ _ 0 = 1
h n a b = h (n-1) a (h n a (b-1))
EDIT: Changed the first parameter to Int (as if I could cope with n that big!)
alt 24 = ↑. So 3↑3 or 3↑↑↑↑3 is possible to write on reddit. The ASCII set involves a lot of quite useful characters, including →, –(compared to the shorter - –) or bullet points •►.
Quick formatting trick to share: if you want to have a superscript letter immediately followed by a non-superscript letter you can put brackets around the bit you want superscripted.
Didn't Graham's Number use arrow notation? Like OP's example, aaaa... with an n number of a's, would be a↑↑n.
And with this method, WE CAN GO DEEPER. a↑↑↑n = a↑↑a↑↑a↑↑a... with n a's. a↑↑↑↑n = a↑↑↑a↑↑↑a↑↑↑a... with n a's.
For Graham's number, you start with 3↑↑↑3 (already pretty huge), but that describes the number of arrows between two 3's. And THAT number describes the number of arrows between two 3's. Recurse 62 more times any you have Graham's Number.
Edit: More about Graham's Number.
[deleted] · 5 points · Posted at 02:07:33 on February 14, 2016 · (Permalink)*
[deleted] · 1 points · Posted at 11:43:16 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 1 points · Posted at 15:08:16 on February 14, 2016 · (Permalink)
The first identity you stated is incorrect so the second identity doesn't apply. ba = aaa...} b times. Exponentiation is right-associative meaning the tower is evaluated from the top down. Strangely, this function is presently defined only for integer and infinite b. The problem is that there is no known functional square root f(f(x)) = ex otherwise it would be easy to exponent a number, say, two-and-a-half times.
cManks · 6 points · Posted at 01:26:36 on February 14, 2016 · (Permalink)
4 years of a math and computer science degree and I've never come across this before.
I remember discovering this on my own and thinking I had invented it for several years, because I didn't know what it was called so I couldn't google it.
Atario · 1 points · Posted at 11:01:50 on February 14, 2016 · (Permalink)
A guy I knew in college came up with it too, and he called it "macho" (with a corresponding "wimpo" function which was just incrementation).
beenoc · 1 points · Posted at 02:23:52 on February 14, 2016 · (Permalink)
I learned about this from a question that asked "What number can you write that is a bigger number than the amount of carbon atoms you just laid on the paper?" (was either reddit or What If XKCD.) The answer was 99, or 9999999999 . I'm pretty sure that's more than the amount of atoms in the known universe, considering every calculator I can find just returns "infinity" after 9999.
Isn't that similar to Knuth Notation, where "A ! B = AAAA..."? And "A !! B = A ! (A ! B)" which is how Graham's Number (largest number known to have any sort of use in mathematics, it's the answer to a geometry problem) is calculated?
It's basically analogous to a mobius strip. It's getting a tube to "twist" (or invert) before connecting. It only works in 4-D without crossing itself, but it's 3D shadow forms a bottle
It's a 2D manifold which can be embedded in a 4D Euclidean space (but not a 3D Euclidean space). Technically doesn't make it 4D, but nobody really cares anyway.
I care. This AskReddit is making me, as a mathematician, both happy at people learning fun facts, and angry at people who think they know things but are wrong.
A Klein bottle itself is 2d. But if you want to embed it without self-intersection, you need a 4d ambient space.
Of course, I think you were still answering correctly in the spirit of the post you were responding to, but I think it's a point worth making anyway.
[deleted] · -16 points · Posted at 00:45:16 on February 14, 2016 · (Permalink)*
[deleted]
NullRad · 13 points · Posted at 00:48:44 on February 14, 2016 · (Permalink)
But no volume. It is like the black hole of containers.
[deleted] · -15 points · Posted at 00:52:09 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 13 points · Posted at 01:48:05 on February 14, 2016 · (Permalink)
Thats not an actual klein bottle. A true, mathematically correct klein bottle doesnt actually pass through itself, and can't actually exist in our universe.
That's great and all, but this thread is about mathematics. Mathematically, a Klein bottle is a two-dimensional object, which can be embedded without self-intersection in a space of at least 4 dimensions. Even a square is 3d by your criterion because we can't make an infinitely thin square in real life, but that's missing the point spectacularly.
[deleted] · -19 points · Posted at 01:13:55 on February 14, 2016 · (Permalink)
No, you're ignoring what I'm saying and defining all terminology so that you are right.
In mathematics, the Klein bottle /ˈklaɪn/ is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
Literally the first sentence of the wikipedia article for "Klein bottle." You can complain about the definition of "dimension" all you want, but it turns out mathematicians don't care.
[deleted] · -17 points · Posted at 01:20:14 on February 14, 2016 · (Permalink)*
No. I'm not guessing at what the wikipedia article means. I know what two-dimensional manifold is. It's a second-countable, Hausdorff topological space such that every point has a neighborhood which is homeomorphic to an open set in R2 (equivalently, all of R2 or an open ball in R2 ). A Klein bottle satisfies this. Hence, it is two-dimensional. The image you linked is a projection of a Klein bottle embedded in three-dimensional space, but the definition of a Klein bottle does not require that it be embedded in any higher space 3d space. It is a space in its own right, which is two-dimensional because every sufficiently small piece looks like two-dimensional Euclidean space.
A Klein Bottle is this: [0,1]×[0,1]/((0,x)~(1,x) , (x,0)~(1-x,1)), and nothing else. It is a two-dimensional topological manifold, as is easily seen by explicitly presenting charts.
[deleted] · -16 points · Posted at 01:26:45 on February 14, 2016 · (Permalink)
Once again, failing to distinguish between "the mathematically defined entity known as a Klein bottle" and "a neat math-inspired desk ornament." No one is talking about making Klein bottles in real life here (well, except you). This is a thread about mathematics.
You continue to try to lay some kind of pithy smackdown while failing to make any substantive argument that might refute why, for instance, Wikipedia might refer to a Klein bottle as "a two-dimensional manifold."
A Klein bottle is a 2D surface embedded in 4-space. With self-intersection, you can depict any lower dimension object into a space as small as it's minimum dimension.
What's the difference? The simplest example is the Mobius Strip. This is a 2D object embedded in 3D. Why and how? Well it identifies edges by wrapping around. Imagine a square. The side edges are considered boundaries while the top and bottom edges are identified with reverse orientation. Therefore you can express the object in 2D without losing any information. However, to draw a real object with these properties, you need to draw in a 3D space.
Klein bottle is the same. It's a 2D object with more complicated identified edges. If you draw it in 2D, you have lots of identified edges. If you draw it in 2D you have fewer overlaps, but in the minimal case you still need that bottle neck overlap. In 4D you can draw it without overlap.
Doesn't change the fact that it is a 2D surface area type object.
[deleted] · 3 points · Posted at 23:35:17 on February 13, 2016 · (Permalink)
AFAIK, at some point the bottle has to go inside itself (because the inside is the same surface as the outside) but the only way you can do that in 3d space is to create an intersection or join. In 4d space, as difficult as it is to conceptualise, there is a way for the bottle to go inside of itself without creating a join
Like I said, it's hard to think about it because we live in a 3D space but the gist of it is that extra dimension allows the bottle to kind of circumvent itself, if that makes any sense. Maybe it's a bit easier to think about it in 2d-3d. If I have a circle on a sheet of paper and I put the tip of my pencil on the outside of the circle, there's no way for me to move the pencil inside the circle without going over it, which is against the rules. But, if I can use 3 dimensions, I can just lift the pencil off the paper and then put it on the inside of the circle. I have gone from the inside to the outside, without crossing over. It's the same concept with the Klein bottle, just this time using the 4th dimension
Think of in terms of things that are easier to conceptualize: Mobius Strip and 2D to 3D.
In 3D we can construct a Mobius Strip. But a Mobius strip is a 2D manifold, so we can write a 2D definition of a Mobius strip, we just have to identify the top and bottom boundaries of a square. Over the arrows we wrap around and our direction moves to the opposite. Every identification like this is an intersection with another dimension above 2D. Essentially wrapping over infinity, and when we do flipping over to swap direction, then connecting again; the wrapping over infinity is what requires us to move up a dimension to draw the object.
Exactly the same thing applies for a Klein Bottle (a 2D manifold embedded) in 4D space. In 4D we can draw it with no intersections, in lower dimensions we can draw it by wrapping stuff around and creating intersections (essentially points that are identified).
No!! A klein bottle is technically 3D, but it has to exist in a 4D space. Similar to how a mobius strip is 2D, but has to exist in a 3D space. (Paper may be 3D, but an actual mobius strip is theoretically 2D.)
[deleted] · -1 points · Posted at 02:37:02 on February 14, 2016 · (Permalink)
[deleted]
mirjak · 3 points · Posted at 03:44:18 on February 14, 2016 · (Permalink)
That's just a representation of one. A real Klein bottle wouldn't have the intersection.
Mobius is a 2d object with 2 surfaces, bent through the 3rd dimension, to create a 3d object with 1 surface.
Klein is a 3d object with an inside and an outside (2 surfaces), bent through the 4th dimension, to create a 4d object with 1 surface.
1 surface here means that you can take a pen and drag it around - without picking it up - to cover the whole object. Ad a contrast to this, on a regular piece of paper, you have to pick up the pen to start drawing on the backside.
Right - because it only has one side! You could also say it has no outside,which is pretty trippy because you're clearly looking at something. It's super cool stuff.
it was on the front page of /r/pics yesterday or today, I think.
Jdrawer · 1 points · Posted at 08:22:27 on February 14, 2016 · (Permalink)
The loopy cousin of the Klein stein, who has earned the title of "The best way to drink at work."
Seifty · 1 points · Posted at 09:54:37 on February 14, 2016 · (Permalink)
What is a Möbius Strip?
Rehovak · 1 points · Posted at 16:40:14 on February 14, 2016 · (Permalink)
It's a strip with only one side. Basically take a long piece of paper, twist it once, and tape it to it's other end. If you drag your finger along it, it'll eventually end up at the same place it started!
judgej2 · 1 points · Posted at 09:57:31 on February 14, 2016 · (Permalink)
A bottle with one surface - the inside is the outside. It is a real thing and can be constructed. Trying to buy one is a pain though, just not enough are made.
This except that the part where it crosses itself isn't actually an intersection. Imagine being a ghost and putting your arms through your belly and shaking your own hand (though that's not a Klein bottle thing, that's just because we can't have a real one in 3-D space).
A Klein bottle only has one "side": Imagine being an ant and crawling from any point on the "inside" to the "outside".
[deleted] · 1 points · Posted at 14:12:33 on February 14, 2016 · (Permalink)
A doughnut with a 4d twist.
Ralvald · 1 points · Posted at 14:40:12 on February 14, 2016 · (Permalink)
Slice a bagel down the middle with a half-twist that meets up where you started. Which side is the one side of the Möbius bagel, the flat side or the curvy side?
[deleted] · 2 points · Posted at 04:49:36 on February 14, 2016 · (Permalink)
The "moebius" bagel contains two rotations (one for each times it winds around with the moebius cut).
In addition to having one face, a mobius strip has only one edge. If you glue together a disk and a mobius band along their edge, you get a projective plane.
If you take scissors and cut a Möbius strip in half along its centerline, you end up with a loop with two twists -- no longer a Möbius strip. If you cut it one third of the way from the edge you end up with two connected loops -- one a Möbius strip and the other a longer loop with two twists.
That's not correct. If you extend the edges of a mobius strio so that they connect to each other it creates a Klein bottle.
Rehovak · 6 points · Posted at 23:06:48 on February 13, 2016 · (Permalink)
That's why I said topologically. Topologists don't care about the exact look of things, just their properties. You are right in that you would have to extend or stretch edges. There's a joke that topologists get their coffee cups and their donuts mixed up because topologically they are the same!
You weren't really clear. All you said was "glue two mobius strips together," and you didn't specify at all which parts of the two strips were to be glued together.
Rehovak · 1 points · Posted at 16:42:12 on February 14, 2016 · (Permalink)
Sorry! It's kind of hard to describe without pictures, but I'm terrible at drawing, it's why I chose Math! :P
If you cut a Möbius strip lengthwise, you get a longer Möbius strip that is twisted twice. If you then cut that Möbius strip lengthwise, you get two double-twisted Möbius strips interlinked. This is fun to do with paper an scissors.
[deleted] · 1 points · Posted at 03:33:38 on February 14, 2016 · (Permalink)
spazzes internally
_Psyki · 1 points · Posted at 05:19:07 on February 14, 2016 · (Permalink)
Also, if those Möbius Strips were not of the same chirality, when you cut down the centre line of each you will be left with two entwined hearts.
If you glue three Mobius Strips together, it creates a mess.
233C · 1 points · Posted at 09:27:30 on February 14, 2016 · (Permalink)
Anybody who has never done this, please try:
Make a comfortably wide Möbius strip.
Cut is along its middle line and see what you got (1 trip, 2 strips? are they Möbius strips or not?)
Than cut it again, along its middle line.
be amazed.
[deleted] · 1 points · Posted at 10:12:36 on February 14, 2016 · (Permalink)
Nice! I knew about both objects, but not about this fact. Pretty neat :)
EDIT: for those confused mobile users, the 2 at the end of each starting number is supposed to be an exponent. Sorry for the confusion - I'm not a witch!
The length of the first one is 4, the length of the second is 6.
This means that the highest number is 4 (the shorter of the two). The number is repeated 3 times because 6 - 4 + 1 = 3. (the length of the longest - the length of the shortest + 1)
Wow - what an interesting dose of perspective! The trick I cited above I learned back in maybe 4th or 5th grade just for shiggles. Obviously I've remembered it since then. But I never thought to keep pushing it until the rule breaks. I had always just assumed, but even today I got to learn even more about it. Thanks, and not in some sarcastic or ironic way - this was surprisingly enlightening.
Actually it doesn't break at all. What he's doing wrong is that he's doing it in base10. When you encounter a number greater than 9 it can't be represented by a single digit in base 10 so it fucks up everything.
You (and others) are correct about just moving to a higher base system to extend this pattern further. However, no matter what finite number you use as a base, there will be a point at which this pattern stops being obvious (i.e. "breaks", if you decompose the digits, you can probably see the pattern again but it's not immediately obvious as it is before that point).
If you can find a finite base where this works for an arbitrarily long string of 1s, I would be very interested in a proof.
I am not quite sure what the first part means, but proving your second part would be rather trivial. While I am not sure how to write proofs, but what you're simply doing is shifting 1111..s by 1 position and adding. This would always hold true for any base.
The first part is essentially that if you start in one base system (i.e. base 10), you can follow the pattern of a string of x 1s squared being equal to 123...x...321 until you get to x > your base (i.e. x = 11 in my previous example). However, if you increase the base (say from 10 to 16), the pattern will once again hold for some strings that broke it in the old base. My point was that no matter how large you make the base, as long as it's a finite number (i.e. as long as it makes sense), there will be a string of 1s long enough to break the pattern. For example:
111111111112 = 123456790120987654321 in base 10 (pattern broken) but 111111111112 = 123456789ABA987654321 in base 16 (pattern works for the same string of 1s). Then you can increase the string to 11111111111111111 to break the pattern in base 16.
The second part was asking for if there is a specific base system where the 11...12 = 123...321 pattern will hold no matter how long you make the string of 1s.
I can see why it holds true. That doesn't really cause it to lose its charm for me, it just changes it from "charming due to mystery" to "charming due to neat math stuff".
Actually it doesn't break at all. You're doing it in base10. When you encounter a number greater than 9 it can't be represented by a single digit in base 10 so it fucks up everything.
It works if you write it out! 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 4 3 2 1. It just happens that you carry the 10 to the next digit (the nine), which also carries to the eight making it a 9, so you end up with 1234567900987654321
It makes more sense to write it out before you figure it out, 12 ones would be: 1 2 3 4 5 6 7 8 9 10 11 12 11 10 9 8 7 6 5 4 3 2 1, then we just have to carry all the ones over to get 1234567901232098765432.
Domriso · 1 points · Posted at 17:16:25 on February 14, 2016 · (Permalink)
also very interesting to this is that these numbers from the generated sequence can be structured into Pascal's Triangle, which is then used to determine the coefficients of binomial expansions.
Thank you. I couldn't figure out what kind of crazy math was happening and I thought people were just messing with non-math people. On mobile it looks like 12=1, 112=121, etc. That makes way more sense.
Crazier if you ad the "1s" together on the left and square it, the result will be the sum of the numbers on the right:
112 = 121 same as (1+1)2 = 4 (1+2+1)
If you use lattice multiplication this makes a lot of sense. Since each box will only contain 1 the highest digit in the product will be number of boxes in the longest diagonal.
Oh, gotcha. What your phone isn't showing you is that the 2 at the end of each first number is supposed to be an exponent. So the numbers should read 11-squared, 111-squared and so on. Apologies to the mobile redditors.
For base n, it breaks down for n digits or more, i.e. 11 x 11 != 121 in base-2 because there is no 2 in base-2 notation. Similarly, won't work in base 10 for 1111111111 x 1111111111.
Sorry, I thought my previous answer was enough - it's just the way the math works out every time. Just like 2+2=4, 11x11=121, and 111x111=12321... it just is. But if you want a better visualization of how those numbers stack up, /u/t17dr shows it off really well in this comment below.
Pi4zza · 1 points · Posted at 01:05:37 on February 15, 2016 · (Permalink)
He edited his comment saying that the 2 at the end of each number is an exponent. I didn't see that because im on mobile, i actually inderstand this. My bad man.
[deleted] · 1799 points · Posted at 19:15:55 on February 13, 2016 · (Permalink)
The smallest uninteresting number is 14972. It's uninteresting because it currently appears in no number sequences (minus the sequence of natural numbers, of course).
The number gets bigger as people figure out new sequences with that number.
[deleted] · 1 points · Posted at 03:51:27 on February 14, 2016 · (Permalink)
Not really. You just define an uninteresting number as a number that appears in just two sequences:
The sequence of natural numbers and the sequence of uninteresting numbers.
Although I'm not sure what set of sequences /u/HowdyDoodlyDoo is talking about, as 14972 also appears in the sequence of even numbers, which is a pretty obvious sequence to have in any collection of sequences.
[deleted] · 1 points · Posted at 04:52:57 on February 14, 2016 · (Permalink)
That's not merely a paradox, that's a contradiction. Clearly we have not defined interesting consistently
sim642 · 1 points · Posted at 09:30:11 on February 14, 2016 · (Permalink)
Clearly the number being interesting leads to a contradiction but so does it being uninteresting because that leads to the same contradiction as the interesting case. Both cases are contradictory, thus a paradox.
"What if I add the sequence of (natural) numbers that aren't in any other sequence?"
zarraha · 8 points · Posted at 23:41:34 on February 13, 2016 · (Permalink)
It's not. Being the first uninteresting number isn't very interesting. It's half interesting (and thus only half qualifies as uninteresting). Paradox solved.
[deleted] · 3 points · Posted at 02:22:51 on February 14, 2016 · (Permalink)
It's not really a paradox either way. It's a joke proof that there are no uninteresting numbers, because if there are then there has to be a lowest uninteresting number, which immediately makes it interesting. And so on.
If I is the set of all numbers that belong to known sequences (except natural numbers), let U be a sequence of all elements of the negation of I. Now, all numbers are interesting.
I argue that any interest it should recieve for being the first uninteresting number really belongs to the last interesting number, and thus the first uninteresting number remains uninteresting.
That's a cop-out. You can say that any number divisible by X is in the set of Xn and therefore is "interesting". The only exceptions are primes, but they're interesting already.
This entire idea is probably the most ill-defined thing I've seen in a while. Are you being serious? This is totally ridiculous on several accounts. First, there's no way to define when a sequence is interesting. Second, the even numbers are certainly interesting (for instance, they are the "largest" proper subgroup of Z). Third, the idea that some constant (the "smallest uninteresting number") should be defined in terms of human mathematical knowledge is totally antithetical to the central goals and philosophy of mathematics. As discussed above, it even leads directly to a paradox, in that "the least uninteresting number" is certainly an interesting property to have.
I think you are taking the word "interesting" a bit too literally here. It's not uncommon for professions to take common words and derive a more specific meaning for their field. In this case, "interesting" just means it's apart of a sequence used in non-elementary mathematics. Useful is another way to look at it. There's no paradox if you understand that much. Getting picky because "interesting" means something else in other contexts isn't useful. Our legal system would fall apart if that were the case :)
db0255 · 1 points · Posted at 05:07:14 on February 15, 2016 · (Permalink)
Yeah, the term "interesting" would definitely be void-for-vagueness if it were part of mathematical US case law.
-Samba- · 2 points · Posted at 14:53:48 on February 14, 2016 · (Permalink)
Another example is the difference between a proof in science and a proof in mathematics. In science a proof is just overwhelming evidence to support the theory, while a mathematical proof is a logical certainty.
db0255 · 3 points · Posted at 05:05:26 on February 15, 2016 · (Permalink)
This is how I imagine the conversation at an average lunch goes for grad students in a college math department.
Sequences that include all real numbers, all numbers greater than a certain number, all numbers that don't fall into a certain sequence, etc. don't count.
So regarding 9 the answer is 2. The right side symbolizes negative while its left side is positive. However 9 cannot attain 2 without -7.
14972
Which draws the question, does 1+1=2? If so then 14972 can really be seen as (597)2.
9-7 = 2.
5+9-7 = 2.
But this is pointless because this number is special.
1+4+9-7=2
9-7 = 2.
With this number, we can break the rule of equality, in that by removing the positive side of 9, we keep equilibrium.
But we all know, this isn't the same. What happened to 1 and 4?
9 decided to drop 7, but became worried. How will he achieve 2? He called up his friends still on his speed dial, 1 and 4.
After a while, 9, 4, and 1 went out together. The resulting night, 9 was reminded of 7, as the resulting night equated to 14. 4 and 1 tried putting their heads together, but it wasn't the same. 14/5 was missing 2. But 9 met a number that was out of this world that night, she was more than just a number. She opened his world past just whole numbers, and suddenly, 2 didn't seem all that anymore. And on that day, 9 said fuck valentines day and went home.
Sequence of numbers, not sequence of digits. "56345" isn't a sequence of numbers; it's just one number, equal to 5 × 59 × 191.
It's also apparently not a very interesting number, as it only pops up in a couple of obscure sequences involving Molien series, whatever the hell those are. (Beyond a reminder that I really should read generatingfunctionology sometime, I mean.)
BiggerJ · 2 points · Posted at 07:19:32 on February 14, 2016 · (Permalink)
He was referring to the Online Encyclopedia of Integer Sequences, presumably because, like Wikipedia, archive.org's software collection and so forth, it will destroy your free time.
rcheu · 1 points · Posted at 03:14:12 on February 14, 2016 · (Permalink)
For those wondering what this actually means, 14972 is, as of time of writing, the smallest number to not appear in any sequence in the Online Encyclopedia of Integer Sequences, which is a real thing that exists for some reason.
Note that the OEIS only lists so many values in each sequence, so it does appear in some sequences, just at points not listed in the OEIS.
Interestingly enough, the last time I had check, that number was 12407. So I had to check now and the learnt that the number changes; and as for now it is indeed 14972.
Suppose for contradiction there is an uninteresting natural number.. Then there must be a first one. By nature of being the first of this type, that number is interesting. Contradiction, as was to be shown.
squrr1 · 1 points · Posted at 07:16:30 on February 14, 2016 · (Permalink)
Doesn't that make it the first member of the sequence of uninteresting numbers?
sherlip · 1 points · Posted at 07:21:13 on February 14, 2016 · (Permalink)
jmt222 · 335 points · Posted at 21:03:59 on February 13, 2016 · (Permalink)
Rational numbers are countable which essentially means we can associate to each one a natural number n where no two rationals are associated with the same natural number.
Let ε be a positive number that is as small as you would like. For the rational number r associated with 1, we "cover" r with the interval (r-ε/4,r+ε/4) which has length ε/2. For the rational number s associated with 2, we again cover it, but with an interval half as small, i.e. the interval (s-ε/8,s+ε/8) which has length ε/4. Continue in this way to cover all rational numbers. The total length of all the intervals in this cover is:
ε/2+ε/4+ε/8+ε/16+... = ε
So we can cover all rational numbers with a set that is as "small" as we would like. What I have described minus some very technical details is that the set of all rational numbers has measure 0, meaning they account for a "small" small subset of all real numbers. For rationals to be a "small" subset of real numbers, irrationals have to be a "large" subset of real numbers which is to say in the measure sense, almost all real numbers are irrational.
The Simplify function absolutely amazes me. That it decides reasonably what is most easily interpreted by a human is astonishing. Like all the other stuff I can guess at some algorithm to implement, but that one is just so open ended.
Am currently in a numerical methods class that uses Matlab. Screw Matlab. There are five distinct ways to pass functions to functions in that accursed language.
eskuvai · 3 points · Posted at 04:49:06 on February 14, 2016 · (Permalink)
accurate af
[deleted] · 2 points · Posted at 03:31:15 on February 14, 2016 · (Permalink)
Did we really see it much in complex? We're certainly using it for Real, but my hilarious memories of complex were not knowing a question on the test, so I just wrote "pi/2".
Got it back: "You're right, but you have no work, so no marks."
I often tell my friends, "When starting off a proof, just let epsilon be greater than zero. I don't care what you're trying to prove, you can't go wrong by doing this."
Can you ELI engineering student with some undergrad math?
[deleted] · 1 points · Posted at 20:16:50 on February 14, 2016 · (Permalink)
Suppose you have a particle confined to a line. The particle gets hit randomly by other particles around it, causing it to move back and forth( Brownian motion). If you look at the trajectory of the particle, with time in the x axis and position in y, you will get some continuous function ( motion is continuous). Now we could ask the question: what is the probability that the particle's trajectory is one of a given collection of continuous functions?
To assign such probabilities in general is a pretty hard problem.
What can be proved is that with probability 1, the trajectory of the particle will be a function which is not differentiable anywhere. This is the 'measure theory' part.
Look at the set of all continuous functions on the interval [0,1]. If you have a continuous function on this interval, |f(x)| has a maximum, from basic calculus. If you have two functions f and g, you can talk of how "close" they are: the distance between f and g is the maximum of |f(X)-g(X)|. Now that you have a notion of distance, you can talk of limits of functions, etc. The collection of nowhere differentiable functions is large in the following sense: given any continuous function and a error bound, you can approximate it by a n.d function. Also, all functions close enough to a nowhere differentiable function are nowhere differentiable. This means that functions which are differentiable at atleast one point are sparse, just like the set of integers is sparse in the real line.
A more intuitive explanation (for non-math people) would be that there is a method for creating a list that contains all the rational numbers. No such method exists for the irrational numbers. Any attempt to do so will result in a list that excludes nearly all irrational numbers.
Any countable set of numbers yes. But if you have an uncountable set this won't work. For example there is no way to cover the interval (0,1) by countably many subintervals so that the sum of their lengths is less than one.
This is really how we define "length" for sets that are messier than intervals.
[deleted] · 1 points · Posted at 13:37:14 on February 14, 2016 · (Permalink)
These words seem to make sense but I can't seem to pray what any of these sentences mean. Sorry.
I remember the days I used to think I was pretty smart.
When you 'cover' an interval, there are many rational numbers that fall within it. So if you cover the interval around r = 1 (so 3/4 to 1 1/4 in your example), there are many rational numbers that fall within that range.
So for each epsilon term in the summation, you associate a large number of rationals.
jmt222 · 1 points · Posted at 14:31:56 on February 14, 2016 · (Permalink)
You are correct and we could actually change the process to skip those rationals already covered unintentionally in a previous step, but this does not actually gain you anything meaningful towards the result and so no effort is made to do this in proofs usually. The process still contains all rationals with an arbitrarily small cover so it follows that rationals have measure 0.
Umm. No. The rationals are uncountably infinite. I didn't read the rest of your post so the rest may be correct. But rationals are definitely uncountably infinite. Because there's ALWAYS one more between the two you just counted.
jmt222 · 2 points · Posted at 23:30:51 on February 18, 2016 · (Permalink)
You are in error. A proof can be found in any basic analysis text or more easily found with an internet search.
Maybe you and I have different definitions of countable. Countable is the whole numbers. You can go from one to the next, an infinite number of times.
Uncountable is rationals, or irrationals. You can pick any two, and never count from one to the next. Yes I have seen the diagonal proof. But no, that is a different kind of countable. In the same way a space filling curve is "two dimensional" technically. But it's really not a 2d object.
More than that! Most numbers aren't even computable!
A computable number is a number that can be generated by a finite program - to be precise, if you give it enough time, it'll calculate the number to however much accuracy you want. For example, 3 is computable, the program that prints 3.00000... (while(1) print 0) satisfies the requirements.
Even pi is computable, it can be shown that pi/4=1-1/3+1/5-1/7... so the program that calculates 1/(2n+1) and adds or subtracts it from our result and keeps updating the result computes pi to arbitary accuracy.
However, almost all numbers aren't computable (the amount of computable numbers is countable), the absurd thing is we never meet a noncomputable number, since we meet numbers in everyday life through equations, integrals, and the like, and all of those are computable.
Asdanf · 96 points · Posted at 01:29:31 on February 14, 2016 · (Permalink)
We do occasionally encounter noncomputable numbers, such as Chaitin's Constant. But it is true that we only ever "meet" describable numbers, and there are only countably many of those.
This can be seen from the fact that descriptions are countable. For instance, you can write each description in English, and then sort them by length and alphabetically. The real numbers aren't countable, so most real numbers cannot be described by a finite amount of English text.
It's impossible to provide even a single example of an indescribable number, and yet they constitute almost all real numbers.
Help me out, I have some basic theory of comp sci experience but reading that was a huge mindfuck
So basically you make a bunch of random programs by spitting out random 1's and 0's, run that program, and the Chaitin constant is the chance that the program will halt, lets say under a Turing machine? And the chaitin constant is not computable?
NotInVan · 11 points · Posted at 06:00:30 on February 14, 2016 · (Permalink)
Pretty much.
And it's not computable because if one could compute it one could solve the Halting problem.
[deleted] · 2 points · Posted at 10:08:35 on February 14, 2016 · (Permalink)
that's probably not a good definition, since you can "describe" any integer number in one word simply by writing it down, for example :)
Bobius · 1 points · Posted at 18:03:50 on February 14, 2016 · (Permalink)
Not a word. What if I change the question to "The smallest describable number with a description of at least fifteen words in English"?
I mean 1,000 has plenty of descriptions, all at least 2 words - ten cubed, one thousand, a thousand etc.
Given there's a finite number of English words there's a finite number of 15 word sentences. Only some will make sense, so there's certainly only a finite number of such sentences!
that works (if your set of acceptable definitions is finite therefore you know that the set of positive integers definable in under sixty characters is non-empty)
Asdanf · 1 points · Posted at 07:06:17 on February 15, 2016 · (Permalink)
It's good to see other folks are interested in the Berry Paradox.
nyando · 2 points · Posted at 08:42:03 on February 14, 2016 · (Permalink)
Maaan I found out like a month ago that most numbers are transcendental, and I thought that was the end of it. Now this crops up. It's not in my degree, but shit like this is why I want to take more math classes.
Atario · 1 points · Posted at 11:09:59 on February 14, 2016 · (Permalink)
But English lets you cheat your way around this limitation. "A random indescribable number". There, I just described one.
No you didn't. There is a precise definition of "describing a number" in this context, and it means to be able to find approximations of the number with arbitrarely high precision.
[deleted] · 2 points · Posted at 14:36:46 on February 14, 2016 · (Permalink)
No you didn't. If you managed to describe it then it's not indescribable and therefore doesn't fit your description of it.
Karoal · 6 points · Posted at 00:01:31 on February 14, 2016 · (Permalink)
There is a very interesting book that goes over Alan Turing's paper which includes this topic, it's called The Annotated Turing by Charles Petzold if I remember correctly.
One of the ways which is cool to think about this is that every single real number can be represented by an (infinite!) sequence of numbers, with a decimal point somewhere.
For now let's only think about what happens for each number after the decimal point. You could map the position of the first digit after the decimal point to the number 1, the second position to 2 etc. For each position you have, there are 10 possible choices of digits. So the number of possible combinations of digits is multiplied by 10. Since this sequence of numbers is infinite, it is unreasonable that you could expect 'most' real numbers to be able to be computed by a machine!
This is obvious if you consider the fact that the real numbers are uncountably infinite, but programs are countably infinite (they are just made up of symbols one after another, after all).
Isn't this likely to be a gap in our mathematical understanding? If they "exist" ( assuming you have to take the philosophical approach that math and numbers aren't abstractions but rather an actual expression of nature), and we can't get to them, this seems like we're up against a fundamental wall in knowledge or our computational methods are incomplete. Does the general math community favor the former or the latter?
So wouldn't that be a form of computation? What I was trying to say before is that if you say most numbers aren't computable, that seems like a large gap in computation. If they're just not computable without using special tools that's not quite the same as what you initially said. Perhaps I'm misunderstanding though?
I don't exactly see what is the issue with uncomputable numbers, you can still think of them as an infinite decimal, just one that has no freaking pattern (by pattern I don't mean something repeating, I mean something even stronger, no finite program can come up with the next term).
So if there's no pattern whatsoever, that doesn't strike you as strange? Generally speaking if we can't predict something, that means our knowledge is incomplete not that it's inherently unpredictable. However there seems to be a swing lately for many communities, mostly in physics and computer science (because of things like the Halting problem and quantum mechanics), to take findings and proofs as hard evidence that nature is inherently unpredictable.
The philosophical implication of the universe taking on properties that are inherently unable to be computed is that there are knowledge limits built into the universe, there are things that we could never know. I personally find this a bit unlikely for various reasons (such as why the hell would there be?), thus the other conclusion is that our ability to compute, and thus make predictions about the next in the sequence, isn't sufficient.
Anyway, the original question was just a wayward fishing line hoping to ensnare a mathematician (or I suppose just math enthusiast) to enlighten me to potential reasons why my intuition may be mistaken.
Not all Dedekind cuts can be generated by a finite program simply because there are only a countable amount of finite program.
Math has not issue with things being called uncomputable, if you removed the requirement that the program be finite then we could generate every number.
I'm not much into philosophy, sorry, but I don't see any problem with the existence of those numbers (of course I'm not talking about physics, in math we just invent stuff and look at their properties).
Got ya, I suppose the answer may be that most Mathematicians share your sentiment. It's a bit like asking construction workers how a screw is made. They don't care, nor does it pose any problem to them if I told them it was made of some random concoction of metals that couldn't be known. They just need the screw to build a wall.
But, as for why it's a problem, it's a problem because Math is a tool that we expect to predict and represent the universe. If we find we can't do something, we should determine if we just don't have the right tool or if the universe doesn't allow us to do it. Not just for the philosophical implications, but so people actually pursue seeing if they can build a new and better tool that does what we couldn't before. Unknowable vs not known is an important distinction for pragmatic reasons as well.
computable numbers have no bearing on physics if that's what you mean, there is never a need in physics for an exact number, just a close approximation (and for examples the rationals are well defined and dense).
That is the most interesting thing I've heard in a long time. I've always had a thought with calculus and using infinities everywhere in physics that it could be done better. Is there such a thing as a computable calculus? One that uses only computable numbers?
I'm afraid I don't know much about computable numbers except for the fact that they are countable. I do know one really cool fact though:
Although they are countable, they aren't effectively countable, that means that there isn't a finite program that generates a list of all computable numbers to arbitary accuracy (meaning: let f be a bijection from N to the countable numbers, then there isn't a finite program so that given M, and epsilon calculates f(1),f(2)..f(m) to accuracy of e after enough time. This can be proved by a neat cantor diagonal argument.
When you get down to the atomic level atomic vibration, diffusion, sublimation, the uncertainty principle and all kinds of other things come into play, so you can't really have a 100% precise and accurate description of the length. It wouldn't be a non-computable number so much as a probabilistic length distribution though.
The uncertainty principle does not generally apply to things as large as atoms locked in matrices. And everything else only matters if you care about the length over time. You could definitely get a perfect snapshot of the fence length if you had a large enough electron microscope.
The uncertainty principle does not generally apply to things as large as atoms locked in matrices.
It may not have a large effect on say a hydrogen atom, but it does have enough of an effect that you couldn't define the length of the fence to arbitrary precision, which is necessary for your argument.
rmxz · -2 points · Posted at 03:45:24 on February 14, 2016 · (Permalink)
Not really.
Remember there are all sorts of continuous phenomena too -- like the universe itself expanding, or gravity waves from distant black holes stretching and smushing the earth -- that will be changing the length of the fence so most of the time it'll be a non-computable length.
Even weirder, almost all real numbers are undescribable. We have literally no way to pin down most real numbers (for a definition of "pin down" fairly close to the intuitive one)
Oussl · 1 points · Posted at 04:29:17 on February 14, 2016 · (Permalink)
In a fundamental sense, can a number that is undescribable truly be said to exist? Its existence is not a meaningful concept as an individual entity
Nothing in mathematics exists. We made it all up. Mathematics is the study of abstract sets of rules and their logical consequences.
[deleted] · 3 points · Posted at 01:22:48 on February 14, 2016 · (Permalink)
More than that, in fact. Almost all are transcendental - you can't get them as roots of aimed polynomial with integer coefficient. ( the square root of 2 is irrational, but not transcendental).
Despite this, there are very few numbers that we know are transcendental. Pi and e are two of them.
Godd2 · 2 points · Posted at 02:59:15 on February 14, 2016 · (Permalink)
If you want something even better: almost all real numbers are not definable...
This is actually the starting point of the best intuitive explanation I heard as to why the continuum hypothesis is independent of ZF.
[deleted] · 2 points · Posted at 02:53:17 on February 14, 2016 · (Permalink)
It follows that if you randomly choose any real number, the probability of it being 2 (e.g.) is equal to zero.
Atmosck · 2 points · Posted at 05:23:28 on February 14, 2016 · (Permalink)
Well, yeah. The rational numbers are countable, and the definition of "almost all" is everything except a measure zero set, and countable sets have measure zero.
I find it amusing that we can say things like "almost" and "most" to describe infinite sets of numbers. Gets into the cardinality of infinity which is super fascinating.
[deleted] · 1 points · Posted at 11:25:56 on February 14, 2016 · (Permalink)
Even much worse: Almost all real numbers cannot be computed by any kind of finite algorithm.
Vryl · 1 points · Posted at 15:04:07 on February 14, 2016 · (Permalink)
I like the fact that most numbers are uncomputable - that there are vastly more uncomputable numbers than computable ones.
When I was a kid, when we said, Hmmm..., which in our language means both the normal Hmmm... and one, everyone said two. We would get up to some high number, and then just throw infinities like : Infinite times two, Superinfinity, Super Infinityjin, etc...
osadon · 1 points · Posted at 01:49:26 on March 14, 2016 · (Permalink)
The most interesting part is between every 2 rational numbers theres an irational number and between every 2 irational numbers theres a rational number, also theres more irational numbers than rational numbers.
I'm sure they have infinite house keepers, so each one only has to clean a hundred rooms. Or a billion. Or one. Whatever.
BlLE · 1 points · Posted at 12:22:12 on February 14, 2016 · (Permalink)
Actually, each of the infinite housekeepers would have an infinite rooms to clean. Infinite is counterintuitive and this is why I avoided math and went straight to evolution & ecology.
Eh. It didn't explain Gabriel's Horn at all. I saw it mentioned elsewhere and was hoping this video would actually give some kind of explanation, but it just said the surface is infinite, but the space it encloses is finite. Thus far, I'm not a fan.
imagine talking a horn and extending the mouthpiece infinitely. past a certain point the volume you add becomes negligible (because by the end the sides of the horn are technically still apart, but infinitesimally close together), but you keep adding surface area because you keep adding "outside" of the horn.
repeat ad infinitum (literally), and you have a finite volume and an infinite surface area!
See, but that doesn't make sense to me, because even if the volume you add to the interior is negligible, it's still there. Even if it adds .000000000001cm3 to the volume, and 999,999,999m2 to the area, it's still adding both infinitely, so they would both be infinite.
EDIT: I know that's not right, but I don't understand the actual mathematical logic behind it, and that's what I got from your explanation.
If you were consistently adding .000000000001cm3 to the sum, then it would approach infinity. However, we are adding smaller numbers each time. The sum of these values can be bounded above and below, hence it is finite.
Consider a sum where it begins with 1. I always half the previous term, and add that to the sum.
1 + 1/2 + 1/4 + ..
Its clear that this sum is larger than 1, and must be less than 2 (any partial sum will never be larger than 2). We then can conclude that the sum is finite.
h4n4_LOL · 0 points · Posted at 03:23:08 on February 14, 2016 · (Permalink)*
the video fails to explain why you would even need the step n to 2n at all (and in all laer stages of the example). Becaus if there is a an infinite number of guests moving in you still can do n to n+1 and just reapeat the step infinite times. so m(n to n+1) (or n(n tp n+1) im not sure how to note that stuff). SO it fails to even explain in the sligthest that infinite =! infinte+1 and why. If you can write it like that sure it seem ok in and mathematical way but as soon as you remeber that n=infinte it doesnt make sence at all QQ (btw i get the fact that the video was probably not meant to explain what i said but i buffels my that no matter what simple source oyu wanna find to the topic of infinity most of them dont even can or try to explain the basic concept and just take it as giventhat you can use simple math on it. This buggs me in so many other fields of since too. Like Entropy in physics for example)
MrXian · 1 points · Posted at 17:15:39 on February 14, 2016 · (Permalink)
I kinda dislike the idea of a simple explanation for something as complex as infinity.
Think of whole numbers. Every single one. 1, 2, 3, 4, 5, 6, 7... on and on and on. It doesn't stop. There are an infinite number of whole numbers. Now think of the number of not-whole numbers between 1 and 2. 1.1, 1.01, 1.02, 1.002, 1.0035... It keeps going on and on into infinity. So the number of whole numbers and the number of numbers are both infinite, but the number of numbers without the whole requirement is a larger infinity. Denser infinity, if you will.
So there are actually two types of not-whole numbers. One type is rational numbers (they can be written as a fraction of whole numbers, like 1/4, or 3/7), and it actually includes all of the whole numbers, too (2 = 2/1 = 4/2). The other is irrational numbers. These numbers can't be written as a fraction, like the square root of 2, or pi. They have an infinite number of digits after the decimal point, and those digits never repeat.
So let's start with the rational numbers. The way you can tell if infinities are the same size is by seeing if you can matching up each number from one set with a number from the other set. If none are left over, those sets are the same time.
You can write all of the fractions like this:
0
1
2
3
4
5
6
1
1/1 =1
2/1 = 2
3/1 = 3
4/1 = 4
5/1 =5
6/1 = 6
2
1/2 = .5
2/2 =1
3/2 = 1.5
4/2 = 2
5/2 = 2.5
6/2 = 3
3
1/3 = 0.333...
2/3 = 0.666...
3/3 = 1
4/3 - 1.333...
5/3 = 1.666...
6/2 = 3
If you start from the top left, you can zig zag along the diagonals and number them, skipping over the duplicates (which I've crossed out). So, in this case, we'd say that:
1 matches with 1
2 matches with 2
0.5 matches with 3
0.333 matches with 4
Skip 1.
3 matches with 5.
4 matches with 6.
1.5 matches with 7.
0.666 matches with 8.
and so on.
You'll hit every fraction eventually, so there are the same number of rational numbers as there are whole numbers.
Then there's the irrational numbers. Let's only look at the irrational numbers between 0 and 1. This one you have to prove the size of differently.
Let's assume that you have a list (which you can number) of all of the irrational numbers like:
1) 0.1238975209825983240982452...
2) 0.123579872456982734....
3 0.90752348974260825...
4) 0.32579829587234...
5) 0.23579872340981234...
If we have a list of all irrational numbers, then it's not possible to make a new irrational number. Therefore, if we make a new irrational number, there are more irrational numbers between 0 and 1 than there are whole numbers.
So let's just try to generate a new number and see if it's possible. We'll start with the first digit after the decimal, and keep an eye on the bolded digits in my list.
If we make sure that the first digit isn't 1, then it's not the same as the first number. So we'll start our number off as 0.2...........
Then the second digit. If we make sure that the second digit isn't 2, then it's not the same as the first number. So we'll continue the number to be 0.24..........
Then the third digit. If we make sure that the third digit isn't 7, then it's not the same as the third number, so now let's make our number 0.243........
If we make sure that the fourth digit isn't 7, then we know the new number isn't the same as the fourth number. So our number is now 0.2439........
And if the fifth digit isn't 9, then the new number isn't the same as the 5th number on our list. So we'll say our new number is 0.2438.....
If you continue with that pattern, then you know that your new irrational number isn't any of the numbers we listed yet, but we don't have any more whole numbers to number this irrational number with! Therefore, there are more irrational numbers between 0 and 1 than there are whole numbers!
[deleted] · 2 points · Posted at 15:06:37 on February 14, 2016 · (Permalink)
Hahaha, no, I just forgot to change to the right account.
trevour · 1 points · Posted at 22:30:12 on February 15, 2016 · (Permalink)
This is a much more correct explanation than the guy you're replying to. It's all about whether the sets are listable or not, not about "density" or whatever that guy is talking about.
I mean, the denser infinity does make sense, mine's just more technically correct, and gets around the annoying gut feeling of "it's not possible for there to be more numbers between 0 and 1 than between 0 and infinity."
Eh, that's not really true. There are as many whole numbers as there are fractions.
But the set of irrational numbers is larger than the set of whole numbers/fractions (uncountable vs. countable).
But where it gets interesting is, that in any arbitrarily small neighbourhood of an irrational number you'll find (countably) infinite many rational numbers!
After doing this for all natural numbers, every single positive integer has been paired with a unique decimal number. Every single one.
Now, define a decimal number that is unique from all others in this set in at least one spot. This is done by taking the tenth column on the first decimal number, and incrementing it. Do the same for the hundredth column on the second number. And the thousandth column for the third, and so on. Take those new decimal places and put them into a brand new number. Here's what it looks like:
You now have a number that is unique from all others in the sequence, and it still counts as a real number between 0 and 1, but it has nowhere to go on the set. Every natural number is already paired up.
This proves that there are more numbers between 0 and 1 than there are natural numbers, because you can always find a new decimal number in a set like the one just described.
rawling · 1 points · Posted at 13:07:28 on February 14, 2016 · (Permalink)
thatJainaGirl's comment is deficient in that
it just lists rational numbers between 1 and 2
it claims that because there are infinitely many of these, there are more of them than there are whole numbers
Between the two of them, this doesn't prove that there are "more" reals than integers.
You're not contradicting an7agonist, you're just providing a proper proof to thatJainaGirl's point.
taedrin · 8 points · Posted at 02:55:15 on February 14, 2016 · (Permalink)
in any arbitrarily small neighbourhood of an irrational number you'll find (countably) infinite many rational numbers!
Or put in simpler terms, between any two different irrational numbers, you can always find a rational number, no matter how close they are to each other.
You are wrong to assume you are wrong. For any number in the reals and any open interval around said number, there exists a countably infinite number of rational numbers in said region.
Proof sketch: We know if the rationals are countable, thus we get countably. Also rationals are dense in reals. If we take any region around a point, we can find at least one real. We use that fact and induction to get infinite rationals.
there are also a countably infinite number of algebraic numbers (sqrt(2)for instance, any number that is a root of a polynomial with rational coefficients) which are the majority of the irrational numbers you would think about.
klod42 · 3 points · Posted at 11:38:41 on February 14, 2016 · (Permalink)
Hey, that's cool, I never really thought of that. Transcendentals are the ones ruining the party.
antsugi · 2 points · Posted at 05:01:10 on February 14, 2016 · (Permalink)
That doesn't add up right. If you tack on another whole number, you get an infinity between it and the last. And as you continue to add number after number you will get another and another infinite, while in the process of building the whole number infinite
klod42 · 3 points · Posted at 11:34:06 on February 14, 2016 · (Permalink)
Infinite is infinite. Infinite number of infinities is still the same infinite. Comparing infinities isn't about what "feels" bigger. The idea is, since we can't just intuitively comprehend the sizes of the infinite sets, we compare them by trying to "connect" their elements.
For example, N is a set of natural numbers. N={1,2,3,4,5,6,...}. We call its size "countably infinite". Now, imagine a set 2N={2,4,6,8,10,...}, a set of even numbers. I can "connect" their elements with a simple function f(n)=2*n. So, we have pairs: (1,2), (2,4), (3,6), etc.
That function is a bijection: it covers all elements in both sets, and every element in one set has exactly one pair in the other set. We never run out of elements, so we call those sets equal in size. One such function is enough to prove that the two sets are equal.
You can make such bijections for whole and rational numbers as well, but not for irrational numbers.
[deleted] · 3 points · Posted at 00:49:00 on February 14, 2016 · (Permalink)*
They're the same size infinity! If you take a list of all the natural numbers, and multiply each of them by two, you end up with a list of every even number. Any time you can take one set and map it onto another set (pair up the members of the set, with none left over in either set), they're the same size. That still holds for sets with infinite numbers of members.
Watch out using that word "onto." It has a mathematical meaning in context of functions and set theory, synonymous with the more technical sounding term "surjective," meaning that every element of the codomain (the "y" part of the function f(x)=y, with "x" being the domain) has a corresponding element in the domain that maps to it. Or, if a function is defined from the set X to the set Y, then every possible y in the set Y has an x in the set X such that f(x) = y. If a function is surjective or "onto," then X is cardinality-speaking at least as big or bigger than Y.
Intuitively it is obvious that the natural numbers are at least as big if not bigger than the even numbers, so there of course exists an "onto" function from the naturals to the evens. What is a little less obvious is showing that your function, take a natural number and double it, is not only "onto" or surjective, but also injective or "one-to-one," (in graphical terms, an injective function passes the horizontal line test), and thus bijective, which would imply that the natural numbers and the even numbers have exactly the same size or cardinality.
Thanks for the clarification! I actually used "onto" specifically because I knew that the two sets mapped one-to-one, but I'd forgotten to mention that you needed to be able to map A onto B AND B onto A. :)
Onto and one-to-one aren't the same, just to make sure, and one doesn't imply the other
[deleted] · 3 points · Posted at 01:11:43 on February 14, 2016 · (Permalink)
What about an infinity of all natural numbers and an infinity of even natural numbers? One would be half the size of the other, but both are infinite.
Same size. There are as many even natural numbers as there are natural numbers. Also, there are as many integers (..., -2, -1, 0, 1, 2, ...) as there are natural numbers (0, 1, 2, ...). These are examples of countably infinite sets.
[deleted] · 2 points · Posted at 02:29:26 on February 14, 2016 · (Permalink)
It's true in another sense of size called natural density. You can look at the natural numbers as having natural density of 1 (in the natural numbers) and define the density as the limit of the number of numbers from the other set occurring in the natural numbers. So in this sense the even numbers are half the size of the natural numbers.
Id like to see you type out a decimal representation of an irrational number.
GeeJo · 6 points · Posted at 06:01:03 on February 14, 2016 · (Permalink)
Who said that the examples had to be decimal representations? e, pi, and root 2 would have worked fine. Irrational numbers weren't even mentioned by OP, just "not-whole" numbers, which was the problem. It was just all-around a very unclear explanation of cardinality.
Although you could say that "not-whole numbers" is the set of all numbers that aren't whole, which includes all irrational numbers and and all fractions. The set of "whole numbers" is infinite, but the set of "not-whole numbers" is both infinite and larger than the set of "whole numbers".
I find that the easiest way to explain this concept without having to refer to irrational numbers is to compare the set of all whole numbers to the set of all even whole numbers. Both are infinite, but even common sense says that the set of only even whole numbers is smaller.
Ibbot · 2 points · Posted at 02:42:35 on February 14, 2016 · (Permalink)
It's still abundantly clear that he's referring to the set of all numbers that are not whole numbers, whether or not they are irrational.
The issue is that saying it's a larger infinity because there is an infinite amount of numbers between 1 and 2 is wrong. He pointed out there are also an infinite number of rational numbers between 1 and 2, but the set of rational numbers is the same size as the set of whole numbers which is a counter example to that logic.
Ibbot · 1 points · Posted at 09:59:33 on February 14, 2016 · (Permalink)
And even worse, what I said makes even less sense when you consider what the person I was replying to was replying to.
What do you mean? The real numbers have the same cardinality as just the irrational numbers (Card(Q x R) = Card(R\Q) = Card(R)).
ratwing · -7 points · Posted at 01:28:02 on February 14, 2016 · (Permalink)
outsider (of math) looking in. I always find it entertaining when people add exclamation points to the ends of sentences like yours. Yes, it is interesting, but no, you probably would not shout it if you were in a room full of people.
As a small addendum, Hazel is partially correct and partially incorrect in TFIOS. The set of numbers between 0 and 1 and the set of numbers between 0 and 2 are the same size.
[deleted] · 1 points · Posted at 09:36:54 on February 14, 2016 · (Permalink)
Intuition isn't great for dealing with infinity. Let go back to whole numbers. We have 1, 2, 3, 4... Now just take half of those, the even numbers: 2, 4, 6, 8...
Now, you can pair each whole number x with an even number 2x. So we get pairs like (1, 2), (2, 4), (3, 6), (4,8)... So you know there's the same amount of even numbers as whole numbers, even though the even numbers are part of the whole numbers.
What's fun is taking this to the next level. We've just shown that 2×∞=∞, but what about ∞×∞? If you take the set of fractions between 0 and 1, you can prove that there are as many of these as there are whole numbers. So then you take all the fractions ever, so you have the fractions between 0 and 1, the ones between 1 and 2, and so on. We now have an infinite amount of infinite groups of numbers. How many are there over all? Exactly the same as the number of whole numbers.
You are so close to being right. But all of your not-whole numbers are rational. And there are just as many rational numbers as there are integers, it's the same.
You can prove this by putting all of the rationals into a list going 1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1 ... This is called Cantor's Diagonal Argument.
But irrational numbers like pi and e are outside of that collection of numbers. And when you count all of the irrational numbers as well, you really do have more, a bigger infinity, than your 1,2,3 counting numbers.
[deleted] · 7 points · Posted at 00:39:13 on February 14, 2016 · (Permalink)
Also, if my memory is right, there are more real numbers between 0 and 1 than there are natural numbers.
Querce · 3 points · Posted at 05:18:56 on February 14, 2016 · (Permalink)
and there are as many numbers between 0 and 1 as there are between 0 and 2
Right because the reals between 0 and 1 are uncountably infinite there is no one to one correspondence to the natural numbers. To be countably infinite there must be a one to one correspondence with the natural numbers (so obviously the natural numbers are countably infinite)
This is completely wrong...? You're perpetuating a common misunderstanding when people say "there are different sizes of infinity", sorry.
mloos93 · 1 points · Posted at 07:03:44 on February 14, 2016 · (Permalink)*
So, someone else may have said this, but the fractions infinite is the same size as the whole numbers infinite. Same as the all negative and positive numbers infinite with the only positive numbers infinite.
Where the infinites become different sizes is in set theory. In the whole, positive numbers infinity, you can group the numbers together in different ways, called subsets. These subsets, when you take all of them also create a set.
You know what, watch this video. It explains it better.
mhblm · 1 points · Posted at 00:19:21 on February 15, 2016 · (Permalink)
That's not quite correct; both of your example sets are countably infinite and have the same cardinality of aleph naught.
If you included irrational numbers you would have an uncountably infinite set with a larger cardinality of aleph one.
[deleted] · 1 points · Posted at 10:24:50 on March 8, 2016 · (Permalink)
No, the density has nothing to do with it. There are as many decimal numbers of finite length as there are integers, even though they're dense everywhere. What you want to talk about is the infinity of infinitely long decimal numbers, that is, numbers that you can't completely write down. Because they are so long there are a lot of choices for them. The integers are only finite in length, so there are fewer (but still infinite) choices.
Accountably infinite vs Unaccountably infinite. Essentially, the first example we can map the whole numbers to every item in the infinite set. In the second example, we can't map a whole integer to every number in its infinite set.
Also there are several levels of uncountably infinite, beyond the number of reals. A still open question is where there's an infinity between countable and the size of the reals.
[deleted] · -1 points · Posted at 01:39:50 on February 14, 2016 · (Permalink)
[deleted]
108241 · 1 points · Posted at 03:26:41 on February 14, 2016 · (Permalink)
People are downvoting you since they think you're joking.
[deleted] · 1 points · Posted at 04:04:27 on February 14, 2016 · (Permalink)
Or because it's a vaguely correct factoid perpetuated by people who saw one math video or one TIL post and don't understand that it only "equals" -1/12 in one sense so it's misleading if not outright incorrect to say it equals -1/12 as if it converged.
mrill · 0 points · Posted at 06:48:22 on February 14, 2016 · (Permalink)
That doesn't make any sense. It depends on what your defining one as. Both infinities are the same. They're both just ifinitely subdividing something. There is one cosmos and numbers are our way of subdividing objects and patterns into existence. An apple can be 'one' or it could be subdivided ifinitely into particles nonstop. After all there is an infinite amount of numbers between zero and 1. You can subdivide in that infinite amount into more infinity. So yeah both infinities are the same thing it just depends on scale and what you pick 'one' to be.
rawling · 1 points · Posted at 13:09:13 on February 14, 2016 · (Permalink)
Each digit is an infinity unto itself. It's infinitely precise at 1.000~repeating. Also, it might be better to say that between the numbers a and 2 there are an infinite number of decimal numbers. Between 1 and infinity, however, there are all of those decimal numbers for every digit. And between -infinity and infinity there are even more. Really you can even say that between 1 and infinity is an infinity, but between 2 and infinity is a smaller infinity.
Still, the best way to explain it is by just showing them two circles of differing sizes. Each is an infinite loop, but one is smaller than the other. Both have infinite points, but somehow one has less points than the other. Any line works due to infinite precision, but circles help people grasp it better.
ohaiya · 0 points · Posted at 09:44:46 on February 14, 2016 · (Permalink)
Alternatively, think of the sequence of whole numbers: 1, 2, 3, 4, ...
Now double each number in that sequence to produce the subset that is even numbers 2, 4, 6, 8, ...
Since the first sequence is infinite, so is the second, but it's only half the set of numbers as the first set
[deleted] · -2 points · Posted at 02:40:02 on February 14, 2016 · (Permalink)*
There are an infinite number of numbers between 1 and 2.
And it can be shown, there are twice as many numbers between 1 and 3 as there are between 1 and 2.
By induction, there are infinitely many times as many numbers between 1 and infinity as the infinite number of numbers between 1 and 2.
EDIT - Nevermind, these are all the same uncountable infinity.
there are twice as many numbers between 1 and 3 as there are between 1 and 2
Not so! That's what's so cool about this stuff. The set of rational numbers between 1 and 2 is exactly the same size as the set of rational numbers between 1 and 3; in fact, each of these is exactly the same size as the set of all rational numbers! (The same goes if we substitute "real numbers" for "rational numbers" throughout.)
By analogy, the set of positive whole numbers isn't any bigger than the set of positive even whole numbers.
One way to understand this latter example is to imagine a function y = 2x, where x is populated by positive whole numbers. That means y must be populated by only positive even numbers. If the set of even whole numbers were smaller, then this function would have gaps--in other words, if the set of x values were bigger than the set of y values, then there would be a whole number that was missing a double! The graph y = 2x would have holes in it.
So our intuitions about infinity often turn out to be misleading upon closer inspection.
A key concept here is that of countably infinite sets. A set is countably infinite if it is the same size as the set of whole numbers (and thus, in theory, its every member can be paired with a specific whole number and thus counted). All countably infinite sets are the same size. Some countably infinite sets include:
Natural numbers
Integers
Positive integers
Positive even integers
Positive even integers that are also divisible by 7
Rational numbers
An example of a set that is bigger than any of these is the set of real numbers. The coolest proof of this, in my opinion, is Cantor's diagonal argument.
I explained it to my little cousins as: there are an infinite amount of negative numbers (-infinity to -1), and an infinite amount of numbers in the positive direction (1 to infinity), both are logically the same. But there's also an infinite amount of numbers between negative infinity and infinity, which would logically he greater than both of those other infinities.
Or think of all the whole numbers and then think of just the even numbers. Both sets are infinite but one has half the numbers in the other.
mhblm · 1 points · Posted at 00:47:12 on February 15, 2016 · (Permalink)*
Actually, they have the same number of numbers. Half of infinity is still infinity. I would get into it but vsauce explains it better than I ever could:
The way I understand it is this (excuse me because I'm only a college student taking higher level math courses) infinity is more of a concept of endless than it is an actual number. Because of this, infinity and infinity plus one represent different concepts of endlessness. It is clear which one is larger(the plus one).
adding one to infinity doesn't make it larger in itself, it makes it larger than infinity. So A=infinity and B=infinity+1 so B is larger than A. This is used in things like finding the convergence of a limit where 1/(r+1) as r goes to infinity is smaller than 1/r and 1/r converges to zero so 1/(r+1) must also converge to zero.
I'm not exactly sure what you mean here. The limit of 1/(r + 1) and the limit if 1/r are both zero as r approaches infinity.
it makes it larger than infinity
It does not, and "larger than infinity" does not really make sense because there is more than one infinite set. What does make sense is to specify which infinite set you're referring to (e.g., the set of natural numbers); then we can discuss whether adding a finite quantity to it will make it bigger (it will not, as Hilbert's Hotel demonstrates).
In fact, even adding another infinite set to the set of natural numbers won't (necessarily) make the resulting set larger. For example, combining the set of the natural numbers and the set of all rational numbers will not result in a set larger than the natural numbers. The rational numbers are countably infinite, just like the naturals are.
[deleted] · 33 points · Posted at 00:07:53 on February 14, 2016 · (Permalink)
Correct. I had a theoretical statistics professor that explained this really well. Essentially, there is a countable infinity, and an incountable infinity. Coutable is the infinity thay we all typically think of when we hear the word "infinity." I start counting at 1, eventually get to a million, then a billion, trillion, quadrillion, etc. Uncountable infinity is, for instance, the number of numbers between 4 and 5. It's impossible to count how many there are, because it's impossible to find the "starting number" in the first place. I could start at 4.01, but 4.0001 is smaller, with 4.0000001 being smaller than that.
There's an operation called the "power set", which takes some collection A to the set of all of its subsets P(A). So P({1, 2, 3}) = {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {1, 2, 3}}.
Intuitively, the power set of a set will always be bigger than the set itself. By Cantor's Theorem, this holds even for the power sets of infinite sets.
Take the natural numbers. They're infinite, but "less infinite" than the real numbers. In fact, there are as many real numbers as there are subsets of the natural numbers! So the power set of the naturals is as large as the set of reals.
But what if you take the power set of the real numbers? You get something that's even bigger than uncountable.
[deleted] · 7 points · Posted at 01:28:19 on February 14, 2016 · (Permalink)
but wait, there's more
thmsoe · 4 points · Posted at 01:42:15 on February 14, 2016 · (Permalink)
Your explanation is almost true, but your last sentence also applies to the rational numbers between 4 and 5, which are countable. The classical argument to illustrate why the real numbers aren't countable is Cantor diagonalisation, which requires a bit of mathematical knowledge.
[deleted] · 1 points · Posted at 02:14:34 on February 14, 2016 · (Permalink)
Yes...the number of rational numbers between 4 and 5 is countably infinite. The number of numbers between 4 and 5 is on uncountably infinite. Cantor's diagonalization has to do with the fact that infinite sets don't necessarily coincide with the infinite set of natural numbers. That's where the expression of "uncountable sets" came from in the first place. This is where cardinal numbers come into place to help with more complex set theory.
The number of numbers between 4 and 5 is on uncountably infinite.
I think what he was trying to say was that your argument for why this is uncountable doesn't really add up, since the same trick should apply to the rationals, but those are countable.
Also, you should be more careful with how you toss around "numbers" as though the reals are the end-all be-all number system.
For instance, in the surreals, there are so many numbers between 4 and 5 that you can't describe them with any infinite cardinal, because they form a proper class.
[deleted] · 282 points · Posted at 20:34:48 on February 13, 2016 · (Permalink)
I once heard a physicist say he hated "infinity" because he felt it was a lazy mathematical concept that was a fancy way of saying "I don't know what goes here, so I'll just say 'infinity'"
That's not how it works at all. Infinity has a precise definition. A set S is infinite if and only if you can choose one of its proper subsets and then make a bijection between S and the chosen subset.
A proper subset is just a collection of things that are all members of a set, but not the entire set. For instance, some proper subsets of {1,2,3,4,5} are {2,4,5} ; {1,2} ; {4} ; and {}.
Some examples of things that aren't proper subsets of {1,2,3,4,5} are {2,4,9} and {1,2,3,4,5}. (The last one is a subset, but not a proper subset.)
A bijection is a rule that pairs up things from one set to things from another. For instance, a bijection between {A,B,C} and {1,2,3} could be
Letters
Numbers
A
2
B
1
C
3
Nothing is repeated or left out on either side, so we have a bijection.
Now let's try it out with the natural numbers: {0,1,2,3,4,5,6...}. What subset could we pick? There are several good choices, but I'm going to demonstrate with the even numbers. Here's my bijection:
Natural
Even
0
0
1
2
2
4
3
6
...
...
(You could also write this as f(n)=2n.)
All natural numbers appear on the left side and all even numbers appear on the right. Nothing repeats on either side. This means we have a bijection between naturals and evens, so the natural numbers are infinite.
(This also shows that there are the same number of natural numbers as there are even numbers!)
There are various types of infinite numbers - cardinals, ordinals, surreals, hyperreals... all of them are precisely defined and used in different contexts.
FUZxxl · 18 points · Posted at 23:05:28 on February 13, 2016 · (Permalink)
Finiteness is usually defined as “not admitting a bijection into a proper subset of itself” because that definition is equal and does not rely on the definitions of set size, real numbers and an ordering relation that allows you to order cardianls
magus145 · 18 points · Posted at 00:29:59 on February 14, 2016 · (Permalink)
That's the definition of Dedekind finite.
The standard set theory definition of an infinite set is "does not have a bijection with a finite cardinal", i.e., it is not the same size as a natural number.
The two definitions are only equivalent using the Axiom of Choice, so you don't want to take Dedekind finite as your definition of an infinite set unless you're sure you're working over a set theory where they're equivalent.
zomenox · 4 points · Posted at 01:06:50 on February 14, 2016 · (Permalink)
As I can't accept well ordered real numbers, fuck the axiom of choice.
Right, but which uncountable? You've heard of the cardinal numbers, I'm sure? You would think it would make sense to talk about the "size" of the reals, right?
Without choice, we have no way to compare the "sizes" of arbitrary sets. We know we can't inject R into N (so under the usual definition, |N|<|R|, but we have no idea what functions may or may not exist between R and any higher cardinality, meaning |R| might not even be one of the usual cardinal numbers. Without Choice, some sets don't even have sizes in any usual sense of the word.
Reddit is a hard medium to show sarcasm in. I probably should have italicized what I wrote. ;)
FUZxxl · 7 points · Posted at 23:48:31 on February 13, 2016 · (Permalink)
Not just “pairs up things” but “pairs up each thing from one set with one thing from the other set using each thing exactly once,” but maybe “pairs up things” is precise enough for the layman.
Yeah, I explained the "uses each thing only once" after the table for ℕ vs 2ℕ. I figured that it would clutter up the definition too much if I explained it in-definition - I already had to explain proper subsets, and too much explanation would lose people. When people think of pairing things up in real life, most assume that you don't repeat anything. Hopefully that's good enough to get the point across.
(Even though the condition of not repeating anything is necessary, it may be seen as pedantic by "laypeople".)
FUZxxl · 1 points · Posted at 23:57:38 on February 13, 2016 · (Permalink)
maybe say “Nothing is repeated or omitted on either side” instead of just “Nothing is repeated on either side.” That should be sufficient.
Oh, I see what you mean. I was referring to after the table for ℕ→2ℕ. Thanks for the suggestion! I put "left out" instead of "omitted" to keep the wording simple.
FUZxxl · 1 points · Posted at 00:14:27 on February 14, 2016 · (Permalink)
So, my maths knowledge fits nicely into a shotglass but isn't that the definition of countable infinite sets? For uncountable infinite sets there is no such bijection but they're still infinite sets.
I think I learned that infinite sets are all sets that are not finite (and finite being defined as whatever. Cardinality or what have you).
You wouldn't be able to make a chart like that, but it doesn't matter - all you need is for there to be a rule. So if you were looking at the real numbers from 0 to 1, you could do something like f(x) = x/2. If you were looking at all real numbers, you could do this:
if x is positive, f(x)=x+1
otherwise, f(x)=x
This is fairly easily reversible, and ℝ\[0,1) is a subset of ℝ.
Thanks, got it. Must've remembered it wrong. (It's a very small shot glass.)
DXvegas · 1 points · Posted at 02:04:39 on February 14, 2016 · (Permalink)
This is a really neat explanation. I know how infinity was defined in reference to limits of functions/sequences, but not set sizes. I'm curious, what would a bijection of S and a proper subset of S look like if S is infinite but not countably infinite?
You wouldn't be able to make a chart like that, but it doesn't matter - all you need is for there to be a rule. So if you were looking at the real numbers from 0 to 1, you could do something like f(x) = x/2. If you were looking at all real numbers, you could do this:
if x is positive, f(x)=x+1
otherwise, f(x)=x
This is fairly easily reversible, and ℝ\[0,1) is a subset of ℝ.
I've always wondered why we can do this because it feels like cheating. Why not take any function and just say that the codomain is the range of the function and then call it onto?
I suppose I could try to answer my own question. The set of evens we can easily generate, and some functions would be more difficult to generate the range. I suppose I've seen the notation 3N and 4N for multiples of those numbers. for a function f(n)= 2n2 +3 could we just define the codomain to be 2N2 +3 (or probably just 2N2 )?
Things just not need to repeat on their own sides. We're trying to perfectly pair up the natural numbers with the even numbers - before pairing up we start with two "copies"
of all the evens.
[deleted] · 1 points · Posted at 17:24:11 on February 14, 2016 · (Permalink)
Infinite sets are weird. The names of the objects shouldn't matter in determining how many of them there are, right? But if you rename the even numbers to "A, B, C..." (and start making up your own symbols after a while) then there's no way to tell that they were originally every other natural number. So you can't compare things by looking at what they are - after all, renaming things shouldn't change how many of them there are.
So how can we compare things? We pair them up! If you can match everything from one side to everything from another without repeating, then there are the same amount of things on both sides.
This lets us compare things without worrying about their structure or anything else. Again, structure shouldn't matter when we're just looking at how big something is - you could "squish" the even numbers to be paired up perfectly with the naturals, so they have the same size.
But there is a sense in which there are half as many evens as naturals. It's not size though. It's natural density. Natural density is a property of subsets of the natural numbers. You can measure it by picking bigger and bigger intervals and checking what fraction is part of the subset you're looking at.
Here's how we'd check the natural density of the evens:
First, we look at the interval {0}. 100% of those numbers are even.
Then we look at the interval {0 to 1}. 50% of those numbers are even.
Then we look at the interval {0 to 2}. 66.66...% of those numbers are even.
Then we look at the interval {0 to 3}. 50% of those numbers are even.
As we keep getting bigger, everything after a certain point gets closer and closer to 50%. The limit of the density in the interval {0,n} as n goes to infinity is 1/2. So the evens have a natural density of 1/2.
[deleted] · 0 points · Posted at 02:14:38 on February 14, 2016 · (Permalink)
175gr · 112 points · Posted at 22:08:51 on February 13, 2016 · (Permalink)
That's not really true mathematically. Infinity is a rigorous concept. Whenever you see it, it means something specific, no matter what it is.
Being a physicist, he might be referring to different ways physicists deal with infinity. There are ways to assign finite values to divergent series, and these often give results that match experiments - a famous one is the use of zeta regularization to replace "1+2+3+..." With "-1/12".
I love physicists and mathematicians fighting. Every time I learn one of these in physics or math the next day my prof will tell us he'll get mad if he ever sees it in his course since math is usually theoretically correct while physics is practically correct
[deleted] · 5 points · Posted at 02:07:24 on February 14, 2016 · (Permalink)
I love physicists and mathematicians fighting.
It's even more fun if you're a chemist, because then you get to laugh at both of them for even bothering in the first place. As we all know, the only real data is empirical data.
But there seems to be a mathematical way of deriving -1/12th from infinite numbers if you include all of them including fractions and negative numbers.
If you minus the area under the graph above the x axis on the left from the one on the right you get zero leaving the sum of all numbers through to infinity at -1/12!
Folks who reply with objections that infinities are precisely defined mathematically misunderstand the point being made.
In physics when infinities arise as a consequence of the mathematics being used many physicists believe this indicates the physical theory is incomplete or flawed, otherwise there would be no infinities present.
nerga · 2 points · Posted at 02:04:16 on February 14, 2016 · (Permalink)
Was this physicist a college freshman?
[deleted] · 2 points · Posted at 03:00:06 on February 14, 2016 · (Permalink)
University professor.
drunz · 2 points · Posted at 22:38:38 on February 13, 2016 · (Permalink)
"Ugh, what a cop out. They just use infinity as a Deux ex Machina. Worst theorem ever."- how I imagine this conversation going
The physics of infinities are fairly well understood too since like the 60s.
[deleted] · 1 points · Posted at 20:59:03 on February 13, 2016 · (Permalink)
That's how I feel when I think about infinity, it's like a definite idea but obscure at the same time :p
[deleted] · 2 points · Posted at 21:19:21 on February 13, 2016 · (Permalink)
I'm the same way when I think about the concept. I'm not a mathematician in any sense of the word but infinity is quite fascinating as a concept.
georgeo · 3 points · Posted at 23:33:51 on February 13, 2016 · (Permalink)
Georg Cantor, the mathematician who did a lot of pioneering work on the topic, went insane. It's easy to see why.
[deleted] · 2 points · Posted at 01:25:08 on February 14, 2016 · (Permalink)
Yeah I think anyone would have some issues staying sane when numerous colleagues tried over and over to prove that their life's work was bullshit and in the midst of all this their kid died.
Yes! When I was in the seventh grade, I read about this in "Asimov On Numbers." It blew my freakin' mind.
The concept that you can have something more infinite than infinity was so damn cool to me that I took it for my own pseudonym. Been using it for over twenty years!
[deleted] · 1 points · Posted at 02:16:31 on February 14, 2016 · (Permalink)
I know this. However, I chose this phrasing because it's more accessible to the layman, I didn't want the Hebrew connotations of Aleph One, and lim (x -> inf) f(x)=x2 doesn't work well as a username.
Plus ∞2 makes for a pretty cool-looking monogram. I had it embroidered on a ballcap.
I think the problem with this is the naming - when we say infinity we talk about the natural number infinity perhaps, but then sometimes different infinities without really defining our terms.
infinity like other numbers is a mapping, the number 2 for instance is a mapping onto reality and represents some physical thing, we say have 2 pints of lager, and we all know what that means. So when we are kids and hear infinity we naturally think of infinite pints of lager, as others have mentioned this is the countable infinity, because we map this onto a succession of pints of lager.
Now there are different sorts of infinity and mathematicians name them differently, because they represent different mappings onto different number systems and so have different qualitative properties. Kids intuitively know this when they argue about something being infinity true, uh uh it's infinity times infinity, and so on. Intuitively the first infinity maps to the number of integers, the other infinities get closer and closer to the reals, which (if my memory is correct and its been a while since i studied this) is about as many infinities as you can get.
It makes sense the second you think about it. You cannot count to the end of all numbers because there is no end, you just keep counting and counting. We know from this that there is an infinite amount of numbers because it never ends.
Imagine that you count up all the odd numbers, you still can never get to the end, because it just continues into infinity, so this number is also infinite.
However, you also know that even though both sets are infinite one set has twice as many items within it.
Not true. Both sets are countably infinite, meaning that you can list all of them in order (1, 2, 3, ...) vs (2×1-1, 2×2-1, 2×3-1, ...). Because you can map each whole number to an odd number bijectively using f(x)=2x-1, these two sets have the same cardinality - they're both countably infinite
A friend of mine, who terrifyingly intelligent and loves really complex math, explained this to me once. Failing to grasp the concept in its entirety, I simply said "so its infinity+1" and she became very flustered.
I remember in my Calc II classes, people couldn't wrap their heads around why infinity/infinity was undefined and not 1 or some other number. After the prof explained how some infinities are bigger than the others, it blew my fucking mind. I basically spend the entire day thinking about it and trying to wrap my head about it, but I still don't think I entirely get it. Like I understand the explanations on a logically level, I just can't seem to "get" it.
retief1 · 2 points · Posted at 05:01:06 on February 14, 2016 · (Permalink)
There are as many whole numbers (0, 1, 2, 3 ...) as there are integers (..., -2, -1, 0, 1, 2, ...), but there are more real numbers between 0 and 1 than there are integers. The proof of that is even more fun.
salgat · 2 points · Posted at 06:55:59 on February 14, 2016 · (Permalink)
It's more accurate to say there are different ways to approach infinity, some being faster than others.
BiggerJ · 2 points · Posted at 07:17:10 on February 14, 2016 · (Permalink)*
Imagine counting up from zero to any number ever by whole numbers. As long as your target is part of the set you're counting through, then given enough time, you'll eventually reach it. The set is countably infinite.
Now imagine counting up from zero to any number ever by decimals. You'd start 'zero, zero point zero zero zero zero zero zero...' ad infinitum. You couldn't even start. The set is uncountably infinite.
Lareine · 2 points · Posted at 07:46:16 on February 14, 2016 · (Permalink)
Yes, but that goddamn quote in Fault in Our Stars gets it wrong. Get it together John Green.
[deleted] · 1 points · Posted at 00:50:21 on February 14, 2016 · (Permalink)
Infinity is as much a number as the color purple is. People don't always get that. It's a concept, not a specific number, all infinity means is that something is uncountable.
The easiest way to imagine it is you have a string of infinite length. Next to it is a much thicker string of infinite length. They're both infinite but one is bigger. I think.
hlposts · 1 points · Posted at 02:13:01 on February 14, 2016 · (Permalink)
If someone hasn't mentioned it already, check out The Mystery of the Aleph. Interesting mix of historical novel and math investigation. The story of Gregor Cantor investigating this idea, his madness, and his persecution by the church for investigating infinity at a time when the idea was reserved for theology.
Furthermore, contrary to popular-ish belief, there actually aren't more numbers between 0 to 1 lets say and 0 to 2. As long as you can make a direct mapping between items from one set to the other, then the two sets have an infinite but equal number of elements.
Simply put you could repeat "12" infinite times or "123" infinite times. "123" would be "bigger" but that doenst apply to infinity long constructs. They are all the same length; forever.
msstark · 1 points · Posted at 03:00:34 on February 14, 2016 · (Permalink)
I read that in a John Green book and I had to put the book down awhile and think about it. It was probably the most time anyone probably spent thinking while reading a John Green book.
Sakinho · 1 points · Posted at 03:11:23 on February 14, 2016 · (Permalink)
Not only are there infinities larger than others, but there is an infinitude of infinities. These can be understood with set theory, where infinities are described as infinite sets whose sizes can be compared. In particular, from an infinite set, it's always possible to create a strictly larger infinite set by creating a set of all subsets of the starting infinite set. Therefore, set theory can generate and handle an infinite hierarchy of infinite sets.
Now, here's the crazy part. If there is an infinitude of infinite sets, how large is this infinitude? Turns out that even though you can make sets for very, very large infinities, the infinitude of infinite sets describes such a vast concept that it's too large to even form a set.
And that the infinity between 1 and 2 is larger than the infinity of all natural numbers.
[deleted] · 1 points · Posted at 04:22:47 on February 14, 2016 · (Permalink)
I'm a college undergrad. I got an A in calculus. I thought I had a grasp on math, now I am very very confused and sad.
[deleted] · 1 points · Posted at 04:25:31 on February 14, 2016 · (Permalink)
Me too, currently in discrete math. I'd recommend snagging a discrete math book or looking online, if you like math I think you'd find set theory/number theory interesting (if you haven't been exposed to this stuff before)
[deleted] · 1 points · Posted at 04:24:41 on February 14, 2016 · (Permalink)
to those confused, imagine a bunch of holes that are an infinite amount of miles deep as these different kinds of infinity. the larger infinities are holes with wider diameter than other holes.
Correct me if I am thinking about this wrong but I always use a thought experiment for this one. Imagine a grid with a one square line. The line continues infinitely. Now picture a line that is 2 squares thick. The one square line could be subtracted from the 2 square line and we would be left with a one square line, even though both are infinite. Thus one infinity is larger than the other.
Stopped 2+ years of lurking to make this comment. The Riemann Rearrangment theorem is pretty cool and explains a lot of the unintiutive things that happen when dealing with infinite sums. https://en.wikipedia.org/wiki/Riemann_series_theorem
It can be sometimes. Doing the basic sin and cos are easy, but I learned in an Analog and Digital Communications class (AM/FM transmission stuff) that it can get very hairy when you're dealing with a complicated signal that is then encoded within another trig function.
[deleted] · 3 points · Posted at 14:56:50 on February 14, 2016 · (Permalink)
Yea real waves are hard but trig sub isn't so hard that it's worth skipping as a whole.
qwrty42 · 3 points · Posted at 08:31:07 on February 14, 2016 · (Permalink)
Depends on the school. My college didn't even get to antiderivatives until calc 2
I saw a giant "E" with an infinity on its head, skateboarding on top of n= something, and noped outta there fast.
[deleted] · 2 points · Posted at 08:35:11 on February 14, 2016 · (Permalink)
Was gonna answer this. For anyone still scratching their head at it, it makes a lot more sense when you consider that an "infinite sum", formally, is actually a limit of a sequence of partial sums. Students usually think of series as just being infinitely many terms added together, but this is a misconception.
Tharn11 · 4 points · Posted at 01:39:27 on February 14, 2016 · (Permalink)
Had to prove this as a homework assignment last year. That succckkkkeeedd
I get that, but that means he didn't have an account for two years right? Like why the fuck not, it lets you make comments, upvote stuff you like, make shitposts, whatever.
Also I'm not sure what the age of the account has to do with the length of the lurk.
/u/kandarr thinks lurking means having an account but not posting for some reason
But yeah I agree with you. I lurked on reddit for a few months before finally making an account circa one year ago
Damn I'm never going back
usthcd · 3441 points · Posted at 19:41:33 on February 13, 2016 · (Permalink)
If you put 23 people in a room, there's over 50% chance that at least two of them have the same birthday.
WildxYak · 2773 points · Posted at 21:20:09 on February 13, 2016 · (Permalink)
/u/TYLERvsBEER had the best ELI5 description of this IMO
(The most ELI5 way I know how...
Imagine there's a room with 70 people in it. They are in a straight line standing side by side (shoulder to shoulder) facing forward. They are numbered in order. 1 to 70.
The #1 person turns to the to the #2 person and they check to see if their birthdays match. They don't, so #1 then goes to #3 and then 4 checking with each person down the line until he reaches person #70. None match. #1 has met everyone and there were no matches so they all wave goodbye to #1 and he skips off. That was a total of 69 "birthday checks". Are we done? NO!
#2 has been sitting still and has only met #1 and no one else! Everyone is still in the same order, only difference is that #1 is now gone. So #2 turns to #3 and they see if their birthdays match. They don't, so #2 goes to 4, and 5 and 6 until he's reached #70 and still no matches. Darn! #2 has now met everyone so they wave goodbye to him and he skips off. That was a total of 68 "birthday checks". #1 did 69, so together we've got 137 checks...and we've only gone through two people!
Repeat this until you get to the final "birthday check" with persons #69 and #70.
This is how I explained it to my cousins anyhow and it worked.)
That's the wrong way bro
Traditionally monks brew extra strong Beer during lent and eat less
Source i'm German and live in a very catholic region
There are a lot of feasts now with really good Beer 😃
Succinct and intuitive explanation, and correct to boot. Too many people cite the "253 possible pairs" argument without really understanding the problem. Your post will come in handy in the future whenever this problem comes up, so thanks.
Too many people cite the "253 possible pairs" argument without really understanding the problem.
How do you figure? Understanding that it's primarily about the number of pairs of people, not the number of people, is an enormous part of understanding the problem.
253 isn't much more than 50% of 365. In terms of orders of magnitude, it's slightly bigger than 50% of 365.
Unfortunately, I don't know whether I can give you a short answer. The shortest answer is just "If you do the math in detail, you end up with 23 people which means 253 pairs."
I can give you some links for further reading, but I don't know what your math background is, so I don't know what level of detail is appropriate for you.
Everything you might need to know can be figured out by reading the links, but depending on your math background, it might take some time.
But it is. 22 people gives 231 possible pairs, which is still more than 50% of 365. Why not say you have over a 50% chance of finding a matching pair with 22 people? Why not say 21? Whatever number of people it takes to get 183 possible pairs should be the 50% number. (I don't know what that is, but it's much less than 23.)
Why not say you have over a 50% chance of finding a matching pair with 22 people? Why not say 21?
Because it's not true.
Whatever number of people it takes to get 183 possible pairs should be the 50% number.
You might guess that it would be, but it's not.
I know I might sound snarky. I know I might sound like I'm not explaining it. But the fact is, explaining it takes time. You have to work through some details.
I gave you some links that explain some of the details, but you might just have to spend some time on it.
What is your math background, if you don't mind me asking? One of the problems with conversations among strangers on the internet is that you don't know what the other person knows.
You're contradicting yourself. You start out saying, essentially, "253 pairs gives a 50% chance because 253 is 50% of 365." But it's not, 183 is. So what's 253 50% of? What's the significance of 253?
You start out saying, essentially, "253 pairs gives a 50% chance because 253 is 50% of 365." But it's not, 183 is.
All I said is that 253 is close to 50% of 365, which provides a rough explanation of why about 253 pairs is enough.
What's the significance of 253?
The significance is that it just happens to work out that way.
You're asking for a quick intuitive explanation, but sometimes there isn't a quick intuitive explanation. You just have to work through the steps.
Probability of two people having different birthdays:
364/365
Probability of three people having different birthdays:
(364/365) * (363/365)
Probability of four people having different birthdays:
(364/365) * (363/365) * (362/365)
Continue in this way. It turns out, after you crunch the numbers, that with 22 people, the probability of all different birthdays is more than 50%, but with 23 people, the probability of all different birthdays is less than 50%.
That's just the way it happens to work out. If you really want to understand this, then work through the details yourself. Don't glibly ask for a simple explanation when there might not be one. Have the patience to work through the specific details, which can be found in the links I provided.
Think about it this way: Anytime a person meets another person there's a 1/365 chance that they share the same birthday. In my example this occurance, or "birthday check", is happening hundreds of times.
I'm actually just a dumb sales guy who tries to simplify things to customers all of the time. This was my crack at it. There are some math guys who I believe explained the way to calculate this. Sorry!
One point to remember is that you're not looking for two people who where born on a specific day i.e June the 7th. You're looking for two people who share a birthday, which could be any of the 365 days.
But it doesn't matter which day. Most people would think of it (incorrectly) like this: Guy #1 is born on June 7th, so now I have to find someone else born on June 7th in the rest of the 22 people. But there is 22 other days that you need to look at.
[deleted] · 0 points · Posted at 06:02:39 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 4 points · Posted at 06:07:25 on February 14, 2016 · (Permalink)
Yes. Now lets say Guy #1 can't find anyone with a June 7th birthday.
THAT'S NOT THE END OF IT!
He checked 22 other people and nobody had June 7th.
NOW, Guy #2 needs to check. His birthday is January 1st. He checks 21 other people with the January 1st birthday.
Now there have been 22 checks (guy 1 checking everyone for June 7th) + 21 checks (guy 2 checking everyone for January 1st) = 43 checks. Continue this down the road and you'll have
WildxYak · 63 points · Posted at 00:07:18 on February 14, 2016 · (Permalink)
I'm no mathematician by any means, this just happens to be one I've spent time trying to get my head around. /u/Frtipachi explained it well too with a more visual example that might help.
Another fun way to picture it visual can be this. Imagine a giant spinner wheel, like a prize wheel at a carnival. There are 367 pegs making 366 slots (we'll pretend the 366 slot is 1/4 the size of the others to signify Feb. 29) for the pointer to land on. Once someone lands on a slot it is colored in before the next person spins. For the first 10 or so spins you have 1/366, 2/366, 3/366, etc chance of landing on a colored in slot, quite low odds. However, at say the 60th person around ~1/6 of the wheel will be colored in. Using these crude numbers, would you not expect to hit a ~1/6 chance sometime in the next 10 spins? Landing on the non-colored slots would equate to roughly (5/6)10 which is about a ~16% chance just in those 10 spins. This would mean in those last hypothetical 10 spins you would have ~84% chance of landing on at least 1 previously landed on slot. In this example the 'randomness' of the spin indicates the perceived 'randomness' of each persons birthday in the selected group. As a more visual learner myself, I hope this might have helped.
Still don't get it. Why is it using 60 people. If we're using 23 people at around 20 people you're going to have the board about 1/16 colored. So confused.
It's because you have to add up all the probabilities as you go. 60 is an easier number to visualize.
So yeah, the 23rd person has a 94% chance of missing, but when you combine that with chances that each of the 23 of the others also missed, it comes to about 50%.
It's like if you have a spinner with only 1% chance of winning, but you have 70 spins, you have a much better chance of winning.
At 60 people it becomes a ~99% chance. That's what the discussion was about when the original answer was posted.
The theory and method can still be applied for 23 people and getting the 50% chance.
Except in the real world with birthdays the chances are a little higher than the math shows, because human birthdays tend to be clustered due to events (~9 months after valentines, christmas, snow-ins, large economic booms, disasters, etc).
I couldn't wrap my mind around it either, so I wrote a program that randomly generates a number from 1-365 23 times and checks if any numbers match. I had it loop 1000 times. Every time I ran the program, a match was found 50% of the time. I still don't understand it, but it definitely is true.
That's exactly why it works. You're not generating a number from 1-365 and looking for, say, 77. You generating 23 numbers.
Say you generate one number, eg. 5. The second number has a 1/365 chance of being 5. But it's not, maybe it's 143. Now the third number has a 2/365 chance of matching, since it could match either 5 or 143. And so on. By the time you get to the last number, you have a 22/365 chance of matching the previous numbers.
I think(hope) I got it now after reading all these explanations. Correct me if I'm wrong. Say there is 23 of us spinning a wheel 1-365. Say all 23 of us spun the wheel and all landed on different numbers. That would be 23/365 of the board selected, or approx 1/16. So the next guy is going to have a 1/16 shot of landing on the same numbers as one of us. Not great odds, but all 23 people have those same odds. So if 23 people people spin the wheel with 1/16 of it taken, after 23 spins, someone is more than likely going to win that 1/16 odds. Yes? No?
HhmmmmNo · 2 points · Posted at 07:13:34 on February 14, 2016 · (Permalink)*
OK, think of it this way. In a room of 23 people there are 253 different pairs. That's (23 x 22)/2. The chance of any pair having the same birthday is 1/365, thus the chance of them not having the same birthday is 364/365 or 99.726%. But that chance needs to be multiplied by itself for each pair. That means the chance of no match is (364/365)253 or 49.95%. What's the chance of having a match? The reverse, 50.05%.
The people who spin the wheel don't have the same odds. The odds go up steadily each time and you need to combine them. The math I did above is a simple way to do that.
[deleted] · 0 points · Posted at 05:57:54 on February 14, 2016 · (Permalink)*
I don't get it because there's 23 people, and 365 days. Therefore there should be roughly a 23/365 chance that there's a match. That would mean that it should only match around 1/16 of the time.
All these helpful people and i still don't get it.
Therefore there should be roughly a 23/365 chance that there's a match.
Yes, but only for the first guy. The first guy has a 22/365 chance, not including himself. But then the next guy has a 21/365 chance, and the next guy a 20/365 chance, then 19/365, 18/365, 17/365, etc. Keep going through all 23 people, dropping one number each time. That adds up.
You're trying to get the same number twice with 23 attempts. The second number has a 1/365 chance to be the same as the first number, obviously, but let's say it isn't. Now the third number has a 2/365 chance, because there are already two different numbers it can match to. The fourth one has 3/365 possible matches, and so on up to the twenty-third number having 22/365 possible matches. You add all these chances together and it comes out to a bit over 50% total for at least two of them to have been the same number.
Don't think of it as trying to find a match to a specific number of your choosing. With 23 people, there are over 250 possible pairings. All you need is one of those 250+ pairings to produce a match.
[deleted] · 0 points · Posted at 07:17:13 on February 14, 2016 · (Permalink)
I still don't get it. There should (logically) be 23 different numbers, with around a 1/16 chance of match.
My brain fails to understand anything else. Thanks for trying though.
It's just adding up the chances for each number to match one of the previously-generated numbers. It's just (1/365)+(2/365)+(3/365)+...+(20/365)+(21/365)+(22/365). That adds up to a bit more than a 50% probability.
Your 23/365 is a single chance for a number to match one of 23 other numbers. Not the combined chances for any two of those 23 numbers to match each other.
doogie88 · -1 points · Posted at 06:26:47 on February 14, 2016 · (Permalink)
I looked at a few replies to you but none seemed to really ELI5.
Take 23 darts, a poor darts player, and a large calendar.
The poor darts player is just good enough to hit the calendar every time but it randomly hits a date on the calendar, he hits each date with the exact same chance, whether or not he's already hit it.
Now he throws the first dart, since there are no darts already on the board he will definitely NOT hit a date that already has a dart on it. (Probability 1 = 365/365)
He throws the second dart, there is a 364/365 chance of not hitting a date with a dart already in it, since he has thrown one dart in one date.
He throws the third dart, there is a 363/365 chance of not hitting a date with a dart in it, since he has thrown two and hit two dates.
he throws the fourth, 362/365 chance of not hitting a date with a dart already in it, since he has thrown three already and hit three different dates.
so on, so forth, until he throws the 23rd dart into a different date with probability 343/365.
So the chance that we manage to throw 23 darts into all different dates is (365 * 364 * 363 * ... * 343) / (365 ^ 23), which WolframAlpha tells me is approximately 0.49. Hence the chance that we do NOT manage to throw 23 darts into all different dates is 1-0.49, or about 0.51.
kevms · 11 points · Posted at 02:17:55 on February 14, 2016 · (Permalink)
Here's my explanation:
Let's say there are 23 people standing in a line, all facing the same way. #1 checks with #2-23 to see if they have matching birthdays, then #2 checks with #3-23, and so on, all the way to #22 checking with #23. That's 253 checks. Keep this number in mind.
Now, let's say we DON'T want any of the birthdays to match. What are the chances? For any of the aforementioned checks, the chances that the birthdays DON'T match is 365/366, around 99.7%. Since we don't want ANY of the checks to get a match, the chances are (365/366)253. That's 50%.
Since there's a 50% chance that there would be NO matches, there's also a 50% chance that there's at least a match somewhere.
This explanation isn't actually correct although it gives a very similar answer to the correct one. Assuming 366 days, the first person can have a birthday on any one of 366 days, leaving 365/366 for the next person to have a different birthday. But if this check is failed, the second person only has 365 days available, leaving 364/366 for the third. This continues until the nth person can have a birthday on any one of (366 - n) days.
P(n) = 1 - (366 * 365 * ... * [366 - n]) / 366n
P(23) = ~0.506
kevms · 1 points · Posted at 07:57:34 on February 14, 2016 · (Permalink)
Oh yeah, you're right. Forgot to account for that.
Each person has 22 chances of having a matching birthday. That means 23 different people have 22 potential chances to have a birthday match in the room. Think about it like that and it's easier to conceptualize.
Edit: In reality, only one person actually has 22 chances, considering that once he goes through all 22, then he's now out of the picture as a match for the other 22 people. But it still makes it easier to conceptualize. 22/365, 21/365, 20/365, etc. It's likely that you'll eventually get a match.
[deleted] · 1 points · Posted at 01:30:21 on February 14, 2016 · (Permalink)
Each person has 22 chances of having a matching birthday. That means 23 different people have 22 potential chances to have a birthday match in the room. Think about it like that and it's easier to conceptualize.
In reality, only one person actually has 22 chances, considering that once he goes through all 22, then he's now out of the picture as a match for the other 22 people. But it still makes it easier to conceptualize. 22/365 chance for the next guy, then 21/365, 20/365, etc. It's likely that you'll eventually get a match because it adds up. There are a ton of chances.
Same, that explanation was great, but still doesn't fully make sense. Like you said, if you take 23 random numbers from 1-365 how can there be a 50% chance out of 365 numbers, two people are going to land on the same number. :(
1) You pick a number 1-365. You're the first to pick one, so you know that nobody else has picked it: probability 100%.
2) Person 2 picks a number 1-365. They have a whole 364 other numbers to choose, or the 1 number that's already picked. Probability of them picking a unique number: 364/365.
3) Person 3 picks a number 1-365. They have 363 unique numbers to choose, or the 2 numbers that have already been picked. Probability of them picking a unique number: 363/365.
However, that number (363/365) is the probability of that third person picking a unique number provided the first two people have already picked two different unique numbers. In order to find the probability of the first, second, and third people all picking different numbers, we multiply the probabilities for each event:
That can be generalized to n people: P(n) = (365 * 364 * ... * [365 - n]) / (365n ). This number P(n) is the probability of n people all picking different numbers (randomly) out of 365 total numbers to pick from. The probability of some two people picking the same numbers is the opposite of this number: if it is NOT true that everyone picks unique numbers, then it IS true that some two people picked the same number.
So the probability of two people picking the same number out of 365 possible choices is 1 - (365 * 364 * ... * [365 - n]) / (365n ). It just so happens that at n=23 (where you have 23 people), that number exceeds 0.5, meaning the probability passes 50%. At 70 people, that number passes 99.9%.
The odds of person 6 having the same birthday as person 14 is 1 in 365. But we're not talking about matching a specific person to another specific person. We're talking about any of the people in the room having the same birthday as any of the other people in the room.
JuntaEx · 32 points · Posted at 00:23:15 on February 14, 2016 · (Permalink)
Well, ok, in a room with 70 people, but the first post says in a room with 23 people... the same principle still applies? The chances are as high as in a room with 70 people?
WildxYak · 60 points · Posted at 00:38:58 on February 14, 2016 · (Permalink)*
Sorry about that, the example was a direct copy and paste. The principle is exactly the same for trying to find two people with the same birthday.
The 23 person example is the ~50% chance, the 70 people is for ~99.9% chance.
You can see a tables here (1)(2) with the probabilities.
Probability of an unshared birthday is also listed first because when the actual math is done you're actually working out the chance of people not having the same birthday, the way it's spoken about (50% chance of having..) makes it sound more impressive (50% chance no one will have...)
No, the chances increase the more people you have in the room, he was just using 70 as an arbitrary number for the example. However, with 23 people you'd have roughly 250 unique birthday comparisons using the same methodology.
jepZack · 3 points · Posted at 02:20:07 on February 14, 2016 · (Permalink)
The chances will be higher with 70 people, as you will have had more 'checks'.
I realise this was a joke, but it's important to note that it's not a 50% chance that someone has YOUR birthday, but that two strangers will have each other's birthdays, which is unlikely to be you.
[deleted] · 6 points · Posted at 04:27:52 on February 14, 2016 · (Permalink)
Every individual in the room shakes hands with every other individual in the room. How many handshakes are there? We solve for the number of students and teachers in the room, and then find an algebraic solution that works for any number of people.
Sweet! They enjoy challenges. Some of them find the algebraic solution within a few minutes. Kids are capable of a lot more than they're given credit for.
I don't find this one that much intuitive personally (one would assume that many of the "checks" are very similar and still don't understand).
I prefer to simply to picture "filling a room with people", and starting at 10 people already in the room. At this point it's more or less choosing a number between one and 30 and there's one in there that if you pick, you have the same birthday as someone else. But you're not alone, there are still 13 people who have to choose. They're going to fill about half of the 30 numbers, so there's about half a chance.
metju · 1 points · Posted at 03:08:25 on February 14, 2016 · (Permalink)
Even with all the explanations in seemed like bullshit to me, so naturally I engage smartass mode and write some code to prove it in practice... but fuck me, you're right.
Thanks! I tried explaining it to my stepdad who believes in bigfoot and aliens on the moon. He confidently told me this was impossible. Maybe this explanation will help.
Please someone help me get this. If 1 person was born with a 1/365 probability of being born on any day, and they don't share a birthday with 23 people, then everyone else's birthday could land on 364 out of 365 days of the year. So now the remaining 22 people have a 1/364 probability of sharing the same birthday, because we have only deduced what day they weren't born. If we do this for all but the last 2 people, the probability that they'll share a birthday is 1/344. How have we deduced more than 342 extra dates (since you claim the odds are greater than 1/2)?
Can some one explain this to me further? If the probability is based on the number of checks, does it matter that the method for checking is horribly iinefficient? Its a bubble sort algorithm.
[deleted] · 1 points · Posted at 06:35:23 on February 14, 2016 · (Permalink)
I almost freaked my wife (an event planner) out when I was helping her with a networking event and I told her that the event would give people 2 seconds to talk if she wanted everyone to meet each other.
I had forgotten that more than two people can shake hands at the same time.
keboh · 1 points · Posted at 07:13:46 on February 14, 2016 · (Permalink)
Heh, number 1 did 69
omniron · 1 points · Posted at 07:29:12 on February 14, 2016 · (Permalink)
This is the best explanation I've seen for this. Makes it really easy to derive the algebraic proof too. Can't believe after take college level math classes I haven't seen such a concise explanation.
Also I just realized you can frame the question as "how many people need to be on a room for at least 1 to share a birthday" and "how many people have to be in a room for you to share a birthday with them". 2 similar worded questions with very different answers.
[deleted] · 1 points · Posted at 08:20:15 on February 14, 2016 · (Permalink)
This is one of those things like the game show with the 3 doors and the car and the goats and the host asking you if you want to change your mind.
It relies on the concept that you can apply the probabilities from a smaller pool of unknowns where definite "no" results have been eliminated to the original pool of results. Which seems fucking ridiculous to me. Plus it suggests that the theoretical probability of a match increases with the number of checks you do, which isn't fucking true either.
GAH. MATHS IS SO ANNOYING WHEN EVERYONE SAYS IT MAKES SENSE AND YOU JUST DON'T SEE IT.
I'm not a math but 70 people is higher than 23 people
[deleted] · 1 points · Posted at 13:27:21 on February 14, 2016 · (Permalink)
This person only picked the number 70 to write "number 1 did 69, and that's only the first one!" in an ELI5. He made trolling the moderators into a sport. Good job mister TYLERvsBEER.
The math behind that explanation is incorrect; you're double counting handshakes.
The intuition for why that answer is incorrect is quite simple:
Suppose there are 28 people in the room. Then the number of handshakes is 27+26+...+2+1 = 378.
This implies that we've checked more than all possible days in the year, and thus there must be at least one collision.
This is clearly not true (by the pigeon hole property), but as an obvious counter example, they may have all been born on consecutive days in January.
So handshakes must not solve the problem.
Edit: the reason the handshakes method didn't work is because you're changing the conditional probability at each step, but incorrectly assuming it remains constant. If you don't share a birthday with anyone in line, then it's slightly more likely that someone in line shares a birthday with someone else.
For example, if everyone in line uses Steam, and you don't, then all of their birthdays are January 1. So you think you've checked 27 days, but you only checked 1. The next person also only checks 1. And by the end, the only collision checked is if your birthday is January 1st or not.
Well now I feel stupid, because this eli5 version makes zero sense to me. Why 70 people? Why do the total number of asks matter? Where does 23 come in to things?
The particular example uses 70 people to get to a 99.9% chance, 23 people is where it is a 50% chance. The theory and process is the same just a different number of people to get a higher chance.
The total number of asks is so that everyone asks everyone at the end and it's not just one person asking everyone. If that was the case #1 would ask 22 other people but those other 22 people wouldn't ask each other so you'd miss all those potential matches.
Why don't they each just write it down on a card and stand in a circle? Then everyone could check at once.
[deleted] · 0 points · Posted at 22:48:15 on February 13, 2016 · (Permalink)
[deleted]
robson- · 1 points · Posted at 23:13:44 on February 13, 2016 · (Permalink)
No, it's 2,415.
Vekom · 0 points · Posted at 01:17:43 on February 14, 2016 · (Permalink)
Not sure, but I think there are way less comparisons, because the problem is transitive. When #1 and #2 dont match, and #2 and #3 dont match, you wouldnt have to check between #1 and #3.
Adarain · 3 points · Posted at 02:05:34 on February 14, 2016 · (Permalink)
Scenario A: People 1 and 3 share birthday, person 2 is different.
We compare 1 and 2 and find they have different birthdays. We compare 2 and 3 and find they have different birthdays.
Scenario B: All three have different birthdays.
We compare 1 and 2 and find they have different birthdays. We compare 2 and 3 and find they have different birthdays. (same as before)
Only if person 2 shares their birthday with one of the others do we not have to check the relation between person 1 and 3, but if both checks result in a "different" then we need to do the third check.
Vekom · 2 points · Posted at 03:34:23 on February 14, 2016 · (Permalink)
The theory and method is the same for 70 people as it is for 23.
The reason the example (I've directly copy and pasted and not adjusted) is talking about 70 people is because that 70 people will give a 99.9% chance of a same birthday and that's what that discussion was about.
Back in havo (european(dutch to be more specific)) high school(?) age 12 to 16 I needed this explanation so bad in my life now that I read it years later I hope I can recall this trick or e able to go to my liked reddit comments and finding this particular one to explain it to whomever needs it, this concept was explained terrible by our math teacher i remember like 20% of the class getting it and the other 80% just giving up on it(myself being part of that. we used self written TI83 calculator programs to just calculate those answers for us by manualy imnputting the vallues).
IAmScare · 293 points · Posted at 19:47:37 on February 13, 2016 · (Permalink)
I've heard this one before, but it still confuses me.
(and yes, I have read the explanation and I understand the math behind it. It is just one of those mind bending questions)
The most intuitive explanation for it is that with 23 people, there are over 250 PAIRS of people. With 250 pairs, you would expect there to be at least one pair with a matching birthday.
(This isn't quite rigorous, because the pairs aren't independent, but it provides a pretty good intuition for the answer).
I think some people get confused as to what is being said. If you walk into a room of 23 people it is likely 2 will have the same birthday but it is unlikely any will have the same birthday as the person asking
actually this important distinction is how this finally made sense to me in my probability theory class back in school: one specific person asking if anyone has the same birthday as them is a different probability function than asking if any two individuals in the room have the same birthday
It's so unintuitive that even many scientists get it wrong. One of the most common intuition errors we make in this area is inverting the probabilities. The common one in both the above links is the difference between, "Given you have the disease, what are the odds of getting a positive text result?" and "Given you have a positive test result, what are the odds you have the disease?"
A highly accurate test result in the first question can still be a very low accuracy in the second question.
easy example here. your test ALWAYS says you have the disease. so when you have the disease it will always tell you that correctly, but just because it says you have it doesnt mean you actually have it.
[deleted] · 1 points · Posted at 04:18:01 on February 14, 2016 · (Permalink)
My frustration with combinatorics is how fast the numbers get very large. I have some nCr formulas that excel just totally shits the bed on.
For anybody who still doesn't get it, even though the two sound similar, they're totally different. 23 people in a room and trying to find any two of them having the same birthday is 250 potential matches, each of which has 365 potential birthdates. That's a 250/365 chance, or approximately 68%. 1 person in a room with 22 other people looking for somebody with the same birthday is only 22 potential matches, each of which has 365 potential birth dates. That's only a 22/365 chance, or approximately 6%.
kbtrpm · 1 points · Posted at 14:23:36 on February 14, 2016 · (Permalink)
Me too. If I have 23 bowls with 365 numbers in each, and I draw one number from each, there can't possibly be 50% chance for me to draw two identical numbers.
I'll assume the reader is familiar with any reasonable programming language but I'll be using R, which is great for math problems like these.
# sample the range 1 to 365
# twenty-three times,
# with replacement
draw = function(n = 23, range = 1:365) {
return(sample(range, size = n, replace = T))
}
# if the number of unique elements in the drawing
# is equal to the number of total elements in the drawing
# => then all elements are unique
all_are_unique = function(drawing) {
return(length(drawing) == length(unique(drawing)))
}
# a duplicate exists if not all elements are unique
duplicate_exists = function(drawing) {
return (!all_are_unique(drawing))
}
simulate = function(trials) {
results = sapply(1:trials, function(i) duplicate_exists(draw()))
return(table(results))
}
Basically, as you draw each number, there's more numbers for it to match with. The last number matching with something alone has a 22/365 chance. The one before that has a 22/365... sum that up, and you get over 50%
Me too. If I have 23 bowls with 365 numbers in each, and I draw one number from each, there can't possibly be 50% chance for me to draw two identical numbers.
Sure there can.
You're underestimating how many chances for a match there are.
Doe the number from bowl #1 match the number from one of the other bowls? Maybe, maybe not... but the probability of that happening is not 1 in 365. It's more like 22 in 365, which is about 1 in 16.6.
(Actually, if you want to get technical, it's not exactly 22 in 365 -- you don't just add, because there is the small probability of an overlap, but that probability is small, and 22 in 365 is in the right ballpark.)
Okay, so 1 in 16.6 means it probably won't happen. But that was just bowl #1!
If the number from bowl #1 doesn't match the number from any of the remaining bowls, we move on to bowl #2. Maybe the number from that bowl matches bowl #3, or maybe it matches bowl #4, and so on. Bowl #2 could match any of the remaining bowls, and it has 21 chances to do so, so the probability of bowl #2 matching one of the later bowls is about 21 in 365, which is about 1 in 17.4.
So, to summarize:
Probability of bowl #1 matching one of the later bowls: about 22 in 365, or about 1 in 16.6
Probability of bowl #2 matching one of the later bowls: about 21 in 365, or about 1 in 17.4
Probability of bowl #3 matching one of the later bowls: about 20 in 365, or about 1 in 18.3
Probability of bowl #4 matching one of the later bowls: about 19 in 365, or about 1 in 19.2
And this continues for all the bowls. Yes, it usually won't be bowl #1 that matches one of the later bowls. That only happens about once in every 17 times. But of course, bowl #2 also has a chance to match one of the later bowls, and bowl #3 has a chance to match one of the later bowls, and bowl #4 has a chance to match one of the later bowls, and each of those chances is better than 1 in 20. (Not 1 in 365, by the way.) When you start adding up all these chances, you get a number that's not very small.
"Who in this room has the same birthday as me, February 12th"
and:
"Do any two people in this room have the same birthday of all the 365 days possible?"
You alone asking is a single case. Consider instead if every person in the room asked that question. That's many more cases and the probability that any two will share a birthday is much higher.
Compare no.1 with 2-70. That's 69 possibilities. Now compare no.2 with 3-70. That's another 68 possible matches. Now no. 3 with the remaining 67. And so on and so on. (By only comparing three people to everyone in the room you'd allready have 204 possible matches)
The probability of a person having any given birthday is obviously 100%, 365/365. Add a second person. The probability of them having any birthday EXCEPT the first person's is 364/365. The probability of those two independent events coinciding is their product: 365/365 * 364/365. Continue on until you have 23 people: 365/365 * 364/365 * 363/365 * ... * 342/365, or otherwise: (365 * 364 *363 * ... * 342) / (365n).
Consequently, the probability of n people all having different birthdays is [365 * 364 * 363 * ... * (365 - n)] / (365)n.
In other words, that's [365! / (365 - n)!] / 365n
or P = 365! / [(365 - n)! * 365n ]. That's the probability for n people having different birthdays. The probability that two of n people share a birthday is 1 - P. Toss that into Wolfram Alpha and evaluate it at different points and you'll see that 1 - P > 0.5 at n=23.
Dd_8630 · 1 points · Posted at 01:11:48 on February 14, 2016 · (Permalink)
The guy's reply to that is pretty helpful. Imagine you have all 23 bowls and you go down and one by one you pull out one of the numbers.
After you draw a number from the second bowl it is very unlikely that you will draw the same number as you drew from the first bowl.
Now you draw a number from the third bowl. Well that number can match with either the second or the first. Now you draw one from the fourth bowl. There's a chance that it will match with either the third, the second or the first. The pattern will continue, with each successive draw increasing the number of numbers with which the next draw can match.
As you move down the line of bowls, the number of possible matches increases because there are more numbers with which it can match. By the time you get to the 23rd bowl, there's a 50% chance that the draw from that bowl will match any of the previous 22 numbers you've already drawn. Does that help at all?
Dd_8630 · 1 points · Posted at 02:25:48 on February 14, 2016 · (Permalink)
But that still doesn't explain what part baffles you.
If I have 23 bowls with 365 numbers in each, and I draw one number from each, there can't possibly be 50% chance for me to draw two identical numbers.
'It can't possibly' - why can't it possibly?
If you have 4 points, you can draw 6 straight lines between them. 5 points have 10 lines. 6 dots have 15 lines. 22 points have 231 lines. 23 points have 253 lines.
If you have 23 people in a room, there are 253 possible pairs. There's a 1-in-365 chance any one pair of people will share a birthday.
So 253, each with a 1/365 chance of being a success, means we expect at least 1 to be a success (253 x 1/365 = 0.693).
FYI, your logic is flawed despite that it leads you to a more-or-less correct answer. The birthday problem can be considered a series of independent events yielding the formula:
1 - (365 * 364 * ... * [365 - n]) / (365n )
or
1 - 365! / [(365 - n)! * 365n ], which is greater than 0.5 at n=23, having a value of ~0.507297, not ~0.693 as your process led you to believe.
[deleted] · 0 points · Posted at 23:17:24 on February 13, 2016 · (Permalink)
This exact distinction is what confuses me about Monty hall
caried · 1 points · Posted at 01:36:18 on February 14, 2016 · (Permalink)
That made it make sense for me. Thanks
db0255 · 1 points · Posted at 05:31:23 on February 15, 2016 · (Permalink)
I think I actually learned the explanation from the real hustle, and gold lasts 30 days but I have little idea what it does apart from know someone spent money for me
Firehed · 0 points · Posted at 01:22:30 on February 14, 2016 · (Permalink)
This messed with me for a while, because when my freshman math teacher explained the problem, I was one of the two students in the room that shared a birthday. It's really easy to go from "do two people share a birthday" to "does anyone share my birthday", where the latter works exactly as you'd expect.
Here's a simpler example. Say the year only had 10 days. If you gathered 5 people in a room, then, you might expect there to be a 50% chance of there being a shared birthday. There isn't -- it's actually 84%.
But you don't have to take my word for it. This link will generate 10 rows of random integers, with each integer somewhere between 1 and 10 inclusive. Each row has 5 integers. Count up how many rows contain a duplicate number (for example, a row that contains
1 2 3 4 2
contains a duplicate) and then divide your answer by 10. You will probably get a number pretty close to 0.8.
One of the things that is helpful in this problem is that a degeneracy of pairs is a victory;
that is, if person A has a different birthday from persons B and C, but they don't use up two possible different birthdates, then that is because B and C have the same birthday which is a victory.
I understand why there are more chances than it seems but I don't get what this kind if example means, with 28 people there's over 366 pairs, so what? They can still have 28 different birthdays.
Which is why it isn't rigorous, as I said. The real reason is because each new person you consider has to be compared against the bevy of other people that have already been looked at. But in terms of intuition, it's easy to see why your probability of an overlap would grow very fast as you add more people (up to a point) by looking at how many pairs there are.
db0255 · 1 points · Posted at 05:38:22 on February 15, 2016 · (Permalink)
So put in to mathematical terms.
In a room full of 23 people, you'd have (22+21....+2+1) unique "birthday checks." That amounts to 253 chances someone could have the same birthday. If the odds of a person being born on a single day is held to be 1/365 (not true technically), then the odds two people have the same birthday are 253/365, ~69%. If you had 20 people, the odds are ~52%.
Is this correct? Also, while doing this I stumbled upon an easy way to calculate the sum of integers from 1 to any number. Apparently the formula for "triangular numbers" is n(n+1)/2. So if you had 53 people in the room, there would be 52*53/2 birthday checks.
It provides a "pretty good intuition" in that it leads you to the right answer without providing actual understanding. It doesn't actually explain the correct answer properly.
Except it does provide actual understanding. It just doesn't explain all the details. At a basic level, the issue is that as you consider more people, you have to match them against all the other people that have already been looked at. That is basically equivalent to pairing up every possible pair of people and seeing if a pair exists which has matching birthdays. No, that process won't give you the correct probabilities, but it is absolutely the right general way to think about it.
You're giving a tangentially-related process to obtain a similar-to-correct value that might as well be coincidence. It's only easily believed because it happens to give an answer that is close to the correct one despite not actually representing the probability calculations involved.
It's not a coincidence that it gives an answer close to the correct one. I could explain why, but the explanation requires a bit of math, and I'm not sure what your math background is.
But here's the basic idea.
Suppose I have a 20-sided die. One of the sides is red, and the other 19 are not. I roll the die several times, and I want to know the probability of getting red at least once.
Say I roll the die twice.
Exact probability of getting red at least once: 1 - (probability of no reds) = 1 - (19/20)(19/20).
Approximate probability of getting red at least once: 1/20 + 1/20.
It's not a coincidence that the approximation is close to the reality. The reason is as follows: (19/20)(19/20) is the same as
(1 - 1/20)(1 - 1/20)
= 1 - 1/20 - 1/20 + 1/400
and 1/400 is much smaller than 1/20, so this is in fact very close to
1 - 1/20 - 1/20
which, when subtracted from 1, gives 1/20 + 1/20.
Similar reasoning applies if you roll the die 3 or 4 or 5 times, although the algebra gets messier.
You are correct that the explanation from /u/ThereOnceWasAMan was not 100% rigorous, but it's not an accident that it provides a reasonable approximation.
I know why the answer is similar, but I still don't think using the description of 253 pairs gives an adequate understanding of the problem. Yes, a reasonable approximation, in that 3.14 is a reasonable approximation for pi. But understanding why the true probability is slightly different allows for a more complete understanding of the problem in the same way that knowing that pi is transcendental affects the way we consider finitely-long approximations of pi.
Saying "There are 253 pairs" is an excellent way to start the explanation if somebody is completely befuddled by the whole thing and just says "But 23 is so much smaller than 365!"
But understanding why the true probability is slightly different allows for a more complete understanding of the problem
Sure, I agree with that. But approximations also have their place. There are a great many situations where using 3.14 for pi gives good practical results because we don't care about more than two or three significant digits.
Similarly, with the birthday problem, as a start to the conversation, it might be appropriate to begin with some very rough approximations that informally suggest why we might expect the true probability to be closer to 253/365 than to 23/365 (in a rough overall order-of-magnitude sense).
This is true. I wrote most of those replies around 4 AM, so I realize I was being pretty unfair. It's not useless intuition or tangentially related, it is a close approximation and a good starting point. The main reason I find issue with the approach is that it tends to lead to people evaluating (253/365) and getting a completely wrong answer. I always think working with concepts yields a stronger intuitive grasp for laymen than with numbers, so I favor the step-by-step approach of finding each person's chances, generalizing this, and then finding the total probability in general terms. Not only is this (slightly) more accurate but also I think easier to grasp. Of course if it isn't sticking, the binomial coefficient is a different angle.
Really, the tiny inaccuracy just bothers me when an algebraic proof of the problem is arguably simpler. But don't let me stop you from explaining it how you like. There's no reason you or most people should care, it's beyond trivial here.
[deleted] · 0 points · Posted at 01:42:31 on February 14, 2016 · (Permalink)*
It isn't. Here's a simpler example. Say the year only had 10 days. If you gathered 5 people in a room, then, you might expect there to be a 50% chance of there being a shared birthday. There isn't -- it's actually 84%.
But you don't have to take my word for it. This link will generate 10 rows of random integers, with each integer somewhere between 1 and 10 inclusive. Each row has 5 integers. Count up how many rows contain a duplicate number (for example, a row that contains
1 2 3 4 2
contains a duplicate) and then divide your answer by 10. You will probably get a number pretty close to 0.8.
You're overcomplicated things. Walking into a room with 22 people and comparing yourself with 1 person is wrong. There's 250 possible combination of pairings in that room of 23. Each of the 250 possible pairs has a small chance of sharing a birthday. Those chances add up.
Edit: or if you're really interested, search up football squads. Statistically, over half will have 2 people sharing a birtbday
Give me a link that will give me 23 numbers, selected from 1-365
I mean, that's easy enough. Here is a link with 40 rows, 23 numbers per row, numbers selected from 1-365 inclusive. Approximately 20 of the rows should contain a duplicate number. Knock yourself out.
Not that I know of. Your options are a) write a program to do this yourself (if you know any programming at all, this should be pretty easy -- you just need a random number generator), b) using the link I gave you and do it manually, c) use math.
Any of those methods will generate the same result.
You can do that experiment, sort of. I'll copy something I wrote elsewhere about this:
Here's a simpler example. Say the year only had 10 days. If you gathered 5 people in a room, then, you might expect there to be a 50% chance of there being a shared birthday. There isn't -- it's actually 84%.
But you don't have to take my word for it. This link will generate 10 rows of random integers, with each integer somewhere between 1 and 10 inclusive. Each row has 5 integers. Count up how many rows contain a duplicate number (for example, a row that contains
1 2 3 4 2
contains a duplicate) and then divide your answer by 10. You will probably get a number pretty close to 0.8.
kevms · 5 points · Posted at 02:08:54 on February 14, 2016 · (Permalink)
Let's say there are 23 people standing in a line, all facing the same way. #1 checks with #2-23 to see if they have matching birthdays, then #2 checks with #3-23, and so on, all the way to #22 checking with #23. That's 253 checks. Keep this number in mind.
Now, let's say we DON'T want any of the birthdays to match. What are the chances? For any of the aforementioned checks, the chances that the birthdays DON'T match is 365/366, around 99.7%. Since we don't want ANY of the checks to get a match, the chances are (365/366)253. That's 50%.
Since there's a 50% chance that there would be NO matches, there's also a 50% chance that there's at least a match somewhere.
regdayrF · 7 points · Posted at 21:29:47 on February 13, 2016 · (Permalink)*
Simple explanation, you just go through all the 23 people.
You go through the first one. He can't possibly have the same birthday as any other person, because you have checked noone yet.
You go through the second one. He either can have the same birthday as the second one, or could have birthday on another day.
You go through the third one. It would be fitting, if he had the same birthday as the first or the second one, but he still could have on another day.
You already see a certain trend here. Each time, you check the next person, this next person has a higher chance to have birthday on the same day, as the person, who was checked before him.
If you check the twentythird one, you already have 22 fitting possibilities to strike your event.
All the persons being checked later have quite a large number of birthdays, which could be on the same day as their own. This having quite a large chance to to have the same birthday as another person in the room. As it doesn't matter to you, if the second or twentythird one has birthday on the same day as another person, you kinda "add" the chances for all the 23 people on top of each other.
Why did I put "adding" them on top of each other in quotation marks ?
Well, in theory, the second one could have the same birthday as the first one, which is extremely unlikely. Then you don't even care about any other birthday anymore. Third one could have birthday, as the second or first one, then you don't care about any other birthday anymore, etc. pp.
gnorty · -2 points · Posted at 22:48:55 on February 13, 2016 · (Permalink)
Simple explanation
lmao. You spelt "ridiculously overlong and boring" wrong.
I found this fact during the World Cup '14. Have a look at teams on Wikipedia (about 22 people per team?) and more often than not, there are people who share birthdays.
The best way is just to try it. Kind of didn't believe it at first, but then I realised that in our class of 24 people, two girls have the same birthday!
[deleted] · 1 points · Posted at 04:05:06 on February 14, 2016 · (Permalink)
Just go to Red Robin on your birthday. Or any day for that matter.
Basically you have to think as though your not the one comparing to everyone but as everyone is comparing to each other.
[deleted] · 0 points · Posted at 01:32:34 on February 14, 2016 · (Permalink)*
[deleted]
kevms · 2 points · Posted at 02:14:08 on February 14, 2016 · (Permalink)
This problem becomes much easier to understand if there were a million doors instead of 3. Let's say you choose door #421,639. No way you picked the right door, right? Now the host takes away 999,998 doors that don't have the prize, leaving the door you picked and door #392,402. Do you switch to door #392,402? Definitely.
Part of the explanation is that the odds of being born on any particular day are not 1/365. Births cluster on certain days. Some dates are very popular, while others have very few births.
atrd · 3 points · Posted at 00:50:51 on February 14, 2016 · (Permalink)
The same result holds if you assume that birthdays are randomly distributed.
It is supported by both theoretical models and experimental data. Try it yourself at home. Instead of 365 days, try picking a number 1-16 using a random number generator online. Theoretically, you should get two matching numbers ~50% of the time if you pick the numbers in sets of 5. Pick half a dozen or so sets of 5 numbers and you should start to see this. Keep going and you'll get closer and closer to 50%.
edit: Funnily enough, I just tried it myself (using Wolfram Alpha's RNG from 1-16) exactly 6 times and got exactly 3 matches, 3 non-matches. But it would be reasonable to expect a less close ratio at only 6 trials.
The fuck is wrong with you? You need to lighten up. All I did was say something almost but not quite as dumb as what you said, no need to get all worked up.
Does this mean, if i ask 23 people to pick a number between 1 and 365 (1 for each date obviously) i have a 50% chance of 2 people picking the same number? (keeping out psychological stuff)
And it's also very likely they'll be September babies... Christmas is apparently a fun time for a lot of people, and September a very expensive time.
[deleted] · 5 points · Posted at 02:21:48 on February 14, 2016 · (Permalink)
Here's an explanation I wrote up. It isn't extremely complicated, but it does use probability and so there's no way to make it super simple either. I explained all the steps so it's a bit lengthy and goes off at times to explain how things were done:
The odds of someone in a room of 23 having the same birthday as you is pretty low. But any two people is much different.
You have 23 people in a room. You start with the first person and go around to the other 22 people and compare birthdays. That’s 22 pairs. Then you move onto the next person and compare his/her birthday to everyone else. That's 21 more pairs since you’ve already paired the first and second person. You keep doing this, and it continues down to the last two people that make 1 pair.
So the number of pairs looks like: 22 + 21 + 20 + 19… + 1 = 253 pairs.
The shortcut to calculating this is 23 x 22 / 2 x 1 = 253 pairs.
The first person can be any of the 23 people, and the second person can be any of the remaining 22. If I multiply them together, I know how many pairs I can make. However, this includes every “arrangement” of the pairs. So for example, this is counting the pair “Person 1 & Person 5,” but also the pair of “Person 5 & Person 1.” Since these pairs are the same, we need to divide by the number of possible arrangements of each pair to cancel them out. There are 2 ways of arranging a pair, so we divide by 2.
You can also see this works by adding (22+1) + (21 + 2) + (20 + 3)… etc. Each pair adds up to 23. You will eventually get to 12 + 11, which is the 11th pair. So it’s 23 x 11, or 23 x (22 / 2)
At this point, it should be easier to understand how there might be a 50% chance with only 23 people, because 23 people make a lot of pairs. Now let’s calculate the probability.
I want to show the math I’ll be using with coin flips, because it’s much easier to see that it works. If I asked what are the chances of getting at least 1 heads in two coin flips, how would you do that? You need to calculate the odds of getting only tails. This is simple, there’s a 50% chance of getting tails on each flip, so you multiply: .5 x .5 = .25 or 25% chance of getting two tails, or only tails. Then simply take the inverse to find the odds of getting at least one heads. It’s 75%.
Here are the possibilities laid out: HH, HT, TH, TT. It’s obvious that there’s a 25% chance of getting two tails, and 75% of getting at least one heads.
If we flip 3 times it works the same: .5 x .5 x .5 = .125 or 1/8 chance of getting 3 tails, or only tails. So it’s a 7/8 chance of getting at least one heads. If we flip 253 times, it would be .5 x .5 x .5… and so on 253 times, or .5253.
The birthday problem will use the exact same concept since we are only concerned with one matching pair. We know there are 253 pairs, so what are the chances of getting at least one matching pair? Unlike the coin flip though, there’s a 364/365 chance (ignoring leap year) that any single pair do not match (just like the 50% chance of getting tails). So all we do is multiply to find the odds of not getting any matching birthdays, and then take the inverse to find the odds of at least one matching birthday. Again, there are 253 pairs, so it’s (364/365)253 = .4995 or 49.95%. Take the inverse to get 50.05%. It’s slightly off since it’s not accounting for leap year.
Again, there are 253 pairs, so it’s (364/365)253 = .4995 or 49.95%.
This is emphatically incorrect. As opposed to the individual coin flipping, the birthday pairs are not independent. (Eg.with your method, the probability that three people have the same birthday is the probability that each pair has the same birthday (1/365), so you get (1/365)3, but in reality the probability is (1/365)2.
The correct probability for the original birthday problem with 23 people is 49.3% (see wikipedia or wolfram mathworld).
[deleted] · 2 points · Posted at 20:59:42 on February 14, 2016 · (Permalink)
Oops, you're right. It should definitely be (365/365) x (364/365) x (363/365) and so on 23 times out.
Funny that the wrong method worked out as a pretty close approximation though.
Kalima · 2 points · Posted at 02:03:41 on February 14, 2016 · (Permalink)
If there are 46 people does that increase to over 100%?
Some friends and I tried it last night, and we found 2 people had t g e same birthdah, it was cool
regdayrF · 3 points · Posted at 20:50:53 on February 13, 2016 · (Permalink)*
For anyone wondering about the math behind it:
Assumption: Each day of the year is as likely to be a birtday as another day. Every birthday of the people in the room are independent to each other.
AC = No person has birthday on the same day
A = At least 2 persons have birthday on the same day
P(A) = 1 - P(AC ) = 1-(365!/(342! * 36523 ))
Small reminder: 365!/342! = 365 * 364 * ... * 343
( This is the amount of possibilities, that are out there for 23 different birthdays, now you just have to divide it by 36523, which is the amount of possibilities for the experiment. )
It follows the same principle as the possibility for one specific number on a dice to appear. P(B) = 1/6 --> P(BC ) = 1 - P(B) = 5/6. B being the event for one specific number to appear. BC being the event for this specific number not to appear. You have 6 numbers in total, and each number represents one possibilities. In this case 6 ~ 36523 and 5 ~ 365!/342!
Someone else please check my logic. This feels right but probability is weird.
The chance that none of them will have the same birthday as another is 1.4 * 10-147 .
Basically, for each person that enters the room, what are the chances that their birthday matches none of the others that are already in the room. The expression below is what I used to solve it.
Actually, it is basically the only field of knowlodge that you can actually say something is final. I highly doubt you have studied even past Calculus to truly understand why that is true.
edit: correction
[deleted] · -1 points · Posted at 06:56:38 on February 14, 2016 · (Permalink)
One thing any real mathematician knows is that what they study is true. There is no doubt about it. They don't make meaningless assumptions. They do not speculate. They work with logic. It might take them hundreds or thousands of years to actually answer a problem as it has happened multiple times, but they do what they do in order to get something final. Once something is proven and verified by other mathematicians, there is no doubt that it is not a complete, absolute and final result.
[deleted] · -1 points · Posted at 07:57:22 on February 14, 2016 · (Permalink)
math is based on axioms. axioms are theorems. theorems are not final. i mean heck even 1+1=2 is a theory.
It is a theory, but that doesn't mean the results obtained by it are any less true or final.
I have already argued with people who thought the same way you do (some even invalidating centuries of mathematical research) and it just ends up with me having wasted a lot of time and not having accomplished anything, so I think I'm just gonna go to bed now instead of walking around in circles with you (which is almost always how this ends).
[deleted] · 0 points · Posted at 08:10:58 on February 14, 2016 · (Permalink)
true. i was actually contemplating on not answering back either. theory's are always prone to be disproven and respectable mathematical theory have been disproven before. Even if you think something's right, it's only correct within our frame of reference.
I like this one because last year, when I first read this, the average class size at my school was was 20-25 people. So I thought to myself "who in my classes have the same birthdays?" That's when I remembered that one of my classes had a pair of twins, and another class had two of my friends, who I know shared a birthday. So basically, ~50% of my classes, averaging out to 23 people each, had two people that shared a birthday.
[deleted] · 1 points · Posted at 01:24:16 on February 14, 2016 · (Permalink)
There are 24 people in my college class and me and a friend have the same birthday
The best way to prove this is to compute the probability P that no two people in that room have the same birthday. Then 1-P gives you the answer. It makes a lot more sense to me that way.
[deleted] · 1 points · Posted at 02:23:57 on February 14, 2016 · (Permalink)
And if only two of them are twins it becomes a 100% chance!
I love this one! I was at a dinner party with 6 professors and their S.O.s (with me being a student) and I wanted to impress them with this statistical "trick" if you will. I explained the idea to them and we went around the table and no one had the same birthday, until the very last person . Then everyone freaked out and I was a hero for 5 minutes.
I was gonna argue with this because it makes no sense to me (I have a lot of math experience, however discrete math is apparently a different beast). I figured the easiest way to prove the theory right/wrong is just to test it by randomly assigning numbers out of 365 until I get a duplicate result. The 10 tests averaged out around 23 numbers until I got a duplicate, which proves the theory correct, long story short. It's crazy but I can't argue with something I'm looking at.
[deleted] · 1 points · Posted at 04:56:39 on February 14, 2016 · (Permalink)
I teach college composition, with classes that cap out at 24. I pull this trick on my students every semester. More than half the time I blow their minds with my prediction that two people in the room have the same birthday.
They often assume I have access to their records, which includes their birthdays, but I don't. Also, who has time to look up all your students' birthdays for a quick gag?
Had a professor in college who would have us all, on the first day of class, stand in a circle in birthday order to prove this. Sure enough we had some pairs.
[deleted] · 1 points · Posted at 06:00:08 on February 14, 2016 · (Permalink)
In theory. But in practice, think about this. You go to school for almost your whole childhood about from 5-18 years old. I don't know about you, but throughout all my school days not once in all of my classes did 2 people have the same birthday. There were upwards of 23 kids in those classes, and almost every year there was plenty of people joining and leaving those classes.
We did this in my pre-calc class in high school for funsies. There was ony about 20 of us, the teacher went through the math and showed it was about under 50% that we shared a birthday with someone. So naturally we decided to test it. She asked every person, one by one, their birthday. We got to the last row of people, and our chances were looking grim. She asked the second last person, and she says (insert birthday month day here). I shit you not, the last person turns and says the same date. Everyone in the class went nuts, and by nuts I mean a few loud "woah"s and "what"s.
Our math teacher taught us this with a practical example. Schooling in my country has static classes for 80% of subjects and classes at the school were 20-25 students, with 18 classes total. According to the school records 7 of those classes had two students with the same birthday.
It's was quite unbelievable until he explained the maths behind.
Oh, I remeber this. Back in school I bet against my math teacher that we'll never find 2 with the same birthday out of 50 random people, so we ran through the school asking people for their birthdays, later on I won but I remember that their were a row of 15 or 16 people that had birthday in april one after another
arenlr · 1 points · Posted at 11:07:26 on February 14, 2016 · (Permalink)
I still don't get it even after reading all the explanations
Let's say I have 23 jars, each filled with a ball labeled 1 to 365.
If I pick one ball at random from each jar, I would expect in most of the cases not to end up with 2 matching balls
This is unsettling because I've never met someone with the same birthday as me.
kbtrpm · 1 points · Posted at 14:22:10 on February 14, 2016 · (Permalink)
I have always wondered about this: the probabilistic computation is easy, but I think it's wrong: nobody ever takes into account the existence of leap years. Not that it affects the 50% conclusion, but the computed probability is not exact.
Interestingly enough this got brought up in my Physics lecture at college at the start of the semester.
The professor decided to spend a few minutes proving it, we had more than 23 people in the room (maybe 40-50?) so the odds were quite good (more than 50%).
So he started by having everybody with a birthday in January raise their hand, 4-5 people did. The first girl he asked what her birthday was said something like January 13th and a kid a few rows away said "uhhh, did you say January 13th? That's my birthday."
So while the odds were about 50% that two people would share the same birthday in the class, the chances of it happening with the first few people are low.
It's like someone took the Pigeonhole Principle from combinatorics, and decided to try to prove it with bubble sorting from sorting/group ordering theory; and to their surprise, it more or less worked. So they left the special case they'd discovered and skipped off into the sunset for others to explain.
Also, there are about as many 4-digit numbers with a repeated digit as there are without.
If we have 4 digits a,b,c,d, there are 9 choices for b (the tenth digit would be a) , 8 for c (the other two would be a or b), and 7 for d. Of 1000 4-digit numbers starting with the same a, only 9*8*7 = 504 do not repeat a digit.
I've been thinking about this for over a day and I still dont get it. You're telling me that if I had a random number generator spit out 23 numbers ranging from 1-365 that there's over a 50% chance that two will match? That seems absurd.
So you're telling me that randomly waking to an adoption center, picking an adorable tuxedo cat, and then finding out it has the same birthday as me isn't so special after all? :(
Again, that's not an equivalent problem. However I saw your comment on 0.999999…=1 so I realize now that you are trolling. If anyone else wants me to explain why he's wrong I can do that but I won't spend more time on trolls.
You added another condition; in his the 23 people have random birthdays, while in yours you have taken the time to make sure each person doesn't have the same birthday ahead of time. His is random, yours is definite.
Well, you are right to a certain degree. In mathematics you always have to make some assumptions. In this case, you would have to say something along the lines of:
Each day of the year is as likely to be a birtday as another day. Every birthday of the people in the room are independent to each other.
Then you can calculate the chance for each person to have birthday on another date ( AC ),
A = At least 2 persons have birthday on the same day
P(A) = 1 - P(AC) = 1-(365!/(36523 *342!))
[deleted] · 2 points · Posted at 20:53:13 on February 13, 2016 · (Permalink)
After reading the whole thread it's gotten to the point where I now know that every comment below the score threshold on this thread is most likely going to be a comment made by you.
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a roulette, a curve generated by a curve rolling on another curve.
25 years later, I still trace that out if I see something rolling.
That is pretty satisfying, would be even better if it was a perfect loop.
[deleted] · 7 points · Posted at 02:27:22 on February 14, 2016 · (Permalink)
Hahaha. I had a crazy math professor who loved the software Mathematica. He taught it for half of a class and many of the exercises were writing math code to produce the gifs seen on wikipedia. In particular, it was this one.
Follow the end of a spoke on a tire. Within the wheel it moves circularly, but on the flat plane it moves linearly. The two combine to make a nice swirl.
NahSoR · 2 points · Posted at 02:16:04 on February 14, 2016 · (Permalink)
A true lazer
nskll · 1 points · Posted at 09:40:54 on February 14, 2016 · (Permalink)
abedneg0 · 15 points · Posted at 02:44:57 on February 14, 2016 · (Permalink)
The coolest thing about the cycloid is that it is the solution to the following problem. You have a marble at the top of a tower. You want to build a marble run that will get the marble from the top of the tower to the ground some distance away as quickly as possible. What is the shape of that marble run? The answer -- a cycloid.
came here to say this. Aditional fun fact: german pilots in WWII were trained to take this paths while descendin during dogfights giving them a huge advantage.
A very important property of the cycloid is that it is the solution to the Tautochrone Problem: find a curve that the amount of time it takes something to fall to the bottom is independent of the height where it starts. This lead Huygens to realize that a cycloid pendulum should give a more accurate clock than a traditional fixed length pendulum.
For a traditional pendulum, the period of the swing depends slightly on the amplitude of the swing; it is only an approximation of small amplitude that gives period independent of the amplitude. The cycloid pendulum precisely has the period independent of the amplitude of the swing. However, real world effects such as friction make it not practical.
Here is a cool use of the cycloid to explain a neat little toy a researcher is using.
foyf · 2 points · Posted at 04:17:32 on February 14, 2016 · (Permalink)
The really interesting thing about the cycloid curve is that it is the fastest path a rolling object can take down a curve. In other words, a derby car dropped from a cycloid curve will finish before it would on ANY other curve.
foyf · 1 points · Posted at 04:17:29 on February 14, 2016 · (Permalink)
The really interesting thing about the cycloid curve is that it is the fastest path a rolling object can take down a curve. In other words, a derby car dropped from a cycloid curve will finish before it would on ANY other curve.
A hyperbolic paraboloid is a three dimensional shape that when traced onto the three planes in 3D space, yields two parabolas and a hyperbola. It is modeled by the equation "z = (y2 / a2) - (x2 / b2)". Its shape can be visualized easier with Pringles.
Related weird thought: If the wheel in question is not slipping, that means the point on the wheel's edge directly contacting the surface is not moving.
No matter how fast the vehicle is moving, there is a point (or a line, technically) on the wheel at any given time whose velocity, relative to the ground, is zero. That blows my mind.
Another cool thing about these is that it takes the same amount of time to get to the bottom from any point along the curve (if it is inverted in an upside down u shape and a mass is subject to gravity). This makes it ideal for timing things like seconds in a clock, because even if the weight loses momentum along the curve over time and doesn't reach as high (due to air resistance, general friction) it will continue to beat out at the same time interval!
Interestingly if u wanted a slide that would bring u down from A to B (and they aren't on the same axis), a cycloid slide will have the shortest slide time.
Nerfi · 3 points · Posted at 13:55:35 on February 14, 2016 · (Permalink)
I found your use of that line in this context far more emotionally moving than Natalie Portman's attempt to display a similar emotion in the film "Revenge of the Sith."
April 31st would be 76 days away if it existed. Intent of contract is to be respected if the author of the contract makes a minor error based on well known facts to be intentionally misleading.
At our school we have 3 pi days so that every semester can celebrate. April 14th is pi day, November 10th because it is the 314th day of the year where we serve pie, and 7/22 (July 22nd) where we celebrate approximately pi day and serve cake.
I made my account knowing that it represented a fraction close to Pi but wasn't as common as 22/7. It was pure coincidence that I came across this post.
"I made my account knowing that it represented a fraction close to Pi but wasn't as common as 22/7. It was pure coincidence that I came across this post." - from an earlier comment
If I remember correctly, you only need about 20 digits of pi to calculate the diameter of the observable Universe to a precision within the diameter of a single hydrogen atom
EDIT: added "observable Universe"
EDIT 2: as others have pointed out, it's actually 39. Still not all that many in the grand scheme of things
ectish · 1 points · Posted at 04:26:39 on February 15, 2016 · (Permalink)
Because you'll never be invited back and won't get to repeat the sequence?
zacree · 11 points · Posted at 02:50:34 on February 14, 2016 · (Permalink)
My first week at college, there was a meeting with every guy on my floor.
Not even thirty minutes in, they're reciting digits of pi in unison as some sort of contest. They're a couple dozen digits in (more than twenty guys), eyes wide with delight and shaking their fists like they're roman gods watching slaves fight for glory.
ONE. FOUR. ONE. FIVE. NINE...
I have never been further out of my depth. I was really uncomfortable and really wanted to leave but I didn't wanted to be branded as "that guy who left while we were all so happy".
They really were happy, and in a way I was happy for them. Because these were the math nerds from all of our highschools and they were finally meeting other people who they identified with on that level. You could see it in their faces that they were dreading coming to college and having to try to fit in or suffer the consequences and that in this moment it was instantly relieved. They fit in perfectly and nobody in that room was pretending.
Except for me. I was terrified that at some point they were going to notice that I wasn't chanting digits and they were going to ask me to prove some theory that didn't exist and pants me when I stood up and tried.
But then I went and got super high later with some graphic design chick and I forgot all about that until now, about a decade later.
That reminds me of a story a friend of mine told me about.
His middle school had this "Recite pi for pie!" competition. The idea being, whoever could recite the most digits would earn a pie. He wanted the pie, so he got to work and memorized 200 digits.
The thing is, he didn't know how many digits other people had memorized.
The second place competitor had memorized pi to 10 digits.
"How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics."
Boom. Pi to 15 places.
And Mike Keith did it to 740 digits as follows.
Poe, E.
Near a Raven
Midnights so dreary, tired and weary.
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap - the weirdest tap!
An ominous vibrating sound disturbing my chamber's antedoor.
"This", I whispered quietly, "I ignore".
Perfectly, the intellect remembers: the ghostly fires, a glittering ember.
Inflamed by lightning's outbursts, windows cast penumbras upon this floor.
Sorrowful, as one mistreated, unhappy thoughts I heeded:
That inimitable lesson in elegance - Lenore -
Is delighting, exciting...nevermore.
Ominously, curtains parted (my serenity outsmarted),
And fear overcame my being - the fear of "forevermore".
Fearful foreboding abided, selfish sentiment confided,
As I said, "Methinks mysterious traveler knocks afore.
A man is visiting, of age threescore."
Taking little time, briskly addressing something: "Sir," (robustly)
"Tell what source originates clamorous noise afore?
Disturbing sleep unkindly, is it you a-tapping, so slyly?
Why, devil incarnate!--" Here completely unveiled I my antedoor--
Just darkness, I ascertained - nothing more.
While surrounded by darkness then, I persevered to clearly comprehend.
I perceived the weirdest dream...of everlasting "nevermores".
Quite, quite, quick nocturnal doubts fled - such relief! - as my intellect said,
(Desiring, imagining still) that perchance the apparition was uttering a whispered "Lenore".
This only, as evermore.
Silently, I reinforced, remaining anxious, quite scared, afraid,
While intrusive tap did then come thrice - O, so stronger than sounded afore.
"Surely" (said silently) "it was the banging, clanging window lattice."
Glancing out, I quaked, upset by horrors hereinbefore,
Perceiving: a "nevermore".
Completely disturbed, I said, "Utter, please, what prevails ahead.
Repose, relief, cessation, or but more dreary 'nevermores'?"
The bird intruded thence - O, irritation ever since! -
Then sat on Pallas' pallid bust, watching me (I sat not, therefore),
And stated "nevermores".
Bemused by raven's dissonance, my soul exclaimed, "I seek intelligence;
Explain thy purpose, or soon cease intoning forlorn 'nevermores'!"
"Nevermores", winged corvus proclaimed - thusly was a raven named?
Actually maintain a surname, upon Pluvious seashore?
I heard an oppressive "nevermore".
My sentiments extremely pained, to perceive an utterance so plain,
Most interested, mystified, a meaning I hoped for.
"Surely," said the raven's watcher, "separate discourse is wiser.
Therefore, liberation I'll obtain, retreating heretofore -
Eliminating all the 'nevermores' ".
Still, the detestable raven just remained, unmoving, on sculptured bust.
Always saying "never" (by a red chamber's door).
A poor, tender heartache maven - a sorrowful bird - a raven!
O, I wished thoroughly, forthwith, that he'd fly heretofore.
Still sitting, he recited "nevermores".
The raven's dirge induced alarm - "nevermore" quite wearisome.
I meditated: "Might its utterances summarize of a calamity before?"
O, a sadness was manifest - a sorrowful cry of unrest;
"O," I thought sincerely, "it's a melancholy great - furthermore,
Removing doubt, this explains 'nevermores' ".
Seizing just that moment to sit - closely, carefully, advancing beside it,
Sinking down, intrigued, where velvet cushion lay afore.
A creature, midnight-black, watched there - it studied my soul, unawares.
Wherefore, explanations my insight entreated for.
Silently, I pondered the "nevermores".
"Disentangle, nefarious bird! Disengage - I am disturbed!"
Intently its eye burned, raising the cry within my core.
"That delectable Lenore - whose velvet pillow this was, heretofore,
Departed thence, unsettling my consciousness therefore.
She's returning - that maiden - aye, nevermore."
Since, to me, that thought was madness, I renounced continuing sadness.
Continuing on, I soundly, adamantly forswore:
"Wretch," (addressing blackbird only) "fly swiftly - emancipate me!"
"Respite, respite, detestable raven - and discharge me, I implore!"
A ghostly answer of: "nevermore".
" 'Tis a prophet? Wraith? Strange devil? Or the ultimate evil?"
"Answer, tempter-sent creature!", I inquired, like before.
"Forlorn, though firmly undaunted, with 'nevermores' quite indoctrinated,
Is everything depressing, generating great sorrow evermore?
I am subdued!", I then swore.
In answer, the raven turned - relentless distress it spurned.
"Comfort, surcease, quiet, silence!" - pleaded I for.
"Will my (abusive raven!) sorrows persist unabated?
Nevermore Lenore respondeth?", adamantly I encored.
The appeal was ignored.
"O, satanic inferno's denizen -- go!", I said boldly, standing then.
"Take henceforth loathsome "nevermores" - O, to an ugly Plutonian shore!
Let nary one expression, O bird, remain still here, replacing mirth.
Promptly leave and retreat!", I resolutely swore.
Blackbird's riposte: "nevermore".
So he sitteth, observing always, perching ominously on these doorways.
Squatting on the stony bust so untroubled, O therefore.
Suffering stark raven's conversings, so I am condemned, subserving,
To a nightmare cursed, containing miseries galore.
Thus henceforth, I'll rise (from a darkness, a grave) -- nevermore!
-- Original: E. Poe
-- Redone by measuring circles.
Yeah, I forget the exact number, the point was more to demonstrate just how little of it we actually need to discern things to a remarkable degree of accuracy. The trillion-decimal place version or whatever they've got it up to these days is useless beyond demonstrating computing power
20 digits is a precision of 1020, which is 10 million trillion. So you're precise to a ten-million-trillionth of the universe which is presumably smaller than the size of an atom.
Take a ring of atoms that's also the size of the observable universe. Now, a ring of atoms isn't a perfect circle, but let's treat it as such and calculate the circumference. How well do we need to know pi to get the circumference to be accurate within the level of detail a ring of atoms gives us?
An atom is about 1.0 × 10-10 m in size. That means that if we assume atoms behave like marbles (they don't but let's pretend) that the distance from the center of an atom to the center of the next atom in our ring is 1.0 × 10-10 m.
The observable universe is 93 billion light years in diameter, or 8.8 × 1026 m. Let's say we actually have an exact value for it.
The circumference of a circle is pi × diameter.
If you have 37 digits of pi, that reaches past the 10-10 place. So, by the rules for significant figures, if you know pi to 37 places then the error in your circumference calculation caused by the fact that your circle is constructed using physical object and not abstract geometry is greater than the error caused by not knowing the value of pi well enough.
The funny part is if you say, "Well, what if we have it wrong? What if the observable universe is actually 930 billion light years across?" Well, in that case... you need 38 digits. Orders of magnitude are powerful.
Wait. I watched a Numberphile video at one point and the guy said 39 digits if I remember correctly. It doesn't matter much either way, 39 is still a lot lower than most people would expect, including me before watching that vid.
If I remember correctly, you only need about 20 digits of pi to calculate the diameter of the observable Universe to a precision within the diameter of a single hydrogen atom
24 is enough to shoot a bullet at a dime at the edge of the observable universe.
I thought it was 38... But anyways, how am I supposed to then calculate the circumference of the universe? I mean, I know pi up to about 40 digits (3.141592653589793238462643383279502884197169), but I don't know the observable universe's radius. I guess you could derive it from the speed of light (299792.458 km/s) and the universe's age, but then again, we don't really know what that is. It's about 13.72 billion years, with an uncertainty of, like, a few hundred million years, so that's quite a big thing to say that one could calculate the circumference of the earth with a deviation of a few femtometers, when one of the factors is still only so vaguely known...
When I was in middle school, I was in a contest with the rest of my class to memorize pi. The kid who memorized the most got to like 270 digits or something. I was second at 84.
And I thought I had too much time on my hands! pfft
Trezzie · 1 points · Posted at 05:10:42 on February 14, 2016 · (Permalink)
I know up to 3.1415926535897932384626 only because we had an extra credit question on a math test once that we got to know about ahead of time. If we could memorize pi to at least 20 decimal places we got an extra 5 points. I memorized one extra number just because it was easier for me to remember 626 than 62.
At a company bonding day we were doing trivia. One of the questions is what the first 5 decimal places of Pi are. Maths nerd here, I was born knowing that. Immediately I start writing the answer for our team.
EXCEPT the big fat bald CEO who happens to be on my team stops me, and condescendingly corrects me that no actually Pi is 22/7. And he happens to have his cutting-edge Nokia brick phone (this was a while ago) that had a calculator function.
I try to explain that 22/7 is just an approximation you give to school children but he smugly divides 22 by 7 (beep beep bup boop) and writes down his answer while a circle of sycophants at the table nod and compliment him. I try not to vomit with rage. It is still one of the most horrible moments of my life.
As Immortal Technique once said in one of his songs:
'Using numerology, to count the people I sent to Heaven
Produces more digits than 22 divided by 7'
I thought it was kind of clever.
Anyways, we used 22/7 back in school instead of Pi.
Gotta love Euler. Apparently there was a spate of cars being destroyed and fire-bombed in the early 2000s by a bunch of eco-terrorists, who spraypainted stuff like "Gas-Guzzler" on them, you know usual eco-terrorist stuff.
However, completely out of place, one the the patches of graffiti contained Euler's Identity (epi*i + 1 = 0), which the police where able to use to trace back to a student at a local university; when they questioned him, apparently he said that he considered the identity so important that he had to let people know about it, and considered the attention his attacks were getting the perfect opportunity
Another fun fact: Euler was so remarkably prodigious that they decided to stop calling theorems and equations after him due to the vast number already in existence; the theorems are now named after the second person to discover them after him
vambot5 · 23 points · Posted at 04:39:04 on February 14, 2016 · (Permalink)
If I recall correctly from undergrad, many of Euler's theorems had very vague proofs. He would posit the result, do a few calculations, and wave his hands, basically leaving the rest as an exercise for the student. He was, to my knowledge, always right, but he did not lay out full and complete proofs for all of his findings. Learning this, one of my classmates lamented "So you're saying that Euler was just a hand-waving hack?!" in class.
Alright, Euler was a time traveler who went back to claim credit for discovering a shit ton of theories of mathematics to spite his rival in his own time. Calling it now.
I believe I read that he approximated e-pi/2 to the 150th digit in his head when solving for ii
Tyg13 · 17 points · Posted at 05:30:09 on February 14, 2016 · (Permalink)
I think he saw the mathematics working at levels he couldn't fully explain, but at the same time knew to be true. It took people later to come along and lay down the in-betweens of why his arguments work.
Phapples · 18 points · Posted at 12:17:15 on February 14, 2016 · (Permalink)
That's how it works with most people though, everyone who has studied mathematics has had a situation where they know something is true but they have no idea how to prove it - you can feel in your gut this incredible certainty that it's true but you can't articulate why.
Was he going to Caltech? Years ago I read about a case just like that, except for no mention of Euler's identity. Maybe it was in some part of the story I skipped over.
II. MEANS OF THE CONSPIRACY
. . .
7. Defendant WILLIAM JENSEN COTTRELL and other known and
unknown co-conspirators would write "eiπ + 1 = 0" on an SUV
located at Duarte Mitsubishi, 1125 Central Avenue, Duarte,
California.
I would love to take a "History of Math" class. Things like logarithms, natural logs, and e are just buttons on a calculator for me (and so many other people). But I feel like delving into the where, how, why of their creations would really help put there practical uses in perspective.
How the hell did police accomplish this? Is this town so small that there was only a handful of people that could know Euler's identity? Was there only one student at the local college that was passing his math classes?
eulerup · 2 points · Posted at 14:40:00 on February 14, 2016 · (Permalink)
Wooo, a group of people who fully appreciate my username.
This tidbit is what compelled me to click on the link above it.
What is it used for, though? It's considered beautiful simply due to all the constants being packed into one equation?
xERR404x · 59 points · Posted at 00:27:54 on February 14, 2016 · (Permalink)
Interestingly enough, all this is really saying is that cos(pi)=-1 and sin(pi)=0. Euler's formula states that ei*x=cos(x)+isin(x), and Euler's identity is just that formula solved for 0 in terms of pi. Still cool, though.
su5 · 6 points · Posted at 04:16:45 on February 14, 2016 · (Permalink)
And shows that sin and cosine and eix and e-ix aren't linearly indepe
Both. And also the fact that you can stuff addition, multiplication and exponents (i.e. everything that you cover in elementary and middle school) into one equation that only uses the four basic "unit" values for each operation. That is pretty sexy.
No the solution to a differential equation way. It's a DE that should only have a unique solution but ei*x and cos(X)+isin(X) both satisfy the equation.
jofwu · 6 points · Posted at 01:58:01 on February 14, 2016 · (Permalink)
Yeah... People always throw this one out, but when I realized why it's true I stopped being impressed. Euler's identity is a cool equation. But that's all that's going on here. It's not as magical as it looks. The e and i pretty much just drop out of the equation.
[deleted] · 14 points · Posted at 04:17:07 on February 14, 2016 · (Permalink)
It's not amazing because it's supposedly some big coincidence, it's amazing because it shows that all these numbers are connected, and no matter the number system you use they can be connected in a similar way. You have 5 of the most important numbers in any system. The natural exponent, pi, the imaginary identity, the additive identity, and the multiplicative identify. The connection of them all suggests just how integral they are to mathematics.
What makes it so beautiful is that you're taking an irrational number and raising it to another irrational multiplied with an imaginary number and it equals a rational number.
That's crazy.
Just because Euler's formula describes this relation doesn't make the fact that the equation is true any less amazing. At least in my opinion.
The short-version takeaway from Euler's formula is that complex arithmetic has a whole hell of a lot to do with circles. In that context, the appearance of pi is not surprising. It's the geometry and calculus of complex numbers which give beauty to the formulas.
The appearance of e may seem surprising, but its importance can be realized without mention of complex analysis.
jofwu · 1 points · Posted at 12:43:40 on February 14, 2016 · (Permalink)
Everybody else brings up some points, but I'd like to tell you that the equation is used extensively to figure out the energy levels of particles "in a box"; a widely taught subject in most physical chemistry classes. This equation in particular helps understand electrons transition from one energy level to the next and how to calculate them.
jofwu · 2 points · Posted at 12:42:56 on February 14, 2016 · (Permalink)
Like I said, the equation is really cool. But the e/pi/i trick just isn't as magical as it appears, to me.
This is my favourite. It involves taking a real transcendental number, raising it to the power of a complex trascendental number and getting an integer.
And your weird transcendental numbers showed up in completely different contexts "before" (in your mathematical career). Deal with geometry and circles and all that? Use pi. Derivatives, differential equations, and so on? e is what you want. Nowhere do you use both, until you get to complex math/analysis and you pretty much have to use them both.
[deleted] · 4 points · Posted at 02:11:09 on February 14, 2016 · (Permalink)
Nowhere do you use both...
That's not entirely true. e and pi can show up at the same time if you're working with trigonometric differentials.
Especially Laplace sensibly gets introduced after complex numbers (the Laplace transform is a complex-valued function, after all), and even Fourier makes a lot more sense in the complex world.
meodd8 · 1 points · Posted at 15:06:55 on February 14, 2016 · (Permalink)
An identity operation is one where when you perform it, the result is the same thing you performed the operation on, i.e. multiplying a number by 1 does nothing, and adding 0 does nothing.
This seems pretty unimportant, but it's very useful when manipulating equations, because if you multiply something by (x+1)/(x+1), it might help solve your problem, and you're not changing the equation because it's just multiplying by 1. The same is true for 0, because you can add (x+1)-(x+1) to something and all you're doing is adding 0.
That's kind of misleading because what they did in their proof rigorously goes over axiomatic foundations for mathematics, this proof is a better job of showing the complexity of the problem without being too out there.
You can easily prove 1+1=2. Deriving arithmetic over the natural numbers using Lambda Calculus or a similar logic isn't remotely difficult for a mathematician.
No it isn't. Under Russell and Whitehead's chosen axioms it took them 160 pages before they had built up enough framework to decide to include the proof of 1+1=2. That is a specific case and they did not set out to prove that specifically, near any mathematician can derive Peano addition on the naturals in a few pages.
[deleted] · 16 points · Posted at 21:14:27 on February 13, 2016 · (Permalink)
so, if i is defined as x2 = -1, and i squared and -i squared both equal -1, and sqrt(-1) is equal to i and -i, what's the difference between the two definitions?
With i2 = -1, you get 2 choices of i, each opposite to the other. You can choose either one, they correspond to a counterclockwise turn or a clockwise turn.
Using radical notation for numbers besides those in ℝ+ is problematic, since a radical implies principle root and there is no such consistent thing outside ℝ+. You could use sqrt if you're sure to define it explicitly as both of the roots, tho doing that creates ambiguity (you now have extra solutions with a "+/-"). So the standard way of doing things is to just use i as defined by one of the roots of -1 and then specifying a radical as i*sqrt(b) rather than sqrt(-b).
You can define a new "thing" called the imaginary unit, i, and i2 = -1. If you let your numbers have both real and imaginary components (4 + 3i would be such a number), and you define plus and minus and times and division sensibly, it turns out that the system doesn't break: You can still add and multiply and divide, and all the more advanced operations also transfer: You can square numbers, you can take their sine and cosine, and so on. There are even a few things that work better than before.
As an electrical engineering student, I really like Euler's identity. It's very helpful for describing signals. If you have mastered Euler's identity and a Fourier transform, dealing with electrical signals becomes much easier.
ToxDoc · 1 points · Posted at 01:31:25 on February 14, 2016 · (Permalink)
For my college departmental graduation (which included math, chemistry and physics), one of the math professors, who was tasked with "the speech" talked about the beauty of this equation for over 30 minutes before one of the chemistry professors stopped him. It was a memorable experience.
I was going to post the same thing. This fact still fascinates me. I found out about it years ago. Even picked up the book Euler's magic formula to learn more. Sadly I just don't have time to read the book.
aahdin · 1 points · Posted at 01:49:20 on February 14, 2016 · (Permalink)
Hey I posted the same thing a while after you. This thread got me curious and I started googling around for an intuitive explanation of what is actually going on with ei*x. I've gone over the proofs in diffeq but it still felt like black magic to me.
When this was originally demonstrated, Euler assumed that certain math that he knew worked for real numbers also worked for complex numbers. (It needs the complex number versions of some Calculus I.)
He played with the Taylor series expansions of sine and cosine and this just kinda happened. So beautiful that it had to be true.
I do like this one a lot, I like that it makes no sense to me
vambot5 · 1 points · Posted at 04:34:18 on February 14, 2016 · (Permalink)
I had assumed that Euler's identity would be at the top. Maybe the topic is too arcane/intimidating for the average redditor to appreciate. A bit of trivia about rational numbers is easy to wrap your head around. An identity involving the base of the natural logarithms, complex numbers, exponential functions, and the irrational number pi is admittedly more involved. I think one could explain why it is so cool without having to explain the underlying mathematics, but it is hard to avoid the "I don't already understand this, so I will downvote" tendency.
ei*tau = 1, where tau = 2*pi, or the ratio of a circle's circumference to its radius.
It's even more beautiful! Instead of describing going half-way around the unit circle in the complex plane, it describes going one complete turn around.
the most important mathematical constants into one equation.
I would put it stronger than that, it relates the five most important mathematical constants into an extraordinarily simple (although non-obvious) equation.
I got a bunch of comments that kept telling me how I don't know how many constants there are or The most important? Really?, so I just changed it to that.
arakys · 1 points · Posted at 06:09:30 on February 14, 2016 · (Permalink)
This is the post that I was looking for, thank you!
Oh my. euler's identity is integral to electrical engineering. I know that identity (and its uses) like my own dick.
You can use Euler's identity to show quite a few trigonometric identities without even looking at a triangle. I stopped trying to remember those identities when i figured out they could be quickly and easily derived from this equation. Not to mention the applicability to elecromagnetic waves and theory, and field theory in general. Who knew an exponential would make waves and shit? it's awesome
As a BSc in mathematics, I find the frequency that this comes up annoying. That is Euler's Identity
It is a fact that
( * ) et*(pii) = cos(t(pi))+isin(t(pi)).
Set t = 1 and you get
( ** ) epi*i = cos(pi) = -1.
(*) is the more interesting and general statement, but it's also so ubiquitous and pragmatic that it is rendered boring by overexposure.
Euler's identity is just a specific case of this otherwise mundane fact about complex circles. There is much radder and novel mathematics stuff around.
etau*i = 1 is even more beautiful imo as it actually behaves like a identity. When taking the product of two complex numbers you multiply their absolute value and adding their angles. Adding tau wraps around making a full revolution. Hence the angle remains unchanged: An identity.
Cicote · 1 points · Posted at 12:20:37 on February 14, 2016 · (Permalink)
etau*i = 1, even smoother gotta love tau
0theus · 1 points · Posted at 12:43:28 on February 14, 2016 · (Permalink)
It ought to be written eiπ = -1, in my opinion. The 0 in there is completely superfluous - it's just moving all the terms to one side.
Or write e2iπ = 1, since 2π is arguably more fundamental than π in the context of angles.
Or, just write the whole thing: eiθ = cosθ + isinθ, showing how exponential and trigonometric functions are fundamentally related - a far more important and interesting result that encapsulates Euler's identity by setting θ = π.
One of the cooler thing about this is that it can be shown in a direct manner through taylor expansions. Substitute 'ix' for 'x' in the taylor series for ex and it just falls out.
Zero is one of the constants and all of these numbers are hugely important in so many advancements. All of mathematics is based off of the concepts of 1 and 0 so those go without saying, a lot of electrical engineering deals with i, compound interest is based off of e and π has so many applications that I'm not even going to name them.
So I'm not sure what you're getting at, Euler's identity is just an equation that takes some of the most important mathematical concepts and relates them. Read the Wikipedia section on its Mathematical beauty.
[deleted] · 1 points · Posted at 20:40:50 on February 13, 2016 · (Permalink)*
The creators of Futurama actually had to create a new mathematical formula to solve the brain swapping issue they had.
It's called The Futurama Theorem
The theorem proves that, regardless of how many mind switches between two bodies have been made, they can still all be restored to their original bodies using only two extra people, provided these two people have not had any mind switches prior (assuming two people cannot switch minds back with each other after their original switch).
ynnekf76 · 507 points · Posted at 22:10:44 on February 13, 2016 · (Permalink)
In this case that it is brain switches doesn't matter. It could be a variety of tip where you can't tag someone who tagged you. Basically how many extra nodes are needed in a map with only one directional edges
dixego · 601 points · Posted at 23:53:48 on February 13, 2016 · (Permalink)
So you're saying graph theory has applications? Holy shit.
...
...
...
/s in case it wasn't obvious.
[deleted] · 43 points · Posted at 02:07:04 on February 14, 2016 · (Permalink)
As a serious reply to this, graph theory is pretty fucking awesome. It can be used for some pretty creative solutions to problems you might run into.
I suppose my most recent example of this is actually one I used for leisure in a game I've been playing lately, FFXIII-2. In this game are several puzzles, of which one type is based on a clock. There is an arbitrary number of nodes surrounding a center point in a circle (think of a clock), each one with a number associated with it and displayed inside of the node. You may choose any node as your starting point. The number for any particular node represents how many nodes away from the current node you may travel for your next selection (e.g. if you choose a node with a 2, you may choose the next node that is either 2 nodes clockwise from your current position or 2 nodes counter-clockwise). The object of the puzzle is to go from node to node until you've traveled each one. This can be represented as a directed graph, and you can make logical deductions to decide the ordering of certain nodes (e.g. if a node has an in-degree of 0, then it MUST be the starting node; if it has an out-degree of 0, then it MUST be the ending node; otherwise, if a node has an in-degree of 1, then it probably has to be preceded by the node pointing to it (though it's possible that the node under consideration is actually a starting point)). The graph can then be continually reduced to a smaller and smaller subset of nodes representing these orderings (e.g. you might start with A, B, C, D, E, F and then end up with AB, CDE, F) allowing you to reasonably decide an appropriate solution by checking the remaining possibilities. It can be a time-consuming process, sure, but when you have to choose between random selection (likely to fail, and the nodes may change) or brute-forcing your solution (much more time-consuming than the graphing method), it definitely proves to be the preferred alternative!
My personal "graph theory aha" was in Dragon Age: Inquisition. There's a series of puzzles (literally dozens of them) where you have to do a traveling salesmen between a series of nodes, with pre-defined edges to use. The game is that you can only use each edge once, but you can pick which node to start with. (i.e. Konigsburg Bridges Problem, but for DA players: astrariums).
Since we can assume that there is at least one solution, then WLOG we can start at the node with the lowest (or tied-for-lowest) odd degree and solve the problem. I think the first 2 were hard until I recognized it and then the entire rest of the game I breezed through them.
[deleted] · 9 points · Posted at 02:34:17 on February 14, 2016 · (Permalink)
Ha! That's fantastic! It's always incredibly satisfying when you can see these mathematical elements and exploit them appropriately.
mxzf · 8 points · Posted at 04:02:37 on February 14, 2016 · (Permalink)
I've also used graph theory for Ticket to Ride, the board game. I input all of the nodes and links into a graph and then calculated the most efficient route to complete each ticket in the game. I was able to determine which connections I should prioritize claiming for myself due to the large number of routes which travel through that linkage in an optimal path.
Of course, the strategy on any given game is much more dependent on which tickets you actually get and which colors you draw, but knowing which links are used very frequently can be useful for overall strategy.
[deleted] · 3 points · Posted at 04:51:55 on February 14, 2016 · (Permalink)
I've never actually heard of that game and had to perform a quick search to figure out what it was so I could understand your strategy, but that's an interesting way of producing average-case decisions for the game!
mxzf · 4 points · Posted at 05:04:43 on February 14, 2016 · (Permalink)
Yep, that's basically what I was doing. It's impossible to 'solve' the game ahead of time, since you get random routes which may or may not use the most common links, but it does give you an idea of which links are more likely to be needed by other players (and therefore ones you should secure early if you need them yourself) and which ones are much less likely to be in demand. It was definitely more of a "this seems fun" thing than an actual important project, but it was still fun to do and semi useful.
[deleted] · 2 points · Posted at 05:25:59 on February 14, 2016 · (Permalink)
Oh, certainly. Most of my problem-solving exercises are done for leisure. It's just fun discovering solutions to new problems or discovering new solutions to old problems you've encountered before.
[deleted] · 6 points · Posted at 05:13:47 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 2 points · Posted at 05:17:49 on February 14, 2016 · (Permalink)
If you're serious, that sounds like a fascinating read!
[deleted] · 3 points · Posted at 05:36:01 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 05:52:32 on February 14, 2016 · (Permalink)
Oh, definitely. I'm finishing off my last year of a CS major myself, so I've learned all too well the importance of graph theory in networks. For some reason I failed to associate the concept with neural networks, however, and the thought of such an application is interesting.
I'd very much like to be kept up to date on the results, as even though many of the low-level concepts would go far over my head, the high-level details would be of great interest.
[deleted] · 2 points · Posted at 06:28:18 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 0 points · Posted at 07:50:10 on February 14, 2016 · (Permalink)
It appears that my university does indeed allow access. Thanks for the recommended reading! It's quite dense, so it's a bit much to read this late at night, but I will definitely be looking at this. Thank you (:
This still sounds like it might be NP-hard, regardless of your small optimizations
[deleted] · 0 points · Posted at 08:47:22 on February 14, 2016 · (Permalink)
I don't believe I've ever encountered a puzzle with more than 13 nodes, so the time complexity of this kind of problem isn't of major interest. For an arbitrary number of nodes approaching larger numbers, however, this would certainly be cumbersome. I believe we would still be bounded by n*2n-1 possible paths to check (n possible starting nodes, and each node can only point to a maximum of two other nodes), though of course I'm open to being corrected if I'm mistaken. I imagine the amortized complexity will also be much lower than this bound as well, as many paths will have one or both branches of a node in the path pointing toward already-visited nodes (thus ending a path prematurely).
I'm not really the person to ask, though, as I can only speculate (:
[deleted] · 1 points · Posted at 07:54:49 on February 14, 2016 · (Permalink)
I'm very much aware that he was being sarcastic. I was just expanding upon the point by providing an example scenario that many reddit users are likely to encounter (i.e. a videogame). Graph theory is an enjoyable subject, so I wanted to point out a practical application in a non-professional setting.
dixego · 3 points · Posted at 02:11:50 on February 14, 2016 · (Permalink)
The /s is to note that I know graph theory has multiple very useful applications (I'm currently studying Computer Science). I didn't want people to think I was serious about saying graph theory was useless.
As soon as I saw this, I wanted to say "found the first-year grad student"
kblaney · 3 points · Posted at 01:52:18 on February 14, 2016 · (Permalink)
Having never read the actual paper only seen the episode, I thought it was a group theory problem (specifically the problem of the existence of representations of inverses in a subgroup of permutation groups). I didn't know it was actually a graph theory paper.
I haven't read it either but it is the sort of proof that I could use in graph theory, whether they proved it with it doesn't matter as much for applications
That's why they call it a mathematical proof. It's not that the actually experiment is feasible to perform, it's that the hypothetical experiment can be stated in terms that are mathematically rigorous.
This theorem is easily applied to the real world. Instead of switching brains, imagine x number of people each have a pencil. After any number of random swaps in which no two people swap with each other twice, all pencils can be returned to their owners if just two more people (and pencils) are added
Something as simple as "two people can't switch minds with each other more than once" is purely rudimentary logic. Just because it hasn't actually been done doesn't mean that it can't be proven.
So when your elementary school teacher asked you, "if Sally gives you 5 apples and you already have 3, how many apples do you have?", was your response, "how can I solve that, no one named Sally has ever given me 5 apples before?"
Wait, why are the two helpers even necessary? Can't you just take the group of people with switched minds, switch one mind into the correct body, remove the corrected person from the equation, and repeat until everyone is corrected? I must be missing something.
Ken Keeler (the writer of the episode and the theorem) has a PhD in mathematics. There a lot of little math Easter eggs hidden in the Simpsons and Futurama.
cvkxhz · 253 points · Posted at 05:18:27 on February 14, 2016 · (Permalink)
Bender: "Hey, brobot, what's your serial number?"
Flexo: "3370381"
Bender: "No way! Mine's 2716057!"
(Both laugh)
Fry: "heheheheh...I don't get it?"
Bender (annoyed): "We're both expressible as the sum of two cubes!"
Which is a great book that I would recommend to anyone- I read it and it made me a lot more excited about math (a couple years of college math had sucked the life out of me).
hayberry · 12 points · Posted at 22:26:25 on February 13, 2016 · (Permalink)
I love finding those! First one I ever noticed was P = NP in the background somewhere. Think it was a book.
I thought it was commonly assumed he probably made some calculation mistake as we do have solved it but we have no "simple, elegant solution" unless you overlook certain things. I'll have to google it.
I tend to doubt it. Mathematics isn't alchemy or some sort of arcane art and Fermat's last theorem is something many mathematicians have obsessed over. I find it hard to believe that so many people looking for short and simple answers have found all of the erroneous ones but not an equally short but correct one
Something like xxxxxxxx212 + yyyyyyyy112 = zzzzzzzz212 .
I looked at it for one second, somebody asked, "Is that Fermat equation real?" and I was like, "The hell? How dazed are you? That's Even + Odd = Even for you."
30 seconds pass, he goes, "Oh."
In his defense, he was way more drunk at that time.
I know what XOR is. I thought it had something to do with P = NP in context, hence why I asked about XOR SAT. Changing and OR to XOR doesn't really seem that clever if that's all there is to it...
And yet, in the episode where Bender uses the Banach-Tarski printer, the professor says the series modeling Bender's replication is divergent (and therefore he would use up all the matter on earth or something), but the nominator cancels with the exact same expression in the denominator, and thus the remaining series would actually converge.Edit: As /u/wadss said below, it still diverges, I brain-farted and switched terms. Though, still, why would the Professor not show the series in simplest form? But most likely anyone who hasn't taken Differential Calculus, or at the very least Pre-Calculus, wouldn't notice because they probably don't know enough about series.
It is possible whoever did other episodes was either not very well-versed or did it on purpose to make the Professor look not-so-smart. There are other instances in the show and movies where either stuff is completely wrong, makes no sense, or what is on the board has nothing to do with what they are talking about. Edit: There are different instances of things not really making sense, such as in The Beast with a Billion Backs, The Professor and Wernstrom claim to prove a certain conjecture, but the writing on the board has nothing to do with the conjecture.
Still a great show, I love re-watching it (the movies not so much), there is always something new I notice.
wadss · 1 points · Posted at 01:50:35 on February 14, 2016 · (Permalink)
[deleted] · -9 points · Posted at 23:30:14 on February 13, 2016 · (Permalink)
So they didn't do it.
[deleted] · 11 points · Posted at 02:02:25 on February 14, 2016 · (Permalink)
It means they did it, but they never formally proved that this would actually work. They just showed that it worked for the particular numbers that they were interested in and assumed it was a general rule. Futurama proved that it actually does work as a general rule.
They didn't assume it worked generally. The characters in Stargate are typically interested in the easiest solutions to their current life-threatening puzzle, and don't care about generalities.
They didn't build the proof out for people to see, but the actual solution was stated... 2 different things, they were only talking about the solution.
imbogey · 2 points · Posted at 06:08:41 on February 14, 2016 · (Permalink)
I must be missing something.. In sg the extra bodies are already switched bodies so shoudn't this be a different case?
I actually paused that episode towards the beginning when the professor was trying to figure it out. Spent like half an hour scribbling like a mad man trying to figure it out.
Sw0rDz · 2 points · Posted at 07:56:49 on February 14, 2016 · (Permalink)
That was because Futurama had a writer with a PH.D in applied math. The other writers were engineers/physics grads. If you watch that episode carefully. The proof for the theorem is on the green chalkboard.
wardsac · 1 points · Posted at 01:23:13 on February 14, 2016 · (Permalink)
Because 1) This is a mathematical fact.
2)I found this cool
wspaniel · 86 points · Posted at 23:52:50 on February 13, 2016 · (Permalink)
1 + 1/2 + 1/3 + 1/4 + ... diverges. That's standard. But throw out all numbers with a 9 in the denominator, and the series converges.
It gets stranger. You can remove any string of numbers and it still works. For example, you could remove all numbers containing 164812458737002 in the denominator, and that series converges.
It gets even stranger. The series of numbers containing 164812458737002 diverges.
[deleted] · 9 points · Posted at 12:41:09 on February 14, 2016 · (Permalink)
(If there's a number that's not a power of two in the denominator, I'll decrease it until it is. This will increase some parts of the sum, but never decrease any.)
During my next trick, I'll group terms with equal denominators and then cancel the powers of two:
That's actually fascinating. Is there a formal proof of that somewhere?
wspaniel · 12 points · Posted at 08:44:36 on February 14, 2016 · (Permalink)
I remember seeing it here a long time ago. IIRC correctly, the intuition is that almost all elements of the series contain a 9 (once you get to really large denominators), so you basically stop adding stuff at the end. (And I think you can start grouping things together formally and show that each of the elements is smaller than a geometric series that converges.)
The same is true for any string of numbers---once the denominator gets large, basically all of them contain any given string. But since any of them contain the string, they are basically like the harmonic series and diverge.
Basically, 9 of the first 10 numbers do not contain the number 9, 92 of the first 100, and 9n of the first 10n numbers, and a lower percentage after that.
Effectively, the culling of the 9-numbers makes the sequence geometric, and this proof applies from then on.
Certainly not "almost all" elements contain a 9. In fact, exactly 1/9 of the terms contain a 9. For any n-digit string, exactly 1/(10n-1) of the terms contain that string.
But the idea isn't that you are throwing out all the terms, it's that you are throwing out enough terms, since our series "almost" converges.
Edit: I was really high when I wrote this and I overlooked a lot of terms. The density of digits with a 9 is 1, not 1/9, which changes things pretty severely.
That doesn't seem right. It seems to be more than 1/(10n -1).
Take the one digit numbers (0-9). There is one number that contains a 9, and that is the number 9. So that is 1/10 or 1/9 (depending on whether you start counting at 0 [correct] or 1 [heathens]).
For two digit numbers, it is the same for each group of 10 through the 80s (9, 19, 29, 39, 49, 59, 69, 79, 89) = 9 numbers, plus all the 90s (90-99=10 numbers). So there are (9+10)/100 = 19/100 two digit numbers that contain a 9.
For three digit numbers, this repeats for the first 900 numbers (19 in 0-99, 19 in 100-199, ... , 19 in 800-899), plus all the 900s. So there are (9*19 + 100)/1000 = (171 + 100)/1000 = 271/1000.
Similarly, there are 3439/10,000 four digit numbers and 40951/100,000 five digit numbers that contain a 9.
What almightysappling has calculated is probability that given a series of terms that are non zero the probability that a term will contain a given sequence is 1/(10n -1), where n is the length of the term. But the question was asking what is the probability the a series of length n contains a nine, as n tends to infinity.
So yes, if you take the harmonic series and throw away all the terms with a 9 in the denominator, you are throwing away almost all (in the technical sense) of the terms.
Well if you throw out all numbers with a 9 in the denominator, since we are talking about an INFINITE series, eventually, the probability that a term has a 9 in the denominator is ~100%. As it's like 609 numbers long, or 4000 numbers long, or 15 billion numbers long. So you're basically removing almost every single term, as the terms have longer and longer strings of numbers.
Thus why you can remove any numbers like the ones you listed. Eventually, the probability of the term containing THAT is still ~100%
It's a palindrome because it's a number determined to be. It's like saying "The letter L, then thirteen o, then three m, then thirteen o, then a L... Oh my god, it's a palindrome!"
The neatest thing is that it's a prime number.
666 in Roman numbers is DCLXVI, i.e. one of each, except M (which was uncommon back then). It was what they wrote for a fairly large but unknown number, like we sometimes use 123.
OTOH, their algebra was easy. X was 10 all the time. scnr
Belphegor originated as the Assyrian Baal-Peor, the Moabitish god to whom the Israelites became attached in Shittim (Numbers 25:3), which was associated with licentiousness and orgies. It was worshipped in the form of a phallus.
necessity is the mother of invention but Belphegor provides the seed
Seal3824 · 15 points · Posted at 22:36:41 on February 13, 2016 · (Permalink)
Yes, but when most people just heard the words "1000 times bigger" they can't really fully grasp the size of it. You can have a rough idea, but usually people need to see the difference to actually comprehend the size difference.
I don't get why people get so impressed over this. I mean, a billion is a thousand times one million, so 11500 days, which is quite clearly some 30 or so years. Maybe the amazement is product of the words being similar.
… I'm afraid to check Bing for ‘Polish hand magic’ because the results probably involve a woman named Dominika doing something I don't want in my browser history.
[deleted] · -1 points · Posted at 18:26:08 on February 14, 2016 · (Permalink)*
[deleted]
bjb406 · 9 points · Posted at 06:04:41 on February 14, 2016 · (Permalink)
I had never heard of SMBC before. You bastard. How will I ever escape my computer screen now?
OPreco · 3 points · Posted at 07:11:35 on February 14, 2016 · (Permalink)
Along the same lines, you can use your hands to quickly calculate 9*x for 1<x<9.
Hold both hands in front of you. Imagine your fingers are numbered from 1-10 going left to right. I.e. If you are looking at the backs of your hands, your left pinkie is "1" and your right pinkie is "10".
Fold down the finger that corresponds to the multiple of 9 you are trying to calculate. Let's say 9*6, so your right thumb. The fingers to the left of this one represent the tens place(5), the fingers to the right represent the ones place (4). Together, they are your product 54.
If you haven't already memorized 18,27,36,45,54,63,72, and 81, now you don't have to. Notice the pattern in the numbers ;)
A similar trick for the nine times table - say you wanted to do 4 * 9.
Put your 4th finger down. The number of fingers to the left of that finger is the number of 10s (3 times 10, count them) and the number of fingers on the right is the number of ones (6*1).
Add these together to get your number. It only works up to 10*9.
Irru · 1 points · Posted at 11:37:07 on February 14, 2016 · (Permalink)*
Wait, does this work for 6*6 too?
One finger on each hands gives a result in the 20s?
phle · 3 points · Posted at 14:50:08 on February 14, 2016 · (Permalink)
Wait, does this work for 6×6 too?
One finger on each hands gives a result in the 20s?
Ok, let's do this by just copy-paste-ing the instructions, but change the numbers to our task:
Say a palm is worth five, and each finger is worth one.
Represent each number with a hand in our case: one will have one finger up; the other will have one finger up
Count all the fingers that are up on each hand and add them.
This is your tens place in our case: (1+1)* 10 = 20.
Count all the fingers that are down on each hand and multiply them.
This is your ones place in our case: 4 × 4 = 16
Add them together and get the value of the expression. in our case: 20 + 16 = 36
I think the new zealands have pissed of the elementals. Wind in Wellington, Earthquakes in Christchurch, weird water in cape reinga, and lava from them volcanoes. I knew Maui shouldnt have taken all that fire
[deleted] · 3 points · Posted at 03:09:43 on February 14, 2016 · (Permalink)
I'm not sure the Hairy Ball theorem applies to an atmosphere -- couldn't the air travel up and down to produce wind as well? In fact, I'm pretty sure that's what would happen in the "no wind" places, since otherwise the air would just... build up infinitely, I think. I dunno.
Boukish · 1 points · Posted at 06:10:06 on February 14, 2016 · (Permalink)
But air moving up/down isn't "wind" in the conventional meaning of the term (perceptible current); yes it'd translate to an area of higher/lower pressure to be sure, but you'd stand there and wouldn't feel any wind.
[deleted] · 1 points · Posted at 19:54:30 on February 14, 2016 · (Permalink)
You can feel wind if it's traveling up and down. To prove this, lie down when it's gusty.
Admittedly, I don't know if the up-and-down winds would be strong enough to feel; I don't know enough about meteorology.
Yes the theorem is about the surface of a sphere, a 2d object. Our atmosphere is not the surface of a sphere, it is a 3d object. So wind can travel up and down as well as tangentially to the surface and so the theorem does not apply.
Eh, it says that there are is no, non vanishing, tangent vector field on a sphere. It's not clear to me that the space in which wind occurs is topologically equivalent to a sphere.
This would however be true for wind considered at a specific elevation, but not wind overall. This is because the theorem is about a 2 dimensional object, the surface of a (topological) sphere. But our atmosphere, is a 3 dimensional object.
A number divided by itself-repeated gives .x0x9 repeated, with x being the number of times the number after it appears based on how many digits the numerator is. Works for any whole number.
Yes, it would be. I can't give you a strict proof of this, but it makes sense if you consider that a number repeated is 100.....01 times itself (number of zeros is 1 less than the number of digits in the original number)
[deleted] · 1 points · Posted at 06:14:56 on February 14, 2016 · (Permalink)
WITCHCRAFT.
djabor · 1 points · Posted at 12:46:50 on February 14, 2016 · (Permalink)
If you only buy two different styles of socks (for example, white and black or short and long), you will always have at least two that match if you pull three socks out of your sock drawer without looking.
That's the pigeon hole principle. In general, if you have n styles of socks, then you need to pull out n + 1 socks to be guaranteed a matching pair.
(The pigeon hole principle is essentially that if you try to put more pigeons into pigeon holes than you have holes, then at least one hole will have 2 pigeons.)
gozman · 1 points · Posted at 03:27:48 on February 17, 2016 · (Permalink)
What if I had 5 of each pair of socks, couldn't I pull put 3 individual socks that are the exact same?
You could even have infinite of each type of socks, and the pigeon hole principle applies. If you have n varieties of socks, then you only need to pull out n+1 socks to be guaranteed at least one match.
The proof for why this is true is quite intuitive: imagine that this wasn't the case. This would mean that you have n+1 distinct socks. But that's impossible, since there are only n types of socks. Thus we have a contradiction, so you must have at least one matching pair.
Note that this doesn't say that you'll have exactly one match. You could have up to (n+1)/2 matches. Or you could have more than two of one kind of sock. But you are guaranteed to get at least one matching pair.
gozman · 1 points · Posted at 13:53:28 on February 17, 2016 · (Permalink)
Ahhh, sorry. I was really focussed on taking specifically three socks out at a time.
I get it now, cheers
q3w3e3 · 1 points · Posted at 15:25:19 on February 23, 2016 · (Permalink)
Couldnt I pull out three of the same type in a row?
Sometimes the color of your socks can bring together the outfit.
bob85m · 3 points · Posted at 02:51:41 on February 18, 2016 · (Permalink)
That's some solid math right there!
[deleted] · 3 points · Posted at 06:43:37 on February 14, 2016 · (Permalink)
Applied Ramsey theory. Sexy.
[deleted] · 304 points · Posted at 20:39:42 on February 13, 2016 · (Permalink)
The natural logarithm of a number equals the integral of 1/x from one to that number (if I recall correctly). I think it's weird that something as tricky as the logarithm comes from such a simple expression.
LabKitty · 92 points · Posted at 23:17:50 on February 13, 2016 · (Permalink)
It's wild that logarithms were around before calculus was invented.
Then, one day someone asks what the antiderivative of 1/x is. You can't use the power rule (because it would divide by zero) so we decide to make up a new function -- call it blerg(x).
You start checking out the properties of blerg(x) and you realize you rediscovered the log function!
iirc limits help this out a lot but I might not be
NoGardE · 5 points · Posted at 03:04:03 on February 14, 2016 · (Permalink)
Iirc there's a decently easy* way to calculate it from the limit.
*For Euler or Gauss.
[deleted] · 2 points · Posted at 07:42:52 on February 14, 2016 · (Permalink)
There's also a dead easy way to calculate it for anyone.
Derivatives are isomorphisms. That is, their inverse transform is defined. Hence, if the derivative of 1/x exists, so does its integral.
Consider:
y = ex ; dy/dx = ex = y
Hence dy/dx = y
(1/y)dy = (1)dx
Integral of (1/y) = x
y = ex thus x = ln(y)
So the integral of (1/y) is ln(y).
NoGardE · 3 points · Posted at 08:21:02 on February 14, 2016 · (Permalink)
Could you mention that it's integral of (1/y)dx = x? Got a bit confused on that bit,made me think you were integrating on different variables on different sides.
[deleted] · 3 points · Posted at 08:48:16 on February 14, 2016 · (Permalink)
I was integrating both sides according to different variables. According to y on the left hand side, and x on the right hand side to be more precise.
See, if y = f(x) and dy/dx = f'(x), then:
dy = f'(x)dx
Integrating both sides with respect to y and x, we get:
y = f(x)
That's where the dx and dy come from when you integrate. Here, the integral of 1/y with respect to y is equal to the integral of 1 with respect to x, which is equal to x. Going back to y = ex , it becomes clear that ln(y) = x, hence the integral of (1/y) with respect to y is equal to ln(y).
NoGardE · 1 points · Posted at 09:08:47 on February 14, 2016 · (Permalink)
But you can't integrate dy on the left and dx on the right. Pulling away from the limit, that's multiplying by (y-y0) on the left, and by (x-x0) on the right.
I'm pretty sure both sides is integrated dx. Since y is a function of x, it's valid and correct math.
[deleted] · 1 points · Posted at 09:22:53 on February 14, 2016 · (Permalink)
Yes. Yes I can. No offence but I'm math major and I aced my Ordinary Differential Equations class, as well as Advanced Calculus I and II.
There's no pulling away from the limit whatsoever. Integrating y dy and f(x) dx is the exact same thing given you change your range of integration accordingly. Here, there's no range as we are dealing with general forms. We do not seek to find a scalar as an answer.
Here:
y = x
dy/dx = 1
dy = dx
y = x
I integrated with respect to y on the left side, and with respect to x on the right side.
qaisjp · 1 points · Posted at 10:46:16 on February 14, 2016 · (Permalink)
I do A2 further maths and now you have destroyed everything I've learnt in pure maths in the last two years
Good bye.
[deleted] · 1 points · Posted at 15:39:25 on February 14, 2016 · (Permalink)
Allow me to destroy it a little more just to show you that I am not trolling.
Exponential growth or decay is defined as:
dx/dt = kx
(1/x)dx = k dt
ln(x) = kt + u ; u is a constant
x = ekt+u = ekt eu = cekt ; c is a constant
x(t) = cekt is precisely the function for exponential growth and decay, with c = x(0). You can look it up on wikipedia.
To be fair, I shouldn't have renderend anything you've learn so far invalid. You just haven't learn about what I'm showing you yet.
qaisjp · 1 points · Posted at 16:09:47 on February 14, 2016 · (Permalink)
that's just differential equations?
maybe I made that comment too early in the morning, i understand your algebra now
[deleted] · 1 points · Posted at 16:28:34 on February 14, 2016 · (Permalink)
Yes, it's very basic differential equations, which can be used to find the antiderivative of 1/y
qaisjp · 1 points · Posted at 16:30:49 on February 14, 2016 · (Permalink)
But dy/dx is not a fraction, "multiplying by dx" is not a valid justification. You can certainly integrate dy/dx with respect to x, in fact I'm not sure how you could think that you could integrate the right hand side of an equation (f'(x)) with respect to x but not the letft hand side (dy/dx)? Both sides are the same...
I'm well aware of the method. "Multiply by dx" is not a justification, as when defining dy/dx we never define dy or dx separately. Of course you can think of dx as "a small change in x" but I think you would struggle to define it rigorously.
Have you taken any analysis?
[deleted] · 1 points · Posted at 18:49:28 on February 15, 2016 · (Permalink)*
First of all, we'll clarify right off the bat that yes, dy/dx is a fraction, and yes, I can multiply by dx.
First screenshot: implicit differentiation when f(x,y) = c. Label z = c, hence dz = 0. The partial derivative of z(x,y) is dz = F(x)dx + F(y)dy = 0. Dividing both sides by dx and isolating dy/dx gives the formula dy/dx = -F(x)/F(y).
Second screenshot: two integrals with respect to different variables being equal. The original equation was (1+x)dy - ydx = 0 which is the exact same thing as dy/dx = y/(1+x). Had this been dy/dx = 1/(1+x), then dy = 1/(1+x) dx and we'd have integrated with respect to different variable, hence why dy = f(x) dx is perfectly valid.
So all in all, I don't think you are well aware of the method. I don't think you've taken any ODE class either.
dx is perfectly well defined. Integrating with respect to different variables means you're doing the Riemman sum with h times delta(x) or h' times delta y, with h being the height under the curve. dx is the notation we give to delta(x) once we've put lim n-> infinity where n is the number of h times delta(x) aka number of intervals where we approximate the area under the curve. Doing this along the x axis or y axis yields the exact same result.
I am taking analysis right now, but I highly doubt you are. There's no way someone who is taking analysis would have no knowledge of advanced calculus. No knowledge of ODEs, that's fair enough.
So what are your academic credentials? I find it extremely odd that someone would argue that two integrals cannot be equal if they aren't integrated with respect to the same variable... Given he's knowledgeable math-wise.
Edit: let me give you a very basic example.
y = 3x ; 0<x<3 Hence x = y/3 ; 0<y<9
Then int[0~ 3] 3x dx = [0~ 9] y/3 dy =13.5
Which enlighten the fact that the Riemman sum, aka integral, taken along one axis or the other is the same.
If we do not care about intervals and do not seek to obtain a scalar as an answer, then:
int 3x dx = (3/2)x2 = (3/2)(y/3)2 = (1/6)y2
int (y/3) dy = (1/6)y2 = int 3x dx
Tada. So dy/dx = 3 ; dy = 3dx ; int dy = int 3dx ; y = 3x is 100% valid.
Edit #2: Here's a clear example of the procedure I was following for dy/dx = g(x). http://imgur.com/wtsSFtJ
They integrate dy, yielding y, and equate y = int g(x) dx. Clearly, they do not integrate dy/dx, as they multiply both sides by dx first.
Moreover, if T: Rn -> Rn+1 is defined by T(v) = int v dv, a linear transformation which inverse is defined, then:
so y = f(x) implies dy/dx = f'(x) ; dy = f'(x)dx ; T(1) = T(f'(x))
Hence int (1) dy = y = int f'(x) dx = f(x)
I'm pretty sure you thing int (dy/dx) dx is done with respect to x, but it isn't. the dx cancel out and it becomes dy, which is integrated with respect to y, yielding y.
Maths credentials - about to finish my masters in maths. Yes I've taken a course in ODEs which is why I know this method.
I think you're misunderstanding me but that could be me not communicating well. I'm not saying this method doesn't work, I'm not saying its wrong, my original question was just hoping to lead to some discussion about why the method works.
To be clear our methods are the same, however where you would write
dy/dx=f'(x)
dy=f'(x)dx
Integrate both sides
y=f(x)+c
I would rewrite it equivalently (but slightly more rigorously) as
dy/dx=f'(x)
Integrate both sides wrt x
But the integral of dy/dx wrt x is equal to the integral of 1 wrt y. And so we have
y=f(x)
Maybe once you've done some analysis you might see what I'm getting at when I say that "multiply by dx" isn't exactly rigorous. In some cases treating dy/dx as a fraction might work, eg in the chain rule, but it doesn't always. If you want an example of when it doesn't work look up the total derivative.
Sorry if that sounded condescending, but I do think that after a bit more maths you will see that "multiply by dx" isn't exactly the most sound mathematical argument. Incidentally, I don't think I said or at least didn't mean to imply that two integrals integrated with respect to different variables cannot be equal. My point was that it is possible to integrate dy/dx with respect to x, which it certainly is.
[deleted] · 1 points · Posted at 22:59:30 on February 15, 2016 · (Permalink)
Well I thought you and I were doing the same thing in different ways, and you were just treating dy/dx as a function of x hence doing the exact same thing as int f'(x) dx but saying it doesn't equate to int y dy.
I do need more math training regarding Real Analysis, tho.
[deleted] · 1 points · Posted at 09:56:32 on February 14, 2016 · (Permalink)
No, it's very much possible, and it's a very common method in solving differential equations that you learn among the first things there. The integral is just a dumb operator, the dx or dy is an infinitesimal multiple that determines its value.
He just solved a simple, fully separable differential equation. Probably the simplest there is. It gets a lot more complicated when you add second derivatives and functions of x and y; this is about as simple as differential equations get, however. Source: the second applied math course I took in physics.
NoGardE · 1 points · Posted at 15:59:13 on February 14, 2016 · (Permalink)
Ahhhhhhhh, right. Looks like it's been too long since I did any continuous math.
[deleted] · 4 points · Posted at 04:55:27 on February 14, 2016 · (Permalink)
the logarithm isn't really that tricky though, it's just the inverse of exponentiation.
[deleted] · 1 points · Posted at 11:33:07 on February 14, 2016 · (Permalink)*
The logarithm is very tricky when you meet it the first time in school. It's a thing where you put in a number, and another number comes out and doesn't look at all like what you put in, and there's no readily understandable way (for a kid) to know how it got there.
EDIT: Particularly when the first thing you learned was the base 10 logarithm, which you just sort of understand if you tilt your head and squint, but then they dump the totally random natural logarithm on your head, and tell you to use that instead.
[deleted] · 3 points · Posted at 01:37:38 on February 14, 2016 · (Permalink)
If you take 1/x where x>=1 and rotate it in three dimensional space about the x-axis the resulting surface has infinite surface area but finite volume. That is to say you could fill it with a finite amount of paint, but you could never have enough paint to cover its exterior. This surface is known as the Gabriel's Horn or Torricelli's trumpet.
You mean, "something as tricky as the natural logarithm". Logarithms in general aren't tricky, they're simply one of the two inverse operations of exponentiation (the other is root/radicals). For any ab = c, log[base a] c = b.
The logarithms just the start, you get to find all sorts of wonderful functions we define in terms of integrals, Bessel functions, error functions (my favourite), hyper geometric functions etc.
You can actually define the natural log from this integral. But then you have to prove that it is the inverse function of the exponential function.
snkn179 · 1 points · Posted at 04:23:31 on February 14, 2016 · (Permalink)
If you know that the derivative of ex is the y-value (on the graph y=ex), you can see that the derivative of ln(x) is 1/x since the graph is flipped about the x=y line so the new tangent slope is 1/(previous slope) and the derivative is now determined by the x-axis instead of the y-axis. Difficult to explain in writing but this was something that helped me understand it.
Here is what gets me about it. Things are a bit tricky, so beware...
The natural log and ex are inverse functions, and 1/x is its own inverse. ex is a function that is its own derivative. Now, if I take the antiderivative of a function that is its own inverse (1/x) I get an answer (ln x). Take the inverse function of that answer to get a new function (ex). That final function is its own derivative. I find it difficult to express what is happening here, but it feels nifty in terms of the logic.
The result they derive is a bastardization of a true result.
ζ(-1) = -1/12,
and ζ(n) is defined as 1-n + 2-n +3-n +4-n ...
so -1/12 = ζ(-1) = 1+2+3+4....
but that definition only holds for n > 1.
In the youtube video they use some cool infinite sum tricks to show the same thing, 1+2+3+4... = -1/12, and its very understandable and worth watching.
That's pretty interesting but also very obviously incorrect math. If you subtract the sum of one infinite series from another, you have to take the whole sums subtracted from each other. You can't break it up into parts to make certain things cancel out.
So, yes, this is interesting, but it's just wrong. The sum of any infinite series with a rate greater than one is infinity. It can't be stated as a value.
Shaxys · 14 points · Posted at 00:59:00 on February 14, 2016 · (Permalink)
If I remember correctly, it can be done with somewhat correct mathematics, one of the guys in the video had a blog post about analytic continuation and whatnot.
I think the real deal is that zeta of 1 is equal to -1/12 but the sum of all natural numbers can only be said to equal -1/12 if we "force" it to converge (as in, it would be the only thing the sum could converge to, if it were to converge).
So 10*.999... = Sum (n=1 -> infinity) 10*9*10-n happens to be true, but c*Sum(n=1 -> infinity) y =/= Sum(n=1 -> infinity) c*y in general? I don't remember that at all damn
You're really arguing with a bunch of professional mathematicians and physicists about a result that is actually important to physics. Just because it's counterintuitive doesn't mean that it's wrong. The same channel has released a bunch of videos about why -1/12 is actually a worthwhile and important idea and not just a trick of math or "very obviously incorrect". There isn't anything wrong with the math they show.
Obyeag · 15 points · Posted at 04:39:02 on February 14, 2016 · (Permalink)
It is wrong, at least in a general sense. The only reason why it is correct is due to analytical continuation or the assignments of sums to divergent series. The result 1+2+3+...=-1/12 relies on the assignment of 1/2 as the sum of 1-1+1-1+... which is actually a divergent series. The reason why people take fault with the numberphile video is because they don't explain analytical continuation, ramanajuan sums or anything, leading layman to incorrect conclusions.
[deleted] · 0 points · Posted at 07:03:31 on February 14, 2016 · (Permalink)
No, it's called a Ramanujan sum, and it's only true in certain specialized contexts.
Xguy28 · 1 points · Posted at 05:15:48 on February 14, 2016 · (Permalink)
Why not? 1+2+3+4 =10 and 2+3+1+4 =10. The order you add sums does not matter.
Lehona · 2 points · Posted at 06:28:34 on February 14, 2016 · (Permalink)
That's not always true though. I'm on mobile, but the general idea is: You can only do that with a sum if it's absolutely convergent (ie if you can make every term positive and it still converges).
Xguy28 · 1 points · Posted at 06:51:47 on February 14, 2016 · (Permalink)
What about the sum of all real number - the sum of all real numbers. Surely that's zero right? I know that you can't subtract from a diverging series since infinity - any finite number is still infinity, but that doesn't make it wrong to subtract a number.
Anyway I think this
is a good video explaining it in a bit more depth.
Lehona · 1 points · Posted at 05:15:21 on February 15, 2016 · (Permalink)
That's the point though. I will give an example using integers because it's easier: I can write the sum of all integers like this:
(-1 + 2) + (-2 + 3) + (-3 + 4) + (-4 + 5)... + 1.
Every parenthesis evaluates to one and there are infinitely many terms, so the sum is infinite already!
You're only allowed to rearrange terms if it's absolutely converging.
Xguy28 · 1 points · Posted at 06:56:45 on February 15, 2016 · (Permalink)
OK, I'll buy that.
Lehona · 1 points · Posted at 20:10:38 on February 16, 2016 · (Permalink)
Also consider the following: While intuitively it should add up to zero (For every positive number there's a negative one with equivalent magnitude, right?), it's not actually a converging sum. I don't want to bother you with definitions (although I guess they'd be very helpful here?), but depending on where you start, the sum up to the nth term would be either 0, -n/2 or n/2 (approximately). So it's constantly changing between different values, never getting closer to one in particular but actually growing apart as n gets bigger. Thus it's very wrong to assign a particular value to the sum, because it's constantly changing.
There are reason why you'd assign -1/12 to the sum of all natural numbers, but it's in a very specific context.
[deleted] · -1 points · Posted at 03:49:54 on February 14, 2016 · (Permalink)
But they aren't adding positive numbers forever, that's the point. The question is the SUM of ALL natural numbers, not the sum of all numbers up to a point, but the sum of every natural number, of which there are an infinite quantity. Because infinity is a concept rather than a number itself, it has properties that numbers don't have.
This theory doesn't argue that you won't get a forever increasing positive number as you forever add positive integers, it's stating what happens when you reach the end of forever (infinity), that if you literally sum ALL of them, you get -1/12.
Meaning that it is constantly adding a number one number value greater than the one before it. So it is actually adding forever increasing positive numbers.
How can the sum of all of these numbers be less than the smallest number in the series?
neos300 · 2 points · Posted at 06:12:27 on February 14, 2016 · (Permalink)
Short answer: infinity and the equal sign are more complicated than you think.
[deleted] · 6 points · Posted at 08:38:44 on February 14, 2016 · (Permalink)
The video does a pretty terrible job of explaining it. It starts with the assumption that the series (sum)(-1)n is equal to 1/2, but this is never justified. It would also be impossible to justify since it's untrue.
sederts · 1 points · Posted at 16:31:15 on February 14, 2016 · (Permalink)
I said it was a bastardization of a true result, and the video is understandable. Yes, Ramanujan summation does not allow setting the sum of the series "equal" to the value you derive, but what they did was still cool nonetheless.
[deleted] · 2 points · Posted at 17:21:35 on February 14, 2016 · (Permalink)
My reply was meant more for the average person who might click on that link and be horribly misled. Also, not to sound like a curmudgeon, but I really despise that video and the channel it comes from. It tries to pass off that result as a paradox but does so by starting with an assumption that isn't even true for sums of series in the traditional sense. Like, the only way that result could be "astounding" is if you're stuck thinking of series as sequences of partial sums (or informally as "infinite sums"), but it's actually not that interesting of a result if it just flows from the assumptions of Ramanujan or Cesaro sums. The video makes no such clarification, and so you have morons in the comments saying "math is flawed" and feebly trying to refute the video without adequate knowledge of the subject.
What I find most silly is that if viewers think 1+2+3+4... = -1/12 is some shocking result, why do they have no problem accepting 1-1+1-1+... = 1/2 which is also extremely counterintuitive? It would be like if I told my students that 1+1=0, and from that I could show that 2+2=0. But it's not false because they were expressed in mod 2 the whole time (which I casually don't tell them so that they're left thinking math is all lies).
Bobius · 3 points · Posted at 08:51:05 on February 14, 2016 · (Permalink)
Please stop spreading this kind of stuff. My students all think it's true in some form of useful way and it irritates me to no end.
Repeating decimals are basically shorthand for a series, in this case 9*10-n indexed from 0. You can't treat series like that, you can get all kinds of contradictory answers if you do.
Well, that's true that you have to be careful with limits, but every step in the proof is actually valid for dealing with limits. The thing you really need to be careful with is rearranging the terms in a series. The one thing he needs to be careful with is assuming that the limit exists in the proof. But that's fairly simple to show. Since the sequence 0.99... is monotone, it follows from the fact that it's bounded above by 1 that the series converges. The proof above is valid for showing that the limit is exactly 1.
That's a sequence, not a series. 0.999... Is a numerical representation of the limit of the series 910-n (indexed from 1). It doesn't have a limit, it *is a limit. And since the limit of that series is 1, 0.999... must equal 1.
Edit: I swear that your comment called it a series the first time I read it. I then proceeded to make essentially the same point. But 0.999... is still a number, not a series. Numbers don't have limits, they are limits.
That was another guy calling it a series, which is a sum. You can consider it a sequence of partial sums 0.9, 0.9+ 0.09, 0.9 + 0.09 + 0.009, ... but yes.
That was me being sloppy. Repeating decimals can be thought of as a representation of a series, but they aren't really series.
[deleted] · 1 points · Posted at 16:26:07 on February 14, 2016 · (Permalink)
Yes, S(n) -> 1
But if the sum [k: 1 -> n] ~ 9x10-k = S(n)
Then (10-1) S(n) = 9 - 9x10-n
Hence 0.9999... Doesn't equal 1. I mean, its least upper bound is 1 so obviously S(n) isn't equal to 1. The proof above states that S(n) = lub[S(n)] which is laughable at best.
Yes but chances are these proofs are back of the envelope type things for people without an extensive math background, and a truly rigorous proof would glaze their eyes right over.
The Ramanujan summation of the natural numbers is -1/12. The series is divergent.
The -1/12 result basically shows another way of thinking about divergent series and how you can manipulate them. It's important to distinguish between the actual sum of a series (which in the case of 1+2+3+... diverges) and when you're using a different language to describe divergent series.
"It's actually true" isn't true when you're talking about the classical definition of series and summations. It is true when you're talking about other ways to analyze series.
You didn't have to tell us explicitly - we could see that for ourselves.
Sphecks · 1 points · Posted at 05:00:18 on February 14, 2016 · (Permalink)
If you wanted to put it into layman terms, you can try to explain it this way. You can define a number by saying that a number always has to exist between it and another number. For example, 0.98 is a number because there is a number 0.99 between 0.98 and 1.0. In integer form, 1 is a number because 2 is between 1 and 3. However, can anything be possibly between 0.99 and 1? No, so we know that these have to be the same number.
That's just the logician way of doing it, though it may be less convincing, depending on the people, than writing out the proof which /u/WILLYOUSTFU provided.
Yeah, but I can still take a whole pie and convert it to thirds, then make a whole. Putting it into decimal or base notation screws it up because it's infinitely repeating. Not really too earth shattering now is it?
I do not like any of the mathematical proofs but I found a conceptual one that I think is pretty convincing. .999... is a rational number because the digits repeat infinitely and there are no consecutive rational numbers (there is infinite rational and irrational numbers between to rational numbers) since there are no numbers between .99... and 1, .999 repeating must be one.
regdayrF · 177 points · Posted at 21:06:05 on February 13, 2016 · (Permalink)
It's not meant as proof, but I feel like it is the easiest way for some people to grasp it. Believing 0.33... + 0.33... = 0.66... is not difficult in my opinion as you just add every position onto the other. Luckily, you can view every position on it's own as no position affects the other in this scenario, so one just has to believe in 3 + 3 = 6.
Using infinity sums and positional notation is way better than, what I did, but lots of people don't understand it anymore at that point.
It is circular because the important part is not the choice of 1 but the question of whether certain fractions can be perfectly represented by a decimal with infinitely many terms. Appealing to 1/3 instead convinces people because it's what they've been taught and doesn't challenge their intuition, but it only answers the case of 1 and handwaves the underlying question.
It's like if someone asked why ei*pi + 1 = 0 and you answered "because ei*pi = -1". Removing yourself from the conclusion by one trivial operation doesn't mean your argument is no longer circular, since you're still assuming the entire conclusion in a slightly different formulation.
The 1/3 argument relies on the other party already believing that 1/3 = .333... I disagree that it's like saying "ei*pi + 1 = 0, because ei*pi=-1"; it's like saying "ok, you agree that ex expands into the Taylor series centered at 0: x0/0! + x1/1! + x2/2! +..." and continuing to prove ei*pi + 1 = 0 from there.
Agreeing that the Taylor series centered at 0 for ex is xn/n! from n=0 to infinity is the same as agreeing that ei*pi = -1. That doesn't make the logic circular, that's how math works. You start from accepted truths and work towards a new truth using accepted transformations.
For people who aren't deep into mathematics, you start with what they're most familiar with. You don't start by proving 1+1=2, then showing that there are infinities of different sizes to derive the real numbers, and so on. You start from what they know. People know 1/3 = .333... They understand that 1/3 + 1/3 = 2/3 and that 2/3 = .666... And you can get them to agree that .999... = 1 from the starting point of 1/3 = .333...
KSFT__ · 2 points · Posted at 18:40:08 on February 14, 2016 · (Permalink)
Proving [;e^{i\pi}-1=0;] given [;e^{i\pi}=-1;] is very easy, but that doesn't mean there's anything wrong with the obvious proof. A circular argument is useless because one of its premises is also its conclusion. Proving [;0.999...=1;] given [;\frac{1}{3}=0.333...;] is easy too. If that proof convinces someone that [;0.999...=1;], then that person clearly accepts the premises of the proof. If it's valid (it is in this case, as it is not a circular argument) and it satisfies someone, it isn't a bad way to educate them. If they didn't accept that [;0.999...=1;] before the proof, and they do after, the "underlying question" was obviously answered by the proof. If it doesn't satisfy you, you can read a more rigorous proof, but this one is absolutely not circular, and that issue is separate from whether it's useful or requires premises that aren't obvious, which is subjective. I think it's pretty clear that it doesn't, for people who accept the conclusion after reading it.
If they do, they still truly won't understand the end result. This is the problem with education in America. We find some unrelated thing they were told to have bought before (because we all buy that 1/3 = .3333... but only because of dicking around with a calculator) and then use that badly-founded knowledge the be the base for more knowledge. It's why we're fucked. If we truly knew why 1/3 = .333... from the get-go this wouldn't have even been a question.
[deleted] · -2 points · Posted at 01:10:57 on February 14, 2016 · (Permalink)
We can, it's actually pretty simple, you just have to wrap your head around a number that repeats to infinity. Let's start with 0.333... instead of 1/3.
x = 0.333...
10x = 3.333...
10x = 3 + 0.333...
10x = 3 + x,
10x - x = 3,
9x = 3,
x = 3/9,
x = 1/3,
0.333... = 1/3 ⬛
Gufnork · -8 points · Posted at 09:28:58 on February 14, 2016 · (Permalink)
Apparently it's not that simple since you're doing it wrong.
x = 0.333...333
10x = 3.333....330
10x != 3 + 0.333...333 since 3.333...333 != 3.333...330.
You apparently can't wrap your head around a number that repeats to infinity since you don't realize that even though it has an infinite number, it still has an end. It has a start, an end and an infinite series of numbers in between.
There are infinitely many natural numbers. What's the end of the natural numbers? There isn't. There is no maximum natural number (and before you say it, infinity isn't a number). There is no final digit in .333... just like there's no maximum natural number. 10 * 1/3 = 3.33...
You can't append a 0 in there because there is no place to append a 0. There simply isn't an end. It trails on forever. The number 1/3 represented in base 10 does not terminate.
Gufnork · -4 points · Posted at 11:37:53 on February 14, 2016 · (Permalink)
Even if there's nowhere to append a 3, 3.333.... repeating has one more 3 than 0.333... repeating. You added that 3 when you multiplied by 10 incorrectly. That 3 is what makes this math off. That 3 is after an infinite amount of 3's, so you'll never get to it, nevertheless it's there.
You didn't "add" any 3; you moved every 3 forward a decimal place. Seeing as behind every 3 there's another 3, you never reach any 0. You're not grasping that 0.333... indicates an infinite number of threes. There's no such thing as infinity plus one.
What you're saying is equivalent to saying that the set of integers (Z) is one element larger than the set of integers minus 0 (Z\{0}). However, you can make a bijection from the Z to Z\{0} and show that they're the same size. There is no "one more" integer in Z, there is no "one more" 3 in 3.333...
And unless you can grasp this concept, then you're not able to discuss this. I'm sorry, but you're not following the same definitions and axioms we are.
A decimal with infinitely many repeating 3s does not terminate. It is, by the very definition of infinity, endless. This is best represented as 0.333... but if you're feeling bold, you can also represent it as 0.333333333...
0.333...333 (or 0.333333...3333 if you're still feeling bold) terminates. It has an end. It does not repeat. It might be made up with 100 3s, a trillion 3s, or googolplex 3s. Exactly how many 3s? I dunno. It's a poorly defined number. Either way, there are still a countable number of 3s in that decimal.
Not an infinite quantity, not a countably infinite quantity, *but a countable number of 3s.
I don't know. If it's an irrational number, I don't know how to write it out.
Let A = .999..., B = 1, and C = (A + B) / 2. If A != B, then A < C < B and I've found the counterexample you're looking for. If A == B then A = C = B and there is no counterexample.
So right now I've found a number between A and B unless you can show me that A == B.
Let me state it more generally. If you have two real numbers, A and B. How do you show that there is no real number C such that A < C < B without showing that A == B? Mathematical proofs don't end on questions for the reader to answer. You can't just ask "what's the number between A and B?" and act like you've shown A and B are equal. You have to show that there's no number between A and B.
[deleted] · -4 points · Posted at 11:24:17 on February 14, 2016 · (Permalink)
I've always prefered the "limit as x->∞" reasoning.
Alkadron · -2 points · Posted at 01:30:39 on February 14, 2016 · (Permalink)
There are a lot of very interesting discussions to be had surrounding the idea of what, exactly IS meant as a proof, and what that means, and what it means to prove something.
Best I've come up with so far is "a proof is a convincing argument, as judged by a competent audience." Which turns out is super subjective. So. I'll believe that your comments were, in fact, meant as a proof of sorts.
I'm well aware, I've read a lot of their work, which is why I mentioned there being a lot of very interesting discussions.
Having read a lot of their work, I can tell you: There's no real consensus on the matter. I'm not saying "Best I've come up with..." to imply i know better than they do, I'm saying "Best I've come up with... " to imply that there is no single, well-agreed-upon answer, but I know what my answer is.
I'm no math guy, but I feel like something is wrong with the first step...
If x = 0.99 (for simplicity, lets just say 2 decimal places)
Then it's assumed that 10x = 9.99
But shouldn't it be 10x = 9.9?
I know infinity entails an infinite number of decimals in this place. But infinities are not equal, especially continuous numbers, correct? I feel like there's a loss of precision or something.
Yes, that's exactly why you're not supposed to apply the standard rules of arithmetic on infinite (in this case, repeating) numbers. I've heard that being taught pretty early in many schools, but apparently adding or multiplying ".11111..." is common practice in America...
At any rate, you're right. The whole "proof" relies on doing an operation with an infinite number and assume the result is correct. Actual maths will deal with limits instead, but for all intents and purposes, .999 = 1.
Yeah the same thing disturbed me. Basically in base 10 multiplying by 10 means shifting everything to the left and add a 0 on the right. But how do you add a 0 on the right of something infinitely long? Anytime infinite is involved in math, it's really hard to have stuff check out intuitively, you have to rely on abstract conventions that just work. edit: missing word
Basically in base 10 multiplying by 10 means shifting everything to the left and add a 0 on the right.
It doesn't have to.
What's 0.8675309 times 10?
It's 8.675309.
It's also correct to write it as 8.6753090, but you don't have to. You don't need to write that 0 at the end. You just simply shift each digit by one position.
Yes you're right, for non integers the 0 on the right is meaningless. What bother me is how do you shift stuff on the left when that thing has infinite length? You basically add something by doing this, though in this case the somethign is infinitely small.
Lol I feel like a drunk guy talking philosophy in a pub, I should leave that to mathematicians.
What bother me is how do you shift stuff on the left when that thing has infinite length?
Well, it's not a physical task, so it doesn't matter that it has infinite length.
You shift the digit in the second position to the first position. You shift the digit in the third position to the second position. And so on.
Each of the infinitely many digits is in a particular position, and you shift each digit one position.
Really, the answer to the question "How do you shift stuff?" is: You just do it! This is a theoretical exercise, not a physical task.
If I tell you what digit goes in each position, then I've told you how to shift.
You basically add something by doing this, though in this case the somethign is infinitely small.
Why do you think you add something? You're just moving things. You're not adding anything.
You move whatever's in position 100 to position 99. You move whatever's in position 101 to position 100. And so on. You are only moving things. You're not adding anything at the end. (In fact, there is no end.)
In fact I was trying to build an intuition of it by imagining how numbers are encoded as bits in a computer. In binary multiplying by 2 means shifting bits to the left, in a computer's memory kind of physically (sometimes literally). So if you have an inifintely long number, shifting it feels like creating a loophole on the right of it, which would be worth an infinitely small value.
It's like saying that that 0.999... = 1 - 0.000...1, and that this last small number is actually infinitely small and can be ignored.
I agree with you that the whole physical analogy doesn't make sense, I was just trying to build intuition on something that can't be understodd by intuition.
It can be understood by intuition, but you just have to work on developing the intuition.
If you have an infinitely long decimal, then there is a first position, second position, third position, and so on, but there is no infinitieth position.
Because there are an infinite number of 9's, so you never get far enough in the 0's to write the 1.
IthiQQ · 2 points · Posted at 14:42:38 on February 14, 2016 · (Permalink)
The flaw in this line of thinking is the assumption that there is a final number of the sequence. There is no 1 at the end of the sequence because the end of the sequence does not exist.
Although infinite and infinitesimal numbers are not usually defined using limits or rational numbers, there are information-preserving concepts of these ideas. For example, the hyperreal numbers include numbers larger and numbers smaller than any real number, and "normal" operations between them work. Surreal numbers are a little more difficult to construct, but can represent similar concepts.
In the real numbers, there is no .0...1 or "infinity." They aren't real numbers. The limit of 1/x as x goes to infinity is 0. But you can take many approaches to defining numbers outside the reals which lets you do what you're thinking of. In other words, your idea is not stupid.
This should be a thing. 0 repeating 1 could be defined as the limit of 1/x as x goes to infinity...
But that's just the number 0.
Bree899 · 0 points · Posted at 12:08:40 on February 14, 2016 · (Permalink)
I agree. 1 - 0.9 = 0.1, so 1 - 0.99...99 should be 0.00...01. Close enough to 0 that you can almost ignore it, and you definitely won't ever reach the 1 at the end (due to infinite 0s), but that doesn't mean it isn't there. An infinitely small number. Not 0.
Exactly! My explanation of this is essentially equivalent to yours, which is that (from number theory) two numbers are unequal if there exists a number in between them. Therefore, since there is no number greater than 0.999... that is less than 1, it must be that 0.999... = 1.
Neither of these are mathematically rigorous though. For a real proof, we say .9999.... = .9 + .09 + .009 + .0009 +... = .9/(1-.1) = .9/.9 = 1. The formula I used is the formula for the sum of an infinite geometric series, a1/(1-r), a1= first term in the series, r= the common ratio, or the number that each term in the series is multiplied by to get the next term
The problem of "proving" that 0.999... = 0. ̅9̅ = 1 is that it's not a mathematical problem at all but rather a problem of notation. It just so happens that in our notation "0.999..." holds the same value as "1". The actual mathematical entity that these symbols represent is stupefying and incomprehensible in much the same way the concept of an infinite number of 9's after 0. is stupefying and incomprehensible.
Didn't sound like that's what he meant but maybe it was. I thought he was saying that x only equals 0.9...
But obviously it's both
injygo · 1 points · Posted at 21:09:13 on February 14, 2016 · (Permalink)
There's just one solution to the equation and it's the number that's one more than zero, also known as "0.9999999999..." and "1". That's what the person you were replying to was trying to convey with the proof, that both "0.99999..." and "1" refer to the same number.
x = 1 is correct. But x = .99... is also correct because 1 = .99...
The reason it's trickier to work backwards through is when we have 9x = 9 and solve for x, we think x = 1, but x = 1 = .99... Assuming this, the algebra works fine backwards.
Unless you're working with some very strange axioms of algebraic manipulation, 10x - x always equals 9x. And the proof appears less inconsistent if you consider that .999... actually does equal 1; although there might seem to be some contradiction when you get 9 = (9 * 0.999...), there is none. 9 = 9 * 1.
If you can get to 10x - x = 9.99... - x you see:
(since 10x - x = 9x) 9x = 9.99... - x
(since x = .99...) 9.99... - x = 9
9x = 9
x = 1
x = .99... = 1
[deleted] · -1 points · Posted at 12:21:36 on February 14, 2016 · (Permalink)
Infinitely repeating numbers are not irrational. 0.33... is the ratio 1/3. 0.66... is 2/3. 0.99... is 3/3. In fact, every single infinitely repeating number is rational.
I'm still not convinced. My reasoning is that .999... should be treated like it was infinity and therefore can't be modified, otherwise you can do all sorts of crazy things with it.
My second reason is that if .999... = 1, then what number is closest to 1 while also being less than 1?
benful · 5 points · Posted at 05:47:10 on February 14, 2016 · (Permalink)
My reasoning is that .999... should be treated like it was infinity and therefore can't be modified, otherwise you can do all sorts of crazy things with it.
This is actually kind of a valid criticism of that argument. Infinite sums are a bit subtle - some of the techniques you can use with finite sums don't always work on infinite ones. In this particular case everything is fine, but proving that is harder than proving that 0.999... = 1.
My second reason is that if .999... = 1, then what number is closest to 1 while also being less than 1?
There isn't one, just like there isn't a number that is closest to 1/3 while also being less than 1/3, or a number that is closest to pi while also being less than pi.
regdayrF · 0 points · Posted at 12:16:16 on February 14, 2016 · (Permalink)*
In this case, we're dealing with irrational numbers not rational numbers.
For rational numbers, no matter how small the difference is between numbers, you will always find infinite numbers in between both of them. Let's say, we chose the interval [0.99999999, 1]. In this interval, there are infinite numbers in between 0.99999999 and 1. This can be applied for any real number out there, thus, you will never find a number, that is closest to 1 while not being one. For any given real number a, you will find infinite numbers in between a and 1. No matter how "close" a was to 1, you will still find infinite numbers in between them.
0.333.... with an infinite amount of 3's is an irrational number and can be desplayed as 1/3. Then everything applies what I've typed above.
It's just basic algebra. They're subtracting an x from 10x, thus 9x. You can see it's true pretty easily if you just start plugging numbers in. You can take my word that it's true for any number.
[deleted] · 2 points · Posted at 17:46:27 on February 14, 2016 · (Permalink)
This is incorrect, 10x would be 9, not 9.9. 9.9 would be 11x.
Asmor · 1 points · Posted at 03:00:31 on February 14, 2016 · (Permalink)
I still remember seeing this in... like... 3rd or 4th grade. I totally didn't understand what the teacher was trying to get across, and I thought she was just demonstrating a weird trick with math.
Personally, my favorite way of expressing the fact that 0.9... is the same as 1 is to ask someone what 1 - 0.9... is, or alternatively ask them what's a number between 1 and 0.9...
relies on the same principle that /u/regdayrF held to be true. Multiplication is a shorthand for adding together groups. So, saying 10*0.9... = 9.9... is just like saying 9.9... = 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... , which relies on the fact that one must believe that these infinite decimals can be added in such a way. And if that is true, then 0.3... + 0.3... = 0.6... is just as valid.
faaaks · 1 points · Posted at 04:22:22 on February 14, 2016 · (Permalink)
Personally, I've just asked people to name any number between .9... and 1.
sorif · 1 points · Posted at 04:29:56 on February 14, 2016 · (Permalink)
Even taking this a bit further, any repeating decimal can be represented as
(repeating digits)/(10#repeatingDigits - 1)
.999... = 9/9 = 1
.333... = 3/9 = 1/3
.8484... = 84/99
etc
The reason why is the same as your proof. You are multiplying by a power of 10 to move one sequence of the repeating digits to the left of the decimal point to get your multiple of x you can work with. Then subtract 1 from that power of 10 to eliminate what's to the right of the decimal, and you have a whole number multiple of x over the power of ten (less 1).
Edited: Tried to make my explanation as clear as possible.
I don't like this proof since it relies on believing .3...+.3...=.6..., which someone who doesn't believe .9...=1 isn't likely to believe either.
Yeah. If someone thinks that the repeating decimal is an approximation rather than literal, why would they suddenly forget they think this when you add them.
Clyzm · 1 points · Posted at 07:07:13 on February 14, 2016 · (Permalink)*
I'm still not a fan of this one, really;
10x - x = 9.9 - x
10x - x = 9.9 - 0.9...
Is murky at best. You're trying to say you want to prove this to someone who doesn't believe 0.333... + 0.333... = 0.666..., but you multiply 0.999... by 10. Something more fool proof would be to prove by contradiction that if 1 != 0.99..., then that implies 0.999... must be > or <1, and the existence of a number >0.999... and <1 (or <0.999... and >1) by density of R.
I have a problem with this.
X=.9... Right so although this goes on forever when you multiply it by ten you dont add a 9 to the front you add a 0 to the end. So for example maybe its originally .9999999999 when you multiply that by 10 it becomes 9.999999999 NOT 9.9999999999
Redo all the steps assuming that and you end up with .9999999999=.9999999999
This isn't really accomplishing anything mathematically. You're first line says x = 0.9. Next line you say 10x=9.9. You do some algebra then say that based on that algebra x has two distinct values, when you really just declared two different values in the beginning. If x = 0.9 (first line) then 10 * x would equal 9, not 9.9.
I suppose it does help to see how it works. I like to think of it like a limit when your variable approaches infinity. You technically never touch the line, but you eventually converge on the line.
The problem with all of these IMO is that they all rely on axiomatically selecting against the existence of infinitesimals. If you axiomatically choose for them to exist, none of your math is right.
The tricky bit is that by using 9.9... and 10 in the same formula with a layperson without explicitly stating your axiomatic choice, you have primed the layperson to think under the assumption that infinitesimals exist, in which case they are correct in assuming 10 and 9.9... are different numbers.
Yeah that's a good explanation, but I understood it best when I realized that the only reason this question is at all confusing is because we have decided to represent numbers in base 10. I would then explain how half in base 3 has the same problem.
0.111... + 0.111... = 1.
[deleted] · 1 points · Posted at 08:08:54 on February 14, 2016 · (Permalink)
At the stage:
10x - x = 9.9... - 0.9...
How do you get from 10x - x to 9x in the next line? Surely it's 9.1...x = 9?
I used this to explain it to someone once. Their response was "when you multiply it by 10 the last digit of 0.99.... becomes 0. Proof". I said "which last digit of the infinite series is that then?"
If you're dealing with someone that "doesn't believe .333... + .333... = .666..." then there's no way you're going to get them to believe a process that takes a considerable amount of more steps and algebraic manipulation.
I really don't see how 1/3 + 1/3 + 1/3 = 1 isn't the simplest way to show the concept.
[deleted] · 1 points · Posted at 09:43:19 on February 14, 2016 · (Permalink)
Uh... This is technically the same thing as what regdayrf said... You are just hiding multiple additions of '0.999...' under one multiplication, and then subtracting, which is also, kinda, addition... So, basically, your method is just more complex than regdayrf's
This transition is crucial to the intuitive click. On closer observation, though, it's questionable for the same reason that .3... + .3... == .6... seems questionable. If a person does not trust one, I'm not convinced they should trust the other.
I like the pragmatic argument. For arbitrarily small ε, there is a number of digits N such that 1 - 0.9...9 (repeated N times) < ε.
zodiacR · 1 points · Posted at 12:11:49 on February 14, 2016 · (Permalink)
Hate you for that, how is it possible?
Bree899 · 1 points · Posted at 12:30:53 on February 14, 2016 · (Permalink)
Admittedly not knowing a whole lot about math, could I ask for a serious response to my current opinion?
I'd like to think this is wrong because multiplying 0.99...99 by 10 is not the same as adding it to 9 (which the above example relies on when it says 10x - x = 9).
Look at this:
x = 0.9
10x = 9 (and, incidentally, 10x - x = 8.1)
x + 9 = 9.9
so: x+9 > 10x
Let's add another 9 to that:
x = 0.99
10x = 9.9 (making 10x - x = 8.91)
x + 9 = 9.99
again: x+9 > 10x
This stays the same however many 9s you add to the value of x. So even when x contains an infinite number of 9s, you can't simply multiply by 10, then subtract 9 and expect to be left with a number that has the same value as x.
Instead, it would become as follows:
x = 0.99...99
10x = 9.99...99
10x - x = 8.99...991 (rather than exactly 9)
9x = 8.99...991
x = 0.99...99 (not 1)
If I'm right about this, it renders the whole argument invalid, doesn't it?
And that would allow me to go back to my comfortable life of believing 1/3 is not 0.33...33 and 1 is also not 0.99...99 (but rather there is a difference of an infinitely small number, 0.00...001).
The problem with that proof is that 10 times 0.999... is 9.99...0
If you are going to treat a fraction as an infinite decimal, then it doesn't make sense to ignore the decimal way of handling numbers. If you multiply anything by 10, move all the digits to the left and stick a zero on the end.
Also, thinking about the principle that between any two real numbers there exists another real number, you can't put a real number between 0.999... and 1.
Or you can use this, 0.999... is 1 - 0.00...1 right? Well since the one never comes, 0.00...1 is equal to zero, so that means that 0.999 = 1-0 which is 1.
A simpler thing to understand for people who don't like the witchery of algebra is to state the fact that for any two real numbers, there is an infinite number of numbers between them, then as what number is between 1 and .9999999.......
Well it's not quite right to say x is both .9… and 1 because they're actually the same value
[deleted] · 1 points · Posted at 14:52:16 on February 14, 2016 · (Permalink)
since it relies on believing .3...+.3...=.6...
Why's that a problem for them? You just go along the pairs of digits summing them, and it's always going to be 3 + 3 = 6, so no one has a problem with it. It's intuitively very different from equating a recurring decimal with a whole number, which is the leap-to-far for laypersons.
I guess that just means absolute zero is impossible to get to, but then ........I mean............you can just round up to 1 I suppose due to the domino effect going back from the last 9........but if there's an infinite number of 9s............god dammit.
[deleted] · 1 points · Posted at 16:15:47 on February 14, 2016 · (Permalink)
You're cheating tho.
If you define x as the sum of 9 10-k ; [k:1~n] , then multiply by 10 and subtract x, you still haven't eliminated 9 10-n, hence why "x" isn't equal to 1.
You're plugging n = infinity hence n = n-1 before you even start your calculations. So your proof is wrong. As someone said below, these kind of bogus "proofs" are very irritating.
I don't think there's a lot of difference between the two proofs. One relies on adding two infinite series (0.333... + 0.333...), and the other on subtracting two infinite series (9.999... - 0.999...).
Somewhat equivalent to the above: "Any two numbers that are different have a third number that is between them. But there is no number that's more than 0.999... and less than 1, therefore they're equal"
Except phrasing it that way isn't generally very good at convincing people who don't already grasp the maths; they'll try to suggest "0.999...5" without intuitively getting the concept that the infinite chain of 9s doesn't have an end to put the 5 on the end of it.
h_saxon · 0 points · Posted at 23:23:35 on February 13, 2016 · (Permalink)
You must point out that there is supposed to be a theoretical 1 at the 'end' of those infinite zeroes.
KSFT__ · 3 points · Posted at 03:12:43 on February 14, 2016 · (Permalink)*
The word "theoretical" is meaningless in math. Math doesn't deal with theories; it deals with theorems. There's an important difference there. In science, theories are ideas that seem probably true based on empirical measurements. In math, theorems are statements that have been proven based on axioms, definitions, and rules of deduction. In order to be sure that a statement is true, it's important to be precise about what you mean in math, which is why there's formal notation. You aren't precise enough with your claim, "there is supposed to be a theoretical 1 at the 'end' of those infinite zeroes", for me to explain why it's false (I think it's false, but I can't be sure because I don't know what it is).
I love the visual of this method. You can teach this to someone that has very basic math understanding. Ask them what 9/9 is, if they know it =1 then you are good to go. Use a calculator to show that 1/9 = 0.11111.... then 2/9 = 0.222222.... Then ask them to continue writing 3/9, 4/9, 5/9, ect. Instinctively, 99% of the time they will write 9/9 = 0.999999....
If two numbers are not equal, there has to be a number between them, so if 0.9999.... <> 1, there would have to be a number higher than 0.9999.... that didn't equal 1, so 0.9999... couldn't be the next lowest number than 1. So it has to equal one.
Edited because my first version was more ambiguous than it could have been.
I edited my answer; maybe it will make more sense now.
[deleted] · 3 points · Posted at 02:20:53 on February 14, 2016 · (Permalink)
I only assume this isn't true..it think
0.999... = 1. There's something like a hundred different ways to prove that it's true. All of them are a bit awkward, and it never actually matters anyway unless you're planning on a PhD in mathematics.
All of them are a bit awkward, and it never actually matters anyway unless you're planning on a PhD in mathematics.
What? The non-rigorous "awkward" proofs should be accessible to any high school student (1/3 * 3 should be sufficient).
The actual rigorous proof is typically doable at the end of a 2 semester calculus course, once series are covered. That's like college freshman level.
A PhD student should have enough experience under their belt that they understand innately that two different representations may refer to the same thing.
I fully accepted it when I imagined a number line. There's 0 and 1, and 0.999... would be somewhere in between. 0.9 is really close to 1. 0.99 is even closer. 0.999 even closer than that. Now imagine the number 0.99999999... With every 9 you get closer and closer to one, but because this number is infinite you're becoming closer and closer with no end. And 'eventually' you're going to reach 1.
/r/iamverysmart is for people who say things that are wrong, not just for people who say things you don't understand.
jorellh · 4 points · Posted at 03:08:10 on February 14, 2016 · (Permalink)
easy proof. 0.9 repeating will always be closer to 1 than any number you can imagine.
either that or 1/9 = 0.1 repeating so 9*(1/9) or 9/9 or 1 = 0.9 repeating.
[deleted] · 3 points · Posted at 05:18:49 on February 14, 2016 · (Permalink)
The definitions here are complex for laypeople, but I tried to be as honest to them as I could without making this too long. Real numbers are (often) defined as Cauchy sequences of rational numbers. Cauchy sequences are more or less sequences which vary by less as they go on (for any variance, I can find a point in the sequence after which no two numbers in the sequence vary by more than that variance).
1 is just shorthand for the real number {1,1,1,1,1,....}. Now we define addition as an extension of how we define rational addition by adding the terms of the sequence (which are all rational numbers). so {1,1,1,1,...}+{1,1,1,1,...}={2,2,2,2,...}
We define a real number to be equal to 0(real) if it has 0(rational) as a limit point of it's sequence. so {1,1/2,1/4,1/8,...} = 0(real).
Then finally, we declare a=b if a-b=0.
.9999... is shorthand for {.9,.99,.999,.9999,...} and we see that 1-.999.... = {.1,.01,.001,.0001,...} which has zero as a limit and therefore they are equal.
It seems like we cheated because we defined these things in such a way that .99999...=1 so how could we be proving anything, but in mathematics we don't work with anything that we don't define ourselves. If we don't define the things we work with, then there can't BE any proof. The people who have trouble with .9...=1 aren't making a grievous error of logic, they simply haven't been given the definitions, indeed there are ways of defining .9... which are consistent with everything you've learned about numbers so far such that it does NOT equal 1, so try not to be a jerk when you are explaining.
If you're working in such a space that the minute difference between .99999 repeating and 1 is important, then you can't assume that .111111 repeating is equal to 1/9.
While it is true that if you perform long division to find 1/9, you'll get .111111 repeating, it is important to keep in mind that because it repeats, the operation is never completed, and the fraction is never satisfied.
nxsky · 2 points · Posted at 08:23:58 on February 14, 2016 · (Permalink)
You don't need a proof for this. 0.9 and 0.3 recurring are decimal representations of a number. Whereas 1/3 and 1 are numbers.
What people really fail to see (and I don't blame them) is how mathematics can be very tricky without being complicated at all. For example, 2 is a complex number. Not easy to believe until you write it as 2 + 0i.
Naouak · 2 points · Posted at 09:29:07 on February 14, 2016 · (Permalink)
It can be also explained as :
Two numbers are different if you can write a number between them.
What annoys me about this is that I pretty much never see people actually explain this. They either assume that 1/3 = 0.333... or assume that you can treat infinite sums like regular sums and do 10S - 9S.
You have to define what an infinite sum means rigorously and the simplest definition for a convergent infinite sum is that it equals the limit which in this case gives 0.999... = 1 which is like saying that when you walk across a room you've walked half way plus a quarter plus and eighth and so on.
175gr · 11 points · Posted at 21:59:43 on February 13, 2016 · (Permalink)
I like to use the fact that every two distinct real numbers have another distinct real number between them. What's between .999... And 1?
.999... does equal 1, but the burden of proving there's no counterexample is on you.
I could answer: "Let A = .999..., B = 1, and C = A + B / 2. If A = B, then A = C = B; if A != B then A < C < B. I don't know what C is, but if A != B then I've found the number between A and B."
My problem with the "find the counterexample" proof is that I can't think of a way to show that "there can't be a C such that A < C < B" without the logic "A = B, therefore there is no number C such that A < C < B." If you can really show that there is no C between A and B without relying on A = B, then you've shown that A = B. I don't know how you'd do that though.
dreinn · 0 points · Posted at 14:25:46 on February 14, 2016 · (Permalink)
Easy. 0.00....1
Peazy.
That is, an infinite number of zeros, then a one. Lemon squeezy.
175gr · 1 points · Posted at 15:35:16 on February 14, 2016 · (Permalink)
bik1230 · 2 points · Posted at 00:42:22 on February 14, 2016 · (Permalink)
Why are you mentioning infinite sums? That proof doesn't involve any infinite sums.
thmsoe · 10 points · Posted at 02:05:45 on February 14, 2016 · (Permalink)
When you write 0.9999..., you implicitly talk about the limit of the convergent series 0.9 + 0.09+0.009+...+9*10-n, whose limit is 1. Really, this problem all comes down to definitions.
bik1230 · 0 points · Posted at 02:53:24 on February 14, 2016 · (Permalink)
Ok, I could have been a bit clearer. I don't think it makes sense to talk about 0.9... as a convergent infinite sum when any number with predictable digits can be written as one.
They either assume that 1/3 = 0.333... or assume that you can treat infinite sums like regular sums and do 10S - 9S.
Ultimately yes. It is an assumption. But it makes things tidy and has no actual practical downside, so why not? Mathematics is a tool, nothing more.
The correct thing to take away from it is that mathematics cannot and does not need to represent an infitessimal.
nmuna · 2 points · Posted at 04:38:44 on February 14, 2016 · (Permalink)
A lot of proofs here aren't wrong but there's a much simpler and arguably more correct way to do it. For any 2 distinct real numbers a and b, if we without loss of generality assume a<b, there exists a c such that a < c < b. There are infinitely many such c's in fact. In short there's a real number between any 2 real numbers but it's easy to see that theres no number between 0.99999... And 1. Therefore they're the same number.
but it's easy to see that theres no number between 0.99999... And 1
It's hard (in the sense that as a human I don't know how to do it) for me to find a number between 0.999999... and 1. But it's also hard for me to find a number between A and B where A is 1/(G64) and B is 1/(G64 with a random digit I don't know about replaced) where G64 is Graham's number.
I don't like this proof because it seems like you need to prove that A = B before you can say "There is no C such that A < C < B". And I don't really like the whole proof by "it's easy to see there's no counterexample" when there's no work showing that there's no counterexample.
nmuna · 2 points · Posted at 12:53:34 on February 14, 2016 · (Permalink)
That's a very good point. I think that it requires breaking .9999... down into the summation 910-1+910-2+9*10-3+... And see that if any change is made to any of the 9s in the number becomes less than .999... So to find a greater number requires us to start with a c*100 term. I think that would be enough to do it. I studied math in undergrad so I never got past intro to analysis so I could be wrong.
Like saying 2 is basically 3 if you are measuring in inches from a ruler placed on earth from the sun.
Not true, just seems so from our field of reality.
.9999...is not 1. It's damn close but it isn't one. Same as .6667 x 3 is not 2. Because .666666 is VERY close to .667. Does that mean we just round all .66666 to .667 and call it 2/3? Because it is so close? Or should it be .668. So now we can say .665 x 3 is now 2 also?
nmuna · 1 points · Posted at 12:58:47 on February 14, 2016 · (Permalink)
What I said is a property of real numbers though. The same doesn't apply to integers (what you were using in your inches example). .999999... and 1 are real numbers though where that property holds.
Students easily relate to the intuitive notion of an infinitesimal difference 1-"0.999...", where "0.999..." differs from its standard meaning as the real number 1
Idk man. You are a karma whore and a dick. You just want to be right. Downvoting me and all that shit just to look better.
I was just arguing.
Anyways you are still considering .9999 to be a real number. 1/3 is but if you divide them you never complete the problem. You will be deciding infinitely.
I just see no documented proof from scholars saying it's true. Just that it is how it is taught to undergrads for grasping the concept.
And I'm not missing ellipses. In on a phone, and anything repeated 3 times should basically indicate infinity in this context.
Go on. If you really want to believe it I don't mind.
Well, if 0.9999... has infinite 9's then you could say the same about that extra 1 that you'd need to add to the 9 in the infiniteth place to make it hit the ceiling. That's my point. From a sheer philosophical perspective, 0.9999... is never going to hit one. I'm trying to illustrate that by doing it in the opposite direction.
What I meant is that it's curve-like if you consider how all the 9's keep getting closer to 1. 0.9 != 1. 0.99 != 1, but it's closer. On and on into infinity. Same concept as an asymptote. It will never equal one. (Well, it shouldn't, but somehow that proof says it does...)
raugturi · 1 points · Posted at 08:06:28 on February 15, 2016 · (Permalink)*
I'm going to try to use latex, so you might want a plugin for that like this: TeX The World
I'm not sure how rigorous this proof is, but it appears to me that a) we don't need the limit, an b) it only approaches 1 because [;0.\overline{9} = 1;]. Let me see if I can demonstrate. Let's start with 1/9. If you do that via long division you'll see this:
If we did it as a limit the number it's approaching is actually [;0.\overline{1};], the same as the result of the sum of the infinite series itself. And since we can multiply either side by a constant:
Eh. Not really. I mean sort-of. But basically this statement is because the 'repeating' notation is just a way for us to express things that go on forever without using something that goes on forever.
Actually, it really depends. There is not a single canonical choice for what .999... is in *R, and depending on your choice the result may or may not still be true.
There is not because you can't have an infinite number of 0's followed by 1. The 1 never happens. If it did then a) the number of 0's is now finite, and b) the difference between that number and 1 is 0.<however many 0s you put in>1.
jorellh · 1 points · Posted at 15:13:40 on February 14, 2016 · (Permalink)
True it would just be 1+1/10infinity which is just 0
That's what the points are for, this specific pattern will continue endlessly, so what I typed is not an approximation. If you were to read through some math-literature you notice, that points are often used for reocurring patterns. Therefore 1/3 = 0.333...3 . Just try to divide it by hand, no matter how many steps you were to follow, the next number would always be 3.
My two terms are just the thought behind 0.999...9 = 1 . Proving requires using positional notation and an infinite sum.
They are not approximations, they are equivalent to their fraction representations. An approximation would be 0.333...33 for some finite number if 3s.
We can see their equivalence by writing 0.333... as Σ3*10-n for n from 1 to infinity, which is a geometric series and can be summed in the usual way.
YOU CAN'T DIVIDE BY 'INFINITY' LIKE THAT!!!
Even if you're using the Extended Reals (where you have an element x s.t. n<x for all real numbers n) it's not actually dividing by infinity.
What *is* correct is that in the Reals 1/x -> 0 as x -> infinity
First of all we can't write 1/∞ as ∞ is not a number. However if we take the limit of 1/x as x approaches ∞ then that limit is equal to zero. Not infinitesimally near 0, it's exactly equal to zero.
If you actually believe that the limit 1/x as x approaches ∞ is greater than zero then I invite you to write that limit on the form 0.000…0001 and tell me the number of decimal points in that number.
Showing this was part of our Analysis I exam... I just didn't get it and thought I had come to a contradiction. Good thing I'm studying physics and rarely need limits... Oh wait.
gnorty · -1 points · Posted at 23:04:53 on February 13, 2016 · (Permalink)
anone who doubts this should be asked to write down what they think is 1-0.9999''. Anyone who starts writing 0.11111 should be cast straight to hell, everyone else will very soon stop doubting!
This was the very first proof I learned in pre-algebra class in Jr High. I was blown away with the idea. I’ve been into ‘hobby’ mathematics ever since.
for the sake of doing a math problem or a proof, you can say that .999 repeating forever = 1 because it nearly does, and being infinitely close, they are as good as interchangeable, but they are not truly equal, a better way to say it would be that the limit of the difference of these two amounts approaches zero
Again, you are just wrong. They are literally equal and it can be proven. Part of the problem is that calculus is a little counterintuitive, but you're thinking about it wrong:
The number .999... isn't "moving" anywhere. It doesn't get closer or further away from anything over time. It's not like someone is writing all the ones one at a time and each time you write one it gets closer to one, they already all exist. And there's infinitely many of them. Just like Pi. The name ".999..." is a name of a specific number that can be placed on a number line in a specific place. ANd it is provably equal to 1.
here's the actual proof, if you want it:
The number .999... is actually just an infinite sum. .9 + .09 + .009 + .0009 + .00009 etc. Another way to write that is (9/10) + (9/100) + (9/1000) etc.
This can be re-written as a power series "the sum" from 0-infinity of (9/10)(1/10)n.
This is a special kind of power series known as a "geometric series" which is known to equal a/1-r. a in this case is 9/10, r is 1/10. Just plug them in and do the arithmetic:
(9/10)/(1-1/10)=(9/10)/(9/10) = 1.
That is a mathematical proof right there. When you take Calc 2, you do this proof by hand and you can't argue with it.
.999... and 1 are the same number. Literally the same. Not so close we might as well call them the same. Not approaching the same. Not the same for the purposes of doing this problem. They are the exact same number.
Actually, I am not wrong, just a lot more educated than you are, I have a PhD in math. I'm sorry that you never made it much past Calc 2, but had you continued, you would have discovered advanced number theory, after about 5 more years of solid math (once you get into graduate school majoring in math)
The .9999 =1 problem a highly debated point in higher math circles, and illustrates why many conventional mathematical proof models fall apart when it comes to infinite series, I suppose you are one who has also fallen for that 100 year old hoax that 1 + 2 + 3 + 4 + ...., = -1/12 too?
I really don't think this is highly debated in higher math circles. I've studied these types of problems in an academic setting and I've never met a phd who thought .999... didn't equal 1. Please enlighten me, though:
How does advanced number theory change what I wrote above? Are you saying that infinite sum isn't a geometric series? Or that geometric series don't equal a/1-r? The more detail the better, please.
well it is not an ELI5 subject, or it wouldn't be doctorate level, but hyperreals and infintesimals are interesting (if you are geek) - here is a paper on teaching younger students, and if you can wade through it all the way through, you will start to see that .999... < 1 and also that it just falls short by 1/∞ and perhaps rather than saying .999... = 1, math teachers should actually be saying lim .999... = 1
for the sake of simplicity in calculus, for example, we teach that .999... = 1, even though it really doesn't, so we can get on with class and get the rest of the course taught!
.999... is a single number. There's nothing to take the limit of. An infinite decimal is defined as the limit as the number of digits goes to infinity of its truncations. By definition, .999... is exactly 1.
Also, 1/∞ is not a thing. .999... is a real number; 1 is a real number. Reals are closed under addition.
I'm not trying to call you a liar, but a lot of people on reddit claim to have phds in lots of subjects. And your phrasing is just sloppier than I would expect from a math phd (calling zeta function regularization "a hoax" or using limits in sloppy ways).
I'm not saying it's impossible you have a phd, I just have to conclude you don't know what you're talking about. Feel free to prove me wrong if you want.
people often dismiss concepts that go over their head as "he doesn't know what he is talking about" - it's a mental way of battling insecurity, but that is psychology and we were discussing mathematics.
PS - as I am not insecure, I have no need to feel as if I have to prove you wrong - the intelligent folks reading this will do their due diligence and dig deep enough, and that alone will will prove you wrong ;)
I'm not sure we are talking about mathematics, though. I was. I gave you mathematical argument that .999...=1. Instead of actually refuting it, you said "I have a phd. Trust me, if you knew what I know, you would understand that .999...<1."
And all I'm saying is that what you have written in this thread gives me no indication to actually believe you. Here's the kind of thing I mean:
lim .999... = 1
This statement, as its written, doesn't make mathematical sense. You can't take the limit of a number.
I have a degree in mathematics. Not a phd, but I've worked with math phds before and in my experience they're the most precise people around who are very clear about what they mean. I'm trying to give you the benefit of the doubt, but I just can't imagine one of them writing something like that.
apparently you didn't thoroughly read the pdf paper I linked to in its entirety and FYI, you certainly can take the limit of most any number that has in infinite number of digits (normally a series) - I didn't write the entire nomenclature out as a series (which this number actually is) because I thought you could figure out the concept, perhaps I over estimated you.
when someone abbreviates to save time, that doesn't make them sloppy, it just means they have better things to do than dig out all of the appropriate fonts and symbols to get a point across, a relatively easy to comprehend point at that.
you certainly can take the limit of most any number that has in infinite number of digits (normally a series)
No you can't. You can take the limit of a sequence or a series or a function. A number with infinite digits is defined as the limit as n approaches infinity of some series. That doesn't mean you are taking the limit of the number. Those are different things and a math phd would understand the difference.
You're not abbreviating. You're mixing up concepts.
i didn't even click on the pdf and I'm glad I didn't because it seems like it would be a waste of my time. Like I said, respond to the proof I posted above and be clear about which part you disagree with.
see, this is why your knowledge of math is limited to the calculus level, because when someone presents a paper that might expand your knowledge past high school level, you don't even want to look at it - that's sad
It's not that, I love having my mind expanded. But I only have 24 hours in a day and have to budget the time wisely.
When someone who doesn't even understand basic calculus links me to a paper they claim will expand my mind, but refuses to give me an overview of it, it's probably not a great use of that time.
I've been begging you this whole time: explain to me in some condensed form how the proof I posted above is incorrect. Which part specifically is untrue and why. I'll even repost the proof for you:
The number .999... is actually just an infinite sum. .9 + .09 + .009 + .0009 + .00009 etc. Another way to write that is (9/10) + (9/100) + (9/1000) etc.
This can be re-written as a power series "the sum" from 0-infinity of (9/10)(1/10)n.
This is a special kind of power series known as a "geometric series" which is known to equal a/1-r. a in this case is 9/10, r is 1/10. Just plug them in and do the arithmetic:
(9/10)/(1-1/10)=(9/10)/(9/10) = 1.
Don't give me any bullshit about your "phd" or link me to some esoteric paper. Just explain which premise is wrong in there any why.
Lol I'm really not though. I love math and I love learning new math.
I think you got caught exaggerating your knowledge and now are trying to cover that by insulting me.
Either way, .999...= 1. I proved it and you haven't even acknowledged the proof in the dozens of comments here.
Maybe your arrogant and dismissive tone is preventing you from learning something? I dunno, either way I'm done with this. Next time you pretend to have a phd, you should probably make sure you actually understand the fundamentals of the subject you're lying about. Just a thought.
you only "proved it" using the low grade math that is down at your speed - i.e. calc 2 - when you learn higher levels, you'll find that the elementary level "proof" we provided you, doesn't hold
however you are scared to learn more, because you are scared of what you don't know
reminds me of how republicans deal with science - they only want there to be enough so that they can use their iPhone, and drive their car - otherwise, science is BS
and when you call them out - they quickly bail (like you did)
I think you need to read the wikipedia article that you cited, and start at the paragraph titled Infantesimals and read on from there to the end.
This is a highly debated point in higher math circles, and illustrates why many conventional mathematical proof models fall apart when it comes to infinite series, I suppose you are one who has fallen for that 100 year old hoax that 1+2 + 3 + 4+ ...., = -1/12 too?
Woah... I mean, I can see the performance being improved, but that sounds like some pretty potentially dangerous undefined behavior... Is it really worth it?
lw9k · 3 points · Posted at 09:04:34 on February 14, 2016 · (Permalink)
Yes, because small integers are used a lot and this prevents a lot of needless allocations.
You don't use is very much in idiomatic python, it is actually pretty rare, and anyone using it is likely aware of this.
BTW None is None, which is actually faster than using == IIRC
[deleted] · 3 points · Posted at 00:38:06 on February 14, 2016 · (Permalink)
Wait.. What
[deleted] · 53 points · Posted at 02:13:10 on February 14, 2016 · (Permalink)
It's a joke about rounded values. It's not mathematically true.
Usually it goes 2 + 2 = 5 for sufficiently large values of 2 and sufficiently small values of 5. For example 2.4 + 2.4 = 4.8, which would be rounded to 2 + 2 = 5.
[deleted] · 2 points · Posted at 05:50:31 on February 14, 2016 · (Permalink)
I may have missed the reference, but at least I have chickens!
[deleted] · 1 points · Posted at 02:16:16 on February 14, 2016 · (Permalink)
Doesn't really matter. 3.999... = 4, but in no way is it 3. That's just plain wrong. And the only way we ended up with this mess is because someone was trying to retell a joke about rounding that they never actually understood in the first place.
I know that, but it doesn't mean people won't argue.
[deleted] · 4 points · Posted at 02:15:04 on February 14, 2016 · (Permalink)
There is no argument. There's just people who know that .999... = 1 and people who don't understand why and refuse to accept that maybe they're just dumb.
[deleted] · 3 points · Posted at 02:14:07 on February 14, 2016 · (Permalink)
That's not 3 in any sense of any of the words involved. 3 = 4 is a bad version of the joke, because no one actually rounds that way. It should be something like 1 + 1 = 3.
That's not 3 in any sense of any of the words involved.
Except for prices. See a $3.99 price tag? Yea, that's 3 bucks.
[deleted] · 1 points · Posted at 03:53:51 on February 14, 2016 · (Permalink)
Yea, that's 3 bucks.
That's just being gullible and terrible at rounding. If I see a number that starts with 3 in a store, I just assume it's closer to 4. 99% of the time it's true.
Didn't Kia get all the greatest minds together to work this one out?
ersils · 1 points · Posted at 03:35:15 on February 14, 2016 · (Permalink)
5/7=10/10
Drews232 · -2 points · Posted at 03:16:46 on February 14, 2016 · (Permalink)
5 out of 7 = 9 out of 10
aahdin · 317 points · Posted at 20:37:56 on February 13, 2016 · (Permalink)*
Euler's identity always seemed ridiculous to me.
ei*x= cos(X) + i*sin(x)
ei*pi = -1
You just take random constants that seem like they have nothing to do with each other, and then somehow they do. The proofs I've seen don't really explain much either, other than "the math works out".
Edit: Wow, ton of great responses and explanations. After reading most of this I actually feel like I've got a decent understanding of how it all works.
Jorlung · 64 points · Posted at 22:05:40 on February 13, 2016 · (Permalink)
Proving it using the Taylor Series definition for eix , sinx, and cosx is pretty easy to understand.
aahdin · 17 points · Posted at 23:06:49 on February 13, 2016 · (Permalink)
So both of the common proofs for it are easy enough to do, but they both left me without any kind of intuitive reason why they should work out or what's actually going on.
The closest I've been able to get is that eix is actually a way of rotating your function around the imaginary axis, which is even more confusing.
Jorlung · 11 points · Posted at 23:26:21 on February 13, 2016 · (Permalink)
I don't know if there's an intuitive way to think about it to be honest, maybe there is, but I've always just kind of taken it as something that's true.
If you ever take course in Quantum Mechanics or Control System you start getting a lot more comfortable bouncing around from complex exponential and the s-domain to sins and cosines.
healynr · 13 points · Posted at 01:47:20 on February 14, 2016 · (Permalink)
Man, betterexplained is great. Having not had a math class in a decade and a half and having never gotten into calculus, I still don't understand it entirely, but I feel like it's something I could understand - not, as the author says, simply some magical incantation that just works because it works and doesn't inherently mean anything.
(Which, coincidentally, is why I quit math to begin with...)
aahdin · 3 points · Posted at 23:32:23 on February 13, 2016 · (Permalink)
I actually started googling around after reading your first comment, and I found this video.
I'm still trying to wrap my head around it, but it's making a lot more sense to me now than it did an hour ago.
[deleted] · 2 points · Posted at 02:41:00 on February 14, 2016 · (Permalink)
I had a lot of problems with trying to understand the visualisation, but the formulas make sense to me. If you have a spare half an hour, watch this lecture. It requires some basic understanding of calculus though (so does eπi = -1 though)
Think about the definition of ex. It is 1 + x + x2 /2 + x3 /6 ... for a reason. When you take the derivative of the series, each term becomes the previous term and you end up with the same series. That's what makes this particular infinite series special enough to warrant its own name.
eix was defined in a similar way in order to mimic this property as closely as possible. And indeed, we end up with -eix which is at least close to its own derivative. This helps complex exponentiation be as natural an extension of the real numbers as possible, it's why calculus works so similarly on complex equations.
(By the way, people needs to stop calling these "proofs"! Euler's formula is a definition, it is the foundation of complex exponentiation. You cannot prove definitions, you can only prove that the definition carries desirable properties.)
ReidZB · 1 points · Posted at 03:47:57 on February 14, 2016 · (Permalink)
If you have a copy of Needham's Visual Complex Analysis (hint hint, look at the search results...!), then he tries to explain Euler's formula in an intuitive sense on page 10.
It also says there are "deeper" explanations later in the text, but I haven't looked at the text in such a long time that I don't really remember where; my complex analysis course was a while ago now.
However, I can recommend Needham's text for a "visual" explanation of many topics in complex analysis. Sometimes, they are more intuitive than the symbolic approach, though definitely not always. In my complex analysis course, we essentially came to the conclusion that Needham's text would be an excellent companion for a real, rigorous text on the subject, but that it couldn't really stand alone for a rigorous complex analysis study.
I think about it algebraically. The numbers of the form e2pi/n are called the roots of unity, and these are numbers whose nth power is equal to 1. ei*pi is a second root of unity because (-1)*2 = 1.
If you google the phrase, you'll see the geometry of the roots of unity, all of which are complex except 1, and -1, and it'll hopefully give a more satisfying depiction of what's going on.
That isn't a proof though. Technically Euler's formula cannot be "proven" at all, since it is a definition-- that is, it is defined to equal that series in the first place. All you can do is prove that certain properties of this definition hold, which validates the definition is well chosen. The people creating complex numbers wanted the system to have certain properties, such as being an extension of the real numbers.
Think about what properties we'd want ei*x to have when defining it for the first time. Well, in the reals, ex is its own derivative-- that's kind of why ex was named in the first place. Can the complex extension have a similar property?
For the reals, ex was defined as a particularly useful infinite series which has the nifty property that taking the derivative of each term gives you the previous term in the series, which conspires to give you the exact same series you started with, making it its own derivative!! In trying to simulate this clever property, we might try defining eix in a similar way with a similar series in the most intuitive way possible. Sure enough, we get -ei*x as the derivative, which is highly reminiscent. And helps give rise to a concept of complex exponentiation where calculus is very consistent along real and complex axes. Complex analysis is really only possible because this definition was well chosen. (And of course, if you scoop up the terms from the -ei*x series definition, you end up with cosx + isinx)
Really anyone could create their own extensions of the real numbers with differing definitions, they'd just either likely be less useful, or in some sense "boil down" to something that already exists, such as complex numbers. But that's not a guarantee, there are likely many useful mathematical constructions that have yet to be discovered.
That's the much more useful and interesting one, unfortunately it's not used by most people so maths fans (as opposed to maths users) care more about the pretty one they don't care to understand.
What are exponential functions? They are just functions that are some multiple of their own derivative.
For example, the derivative of e3x is 3e3x; that is, just 3 times itself.
Going the other way around, if I told you that the derivative of a function f(x) was 5 times itself, it would be possible to show that f(x) is just an exponential function with "5x" in the exponent.
Now, what's the derivative of cos(x) + i*sin(x)? It's just -sin(x) + i*cos(x). Since i2 = -1, after factoring out an i, we see that the derivative of cos(x) + i*sin(x) is just "i" times itself. Therefore, this function must be an exponential function with "ix" in the exponent.
There's a great video by 3blue1brown on youtube explaining in terms of stretching and sliding. Essentially, instead of thinking of numbers as counting objects, think of them as marking an infinite line. In this system, adding 3 moves zero to where 3 used to be, multiplying fixes 0 and moves 1 to where 3 used to be, and exponents stretch in such a way that adding and then stretching is the same as stretching and then adding.
You can then extend this to the imaginary ( i ) plane by thinking of the real numbers as the horizontal axis and the imaginary numbers as the verticle axis. The same rules apply, except now exponents with imaginary components rotate the plane so what used to be the real axis is now in the complex space. Because of how pi is defined (half the circumference of a circle), an exponent of i pi rotates all the way around to -1.
eix is complex so eix = A(x) + i*B(x) where A and B are real functions. A can simply be zero, or a function.
As stated above, one of the definitions of e is that derivative of ex is ex. By this definition, the similar special attributes of e's and the sin/cosine's derivatives are what make them related.
d/dx(eix ) = ieix,
so d/dx(A(x)+iB(x)) = iA(x) - B(x).
Now, since A(x) and B(x) are in themselves real, d/dx(B(x))=A(x) and d/dx(A(x)) = -B(x).
A=cos(x) and B=sin(x) fit this derivative behavior perfectly.
tldr: eix and the sine functions are related in that they both simply change signs when being taking the derivative of (forever).
_Psyki · 1 points · Posted at 05:32:42 on February 14, 2016 · (Permalink)
It may not be very intuitive, but you should look into Taylor Series expansions for ex , sinx, and cosx. This then leads into proving that complex numbers expressed in polar form r(cosθ+isinθ) can also be expressed in exponential form reiθ .
eiπ can then be shown to be a complex number with modulus (distance from 0) 1 and argument (anticlockwise angle from positive real axis on an Argand Diagram) π, i.e. cosπ + isinπ = (-1) + i(0) = -1.
The only other time the complex number has no imaginary part (so is a real number) is at θ = 0, but this just gives e0 = 1 which is hardly surprising.
Salman Khans video on khanacademy regarding Euler's Identity is what cemented my love for math, it's great to watch.
underr_ · 1 points · Posted at 06:59:07 on February 14, 2016 · (Permalink)
Had to prove this as my uni for our first test. Had never seen it before, had about 4 hours to stare at it. Most gruesome thing I think I've done at that school.
IZ3820 · 1 points · Posted at 08:14:03 on February 14, 2016 · (Permalink)
Okay, best way to think of it: Rotation around the complex plane (in terms of radians). Cos(x) would define the x part of a point on this circle with radius 1. Sin(x) is the y part. i is that awesome variable that doesn't mesh nicely with the real numbers, so it pushes the real numbers, which you know to be on a number line, now onto a number plane! (Want to read more? "Argand diagram".) If you can accept cos(x) being the x direction now and isin(x) being the y (which is clear because of the i part), we can move on! So by adjusting x, we move around this circle, cool, but why is that eix? If you multiply complex numbers together, their angles on the complex plane add up and their lengths multiply. If you force the length to be 1, then, multiplying by more length 1 points, lying on this circle I brought up, you can accomplish rotation. This is incredible that multiplying gives of rotation, so let's reason through it. Positive real numbers multiplied by themselves stay positive. This makes sense because this number is at 0 rotation, and adds 0 rotation to itself. Now take and negative and do the same thing. This makes a positive, which makes sense because negative numbers are a half rotation from positive ones, and two halfs make a whole rotation back to positives. Now, last one: ii. An imaginary squared. That is negative! Positive Imaginary numbers are a quarter rotation, so two quarter rotations make the number just negative! So taking a complex number, one with the real and i parts, to an exponent makes a rotation if the distances are 1. Great! So why e? E is the natural numbers, so think: Natural growth! If the number was 3ix, it would multiply to go out further than one, and if it was 2, it would shrink, but e keeps the exact distance of one around the axis going! And that exponent causes rotation, so eix makes a circle around the complex plane, as does cos(x)+isin(x), so they are the same! Using this, pi is a half rotation, a half rotation from 1 is -1, so ei*pi is -1! It's late for me, so this explanation might feel complicated, but here:
TL;DR: cos(x)+isin(x) makes a circle of radius one, simply by rules of trig. Multiplying complex numbers rotates them. eix always has a distance/magnitude of 1, and is complex with exponent, so rotation occurs. Both then have to be equal since they are same thing!
Imagine a particle in the complex plane moving along the path e{it}. The velocity of the particle is the derivative of position with respect to time which is ie{it}. Now multiplying a complex number by i corresponds to rotating it counterclockwise by 90 degrees, so the particle's velocity is always perpendicular to its position. But this is exactly motion along a circle of radius 1, so e{it} = cos(t) + i sin(t)
It helps a lot more to understand what's going if you know the imaginary definitions of sin and cosine can be defined exponentially over the complex numbers
For example sin(θ) = (eiθ-e-iθ)/2i
Now it seems more intuitive that π can be related to e and i.
mattbin · 1 points · Posted at 14:46:01 on February 14, 2016 · (Permalink)
Last day of first year calculus the prof dropped this on us. It blew my tiny undergraduate English major mind.
There are aproximatly 10 trillion trillion Planck lenghts in the width of a hydrogen atom. So I would guess you would need about 24 more decimal places.
To take it one step further than the size of a hydrogen atom: the circumference of a circle the size of the observable universe accurate to the size of a proton would only need 43 digits.
Which is the GEO600 experiments (lately known for participating in finding gravitational waves) precision compared to the distance of sun to earth. Down to the diameter of a single hydrogen atom.
[deleted] · 0 points · Posted at 02:35:47 on February 14, 2016 · (Permalink)
Irrational numbers go on forever. But most of the time we don't need infinite numbers.
If we only need a number 5 digits long, then we start by looking at the sequence (3.141592653…) and we pick the closest 5 digit number to it. In this case, 3.14159… is much closer to 3.1416 than 3.1415 (i.e. 59 is a lot closer to 60 than 50).
How many digits? I've got 70, but I've found that most people who put in the effort to memorize some digits stop at more "round" numbers. 100, specifically. I'd go for 314 but... That's just way too many for me.
[deleted] · 14 points · Posted at 01:53:45 on February 14, 2016 · (Permalink)
Used to know over 1,000. Only recited 611 for the competition.
It's a neat party trick especially because someone eventually calls you out by saying "Oh you're probably just making up numbers." So I've got a recording on my phone that I'll whip out and recite the digits in sync with the recording.
JPK314 · 1 points · Posted at 06:55:22 on February 14, 2016 · (Permalink)
Any tip on how to remembering the Numbers? I also have a contest coming up
[deleted] · 2 points · Posted at 03:03:53 on February 14, 2016 · (Permalink)
Nope, sorry. I just have a good memory I guess, I don't use any strategies.
UceOnOCE · 1 points · Posted at 09:36:11 on February 14, 2016 · (Permalink)*
I remember them in chunks of about 4 or 5. When I recite them in my head it kind of has a melody to it.
Quaisy · 1 points · Posted at 01:44:58 on February 14, 2016 · (Permalink)
How far did you memorize up to?
[deleted] · 6 points · Posted at 01:53:03 on February 14, 2016 · (Permalink)
I used to know like over a 1,000 but forgot most of it then I heard about this competition the day before so I only managed to memorize up to like 611. (Which sounds like a lot but it's not since it's all kinda in the back of my memory since I used to know it)
Quaisy · 5 points · Posted at 01:59:45 on February 14, 2016 · (Permalink)
Ah wow, when I was in elementary school I memorized up to 28 digits and as I grew older I became less and less interested in mathematics but those digits have always stuck with me. 28 is enough to impress people though!
That reminds me of a story a friend of mine told me about.
His middle school had this "Recite pi for pie!" competition. The idea being, whoever could recite the most digits would earn a pie. He wanted the pie, so he got to work and memorized 200 digits.
The thing is, he didn't know how many digits other people had memorized.
The second place competitor had memorized pi to 10 digits.
The pie sucked.
[deleted] · 1 points · Posted at 03:29:35 on February 14, 2016 · (Permalink)
That's kinda how I felt because second place only memorized like 300 digits.
In university I got a 2-4 of beer for reciting it to 62 digits. That's about a $40 value.
I'd have to say between you and I, I got the better deal ~ $0.64/digit vs $0.51/dgt
[deleted] · 1 points · Posted at 21:12:53 on February 17, 2016 · (Permalink)
Ya, but if I try again next year and get up to 1,000 and something (not sure the exact amount) I get bragging rights for being the most memorized in the University of Waterloo Pi Recitation contest ever... the only question is whether or not it's worth it. Also, I don't really like beer much.
zarraha · 20 points · Posted at 23:43:45 on February 13, 2016 · (Permalink)
You only need to know pi to the 3rd digit, anything more isn't practical. Any calculation that requires more precision than that is going to be a nightmare to do without a calculator, which knows more for you.
[deleted] · 5 points · Posted at 23:39:56 on February 13, 2016 · (Permalink)
I don't like this one. If I make a life decision based on the 40th digit of pi, I have found a real physical application for it (I just prodded someone because it was odd). Pi has applications outside of circles and chaotic systems can 'resolve' circles to higher precision than this. Yes I'm being pedantic but welcome to the world of maths.
ScLi432 · 8 points · Posted at 23:59:51 on February 13, 2016 · (Permalink)
Or be an engineer rather than a mathematician in which case
pi ~ 3ish
I work on a particle physics project, and recently I found some of our code has the wrong value for pi in the 5th decimal place (3.14156 instead of 3.14159), it's not rounded it's just wrong, and while I can't imagine it has any real effect it's still bugging the crap out of me because there doesn't seem to be any reason for it.
[deleted] · 1 points · Posted at 06:03:58 on February 14, 2016 · (Permalink)
In numerical work I do there's no point having pi to huge precision at all since the integrals in the calculations are only accurate to 6 significant figures.
Similarly in "real world science" you're unlikely to know your measurements to more than 4 significant figures.
[deleted] · 0 points · Posted at 14:39:13 on February 14, 2016 · (Permalink)
You have no idea what you're talking about.
[deleted] · 18 points · Posted at 22:58:42 on February 13, 2016 · (Permalink)
Some mathematicians in the 16th century toyed around with the idea of taking the square root of a negative number and almost 4 centuries later it was discovered that system they had made to calculate this perfectly described the mathematics of an alternating currency circuit.
[deleted] · 5 points · Posted at 17:24:39 on February 14, 2016 · (Permalink)
They named the square root of -1 the number i. I is for imaginary (in electronics they use j because I is used for current). Think of it like a new counting system, we have real numbers and we have imaginary numbers. It's best to picture it on an argand diagram - a graph whereby the imaginary numbers are shown on the y axis and the real numbers on the X axis.
We now can imagine a point off the axis and we say that it is a complex number - it has a real and an imaginary part.
For example, 2 in the real domain, 4 in the imaginary domain is expressed as 2+4i.
Well it turns out all complex numbers (and therefore purely real and purely imaginary numbers) can be expressed in terms of sine and cosine.
Turns out in AC electronics, components can also be thought of in this way, whereby the resistance is a complex number. It's called impedance.
Remember the argand diagram? When dealing with electronics, it's not called a phasor.
We have a projection (meaning value) on x (real) and a projection on y (imaginary).
A resistor has a y projection of 0. A capacitor has a positive y projection and an inductor has a negative y projection.
We can plot the current and voltage on the argand diagram, where the village is at an angle with the positive x axis. We can then add the sinusoidal part in and increase this angle (called the phasor angle). This can predict values for voltage and current at certain points in the cycle, by taking the real value.
I figured out in High School somewhat of a shortcut for finding the square of a number.
Say you need to know 142 but don't have a calculator- I realized you could use the square of 13 (132=169) the add the sum of 13+14=27 so you'd end up with 169+27=196.
Another example: Finding 212 - 202=400. 20+21=41. 400+41=212
Does that make sense? I tried write a formula but wasn't able to.
Continuous functions that are nowhere differentiable are in fact fairly typical of continuous functions general. Look up Weierstrass functions when you get a chance.
I was being very loose in my use of adjectives and adverbs.
[deleted] · 2 points · Posted at 01:12:34 on February 14, 2016 · (Permalink)
Ah, the Monsters of Real Analysis! Largely the cause of the modern pure/applied division.
[deleted] · 2 points · Posted at 01:34:51 on February 14, 2016 · (Permalink)
In more ways than one! The set of continuous functions had measure zero in the Weiner measure ( from Brownian motion).
And they are nowhere dense in the supremum topology
[deleted] · 9 points · Posted at 02:49:55 on February 14, 2016 · (Permalink)
"Classical Wiener Measure" is the most giggle-inducing math phrase in my undergraduate-limited experience. Close up would be the Cox-Zucker Algorith or the Tits Group.
[deleted] · 6 points · Posted at 03:08:42 on February 14, 2016 · (Permalink)
There is also the Cuntz Algebra.
nyando · 3 points · Posted at 09:35:44 on February 14, 2016 · (Permalink)
So I've been sitting in front of the Wikipedia article about "Classical Wiener Space" for a solid minute just giggling to myself. Well done.
11669 x 3. Flip it over and you find out what she is afterwards.
Edit A, yes 16 years old. I learned it when I was 14 so it would've been a step up, go fuck yourself you puritanical freaks. B, loose metaphorically not physically, get a clue.
To everyone else commenting confused - girls get loose when they're turned on. Generally giving a girl oral pleasure turns her on, therefore loosens her up.
A girl had 69 boobs and that's too too too many. So she went to see Doctor X on 51st street and he went crazy and ate them all. Now she's boobless.
6922251x8= flip that over
There was a girl with a 69 size bra which was 2 2 2 big, so she went to 51st to visit mister X who gave her 8 pills, now she's boobless! 6922251x8 = 55378008
There was once a girl who was thirteen her breast size was eighty four but she wanted it to be forty five. She went to the doctor and the doctor said "Oh, take these pills two times a day" but she took them four times a day because she wanted smaller breasts and she ended up...
13844502 x 4 x 1 = 55378008
ToxDoc · 2 points · Posted at 01:34:53 on February 14, 2016 · (Permalink)
Can't...turn...iPhone...screen...over. Head going to explode.
[deleted] · 587 points · Posted at 20:11:58 on February 13, 2016 · (Permalink)
Monty Hall problem
Still makes no sense to me, it's one of those things that computer experiments shows to be true, but it has fooled mathematicians and also often makes no intuitive sense (though there are particular ways of thinking about it or framing it that can make better intuitive sense).
memeship · 12 points · Posted at 01:16:15 on February 14, 2016 · (Permalink)
I remember when I was young in college having trouble grasping the concept, so I wrote a program to calculate it for me to prove that it was true. It was.
That was fun. I probably still have the web page I built that simulated the game somewhere online.
The answer to what? Not switching? Cause switching is a 2/3 chance. Not switching is a 1/3 chance of getting it right, but that's usually not the part that people disagree on. Most people argue that switching doesn't matter. They incorrectly assume that their odds of winning remain 1/3.
So I'm not sure if you just had a typo or misexplained, but it sounds like you owe your programmer friend some cash.
Not switching is a 1/3 chance of getting it right, but that's usually not the part that people disagree on.
Yes, it is. Because the people who get it wrong will tell you that they have a 1/2 chance of getting it right (because there are only 2 doors left), when it's still 1/3. So he makes perfect sense to me.
If your strategy is to always switch doors, you will win 2/3 of the time. Not switching will result in winning 1/3 of the time.
Like I said, the part that people typically disagree on with this problem is whether switching increases your chances of winning. The answer is "switching increases your odds of winning."
So I'm not sure why you would bet someone "the answer is 1/3." They either argued a part of the problem that was never meant to be argued, or the person just made a flub in their comment.
The reason why you wouldn't argue "not switching is a 1/3 chance of winning" is because the answer is very intuitive.
Saying switching the doors increases your odds of winning to 50%, while still wrong, is closer to being correct than saying they remain the same. This is because it'll lead you to the correct strategy of always switching. The reason people think this is because they assume that the odds only matter when you're switching (you're either going to win or lose). That's not correct, though, since it ignores the fact that you had to make an initial 1/3 probability guess.
Again, assuming he didn't typo or anything of the sort; at some point during this typical argument, the other person will say "but there are only 2 doors remaining, it's a 50/50!" In other words, "there's a 1/2 chance of my door being the good one!".
I assume that the OP replied "no, you only have a 1/3 chance of winning if you keep your door". At this point, they bet. 1/3 wins the bet, 1/2 loses it.
This whole "initial 1/3 probability" remaining relevant is what people fail to grasp, as they usually equate 2 doors remaining to a coin flip.
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? (Whitaker, 1990, as quoted by vos Savant 1990a)
And what people usually assume:
When first presented with the Monty Hall problem an overwhelming majority of people assume that each door has an equal probability and conclude that switching does not matter (Mueser and Granberg, 1999).
Note how the problem is asking "should you switch." This is equivalent to saying "what are the odds of winning if you switch?" Certainly you can understand why I'm confused that someone would bet "the answer is 1/3" and consider themselves the winner. It's not the correct answer.
If the OP and their programmer friend were really just arguing what the odds of picking the correct door out of 3 possibilities are (not the Monty Hall problem), then I'm surprised it required a computer simulation.
Hey man, I really don't feel like arguing something that's been argued to death for multiple decades.
I'm not arguing the problem itself, we both understand how it works and what the correct answer is. Do take a second to read the previous posts before you criticize someone and tell them they owe money to their friend. Spend an additional second on the context if necessary.
Note how the problem is asking "should you switch."
Which is basically the same thing as asking "should you keep". As I said, you're getting crazy about a simple difference in formulation. To people who get it wrong (and as you pointed out, answer "it doesn't matter") it literally does not matter. Whether you ask "keep" or "switch", it's the same thing.
Put in mathematical terms, their answer is strictly equivalent to "I have a 1/2 chance of winning by keeping my door". To which you'd logically reply, "no, it's only 1/3."
If the OP and their programmer friend were really just arguing what the odds of picking the correct door out of 3 possibilities are
Again, they're (supposedly) arguing their odds AFTER a door has been opened, which is exactly what the problem is about. They just happen to be talking about keeping the initial choice (1/3) rather than the switching possibility (2/3).
"Should you keep" is literally the exact opposite of "should you switch." The answer is, unsurprisingly, completely different.
Not sure why you're trying to argue this so much. Their post was confusing. I asked for clarification. You're incapable of giving that clarification, so why are you still commenting?
Again, they're (supposedly) arguing their odds AFTER a door has been opened, which is exactly what the problem is about. They just happen to be talking about keeping the initial choice (1/3) rather than the switching possibility (2/3).
Are you the person I responded to? No. So perhaps you shouldn't answer for them, since I was asking them exactly what you're trying to say is "supposedly" what they originally argued.
"Should you keep" is literally the exact opposite of "should you switch." The answer is, unsurprisingly, completely different.
From the point of view of someone who didn't get the problem, no, it's exactly the same thing - and their answer is the same; "it doesn't matter".
Not sure why you're trying to argue this so much. Their post was confusing.
Again, the original post was fine, and in context, easy to understand. You're the one making a fuss about it.
I asked for clarification. You're incapable of giving that clarification, so why are you still commenting?
I was capable of clarifying and did so. You appear to be unable to grasp it, don't blame it on me. Next thing we know it'll be the teacher's fault that you landed in a special needs class.
Are you the person I responded to? No.
I took pity on your lack of understanding and tried to give the explanation you asked for (or rather, whined about). I'm starting to wonder whether you were really clueless enough to misunderstand the OP, or whether you just decided to troll and play dumb. Either way I'm done with you.
So in the context of the Monty Hall problem, I'm supposed to know that they were arguing something that's not the Monty Hall problem? There's something wrong with asking them what they were arguing? What the hell are you smoking?
Seriously, you're just being a bit dumb about this.
[deleted] · 5 points · Posted at 03:55:47 on February 14, 2016 · (Permalink)
You also make it sound like a program to simulate that is hard to write. It isn't.
memeship · 12 points · Posted at 02:01:33 on February 14, 2016 · (Permalink)
Humble brag? I wrote this when I was in college. Any CS student would be able to write a program to simulate the Monty Hall experiment. There's nothing to brag about here.
Simply relating to the problem, and how I personally came to understand it better.
Here are the relevant bits if you'd like (Javascript):
var runSequence = function(iterations) {
var numberStayed = 0,
numberSwitched = 0;
while (iterations--) {
didChooseCorrectly() ? numberStayed++ : numberSwitched++;
}
return [numberStayed, numberSwitched];
}
var didChooseCorrectly = function() {
return Math.floor(3 * Math.random()) === Math.floor(3 * Math.random());
}
runSequence(1000);
As you can see, the comparison in the didChooseCorrectly() function illustrates pretty well how the results rely on whether or not you chose correctly first, which you have only a 1/3 chance of doing.
[deleted] · 8 points · Posted at 02:20:31 on February 14, 2016 · (Permalink)
"G-G-Guys, I can do this too! Guys, see, I can do it too! Me! I can do it! Me too!"
chill bruh
jacybear · -13 points · Posted at 02:28:36 on February 14, 2016 · (Permalink)
I actually didn't say that, nor did I imply it. I'm quite chill.
0raichu · 9 points · Posted at 04:26:48 on February 14, 2016 · (Permalink)*
jacybear · -7 points · Posted at 04:47:23 on February 14, 2016 · (Permalink)
A way to explain the problem that everybody understands is to just increase the number of doors. Instead of three doors, there are now a hundred doors. You pick a door at random and Monty then opens up every other door except one. Either the prize is in the door you picked first, or it's in the door that's left unopened. Which should you pick? Everyone knows that they probably didn't pick the right door at the start, and so it becomes much clearer why switching is the better strategy.
I couldn't understand it until I read something similar. Increase the number of doors to one million, choose one, and eliminate 999,998 incorrect doors. The odds of my choosing the correct door were one in a million. I know one of the two remaining doors is the correct door, and the odds are overwhelmingly in favor of it being the remaining door I did not choose.
I like explaining it backwards. Based on the rules of the problem, you have 3 possible initial selections. Based on each proposed strategy, these are the following ways to lose:
Always switch:
You initially pick the winning door.
Never switch:
You pick losing door 1.
You pick losing door 2.
Now just consider the odds of those happening. Remember there's 3 total initial possibilities for each strategy. If you always switch, you have a 1/3 chance of losing. If you never switch, you have a 2/3 chance of losing.
[deleted] · 19 points · Posted at 22:47:10 on February 13, 2016 · (Permalink)
[deleted]
sklos · 34 points · Posted at 23:09:17 on February 13, 2016 · (Permalink)
The door opened being never the correct one is the entire point. Thus, if you originally chose one of the two incorrect ones switching is a winning move, and if you originally chose the one correct one switching is a losing move.
If they choose the door randomly, then yes, switching doesn't change things because 1/3 of the time it will uncover the prize -- but the problem specifies that a door known to not have the prize is opened.
The easiest way to show that switching wins in the normal case is to change the game in two steps:
Step 1: After showing a non-prize door, offer to trade both remaining doors for their original selection -- since one is worthless, this doesn't change the game in any real way.
Step 2: Now just point out that you know of a door you can open to show that it doesn't have the prize, and the player knows this too, so you don't have to actually open any door -- and now, offer to trade both closed doors for their original selection.
The original show never actually had the option to switch. That was a later addition to make it into an interesting problem. The thought experiment was named after the game show just because of the "pick one of three doors" idea.
And yes, your confusion is one of the core reasons people argue about this thing. If the host opens doors at random and happens to open a door with a goat, your odds are 50:50. If the host knows what door the prize is in and always opens the door with a goat, then your odds are 1/3 win if you stay, 2/3 win if you switch.
Which just makes the whole thing more mysterious! The knowledge and actions of the host affect the probabilities!
That doesn't really change anything. Either the host opens the door with the car and it cannot possibly matter what you do, or he opens a door with a goat and you have 2/3 chances if you switch.
[deleted] · 1 points · Posted at 08:38:18 on February 14, 2016 · (Permalink)*
You don't always win by switching. You could still switch to the wrong door.
jmt222 · 2 points · Posted at 13:28:35 on February 14, 2016 · (Permalink)
If your strategy is always switch and your first choice was wrong, then the host eliminates the other wrong door. There is only one door to switch to, which must be the winner.
Oh I get it. It's because if you switch you get the benefit of your host disqualifying one of the doors. If you don't switch then you lose that advantage.
If the host never shows a door between rounds then it would be even odds either way. But since he does, he works for you.
joeykip · 1 points · Posted at 03:49:16 on February 14, 2016 · (Permalink)
This is the perfect response, and perfectly sums up the five-minute, convoluted explanation I always attempt to give when this question comes up.
[deleted] · 1 points · Posted at 04:01:45 on February 14, 2016 · (Permalink)
[deleted]
jmt222 · 1 points · Posted at 13:32:16 on February 14, 2016 · (Permalink)
No. My initials are J.M.T.
[deleted] · 1 points · Posted at 06:11:21 on February 14, 2016 · (Permalink)
HOW. THERE IS A 50 PERCENT CHANCE OF GETTING THE WRONG DOOR.
[deleted] · 1 points · Posted at 06:27:30 on February 14, 2016 · (Permalink)
Okay, ignore the rest of the problem. There are three doors and one car. You pick a door at random. What are the odds that you picked the wrong door?
[deleted] · 2 points · Posted at 06:29:18 on February 14, 2016 · (Permalink)
2/3!!
[deleted] · 2 points · Posted at 06:59:39 on February 14, 2016 · (Permalink)
Right, so say there’s a strategy that gives you these results:
If you picked the wrong door, you win!
If you picked the right door, you lose!
As you’ve just said, the odds that you picked the wrong door are 2/3, so a strategy like this would give you better-than-even odds. Agreed?
[deleted] · 1 points · Posted at 15:47:22 on February 14, 2016 · (Permalink)
The part I don't get is since it's still a 50% chance of getting a wrong door.
I understand what you're saying and why, but also whyyyy.
[deleted] · 2 points · Posted at 16:32:46 on February 14, 2016 · (Permalink)
Where are you getting 50%? If you pick 6/49 lotto numbers, the odds that you won are 1/13,983,816. Telling you 13,983,814 picks that lost based on what you picked, after you picked (maybe this is the part you’re missing? the host doesn’t open the preview door randomly) does not increase the odds that you won. Sure, if the number of options were reduced to 2 before you picked, then you would have a 50% chance. But it’s after.
Clyzm · 1 points · Posted at 07:14:41 on February 14, 2016 · (Permalink)
This is probably the most succinct way I've ever seen this explained.
But since you're deciding again, isn't it 50/50? The choices are basically, if you originally picked door number one and he puts down door three, do you pick door one or door two? Since he offers you another guess, you're making a new choice. That's what bothers me about it.
The odds are based on your initial choice. You have a 1/3 chance of picking the correct door initially, right? If one of the wrong doors is then removed, do you suddenly have a 1/2 chance of your initial choice having been the correct door?
A good way to think about it is that the doors are not removed, they're just marked as incorrect but you can still pick them if you want (even though you know they're incorrect). So you pick a door (1/3 chance of it being right), a door is marked as wrong but is still there (so you still have a 1/3 chance of being correct) - you'd be stupid to pick the one you know is wrong so the only real choice is do you switch to the other unknown door or keep what you've got. Now, you have a 1/3 chance of you initial pick being right, so a 2/3 of it being wrong. You know for a fact that one of the doors is wrong, but there's still three doors so the odds still have to make 3/3. So if your initial choice was 1/3, and one door is known to be wrong, that 2/3 has to be behind the door you didn't initial pick and that hasn't been marked as wrong.
Do you suddenly have a 1/2 chance of your initial choice having been the correct door
Yes, because although when you picked it initially it was 1/3, you are now making a new choice: door number one or two? Picking door number three at this point is as good as picking door number four: since you know that won't get you the prize, you know picking it gives you a 0/3 chance of getting the prize. If door number one remains as 1/3 when door three is marked as incorrect, then door two also remains as 1/3. Before, the prize had an equal chance of being behind any of the three doors. Now there's only two (relevant) doors, and you have to decide if you want to stay on one or pick two. But, at that point, you're making a new decision: door one or door two? If you came on the show and were only offered two doors, it would be the same situation, pick one or the other.
What about this: you come on the show, there's four doors. Before you even make an initial choice, he tells you that door four will be an incorrect choice. Are your odds still one in four? Not to me, because you can make the informed decision of ruling out door four, so it's really just one of three doors. You know it's behind one of the three. 1/3, even when there's four doors. So, with the original problem, it's 1/2, even when there's three doors. Your information makes it 1/2 for you.
Here are all the possible outcomes for the problem in a table. The door Monty opens doesn't affect your choice and doesn't give you any new information - there's no way for you to know whether the door that's being opened is being opened because it's the only one that both doesn't have the prize AND isn't one you picked, instead of just being one that doesn't have the prize (this is why, where possible, the door that Monty opens is "x or y").
You Pick
Prize Door
Monty Opens
Don't Switch
Switch
1
1
2 or 3
WIN
LOSE
1
2
3
LOSE
WIN
1
3
2
LOSE
WIN
2
1
3
LOSE
WIN
2
2
1 or 3
WIN
LOSE
2
3
1
LOSE
WIN
3
1
2
LOSE
WIN
3
2
1
LOSE
WIN
3
3
1 or 2
WIN
LOSE
3/9 wins
6/9 wins
The reason you're getting stuck is because you're "ignoring" the information you have at the start and are treating the two different choices as independent, when in reality the second choice is dependent on the first: whichever door you pick initially has a 1/3 chance of being the one with the prize but a 2/3 chance of NOT having the prize. Removing a door doesn't change the odds of the decision you've already made - if you chose an incorrect door initially (2/3 chance) then the prize MUST be behind the only remaining option once an incorrect door has been removed. If you chose the correct door initially (1/3 chance) then you are guaranteed to lose if you switch, regardless of which door is removed. So 2/3 of the time you'll have picked a losing door initially and switching will be a win, whereas 1/3 you'll have picked the winning door initially and switching will be a loss.
So, if you're doing it multiple times it's best to always switch, because 2/3 of the time you'll get the prize, but if you only doing it once, which is what I assumed because that's how game shows usually work, it's just as likely that switching will get you the prize as not switching. Say the prize is behind door 1. You initially pick door 1. He puts down door 3. Now, it's always been a 100% chance that it is behind door 1. But to you, it was a 1/3 chance for any door, and after he reveals that it isn't behind door 3, it's now a 1/2 chance for either door. I'm talking about making a decision based on what you know. Since you don't know if it's behind door 1 or 2, you have to make a decision that's still uninformed: door 1 or 2?
Now the table: since you're only picking once, only one of these rows is going to get played out. If you pick door one, and he opens door 3, how would you know if you're in row one or two? It's going to be one or the other, and it's 50/50 between winning and losing. If it were a show where you pick nine doors and you get a switch offer each time, then you could expect to see results similar to the table. But that's not what I'm talking about.
So, if you're doing it multiple times it's best to always switch, because 2/3 of the time you'll get the prize, but if you only doing it once, which is what I assumed because that's how game shows usually work, it's just as likely that switching will get you the prize as not switching.
Why would doing it multiple times be any different to just doing it once? If you do it multiple times then each time is independent of the rest. The decisions you make in the first attempt don't have any effect on the odds in the second attempt, or the third, and so on. If you do it multiple times it's exactly the same as only doing it once - it isn't 2/3 of the time it's better to switch if you do it multiple times but it's still 50-50 if you only do it once, because if it was 50-50 how would it end up at 2/3 of the time if you repeat it?
Now the table: since you're only picking once, only one of these rows is going to get played out. If you pick door one, and he opens door 3, how would you know if you're in row one or two?
You don't, you just have to go by how likely it is, but you're using the statistics badly here. If you pick door 1 then he can open door 3 potentially 2/3 times (there are three lines where you pick door 1, two of which have door 3 as an option for him to open). From this, there's there only 1/3 times where him picking door 3 AND you switching results in a loss.
Just because one of the choices is removed, leaving you with one choice, doesn't mean that the odds are 50-50.
I'm going to give a slightly modified example below. Break it down at tell me where you agree and where you disagree.
Imagine there are one hundred doors instead of three. One has a prize car, the other ninety-nine have goats. You pick one, the host removes ninety-eight doors with goats and then you are given the choice to switch or stay with you current door.
Your initial pick has a 1/100 (1%) chance of being the car and a 99/100 (99%) chance of being a goat. The host removes ninety-eight goats, but your initial pick will still have only been a car 1% of the time, yes? So if your initial pick was the car 1% of the times then 99% of the times it must have been a goat, it follows that this is still true once the host has removed ninety-eight goats, because while the host revealing goats is new information to you it doesn't make the choice you've already made any different.
Now you have two doors remaining - one with a car and one with a goat. If you have a car and you switch you're guaranteed (100%) to get a goat instead, and if you have a goat and switch you're guaranteed (100%) to get a car instead. So 99% of the time you'll have a goat, meaning if you switch every time then 99% of the time you'll win a car. 1% of the time you'll have a car from your initial pick, so if you switch then 1% of the time you'll get a goat. So 99% of the time, switching is the better option, versus 1% where you lose. You don't know which applies to you, so it makes sense to switch every time.
I think it's because I'm not looking at it as "door I initially picked vs. doors I didn't pick", I'm looking at it as "door 1 vs. door 2". No matter how many doors there are, if there are only two doors left, then it's one or the other. You are more likely to be wrong that right on the initial guess, but after it becomes a one-or-the-other decision, you now have just as much of a chance of being wrong as being right. It's a new decision, and your initial decision becomes irrelevant.
It makes more sense with the 100 door example, but because it's only 3 doors, it's different. If it were four doors, and two were opened by the host, then it would make more sense to me. But, with the three door example, maybe I'm getting thrown off by it having something be unique about each door: one door is initially chosen by you, one is discarded by the host, and one is left alone by both of you. Any more doors and that wouldn't happen, the host would discard more doors. The idea of picking the one you didn't initially pick works in situations where there are more than three doors, but when there's just three, it stops making sense to me.
With regards to the table being independent thing, I was talking about results you could expect. Overall, by switching every time, you could expect to win 2/3 of the time, but in each individual round, it's going to end up being a 50/50 shot of winning or not if you have to decide between the 2 doors. Yes, your initial pick has a 1/3 chance of being right, but your second pick has a 50/50 chance of being right. Look at the first three rows of the table, where you always pick door 1 initially. After the host puts down a door, it will always end up being one of two possibilities, the third is discarded. For example, you start with a 1/3 chance of being correct. The host puts down door 3. Now the third row is out of the equation. It becomes a new table: first column is you pick 1 for both rows. Second column is it's either in 1 or 2. N/A for third column because he won't open the other bad door. Fourth and fifth columns have Win/Lose and Lose/Win respectively.
I feel like I should talk more about the 100 door example. Say, for simplicity's sake, you pick door 1 initially and the prize is in door 2. The host puts down all the doors except for door 2. The thing is, if you picked door 2 initially, that would be just as uninformed as picking any other. If he put down all doors except #1, and you actually chose correctly initially, then you'd lose if you chose 1. Now, if you did this for 100 rounds, you could expect to win 99 times if you always switched. You could also expect to see one round where not switching would have been the better option. The thing is, you don't know if you're in that round or not. If you made the same table but for the 100 door round, you would still be left with it being "you pick door 1, prize is in door 1, host puts down doors 3-100. Stay=win, switch=lose" and "you pick door 1, prize is in door 2, host puts down 3-100, stay=win, switch=lose". Maybe in the next round it would look like: "you pick door 1, prize is in 3, host puts down 2 and 4-100, switch = win stay = lose". When the goal is to win as many times as possible in 100 rounds and it doesn't matter if you lose one, then it's smart to go with the odds and switch every time. But when the goal is to win every single time when you're only playing once, then it's left up to luck.
I'm not saying it's smarter to not switch, I'm saying that either way, especially in the 3 door game, you're making a random, uninformed guess, and neither choice would be smart.
It's a new decision, and your initial decision becomes irrelevant.
It is a new decision, but the initial decision is still very much relevant because what door is revealed is dependent on your initial choice. Choosing whether to keep the door you've chosen or to switch is obviously dependent on you having already chosen a door, too. The whole point of the game is to make people think it's a 50-50 chance of the prize being behind either door, when in reality switching is always the better choice, statistically, because the second decision is very much dependent on the first. Look at the table I posted a couple of comments ago again: if you pick door 1, regardless of which door is revealed you will win in two of the 3 situations if you switch.
The number of doors changes your odds (more doors is better for you) but it doesn't change how the problem works. There are n doors, you pick one, the host removes n-2 incorrect doors (leaving one winning door and one losing door), you are given the chance to switch. If you switch you'll have (n-1)/n chance of winning, if you don't you'll have 1/n. This is true while n is any natural number.
With regards to the table being independent thing, I was talking about results you could expect. Overall, by switching every time, you could expect to win 2/3 of the time, but in each individual round, it's going to end up being a 50/50 shot of winning or not if you have to decide between the 2 doors. Yes, your initial pick has a 1/3 chance of being right, but your second pick has a 50/50 chance of being right. Look at the first three rows of the table, where you always pick door 1 initially. After the host puts down a door, it will always end up being one of two possibilities, the third is discarded. For example, you start with a 1/3 chance of being correct. The host puts down door 3. Now the third row is out of the equation. It becomes a new table: first column is you pick 1 for both rows. Second column is it's either in 1 or 2. N/A for third column because he won't open the other bad door. Fourth and fifth columns have Win/Lose and Lose/Win respectively.
The problem here is you're only looking at part of the data, which skews it. The doors that the host decides to reveal isn't an independent variable (i.e. isn't a choice made by you) so looking for a specific value in that subset won't give any usable results. If you did want to use door 3 being opened as something to examine, you'd need to take the first and fifth rows as a "half loss" (because both are only a 50% chance of door 3 being opened so they can't count for a full loss each) and take the second and fourth rows as a "full win". And if you do that, you'll get two wins versus one loss in the switch column. The host opening door 3 specifically isn't useful information to you, though - you pick door 1, he opens door 3, but how does that influence your decision? You've still got the switch/not switch choice to make. You have to look at all of the potential outcomes where you pick door 1 initially for it to be statistically valid.
Now, if you did this for 100 rounds, you could expect to win 99 times if you always switched. You could also expect to see one round where not switching would have been the better option. The thing is, you don't know if you're in that round or not.
The problem with statistics is that the universe doesn't give a shit about statistics. If you flip a coin one hundred times, the chance of you actually getting exactly 50 heads isn't 1/2, as you might expect (as demonstrated by Wolfram Alpha). On average you'd expect about 50 heads, but the chances of that happening every time are pretty low, and the chances of the results being HTHTHTHT... (which is what you'd expect if you were going by statistics only- you'd expect that with two coin tosses you'd get a heads and a tails, then repeat that fifty times for one hundred tosses) are very low. So while on average you'd expect to win ninety-nine out of one hundred rounds, it's possible that you could win two hundred times in a row before you lost, and it's also possible that you could only win ninety out of those one hundred rounds. There is no "one round" where you're more likely to lose, because every single round has the same chance of you winning or losing - they're all completely independent of each other.
If you made the same table but for the 100 door round, you would still be left with it being "you pick door 1, prize is in door 1, host puts down doors 3-100. Stay=win, switch=lose" and "you pick door 1, prize is in door 2, host puts down 3-100, stay=win, switch=lose".
Again, you'd need to look at every single possibility that could stem from you picking door 1, not just the two where door 1 and door 2 are the only ones remaining. You'd need to look at your second choice being between keeping door 1 or switching to door 3, keeping door 1 or switching to door 4, keeping door 1 or switching to door 5, etc. as well. Just because there's only two possible outcomes (WIN or LOSE/NOT WIN) doesn't mean that there's an equal chance of both happening, just like how when you get on a plane the outcomes are either "you get off alive" or "you die on the plane"/"you don't get off alive" but the latter is far less likely.
When the goal is to win as many times as possible in 100 rounds and it doesn't matter if you lose one, then it's smart to go with the odds and switch every time. But when the goal is to win every single time when you're only playing once, then it's left up to luck.
Those 100 rounds are made up of one hundred single rounds. Again, they're independent of each other, so it always matters if you lose one. Playing once is no different to playing one hundred times, or one thousand, or more - the odds are still the same, and you still want to win.
I'm not saying it's smarter to not switch, I'm saying that either way, especially in the 3 door game, you're making a random, uninformed guess, and neither choice would be smart.
As I said above, the 3-door game is only different in the odds, the way it works is still the same, so switching is still the smarter choice. Your guesses can definitely be informed - knowing that (in the 3-door game) you're twice as likely to win if you switch than if you don't makes you pretty informed. Luck still comes into it, but you can still be informed.
EDIT: replying to your other comment here, too.
Let me throw out this example, maybe it'll make sense: a coin toss. You call heads or tails, and if you call it right you win. There's no point in trying to decide, because it's one or the other. But, if the game is flipping it 100 times, it's best to pick one and call it until it comes up 50 times, then call the other one until it's over. Or maybe it's better to call that one every time, I don't know. The point is, you can be smart about choosing when it becomes a game of using probability to get the maximum amount of wins possible, but when it's only one chance, and you get one choice, then there's no way to be smart about it. Calling heads is just as random as calling tails.
I've kind of already covered this above. There is no point trying to decide when tossing a coin because it's always a 50% chance of you getting it right, unlike with the Monty Hall problem, where there certainly are different odds if you choose to switch over choosing to stick with what you've already picked. This part specifically is wrong:
But, if the game is flipping it 100 times, it's best to pick one and call it until it comes up 50 times, then call the other one until it's over.
Coin flips are, again, independent of each other. Just because you got 50 heads doesn't mean the rest of the flips will be tails, it's still a 50% chance to be heads on each toss. It's not better to call the same one each time, either, because there's a 50% chance that you'll be wrong, regardless of what you pick.
you can be smart about choosing when it becomes a game of using probability to get the maximum amount of wins possible, but when it's only one chance, and you get one choice, then there's no way to be smart about it.
You can always be smart when it comes to probability, but coin tossing isn't a good example of that. There's no being smart when it comes to tossing coins - the next toss isn't any more predictable because of the last, or because of the last hundred. It's 50-50 every time. The Monty Hall problem isn't 50-50 ever, so you can always be smart about it when it comes to the round you're playing, but looking at past rounds won't help at all because the results of the past round won't influence the results of the next, just like the chance of specific lottery numbers coming up isn't any higher because they didn't come up last week.
The main problem with all of your errors so far seems to be differentiating between dependent and independent probabilities.
Yeah, you're right about all the independent stuff. I still don't get how choosing the other door is better. I get it from a mathmatical standpoint, but the logic doesn't click with me. One of two doors has the prize, pick one. Sure, you have a 2/3 chance of being wrong when you initially pick. You have a 2/3 chance of it being another door. One of them is taken away, so the other door has a 2/3 chance of having the prize, while the door you initially picked retains its 1/3 chance. I get the idea, I just feel like there's more to it. How does the door with a 1/3 probability go up to 2/3 when you take the other door away?
I know the initial decision does impact it, it gets rid of one possibility. However it still leaves two possibilities, and you don't know which is the right one. So I was saying the initial decision is irrelivant because the initial pick no longer has its probability of 1/3. Now it's either the one that happened to be the initial pick or the other one. Yes, it does influence which door gets put down, but because of the chance of the initial pick being correct, you don't know if the other one that you didn't pick that's standing is the prize door or not. Seriously, if you were on a show, and you had one round to guess the door with the prize, and you went through the scenario, how would it not be a 50/50 shot when you made your final decision? Ultimately you're left with two doors, and you don't know what's behind either. It would be the same as not having any third door at all.
It seems like it's a technical issue. Technically you have better odds when you pick the non initial door, but it isn't "initial or non initial", it's "one or two". The game changes when the host discards the door. It goes from a 1/3 game to a 1/2 game. You say the problem isn't 50/50 ever, but if it's a choice between two equally random outcomes, I'd call that 50/50. The game has 9 possible outcomes before anyone does anything. Then after you pick a door, there's 3. Then after the host puts one down, there's two. It would be equally reasonable to change your mind and pick number two than to not change your mind and stay on one, because you wouldn't really be staying, either one is a choice. Your first choice only affected which door got discarded by the host, it doesn't lock in your choice as having a 1/3 probability even when there's only two doors. The door the host revealed is no longer an option. Since the possibility of the host discarding the other door you didn't pick is gone, the table goes from having the three outcomes, where two wins are on switch while only one is on stay, to two outcomes, where one win is on switch and one win is on stay. Again, switch and stay aren't really the right words since its a new choice. The host could say after putting a door down "are you going to switch or stay?", but he could also say, "now, will you choose door one or door two?" as if there were only two choices to begin with. The only difference is you're approaching it as a new decision rather than as an alteration to a previous decision.
And I know the difference between expected outcome and actual outcome. You could do the coin flip thing and get 70 tails, and you wouldn't have to be surprised.
Also, just curious, what would you do if there were four doors but he still only discarded one?
How does the door with a 1/3 probability go up to 2/3 when you take the other door away?
The probably of the door having the prize doesn't go up. You take your initial pick at 1/3 odds, then between them the other two doors combined have a 2/3 chance of the prize being behind one of them - i.e. you have a 2/3 chance of being wrong on your first guess. So then one of those other two doors is removed, leaving you with a 2/3 chance of having been wrong on your first guess but only one door that it's realistic to pick, because you know that the one that was removed was wrong.
It goes from a 1/3 game to a 1/2 game. You say the problem isn't 50/50 ever, but if it's a choice between two equally random outcomes, I'd call that 50/50.
Imagine I roll a six-sided die, and tell you to guess whether it's going to be three or higher OR less than three. The first option will give you a win 2/3 of the time (if the die lands on a 3, 4, 5 or 6) whereas the first will give you a win only 1/3 of the time (if it lands on 1 or 2). There's two possible outcomes - WIN or LOSE - but one of the options has much better odds for you. It's random, but the chances aren't equal, so it makes sense for you to pick the better odds.
The game has 9 possible outcomes before anyone does anything. Then after you pick a door, there's 3. Then after the host puts one down, there's two.
There's never two, because you never know whether the host opened the door because it was the only one he could open or because he randomly selected that from two options. And because you never know that, knowing that door 3 was removed isn't useful information to you at all - door 2 being removed would have been just as useless. Because of the "2 or 3" part of the table, you have to take door 2 being opened into account in the odds as well. So it's only ever three possible outcomes, never two, although two of the three outcomes will result in a win.
Also, just curious, what would you do if there were four doors but he still only discarded one?
So you pick door 1 (1/4 chance of being on the prize, 3/4 chance of being wrong). The host removes an incorrect door, leaving two doors plus the one you initially picked. Those two doors between them now have a 3/4 chance of having the prize behind them. You have to split this 3/4 chance up between the two doors, meaning each has a 3/8 chance of having the prize behind it, versus your 2/8 chance of having picked it initially. So you still switch, but you chances of winning are a lot lower than in the three door version, or in a version where all of the unpicked doors except one are removed.
The formula for your chance to win if you switch when the host only opens a single door instead of n-2 doors is (n-1)/((n-2)*n), where n is the number of doors. As long as (n-1)/((n-2)*n) > 1/n you always want to switch. And it always will be greater. The host removing a door makes it so switching is always in your favour.
There's never two, because you never know whether the host opened the door because it was the only one he could open or because he randomly selected that from two options. And because you never know that, knowing that door 3 was removed isn't useful information to you at all - door 2 being removed would have been just as useless. Because of the "2 or 3" part of the table, you have to take door 2 being opened into account in the odds as well. So it's only ever three possible outcomes, never two, although two of the three outcomes will result in a win.
Yes, it could have been that he had no choice or one other choice. That's only two possibilities, which are dependent on the question of whether the prize is behind the door you picked or the other remaining door. It would be the same if he put door two down, you'd have one possibility of it being behind your initial door and he put a random door down, or you have the other possibility of it being behind another door and he had only one choice of a door to put down. It's one of those two scenarios every time. If door one and door two are left standing, then either they have a 1/2 chance of being correct or a 1/3, either way they're both equal. Each door has always had a 1/3 chance of being correct, from the start. When you pick a door, the other doors each, individually, have a 1/3 chance of being correct.
Let me throw out this example, maybe it'll make sense: a coin toss. You call heads or tails, and if you call it right you win. There's no point in trying to decide, because it's one or the other. But, if the game is flipping it 100 times, it's best to pick one and call it until it comes up 50 times, then call the other one until it's over. Or maybe it's better to call that one every time, I don't know. The point is, you can be smart about choosing when it becomes a game of using probability to get the maximum amount of wins possible, but when it's only one chance, and you get one choice, then there's no way to be smart about it. Calling heads is just as random as calling tails.
Check my edit to my reply to your other comment for my reply to this :)
jmt222 · 1 points · Posted at 13:45:16 on February 14, 2016 · (Permalink)
If you adopt a strategy of always switch, then the only choice you make is your initial one and for the rest of the game you are following your strategy: If you initially chose 1, the host shows you 2, then by following your strategy, there is no guess made here: you pick door #3.
But then if you always pick door number one initially, and the host always puts down door number two, then you're really just always picking door number three. You have no chance of getting the prize if it's behind door number one. The lower odds don't make it impossible for it to be behind door number one, so by always switching you're cutting out the possibility of getting door one every time.
jmt222 · 1 points · Posted at 17:07:34 on February 14, 2016 · (Permalink)
Right. If you initially chose the correct door, then always switching will result in a loss. But you initially chose the correct door 1/3rd of the time so you lose 1/3rd of the time with this strategy.
There is no strategy which guarantees a win, but using the strategy of always switching will always result in a win whenever your initial choice was wrong and always result in a loss whenever your initial choice is correct.
However the degree to which you lose by switching is twice as large as the degree to which you win by switching.
If you have chosen wrong, by switching you gain a 50% chance of getting the right thing.
If you have chosen correctly, then by switching you lose a 100% chance of getting the right thing.
So you take the total probability that you have already chosen correctly, times the expected value of a switch in that case, so 1/3 * -1, then add that to the total probability that you have not already chosen correctly, times the expected value of a switch in that case, so 2/3 * 0.5.
Add those together for the total value of a policy of always switching:
(1/3 * -1) + (2/3 * 0.5) = 0
So your intuition is correct - there is nothing to be gained from switching.
Except I just remembered the Monty hall thing has them eliminating one incorrect box after you make your choice, right? So never mind what I just said.
pixbox · -15 points · Posted at 23:56:46 on February 13, 2016 · (Permalink)
The chances aren't out of three, they're out of two.
Jesus Christ. There are 3 doors. Therefore the chance that your initial door was the winner is 1/3.
pixbox · 0 points · Posted at 05:30:53 on February 14, 2016 · (Permalink)
I know there are three doors. If one door is opened, the chances of you choosing it are zero, so there is no point in it being included other than to increase the probability of picking the "correct" door.
so there is no point in it being included other than to increase the probability of picking the "correct" door.
Yes. Which is exactly what it does, and literally the entire point of the entire Monty Hall problem. Because of the host always opening a goat door, switching gives you the odds of choosing both doors you didn't choose on the first guess, i.e. 2/3.
[deleted] · -1 points · Posted at 02:50:39 on February 14, 2016 · (Permalink)
We play a simple lottery with a million tickets. You buy one. I buy 999 999. I tell you before that I will throw away 999 998 of my tickets. The next day, I check the results. You don't see them yet. I pick a ticket to keep and burn the rest. (None of the ones I burn are winners, of course.)
That is what always bothered me about the Monty Haul problem. It assumes that Monty knows what is behind a curtain and only ever eliminates a loser. I think that is a poorly articulated problem given the way that it is almost always stated. Because the way it is stated usually does not give you the fact that Monty k ows what is behind the doors and does not give you the fact that he eliminates only losing doors.
For the purpose of the problem, Monty always knows that the door he opens is empty (i.e. shows you an empty door). Whether or not he knows that the door is empty or not is irrelevant so long as you SEE that the door he opens is empty.
the way it is stated usually does not give you the fact that Monty knows what is behind the doors and does not give you the fact that he eliminates only losing doors.
Then that's not an issue with the problem, but with the people who incorrectly state it. I've always heard it carefully explained, saying that Monty deliberately chooses one of the "wrong doors" to be revealed.
[deleted] · 7 points · Posted at 01:50:32 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 21 points · Posted at 02:35:15 on February 14, 2016 · (Permalink)
He left out that the tickets thrown away were known to be wrong. We are now left with only 2 tickets and we know one of them is a winner. Odds are, the guy that picked 999,999,999 had the winning ticket, so his one left is the winner. So, it is beneficial for the guy that bought only one to trade tickets with the guy that bought 999,999,999 and threw away 999,999,998 that he knew were wrong.
What makes the problem work is that the person in control of everything knows which ticket is the winning ticket. If you pick the wrong ticket, then the person controlling the lottery is purposefully going to discard all the other tickets except for the winning ticket because he knows the winning ticket. In this case the discarding actually does nothing and you're essentially picking between the set with your ticket and the set with every other ticket.
xereeto · 1 points · Posted at 04:01:21 on February 14, 2016 · (Permalink)
You need to mention that the tickets you burn are definitely not winners, otherwise it's confusing as all hell.
No problem! Plus, it makes the key to the problem immediately obvious - the host's knowledge is important too. If I burned 999 998 tickets, then there would be no benefit in swapping.
It's not 50/50, though. The two tickets are not equally likely to win.
Just because there are multiple outcomes doesn't mean that they're equally likely. If I draw a card from a standard deck, I'm more likely to draw a number than a letter - even though there are only two options, number or letter.
If it was picked randomly from the two tickets left over, then it would be 50/50. But it's not - it's picked at the beginning, then a ton of losing tickets are thrown away. Tickets being thrown away doesn't change the probability of one of my tickets winning versus one of yours winning; I only burnt them after the winner had been chosen! I've just moved all of my "probability mass" over to one specific ticket.
jtlcr777 · 58 points · Posted at 22:26:19 on February 13, 2016 · (Permalink)*
also often makes no intuitive sense
...what? It makes perfect intuitive sense! If you had a 100 doors, and you picked one, you're very likely to pick the wrong door first. Its better to switch when the host narrows it down to 2 doors.
So if there's three doors, theres a 2/3 chance you pick the wrong one first, so its better to switch when the host narrows it down to 2 doors.
It may be the fact that it is typically explained as a game show scenario - people may assume the game show host has chosen to offer the switch, knowing the contestant chose the right door first. However, in a scenario where you are always offered a second choice, it makes intuitive sense.
That is what had me confused when I first had the problem explained to me as above.
Xaxxon · 1 points · Posted at 03:00:17 on February 14, 2016 · (Permalink)
You just said that it's intuitive once it's intuitive.
So it's actually a sociological problem; it's a matter of analyzing the host's behaviour and intentions, not of understanding the math behind it.
rawling · 1 points · Posted at 08:33:18 on February 14, 2016 · (Permalink)
Yeah, you have to know in advance what the rules are, otherwise how do you know he's not only offering because he knows you picked the winning door?
Derren Brown did this as part of his stage show a while back. I was mad at the volunteer for not switching, as switching would've won, but the DB could've been bluffing since he didn't explain the switch option before the volunteer has chosen...
But 1 door is out of the equation after he reveals the 3rd door. So it's a 50/50 regardless if you switch. What am I missing? (to add, I guess I see that you had 33% chance the first time and now it's a 50% chance. That doesn't change the fact that there are 2 unknown doors remaining...)
I took a while on this too. The way i think of it is by grouping the options
First, you have to assume the removed doors are definitely wrong.
Now, "chosen door" has a 33% chance of being correct. "Other doors" which has two doors has a 67% chance of being correct.
When one door is removed from "Other doors" the probability of the correct door being in that group doesn't change. Thus, the remaining door that was not chosen and not removed is most likely the correct answer with 67%.
Okay in your scenario, you're very likely to pick the wrong door first since you have a 1/100 chance, I'm with ya. The host then narrows it down to 2 doors (including your own), so obviously the door that the host leaves is way more likely to be the prize door than your 1/100 first pick. The host reveals 98 out of 100 doors, but only 98 out of 99 possible doors that he could reveal (since he can't reveal your door). So he has a 99/100 chance of having the winning door. So that's an obvious reason to switch doors. In the 3 door scenario, you start with a 1/3 chance of picking the right door. The host has a 2/3 chance of having the winning door, with a 100% chance of always having a loser. My point is that he will always reveal the loser no matter what, that leaves you with a 50/50. Let's say you start on the second phase and the host has already revealed the loser, let's also assume that your default pick is door A and now he asks if you want to switch to door B. In my mind that's 2 unknown doors of equal value, a 50/50. That differs from your 100 door scenario where the host has a 99% chance of picking the winner and leaving it for you to pick between his 99% chance or your 1% chance.
Ohhhhhhhhhhh I get it now.
In the 3 door, he has a 66% chance of having the winning door, and he will always eliminate 1 door. So it's his 66% chance pick that you're switching to. I got it! That took way too long for me to wrap my head around!! :)
Other people have explained it, but here's a different point of view: the 2 remaining doors are not equivalent. The one you choose generally sucks: you chose it with a 33% chance.
We both know that one of the other doors is a "wrong" one (they cant both be "right"). So if the host shows you what's behind that door and you don't switch, effectively you haven't made a decision, you haven't made use of the new bit of information. You're exactly in the same state as you were before the reveal. Your odds are still 33%.
Now the last door, the one that wasn't revealed? That one is a winner. That one has the combined chances of the 2 doors you didn't pick - it's always the best of those 2. Maybe both are bad, in which case you started with the right door (again, 33%). But if either of them was good, then the remaining door has to be good. It "carries" the chance of both doors, i.e. 66%.
like /u/etzophyer was saying elsewhere, I think the hidden key is that the host has 100% chance of revealing an incorrect door.
This means that you will always be left with one incorrect door and one correct door.
This means that switching doors will always switch whether or not you were a winner or a loser.
Finally, like /u/jmt222 said, you have a 2/3 chance of your first choice being incorrect, and 100% chance of switching to the correct door if you indeed did choose incorrectly.
This is very key. The famous incident where mathematicians were yelling at vos Savant that she was wrong had an underspecified problem, so they were both technically wrong. If you don't know that the show ALWAYS opens a wrong door, the result won't be true.
If the show just opens a door at random, and it happened to be the the goat, it's 1:1 odds that your door has a car.
If the show only opens a door if you chose a car, then obviously you should not switch. (But who would watch that gameshow?)
If the show picks a door at random, and only opens it if it's a goat, then it's 1:1 odds.
By opening a wrong door with the "always opens a wrong door" strategy, the host is giving you new info. If you gain no additional information about the doors, the probability cannot change.
It's only confusing because Monty opening a door for you is a misdirect. Picture the game without Monty opening a door for you. Now the choices are to keep your one door, or switch to the other two doors.
Seen this way, you would never choose to have one door when you could have two.
Monty opening the door isn't a misdirect, it's a fundamental part of the concept. The contestant has no information and chooses randomly; Monty has information, when he opens a door now the contestant has information as well.
The information he gives you is that one of the doors you didn't pick is 100% a loser. This is a misdirect because it causes people to assume that the two remaining doors have equal probability of being winners. But it's precisely because Monty's choice of door is non-random that the game is a trick.
The odds when you pick a door are 1/3 - 1/3 - 1/3. Switching doors increases your odds to 2/3. If there's 3 equally likely options, as there are at the beginning, the only way to win 2/3 of the time is to pick two options. And I'm saying that switching "allows" you to pick the door Monty opened and the unopened you didn't select. Since you're now picking 2/3 doors, you have a 2/3 chance of winning.
I see where you're coming from now, I think I just misunderstood. I don't think it's a misdirect per se, I think it's just taking advantage of people who understand the concept of basic stats (a random choice between two options is 50%) but don't understand the concept of information and logic in statistics.
This is the part people get hung up on in my experience. Most people have studied at least the basics of statistics. Most people have not studied the concept of information as it pertains to statistics and logic.
The Opener makes a decision, it's effectively random.
Monty makes a decision, but it's not random; he knows which door has the prize, and opens one of the other doors. He has information you do not.
However, now that Monty has opened a "goat" (ie, no-prize) door, the Opener now has information that was previously unavailable. That is, there was always 66% chance the door was not the one picked, and that doesn't change just because a goat was revealed. This is clearer with the 100 door analogy - there was a 99% chance the correct door was not picked, and that doesn't change if Monty opens 98 goat-doors.
I believe one of the alternative versions of this, the "Monty Fall" problem, has a 50% chance to win whether you switch or not. In this version: Monty trips and opens a random door, revealing a goat.
I totally get the "Monty Hall" problem, but the "Monty Fall" problem drives me nuts. The situation ended up being the same (on the surface at least), but the probability is totally different.
Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation confirming the predicted result (Vazsonyi 1999).
It's easier to think of this way: There are 100 doors, you pick one. The host opens 98 of the doors to reveal goats, and then gives you the option to swap.
You made the first guess with a 1% chance of being right.
When you swap think of it as a different choice; this time with 2 options instead of 100. So a 50% chance.
This logic applies to 3 doors just the same, but with different odds, but still so that it is advantageous to switch.
Edit: My Apologies, I've interpreted it as wrong as well. See replies to my comment for a better explanation
In this scenario the hosts actually gives you 98% if you decide to switch.
In the original scenario, you have a 1% chance of being right, which you pointed out. When he shows you 98 doors, if you make the switch, you essentially picked 99 doors as your initial choice. But you have to realize that of the 99, only one of them will contain the prize
50% should never enter into the Monty Hall problem unless the original number of doors is 2.
If the number of doors is greater than 2, your chance of being right is always less than 50%, and therefore your chance of being right if you switch is always greater than 50%.
In the 100 doors example, you pick a door, you have a 1% chance of being right and a 99% chance of being wrong. When the host reveals the 98 doors with goats behind them, you still have a 1% chance of being right and a 99% chance of being wrong. If you switch, you now have a 99% chance of being right and a 1% chance of being wrong. Knowing what's behind some of the doors does not change the probability of what's behind the rest of the doors, or the probability of you being correct versus incorrect with your initial guess, unless there is exactly 1 door whose contents you do not know.
But this is missing the real confusion; where did all these goats come from?
CanIkeepthegoat?
Ashhel · 4 points · Posted at 22:25:56 on February 13, 2016 · (Permalink)
But this is incorrect. When you switch in the 100 door case, you have a 99% chance of winning. Similarly, when you switch in the 3 door case, you don't have a 50% chance of winning -- you have a 66% of winning.
It's wrong, though. The common misconception is that you're left with two doors so it doesn't matter which door you pick, so there's a 50% chance of winning, and his explanation is exactly this misconception. The way the problem works is that you're giving new information because of how the doors are revealed.
What you have to remember is that the host knows what is behind each door. If he showed a random door, it wouldn't matter if you switched or not.
[deleted] · 2 points · Posted at 19:38:47 on February 14, 2016 · (Permalink)
Just a note about a few people who have told me it never fooled any mathematicians or where I got the idea from:
I had seen Marilyn Vos Savant make references to it, and that's where I first saw the problem. She had posed the problem in her column and had received some letters from people who disagreed with her, and some were professionals with masters and PhDs, including mathematicians and physicists, disagreeing with the correct solution, often quite strongly.
Unfortunately I can't find the quote I had read, I was speaking from memory, but the only one I found today is from wiki, where Marilyn quotes a psychologist as saying, "... no other statistical puzzle comes so close to fooling all the people all the time...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".
The truth is that the human mind is just fucking awful at doing statistics and probability. We have so many built in biases towards this kind of math that it takes a looooooooot of experience and education to be able to handle these well, and even then things can blindside you. That said: The actual math behind this is quite simple when broken down. You just need to actually be willing to set aside your first instincts and actually look at it.
What I think is interesting is people who don't understand this (a 100% true mathematical concept), and instead of saying "I don't understand this. Can you help me understand it?", they instead say "This is wrong!".
That kind of aggressive ignorance is really astounding.
If the host does not know where the losing doors are, then opens a door at random and just happens reveals no prize, then it doesn't matter if you switch or not for your chance of winning.
The 2/3 from switching only occurs when the host knows which doors have the prize.
This isn't true. So long as he opens the empty door and tells you whether or not to switch, you should switch because you have more information.
If you factor in the possibility that the host could possibly open the door with the prize behind it, then your stats change. But so long as you filter out the chances that he opens the grand prize door, then it's no different than monty knowing which doors are empty.
That's not true. If the door opened is a goat regardless of the hosts knowledge you know that the remaining other door is twice as likely to be the car.
I don't understand, if he accidentally always opens a goat door how is that functionally different from opening them with intent?
Oh! Wait nevermind, got it. Thanks for the link!
[deleted] · 1 points · Posted at 23:16:43 on February 13, 2016 · (Permalink)
My computer science class just got finished making an app to test this. It's really mind blowing how that works, when everything you think says directly otherwise.
There's a 2/3 chance that you initially choose a goat.
Assume you have a goat
When Monty opens a door with another goat, then the other door must have a car (assuming you have a goat). It is then a no brainer to switch.
Now 1/3 of the time you have incorrectly assumed that you have a goat, so 2/3 of the time you win, 1/3 of the time you lose.
Korlus · 1 points · Posted at 01:24:54 on February 14, 2016 · (Permalink)
The best way to understand it is to know that the person who gives you the choice knows the position.
Since they cannot/will not pick the correct door, they effectively removed one option from the equation.
It's not that it makes your door any less likely than it was before (it remains just as likely), but you now know that every other door is ever so slightly more likely than the door you picked. This works only because the person knew what was behind each door - if they did it at random, they could potentially reveal the prize.
In the classic problem, you have a 1/3 chance of being right, and a 2/3 chance of being wrong. After the person reveals what is behind the other door, you know that had you picked your door (now), you would have a 1/2 chance of being correct.
However, that is not the case. You picked it before. He didn't make what was behind your door any more likely to be correct, meaning that every other door is now more likely to be the correct answer than yours is/was.
I always find it illuminating to increase the number of goats and doors:
In the original problem, there are three doors: two with goats and one with a car.
In my version of the problem, there are 100 doors. There are goats behind 99 of the doors, and a car behind the last.
The participant chooses an arbitrary door (let's call it Door 37) and then the host opens up 98 of the remaining doors to reveal the goats behind them. Now, only Door 37 (the original choice) and Door 19 remain.
At that point, when the participant chose Door 37, they had a 1/100 chance of choosing a car. That doesn't change. Since the host knows where the car is, opening up all of the other doors means that there is then a 99/100 chance of there being a car (and not a goat) behind Door 19.
Obviously, the best strategy is to switch doors.
ghroat · 1 points · Posted at 02:21:21 on February 14, 2016 · (Permalink)
this makes intuitive sense. the most likeley scnenario is that your original guess was wrong. the host combines the two other doors into one guess by eliminating the other wrong door. the two doors you didnt pick become one option that had two goes at picking the right door
I didn't think to cap the post, but someone on 4chan once told a story about how, for a Statistics project, they made a quick test for this with a deck of cards (or rather, the 4 aces). They got 50 people to take part in the study, told them the rules (one of these cards is the Ace of Spades, choose one, I'll reveal two that are neither your card nor the correct card, you can choose to switch or keep your original guess), and kept track of who switched, for whom switching would be correct, and for whom staying would be correct. Naturally, the switch/stay correctness was a 3:1 ratio, but apparently only something like 3 people chose to switch, and all but one who switched admitted they'd heard of the Monty Hall problem before.
It made more sense to me once I thought of the two options as the complete range options. Staying leaves you with all 3 doors being unaffected, a range of Win Lose Lose, switching removes a losing door from the range because the door opened is always a losing one, the switch range becomes Win Lose.
Just increase the numbers. There's a million doors, and one prize. You pick one door. The host knows where the prize is, and opens 999,998 doors that he knows do not have the prize.
When you started, your odds were one in a million that you were right. Inversely (because the odds of all possible results always add together to one), there was 999,999/1,000,000 odds that you were wrong the first time.
Now you can switch. The door you chose the first time (1 in a million), or the only door left after 999,998 doors were opened (999,999 ina million).
My probability professor literally gave us this problem today! This is insane
[deleted] · 1 points · Posted at 04:12:06 on February 14, 2016 · (Permalink)
So first, you choose one door. The chances you chose wrong is more likely than not (2/3). In such a case, the host eliminates the other wrong door leaving the one and only winning door. So in this more than likely scenario where you chose wrong at first, you guarantee yourself the winning door by switching.
I still don't see how it works. Your odds are the same, whichever door you choose. Your decisions don't affect what's behind the door. Initially, you have a 1 in 3 chance. They reveal the zonk, and you have a 50/50. I don't see how one is any more likely than the other.
Remember, it only works because Monty wouldn't pick the one with the prize behind it, that's what makes the switch a 2/3 rather than 1/3. If he didn't know which one had the prize, you would still have a 1/3 chance for each door.
The trick is to remember the odds don't actually change, I got frustrated for a long time when people try to say things like the odd change BECAUSE they reveal the second door, which isn't quite true. The host say to pick a door. Once you do, he essentially says, "do you want that one, or both of the other two?"
Sometimes its easier to see if you use a bigger number, say 100 doors. Pick one. Thr host opens a dud door, and asks if you want to keep your original pick. You say yes so he opens another dud door and asks again if you want to switch. Because the host will always open a dud door, you this 96 more times until there are two door left. So if you think about it its just one simple question, "do you want the first door you picked, or ALL the other doors?!" You had a 1% chance of guessing the right door at the beginning. Switching at the end would give you a 99% chance you get the prize.
Atmosck · 1 points · Posted at 05:25:16 on February 14, 2016 · (Permalink)
It's not exactly perplexing, it's not like computer experiments betray the existing mathematical theory.
Imagine that, instead of 3 doors, you have 100 doors. You guess door #47, then all the doors except #47 and #62 open to reveal goats behind them. You are then offered a choice: Switch your door to #62, or stay with #47? Obviously, the probability that you correctly picked door #47 is really really small, and now you know for a fact that the prize is either behind that one or #62. Since #47 is almost certainly wrong, it's a no-brainer that you should go for door #62.
[deleted] · 1 points · Posted at 06:34:40 on February 14, 2016 · (Permalink)
I never got it until a friend explained it to me in this way:
Let's say there are 100 doors, and behind 99 of them are goats. Behind one of them is a car. You pick on and the game show guy eliminates 98 goat doors. So there are two doors left, the one you picked and the other one that wasn't eliminated.
The reason you should switch is because you have to ask yourself, does the door that I randomly picked have a greater chance of having the car? Or does the other door that the game show host strategically chose not to eliminate have a greater chance? Out of all the doors besides yours to eliminate, he chose to leave this door. So, do you think your randomly picked door is more likely to have the car, or the other door that FOR SOME MYSTERIOUS REASON was not eliminated like the 98 others? The other door. Because that doors not random like yours.
Think of it this way. If you switch, what you're actually getting is to open every other door. The more doors there are the more obvious it is why its better. But its still better if there's only 3 total, since then you get two instead of one.
For those who don't know the original idea:
So the original is there are three doors. Two of them have junk behind them and one has a new car. You pick door number 1. Monty then says, "Ok, well let's see what's behind door number 3!"
Surprise it's trash.
Now Monty asks you if you want to switch your door to door number 2. Should you do it?
Yes. You should. Why?
Let's scale it up. Let's say there are a million doors and you choose door number 23. Monty then takes away 1 door and asks if you want to switch your door. You say yes. And this continues until your door and two others are left. One has a car and the other two have junk. Monty takes away one other door, leaving yours and another. Do you switch? Well, obviously. I mean what were the chances that you just happened to choose the one door out of a million that had the car behind it?
When has this ever fooled mathematicians? It follows from the basic fact that the host gives you more information than you had. It updates what is called a 'filtration', and changes the probability space that your choice exists in.
I actually wrote a simple Java program myself once to confirm statisticians aren't bulshitting me.
DrMonsi · 1 points · Posted at 10:57:31 on February 14, 2016 · (Permalink)
Easiest way to understand it:
Imagine there being 100 doors (instead of 3). You choose one. The moderator opens 98 false ones (instead of one). You still think it's 50:50 that the door you chose has a probability of 50% being the right one now?
Think about it. It all became clear to me after i was presented this argument.
I get that 1/2 is better than 1/3. What always bothered me about this problem is that with EITHER the choice to change doors or stick to your door, you still making a 1/2 decision. If a person tossed a coin at this point would they not see heads half the time? And yet this seems like equivalent of saying always call heads.
steppe5 · 1 points · Posted at 15:25:05 on February 14, 2016 · (Permalink)
I hope it doesn't fool mathematicians, since I understood the concept in high school statistics.
What finally made it make sense to me is that Monty is giving away a huge amount of information by revealing the door with the non-prize. Probability is basically about making estimates based on available information. New information can and should change your estimates.
Let's think of it in terms of sets of doors, and the odds that the prize is behind one of the doors in that set. That gives us the following table:
Set of doors
Odds
#1
1/3
#2
1/3
#3
1/3
#1 or #2
2/3
#2 or #3
2/3
#1 or #3
2/3
#1 or #2 or #3
3/3
In plain English, the odds are 1/3 that the prize is behind any given door. The odds that the prize is behind either one of two doors are 2/3. (And of course there's a 100% chance that the prize is behind one of the three doors.)
Now, you pick door #1. The odds that the prize is there are 1/3. The odds that the prize is behind door #2 or #3 are 2/3.
Monty reveals that the prize is not behind door #2. The odds that it was behind door #2 or #3 have not changed. There's still a 2/3 chance it's somewhere in that set of locations. But Monty has shown you it's not behind #2, so the odds "focus" on #3. By process of elimination you know that there's a 2/3 chance that it's behind door #3.
That's double your chances if you stick with door #1, so you should switch.
I think this is an instance of mathematics dealing with theory rather than reality. When you're talking about probabilities, you can phrase the question such that it sounds like switching is a better option, but if you were to actually go on the show and put that reasoning into practice, whether or not you switched wouldn't make a difference.
Here's how I'm thinking of it: Let's say we change the rules slightly. You pick one of three doors, and Monty reveals one of doors you didn't pick. However, he doesn't ask if you want to switch your answer. Instead, your original answer is discarded, and you are now asked to pick one of the remaining two doors. There are two unknown doors, 50% of which have a car behind them and 50% have a goat behind them. The third door is now irrelevant. Whichever door you pick, you have a 50% chance of getting the car.
This is essentially the same problem. "Not switching" is the equivalent of picking the first door you chose, and "switching" is the equivalent of picking the second.
[deleted] · 1 points · Posted at 09:44:55 on February 16, 2016 · (Permalink)
it has fooled mathematicians and also often makes no intuitive sense
Source? I really doubt such a simple concept has fooled any rael mathematicians.
It's really simple. When you first choose there are 3 doors and one prize. So there is a 1/3 chance you choose the correct door and a 2/3 chance you chose the wrong door. When the host removes a a door he always removes a door without the prize behind it. So the chances are in your favor to switch because its more likely that your first choice had no prize behind the door.
If you plot all of the choices you can see all the results of switching and not switching.
Let's look at if you do not switch. For picking each door 1 through 3. Let's say the prize is behind door number 3.
1) you pick door 1. The host removes door number 2. You do not switch. The prize is behind door 3. You lose
2) you pick door 2. The host removes door number 1. You do not switch. The prize is behind door 3. You lose
3) you pick door 3. The host removes door number 2 or 1 (it doesn't matter which. He always removes a door without a prize behind it). You do not switch. The prize is behind door 3. You win!
Now let's look at if you do switch
1) you pick door 1. The host removes door number 2. You switch to door 3. The prize is behind door 3. You win!
2) you pick door 2. The host removes door number 1. You switch to door 3. The prize is behind door 3. You win!
3) you pick door 3. The host removes door number 2 or 1. You switch to door 2 or 1 (which ever door the host did not remove). The prize is behind door 3. You lose.
In the case where you do not switch you only win if you pick the door with the prize behind it on your first try. That is a 1/3 chance or 33.33%.
In the case where you switch you win if your first choice is a door without the prize behind it. That is a 2/3 chance or 66.66%.
So it is always in your best interest to switch.
I never understood why people say that it took mathematicians so long to solve the problem. It's really pretty straight forward.
I guess it took them very long to convince normal people of it. And still there's tons that say 50%.
ophello · 0 points · Posted at 09:10:08 on February 14, 2016 · (Permalink)
Ugh... I will never understand why people don't get this.
If a door is opened to you by the host, you've just been given more information. Your odds are now different. You did not pick the prize door because otherwise they would have revealed that you won.
JoshuaZ1 · 62 points · Posted at 20:51:32 on February 13, 2016 · (Permalink)*
I don't know what the coolest is, but I'll try to list a few neat ones that haven't been mentioned yet:
Call a rotation "periodic" if when you keep doing that rotation one eventually gets back to where one started. So for example, on a circle a rotation of 90 degrees (in radians Pi/2) is periodic because you can do it four times and get every point on the circle back where it started. It turns out in two dimensions if you compose two rotations which are periodic you get a third rotation which is periodic (so for example, if I do a 60 degree rotation and a 90 degree rotation I'll have a 150 degree rotation which I can repeat 12 times). Now here's the cool fact: this isn't true on a sphere. I can do two periodic rotations so that I compose them and don't get a periodic rotation. For example, if I rotate 30 degrees on a sphere around a vertical axis and then 30 degrees around an axis that is perpendicular to that axis, you get a rotation across a new axis which is not periodic. (Proving this requires a little linear algebra where you look at the eigenvalues of the corresponding matrix.)
There are the same number of rational numbers as integers. But there are more real numbers than there are rational numbers. (Here I'm using cardinality as the notion of size.)
The number of primes numbers less than or equal to x is very closely approximated by x/ln x. This is the prime number theorem.
We know that one of e+pi and e pi is irrational, but we don't know which (we strongly suspect that both are irrational). (EDIT: Correct version of statement is transcendental for both per comments by /u/tcampion and /u/sniffnoy .)
Here's an "almost" fact. 31, 331, 3331, 33331... are all prime. (Fun programming exercise: make a program to find where this breaks down. Fun number theory exercise: without using any calculator or computer, find a counterexample.)
1729 is the smallest positive integer representable as the sum of two perfect cubes in two different ways. That is 93 +103 = 1729 and 13 + 123 = 1729. There's a famous story about this. Also, worth noting that 1729 is also a Carmichael number.
[deleted] · 4 points · Posted at 01:07:46 on February 14, 2016 · (Permalink)
Upvote for not indulging in Group Theory in polite society. :)
heap42 · 4 points · Posted at 00:02:18 on February 14, 2016 · (Permalink)
The numbers of primes less than or equal to x thing( x/ln x) was conjectured by Gauss when he was FUCKGIN 15 YEARS OLD FUCKING 15... when i was 15 i was looking up boobs on internet. FUCK THAT GUY.... WHAT A LEGEND!!!!
He was 19 (Born in 1777, conjectured it in 1796). Gauss was without a doubt a genius but this accomplishment isn't thaaaat impressive. It's actually kind of obvious if you know what prime numbers are (only divisible by 1 and themselves).
And by obvious I mean logical that as the number increases there is a higher probability of finding another smaller number that it is divisible by, thereby making prime numbers rarer and rarer. Now if he would have PROVED it at 15 (or 19), yeah, that's impressive.
Um, people knew well before Gauss that primes got rarer as they got larger. What is impressive is figuring out the exact rate at which that happens, and yes that was pretty damn impressive.
We know that one of e+pi and e pi is irrational, but we don't know which (we strongly suspect that both are irrational).
I think you mean transcendental, not irrational. I think it's not too hard to show that e and pi are irrational, and probably not so hard to show that they are linearly independent over the rationals. But transcendence is typically a very hard question.
No. I think I meant irrational. I don't see any easy way to prove that e+pi is transcendental or that e pi is transcendental. Is there some way to do that? It doesn't follow in any obvious way from e and pi being transcendental.
(x-e)(x-pi)=x2-(e+pi)x+e pi. If e+pi and e pi were both algebraic, then this would show that e and pi are both algebraic. But they're not, so at least one of e+pi or e pi is transcendental.
Prety sure transcendental is correct here. If r+s and rs are both algebraic, then r and s must also be algebraic since you can solve a quadratic for them. So at least one of e+pi and e*pi must be transcendental (and in particular irrational).
I don't know how you'd get irrationality here without using transcendence; if r+s and rs are both rational, that doesn't necessarily mean rs is rational. (E.g. r=sqrt(2), s=-sqrt(2).)
[deleted] · 1 points · Posted at 05:45:31 on February 14, 2016 · (Permalink)
Are you just claiming that the statement is correct with "irrational" (which I agree with, see above), or are you actually claiming that it is incorrect with transcendental? If the latter, would you mind pointing out the hole in my proof rather than just asserting that I'm wrong?
[deleted] · 0 points · Posted at 06:07:43 on February 14, 2016 · (Permalink)
Number theory approach:
3*(10n +10n-1 ...+10)+1= 30*(10n -1)/9+1=
(10*(10n -1)+3)/3 so we want a prime p != 3 so that there is n so that 10n+1 -7 is divisible by p. Is there an elementary argument to find such p that isn't brute force? I know that for almost all numbers they generate mod p for an infinite amount of p so that we know there is a prime p so that 10n for n=1...p-1 goes through all different values mod p (and 7 specifically), but that isn't elementary at all.
JoshuaZ1 · 2 points · Posted at 23:20:32 on February 13, 2016 · (Permalink)*
I know that for almost all numbers they generate mod p for an infinite amount of p so that we know there is a prime p so that 10n for n=1...p-1 goes through all different values mod p (and 7 specifically), but that isn't elementary at all.
Actually, that's still open. That's the weak form of the Artin primitive root conjecture. But yes, one way is to find a prime that 10 is a primitive root which isn't 7 or 3. A slightly better way is to realize that since the nth term is (10(10n -1)+3)/3 and since 1030 is 1 mod 31 (by Fermat's Little Theorem), and for n=32 one must get a term divisible by 31 since the 2nd term was divisible by 31.
Shit I'm stupid, how did I miss that 10n -1, I was focused on the general case (for any sequence your trick will work, when I say general I mean I've been pondering about artin's conjecture for the last few days) for some reason. What I meant is that there is much progress on Artin's conjecture, so for almost all values this is true.
Yeah, Artin's conjecture is one of those things where we can't prove it, but given the work of Heath-Brown and Hooley, it is pretty clearly true (although I wouldn't be completely shocked if there's some subtle correction factor that actually changes the density of the primes for a given primitive root candidate a when a has a lot of distinct prime divisors).
iSeize · 2 points · Posted at 05:29:50 on February 14, 2016 · (Permalink)
wow that first one was described perfectly. im impressed!
ceriee · 215 points · Posted at 22:00:24 on February 13, 2016 · (Permalink)
Probably too late to the party. Any factor of 9's digital root will always be 9. (A digital root being the sum of all the digits)
For example:
1 x 9 = 9
13 x 9 = 117, 1+1+7 =9
185 x 9 = 1665, 1+6+6+5 = 18, 1+8 = 9
194385 x 9 = 1749465, 1+7+4+9+4+6+5 = 36, 3+6 = 9
This is basically a property of mod n-1, where you write your numbers in base n. Essentially if you have a number with digits a, b, c,... z written abcdefghijklmopqrstuvwxyz base n or any other choose you choose, writing it as powers of n comes out to:
a * n24 + b * n23 + ... + x * n2 + y * n1 + z * n0
Now, because you're in mod n-1, (mod protip: any number in mod k is congruent to its remainder when divided by k - this is not how mod works, but it'll work for the purposes of this) n-1 is congruent to 0, and n is congruent to 1. So essentially,
abcdefghijklmopqrstuvwxyz
=a * n24 + b * n23 + ... + x * n2 + y * n1 + z * n0
=a * 124 + b * 123 + ... + x * 12 + y * 11 + z * 10 mod n-1
=a+b+c+d+e+f+g+h+i+j+k+l+m+o+p+q+r+s+t+u+v+w+x+y+z mod n-1
Where that whole mess is congruent to 0 if it's a multiple of n-1, or some whole number smaller than n-1 otherwise.
If any of you don't know much about modular arithmetic and want to know why it's not as simple as taking the remainder, then continue reading. Otherwise you're good to go.
Modular arithmetic is what happens when you write out the whole numbers and zero from 0 to m-1 inclusive, then cut it at either end, then glue the two ends together to make a loop. When you go past the one end, you end up on the other. There are exactly m numbers in your new number system; that's what the m in mod m refers to. This also implies no fractions; you can't divide anything in mod, because otherwise you have an infinite number of numbers in a system that can only contain m numbers (where m is a finite number; real math is already basically mod infinity). 2 + 6 mod 7 is congruent to 1. The reasoning for this is not just 2+6 = 8, 8/7 = 1 R1. The reasoning actually looks like 2 + 6 = 1 + 1 + 6 = 1 + 7, and 7 mod 7 is congruent to 0, so therefore 1 + 7 mod 7 is congruent to 1 + 0 mod 7.
You can still sort of divide, but there are some workarounds. In regular math, you divide by multiplying by the number's multiplicative inverse. You (technically, most people just skip this step and go straight to dividing) decompose 8/2 into 8 * 1/2 because 21/2 = 1, making them multiplicative inverses. Mod has a similar system, in which you identify the multiplicative inverse q of a number p such that pq is congruent to 1 mod k. This only works for numbers relatively prime to k; you can never, ever create a multiplicative inverse to 2 in mod 2k where k is any whole number, because there exists no number that you can multiply 2 by such that the result is congruent to 1.
You can also exponentiate, and this gets used to create RSA privacy: security based on the concept that you give somebody 2/3s of the system, and that nothing is worth the vast effort that it takes to find the remaining third.
[deleted] · 1 points · Posted at 05:24:15 on February 14, 2016 · (Permalink)
I like to think of it like this: if you add 9 to something, it is basically adding 10 (thus increasing the digital root by 1), and then taking away 1 (thus decreasing the digital root by 1). So adding 9 to something doesn't change its digital root.
A multiple of 9 is just the number 9 with a load of 9's added onto it. So it must have a digital root of 9!
Was going to mention that about 3 but you beat me to it. It's logical since 9 is 32.
However, I can refresh your memory on digital roots of 7.
Take any number. Remove the last digit entirely. Double it and subtract it from the remaining digits of the original number. If the difference is a multiple of 7 then the original number is rooted in 7. If it is not then it is not rooted in 7. If you are unsure then repeat the process.
Example 1:
Let's use a simple multiple first: 14.
Step 1: Drop the last digit.
14 --> 1 and 4
Step 2: Double that dropped digit.
4 × 2 = 8
Step 3: Subtract from the remaining digits.
1 - 8 = -7
-7 is of course a multiple of 7 (7 × -1) therefore the number 14 is a multiple of 7.
Example 2:
Let's try 49 (7 × 7).
Step 1: Drop the final digit.
49 --> 4 and 9
Step 2: Double it.
9 × 2 = 18
Step 3: Subtract from remaining digits.
4 - 18 = -14
-14 is the product of (-1 × 2 × 7). It is rooted in 7.
Try one more? How about... 343?
Step 1 : Drop the final digit.
343 --> 34 and 3
Step 2 : Double that dropped digit.
3 × 2 = 6
Step 3 : Subtract from the remaining digits.
34 - 6 = 28
Hm, I'll play dumb. Is 28 divisible by 7? I'm not sure. Let's do that again.
This generalizes to all other bases too. For example, consider base 8 number systems. In this case, the special property of 9 is replaced by 7. Examples (the numbers below are in base 8):
You can always tell if a number is divisible by three, no matter how big, if you sum all of it's digits untill you get a 1 digit number and it's 3, 6, or 9.
You can use this to do other stuff as well. How can you quickly multiply 38 x 42. The number in between the two numbers is 40 -- 38 + 2 = 40 & 42 - 2 = 40. 402 is 1600. 22 = 4. (The two is taken because it is the difference between 38 and 40 and 40 and 42). 1600 - 4 = 1596. 38 x 42 = 1596.
What is 64 * 56? The middle number is 60. 602 = 3600. 42 = 16. 3600 - 16 = 3584. 64 * 56 = 3584.
This is great because anyone with a decent grasp of algebra can proove and understand it but it seems so cool. It is great to introduce non-mathematical people to the beauty of numbers.
I somehow knew posting a simple formula on Reddit would draw negative comments.
Your comment doesn't match the formula, by the way.
12tales · 1 points · Posted at 06:17:31 on February 14, 2016 · (Permalink)
It does. Your formula is (X-1)(X+1) + 1. That can be simplified to (X x X) + (X x 1) + (-1 x X) + (-1 x 1) +1. Simplified further, that's X2 + X - X - 1 + 1.
I'm just saying, that formula is only cool to the extent that it obfuscates the trivial mathematics going on behind it.
Fuck why cant teachers show us this. Why do teachers suck? While I knew the above, its sooooo easy when you see this.
zekilki · 49 points · Posted at 21:20:48 on February 13, 2016 · (Permalink)
That there are more numbers in the segment [0,1], a subset of the real numbers than there are all integers.
I enjoy that:
1 + 1/2 + 1/4 + 1/8 + 1/16 + ... equals 2
but
1 + 1/2 + 1/3 + 1/4 + 1/5 + ... is infinite.
Infinite!!
[deleted] · 12 points · Posted at 01:17:13 on February 14, 2016 · (Permalink)*
Infinitely many mathematicians walk into a bar: the first one says "I'll have a beer!"; the second one says "I'll take half a beer!"; the third asks for a quarter of a beer...
Bartender shakes his head, pours two pints, and says:
"C'mon guys! Know your limits..."
I'll go ahead and show myself out. I mean, I'd love to tell you the one about the group that commutes. But you've probably heard it abelian times by now...
thmsoe · 3 points · Posted at 02:26:26 on February 14, 2016 · (Permalink)
There is more :)
If in your sum : 1+1/2+1/3+1/4+1/5+... you exclude all numbers which contain 9 as a digit, then your sum actually converges. I believe it works for any combination of digits : for example, if you exclude all numbers that contain '101467' in their digits, then the sum converges.
Even crazier is this : the sum of all 1/p where p are the prime numbers diverges towards infinity. You can thank Euler for that one !
The reasoning behind the "exclude all the numbers with 9" is that 9 becomes more common in numbers as you get larger.
How many numbers between 1 and 10 have a 9 in them? 1. So there's a 10% chance of there being a 9 in the first 10 numbers. What about between 1 and 100? 9,19,29,39,49,59,69,79, 89,90,91,92,93,94,95,96,97,98,99. That's 19. So there's a 19% chance of there being a 9 in the first 100 numbers, and you can see how the ratio to numbers with a 9 vs total numbers is increasing.
Another way to look at is this: Randomly generate a number with N digits. What is the chance that none of those digits is a 9? We have a 9/10 chance of the first digit not being a 9, a 9/10 chance of the second digit being a 9, and so on. So there's a (9/10)N chance of every digit not being a 9. Since 9/10 < 1, then as N goes to infinity, (9/10)N goes to 0.
heap42 · 1 points · Posted at 00:03:59 on February 14, 2016 · (Permalink)
Wait... is the first one right?... Can someone else confirm? I am not really good with Cardinals ordinals and infinities... and someone in an other comment said that this is not true.. or maybe i am confusing somethign.
I never thought of that as amazing, that's just the definition of e. Its like saying if you divide the circumference of a circle by its diameter you get pi.
that there must be some function which is the derivative of itself
And even less obvious, that this should be unique (which it is)
[deleted] · 2 points · Posted at 23:26:36 on February 14, 2016 · (Permalink)
Proving that it must be unique is much easier than proving that it must exist.
Suppose you have two functions f and g such that f' = f and g' = g. and f(0) = g(0) = 1.
Then (f/g)' = (f'g - fg')/g2 = (fg - fg)/g2 = 0
so f/g is a constant and since f(0)/g(0) = 1, then f = g
[deleted] · 1 points · Posted at 23:33:16 on February 14, 2016 · (Permalink)
Because of the Picard–Lindelöf theorem, of course.
But seriously, you can think of differential equations as the continuous analogue to sequences defined recursively.
In the latter, each new value is defined using the previous values.
In the former, at each point, you can think of f'(x) as (f(x+h)-f(x))/h, where h is a small number. The differential equation now gives you a relation between f(x) and f(x+h), that allows you to figure out f(x+h), then f(x+2h) and so on. And as you make the h smaller and smaller, you get a function that gets closer to a solution of the differential equation.
You are wrong, because differentiation is a linear operation on a function space, avoiding going into details here.
So there will be functions that are preserved by the operator, basically exactly like eigenvectors for a regular old matrix, but of course differentiation is an operator on an infinite dimensional vector space.
I suspect, though I don't know, that the existence of such an eigenvector is guaranteed by the kind of space differentiation acts on. which is a Hilbert space with (uncountably) infinite dimensions.
[deleted] · 2 points · Posted at 04:27:44 on February 14, 2016 · (Permalink)*
Kered13 · 3 points · Posted at 14:40:16 on February 14, 2016 · (Permalink)*
Also you can define the exponential function as the inverse of the natural logarithm (which is itself defined as the integral of 1/x from 1 to x). e itself is defined as exp(1) in this approach.
This is how we did it in my analysis class.
sorif · 2 points · Posted at 04:39:54 on February 14, 2016 · (Permalink)
ELI5 for the other definitions and the reason why they're all equal?
fnybny · 2 points · Posted at 07:51:50 on February 14, 2016 · (Permalink)
It is not a definition because e is not the unique complex number with this property. 0'=0
Right. Any student just starting out in ODE can easily derive ex using the differential equation y=dy/dx; i.e., "Some function 'y' is equal to its derivative 'dy/dx'." For anyone who's curious...
y = dy/dx
dy/y = dx
∫dy/y = ∫dx
ln(y) = x
e[ln(y)] = ex y = ex
However, you can also derive e as the following limit:
lim n->∞ (1+1/n)n
Add on a little less to 1 every time, but exponentiate it another time too. This sequence of numbers converges to e (although don't ask me to prove it).
The number e is also transcendental, meaning that it can never be the root of a polynomial with rational coefficients, which essentially says that you can't construct this number with algebra. Numbers that aren't transcendental are, fittingly, called algebraic numbers. Even the imaginary number i is algebraic (x2 + 1 = 0), so transcendental numbers are very special set of numbers indeed. (Fun fact though: Transcendental numbers are uncountably infinite and the algebraic numbers are only countably infinite, meaning that most real numbers are in fact transcendental. It's just really hard to prove that a number is transcendental, which is why it's sort of special.) In fact, the transcendence of e was used to prove that π is also transcendental using Euler's identity eiπ + 1 = 0.
Basically what I'm trying to say is that e is a really neat number.
Well, when you integrate the equation you're using the knowledge that the derivative of lnx is 1/x, and this comes from the knowledge that the derivative of ex is ex. So you can't really use that proof without already knowing about ex. ie you can't actually find the value of ex like that
Kered13 · 1 points · Posted at 14:42:20 on February 14, 2016 · (Permalink)*
Not necessarily. You can also go in the other direction: ln(x) can be defined as the integral of 1/x from 1 to x, and you can then define exp(x) as the inverse of ln(x).
Hmm. That doesn't seem like it gets you anywhere. All you're getting from that is "assume the integral of 1/x from 1-x is defined, and give it a name without figuring out what it actually is. Then the derivative of its inverse (assuming that exists) is its inverse"
In my mind, e has to come from the limit definition
e = lim[x->INF](1 + 1/x)x
Because that value makes sense without using e or ln anywhere in it, and it makes sense why the differentiation property holds.
Kered13 · 1 points · Posted at 15:19:43 on February 14, 2016 · (Permalink)*
Here's a good page that shows you how this approach works, (it was posted elsewhere in this thread for unrelated reasons). Note that while this page starts by talking about properties of logarithms, it doesn't define the logarithm by these properties. It proves the properties after defining the logarithm as the integral of 1/x.
I think part of your problem with this is that you feel like e is the more basic concept, and that it therefore must be defined without the exponential function or the natural logarithm. I would argue that this is wrong. That limit (and other limits that make e) is useful in a few circumstances, but the natural logarithm and exponential function are far more universal. Indeed, you'll almost always find e being used as part of one of these two functions. Furthermore, there's no obvious reason why that limit is important, while both the natural logarithm and exponential function are obviously important from just their definition and basic properties, without even getting into e. Therefore it makes the most sense to define e in terms of one of those two functions. Essentially all rigorous calculus courses do this. (Incidentally, pi is also usually defined as something like the smallest positive x such that sin(x) = 0, since this doesn't require geometry, and even then the circle definition only works in Euclidean geometry).
The next choice is which of the two functions to use. The natural logarithm approach is very natural if you start with integrals before derivatives, while the exponential function is natural if you start with derivatives (most calculus classes do derivatives first, but it's easy to go from the other direction instead). Starting with the natural logarithm is also arguably simpler: The natural logarithm can be defined as a simple definite integral, while the exponential function must be defined as a differential equation. By corollary, this also arguably makes the natural logarithm easier to calculate: The natural logarithm can be calculated using Riemann sums over 1/x, while if the exponential function is defined first it has to be calculated using Euler's method. (Remember, when you've just defined these functions these are the only methods you have to calculate them. Power series and other approximations have to be proved later.)
ln(y) = lim n-> ∞ [ln(1+1/n)]/(1/n) (evaluates to 0/0, thus use L'Hopital's rule)
ln(y) = lim n-> ∞ [(-1/n2 )/(1+1/n)]/(-1/n2 )
ln(y) = lim n-> ∞ (1 + 1/n)
ln(y) = 1
y = e1
L'Hopital's rule states that if the limit evaluates to the indeterminant form of 0/0, then the limit can be substituted with the derivative of the top over the derivative of the bottom.
Atmosck · 1 points · Posted at 05:26:34 on February 14, 2016 · (Permalink)
It is a bit remarkable in that it's not obvious that the function that's it's own derivative is exponential.
And the other definitions are convenient for other problems
klod42 · 1 points · Posted at 16:54:09 on February 14, 2016 · (Permalink)
I never understood why those definitions are equal to each other.
Dinkir9 · 90 points · Posted at 21:23:42 on February 13, 2016 · (Permalink)
Know why this is the case? ex can be defined as 1 + x + x2 /2! + x3 /3! + x4 /4! and so on. Thing is when you derive x4 /4! or something in that vein... It gets knocked down to the term before it. Since the pattern repeats indefinitely, the sequence doesnt get distorted when you derive it and it stays the exact same proving that ex =ex
Btw this was extremely difficult to write out on a phone.
Just FYI, the word for taking a derivative is "differentiate", not "derive". Derive means something totally different,
Dinkir9 · -14 points · Posted at 00:35:20 on February 14, 2016 · (Permalink)
Thats math grammer. The general point is still understood by everybody, doesnt matter if I said differentiate or derive, in the context of the post it was clear what I meant by derive and, it seemed to be pretty well understood. Consider it with literary grammer, the fact that I put a comma in the wrong place or, hell, dont have one isn't gonna change the fact that what I was writing about is still understood almost universally. Only the really anal grammer professors are gonna get confused and that's just because they are trained to do so.
Oh and by the way, I put "grammer" on purpose to get the point across.
I can't offer any profound explanation to why it's e, other than that it follows from a property of exponential functions. I can however show how to find the derivative of x1/x in which a logarithm term appears which explains why x=e is an extreme point.
Let f(x)=x1/x x>0
xx = eln(x1/x ) where ln is the natural logarithm with base e
You could choose any base for the logarithm but as we are about to differentiate, this would be unnecessarily complicated and we would still get a logarithm term with base e.
eln(x1/x ) = e1/xln(x)
d/dx(f(x)) = ( -ln(x)/x2 + 1/x2 )e1/xln(x) =
= x1/x / x2 (1-ln(x)), x>0
We set the derivative equal to zero
x1/x / x2 (1-ln(x)) = 0
1-ln(x) = 0
x = e
There probably is a way to do this where you use the definition of a derivative and reduce the problem to the same as above, thus avoiding the use of logarithms, which would be neater.
jaynay1 · 41 points · Posted at 21:56:48 on February 13, 2016 · (Permalink)
No, e is the value to which the sum from 0 to infinity of 1/n! converges.
But this definition comes from exponential growth, and (to me) is like saying pi is the area divided by the radius squared, instead of the circumference divided by the diameter.
I don't think that's exactly the best analogy. Consider this, why should there be a function that is it's own derivative? On the other hand it's obvious the ratio between the circumference of a circle by its diameter is a number (That doesn't depend on the diameter).
ananori · 1 points · Posted at 22:06:05 on February 13, 2016 · (Permalink)
Why shouldn't be there a function that describes its own rate of change?
I think the burden of proof is on you, why should there? That's not at all a trivial condition, a derivative is a limit, it contains a lot of information about the function. Let's try and build such a function, so arbitrarily set f(0)=0, how do we continue?
Maybe it's intuitive for you, I don't quite see why there should be such a function. For example there is no continuous function which maps rationals to irrationals and irrationals to rationals.
In your case the problem would be solved pretty easily by choosing f as the constant zero-function f(x) = 0 for all x.
But if you are familiar with the Taylor-series you can actually construct it pretty easily for any arbitrary value of f(0):
So, we want to get a function f with f'(x) = f(x) and f(0) = a for some number a.
According to Taylor, f(x) ist equal to the infinite sum f(0)/0! + f'(0)/1! * x + f''(0)/2! * x² + f'''(0)/3! * x³ + ... on the sums radius of convergence. Because of f'(x) = f(x) it also holds that f''(x) = f(x) and so on.
Thus, we get f(x) = a + a * x + a/2 * x² + a/6 * x³ + ... = a * sum(xk / k!, k=0..infinity).
The last sum converges for every real number x, and so f(x) = a * sum(xk / k!, k=0..infinity) for all x.
That sum by the way is equal to ex , so f(x) = a*ex.
We assume, that we have a differentiable function f with the given properties and then show what f has to look like. This assumption is okay because then function we get IS in fact differentiable with these properties.
You can differentiate an infinite sum term by term at any point if the sum converges absolutely at this point (which our sum does).
You have to prove that last thing. What I'm trying to say is that it isn't obvious why such a function exists, when you learned about functions, even when you learned about what is a derivative, did you immediately think that it can be represented by an infinite polynomial?
At this stage I can easily build a function that is its own derivative, but when I learned about what a function is, I did not. I am not saying it takes an incredible genius to think of one, but it is certainly not "just the definition of e".
Kered13 · 1 points · Posted at 14:44:35 on February 14, 2016 · (Permalink)
It's not immediately obvious that that ratio is a constant though (indeed, it's only constant in Euclidean geometry).
Yes you're certainly right it takes work to prove, I think it is much more intuitive though, if you take a triangle and magnify it, than all sides grow by the same factor.
I don't think that's exactly the best analogy. Consider this, why should there be a function that is it's own derivative? On the other hand it's obvious the ratio between the circumference of a circle by its diameter is a number (That doesn't depend on the diameter).
Another reason why it's pretty amazing is the intuitive approach of what that implies. ex being its own derivative implies that the slope of the tangent line at any given point in said function is equal to the value of the function at that given point. I'm sure this can be expanded upon, but I find that initial approach amazing enough.
That's not the definition of e. It's a property of e. There's a huge distinction there and those are not at all the same thing. You can't derive the value of e from f(x) = df(x)/dx.
yes, but now can you PROVE to me that when you divide the circumference by the diameter for ANY circle, its a constant value? which ends up being pi.
Kered13 · 1 points · Posted at 14:47:05 on February 14, 2016 · (Permalink)
If a mathematics course is advanced enough to define e as exp(1) and exp(x) as the function that is it's own derivative, then it's probably advanced enough that pi is not defined as the ratio of a circle to it's diameter. Pi would probably be defined as the smallest positive number x such that ex*i = -1 (or equivalently, the smallest positive number x such that sin(x) = 0).
I don't think that's exactly the best analogy. Consider this, why should there be a function that is it's own derivative? On the other hand it's obvious the ratio between the circumference of a circle by its diameter is a number (That doesn't depend on the diameter).
Zartregu · 20 points · Posted at 23:39:40 on February 13, 2016 · (Permalink)*
ex and a constant function are having a nice stroll.
Suddenly they see a differential operator walking toward them.
"Yikes, he's going to nullify me!" screams the constant function as she runs away.
ex smiles and greets the differential operator.
"Hi, I'm ex"
"Why hello, I'm d/dy..."
bisbyx · 9 points · Posted at 04:25:05 on February 14, 2016 · (Permalink)
I told that joke on the first date with my wife. 8 years later and she still tells people how lame I was on our first date.
xereeto · 1 points · Posted at 04:26:36 on February 14, 2016 · (Permalink)
The integral of 1/cabin is a houseboat... log cabin, then add the c
[deleted] · 1 points · Posted at 23:33:57 on February 13, 2016 · (Permalink)*
No it's not. The derivative is 7. Some guy proved that a while back. The derivative of 7, however, is 7.
There is more to this as well. The natural logarithm of 7 is 7. Or actually it is 6.98989898. Experts are still trying to find out why that is the case; i.e. why it is not exactly 7. Could be proof of a deep error in the way we understand numbers.
If you raise 7 to the 7th power 7 times, what you get is actually not a natural number. It is either irrational or transcendent - nobody knows for sure. Some think it might be divisible by 0.
If you solve the equation 'x + 7 = 0', you get 'x = -7' which is impossible, because the derivative of 'x + 7' is 7 and not 0, which you get on the right-hand side, suggesting complex numbers are somehow involved.
The Riemann zeta-function for even natural numbers can be written as a rational number times a power of 'pi', but there is no similar expression for odd numbers; not even for 7, as one would expect. The numerical value is also no-where near 7.
While the mystery of 7 is way beyond me, I have tried to come up with some answers. 7 is 5 + 2. 2, 5 and 7 are three numbers, giving the sequence 2, 3, 5 and 7 - the first four prime numbers. The derivative of 7 is 7.
Imagine trying to rub all the fur on a sphere the same direction. The direction of the fur corresponds to the wind direction. So if you rub the fur down the whole way around the equator, and then continue to rub the fur in the same direction all over the sphere, the north and south poles will have no direction. There'll be like a little swirl around them, but right at the pole, you'll have the fur pointing in no particular direction.
This isn't a proof, just something to give you a bit of an intuition about it.
Not true. Higher dimensional spaces have options that lower dimensional ones do not.
For example this is why printed circuit boards require two sides to function: it allows lines to cross.
Knots only exist in three and more dimensions.
In the case of wind it means that a given surface might have "zero speed" points but the wind is still moving there it's just moving up or down, ie outside of the "plane" of that surface.
Theorems true in 2D don't necessarily generalize to 3D.
Also, for any great circle of the earth (cross section through the middle), there are two points opposite each other with the same temperature. Pretty sure that's how it goes.
3_14159 · 8 points · Posted at 23:30:25 on February 13, 2016 · (Permalink)
I'm not sure I understand... I've been outside many times when there was absolutely no wind. Do I live in a vortex? I'm not smart. I don't know what a vortex is.
Technically yes, but that's not very useful. Speed is defined as distance over time, so at any point in time the wind vectors must be 0 at some point, but that point could be moving just as fast as the wind is.
dbers92 · 34 points · Posted at 02:14:46 on February 14, 2016 · (Permalink)
As lame as it may sound, last semester in an abstract algebra class we proved:
Anything * 0 = 0
&
A negative * A positive = A negative
22 years old and many years of schooling (aimed toward an applied math degree) and I finally was shown the proof of what is considered trivial by most people.
Obyeag · 29 points · Posted at 04:54:44 on February 14, 2016 · (Permalink)
Proof for those wondering:
x*1=x because 1 is the multiplicative identity.
x+0=x because 0 is the additive identity
A*(b+c)=A*b+A*c due to the distributive property
Prove A*0=0
A*1=A=A*(1+0)=A+A*0
A=A+A*0
Thus A*0=0
dbers92 · 5 points · Posted at 05:15:30 on February 14, 2016 · (Permalink)
I probably should have included this in the original post. Thanks for adding it!
Abomm · 2 points · Posted at 07:36:22 on February 14, 2016 · (Permalink)
Looks a lot like my coq homeworks
[deleted] · 0 points · Posted at 08:44:39 on February 14, 2016 · (Permalink)*
sum{i=1->n}(10i-1) would work for the right side, but it's not exactly elegant.
Edit: similarly, n+9(sum{i=1->n}((i-1)10n-i)) works for the left side but at that point I start to hate myself
narbris · 2 points · Posted at 05:45:57 on February 14, 2016 · (Permalink)
You messed it up after the 9th row.
(1234567900 x 9) + 11 =0
The reason is when you add 10 to the 1 is carried over to the 9 which becomes 10 and carries over a 1 to the 8 which becomes 9.
pikaras · 2 points · Posted at 10:06:12 on February 14, 2016 · (Permalink)
I'm sure you mean 123456780 x 9 and 1234567801 x 9....
The 10 carries over into the next digit and when added to 9 makes it 0. The 11,12,13... also carry over a 1 but add it to the ones place of the last number so it appears to simply skip the 9 and start over
I really quite like Cantor's diagonal argument, to show that there are more real numbers (or even, more real numbers between 0 and 1) than there are integers, even though both are infinite.
If you start out assuming that there's only one kind of infinity, then there's the same infinite number of integers as there is of reals. Hence also there must be some way to count all the real numbers, and make a 1-to-1 mapping from integers to reals and vice versa. So then if that's true you should be able to line them up in order.
and naively we might think that because there are infinite integers, every real number will end up somewhere in that list, even if we just assign them at random - there's an infinity of each type of number so no matter how many reals we think of we're never going to run out of integers to assign to count them with.
But then along comes Cantor and highlights a diagonal line down those rows of digits, to pick out the first digit of #1 and the second digit of #2 (and so on), and says "Consider the real number that we can construct by looking at the nth digit in the nth real and then picking any different digit to be the nth digit of our new number... where does that appear in the numbered list?"
But it can't appear in the list, because it's by-definition different from every entry in the list; different by at least that one digit that was deliberately set to be different from the nth digit of #n. Therefore there are too many reals to count, because we didn't count that one.
[deleted] · 2 points · Posted at 12:58:31 on February 14, 2016 · (Permalink)*
Hmm, you have a point that I'm not sure how to answer... in the general sense that numbers with different digits can nonetheless be equal, so demonstrating differing digits doesn't absolutely prove differing value.
It's a well established enough argument that I would be surprised if there were no answer to that, but being a distant admirer rather than a proper mathematician, I'm not going to be able to furnish you with that answer.
Again, I'm fully aware of this, having studied mathematics.
My point was that one of your premises was wrong for utilization of Cantor's proof.
I'm also impressed by you utilization of ad hominem during this discussion.
If you can't win, just insult. It's a surefire way to prove yourself right. Good on you!
aezart · 1 points · Posted at 08:20:17 on February 14, 2016 · (Permalink)
I've never understood this one. I do understand that there are different infinities, but I don't understand how that diagonal number can't be on the list.
It can't be the same number as #1 because it has a different 1st digit to #1
It can't be the same number as #2 because it has a different 2nd digit to #2
It can't be the same number as #3 because it has a different 3rd digit to #3
...
It can't be the same number as #n because it has a different nth digit to #n
The way that it's defined makes it different to every number in the list, no matter how you assign the numbers.
The Rule of 9's:
You can determine if a number is divisible by 9 by adding up all the digits in the number. If the sum of the digits is divisible by 9, so is the original number. So for 81, 8+1=9 so 81 is divisible by 9. But for 719384715, 7+1+9+3+8+4+7+1+5 = 45, and 45 is divisible by 9, so 719384715 is too. And if you don't know 45 is divisible by 9, all you have to do is 4+5=9 and you know 9 is divisible by 9 (this matters more for super large numbers).
This can also be generalized, so for a base 6 system the same is true for determining if a number is divisible by 5. It works for n-1 in any base n system.
[deleted] · 9 points · Posted at 01:01:20 on February 14, 2016 · (Permalink)*
When you have two complex numbers (which are "real" numbers added to an "imaginary" number (5 + 3i; sqrt(2) + (pi)i; 0 + 0i; etc.) you can describe them (because they are essentially two-dimensional coordinates) as arrows, determined by length and their angle from the positive x axis. When you multiply two complex numbers, their length multiply, and their angles add. So when you multiply complex numbers, they rotate!
An example: 1 + i is a complex number with a length of sqrt(2) and a, angle of 45 degrees from the x-axis:
(1+ i)2 = (1+ i)(1+ i) = 12 + 2i + (i)2 = 1+2i-1=2i
Note that 2i has length 2 and an angle of 90 degrees!
edit: exponents in reddit's text environment don't obey order of operations.
That's a circular argument. You're saying it's cool that complex numbers can use vector mathematics but that's only true because complex numbers are a representation of vectors.
[deleted] · 3 points · Posted at 05:55:18 on February 14, 2016 · (Permalink)*
I really hope you're making a pun with "circular argument". Besides, my point isn't that they are a vector space. I bring that up only to call attention to representing them in polar form. The point is that rotation (one of the dare I say "transcendental" ideas in mathematics) is built into that vector space! In the complex plane rotation is a totally diagonalizable transformation, and accomplished through multiplying by a unimodular constant!
It's possible to ride a square-wheeled bicycle so that your ride is perfectly smooth (your center of mass doesn't bob up and down at all). You have to ride the bike on an upside down catenary curve, which is the curve formed by a rope or chain suspended at both ends (it's not a parabola). Here's CGI of such a bike: https://www.youtube.com/watch?v=0BtZcmEkFsI
So, each time you stack cards, it's very likely that it's the first time in history in which the cards have been stacked in that exact order. Of course, you can never know for sure, but it's still pretty cool.
If your shuffle is truly random, in the sense that each possible ordering of the cards is equally likely. If you start with a new in-order deck and do one or two quick shuffles then you'll be much more likely to duplicate an order that someone else created before by doing the exact same thing.
aezart · 1 points · Posted at 08:11:01 on February 14, 2016 · (Permalink)
According to numberphile, 7 good riffle shuffles is sufficient.
it's very likely that it's the first time in history in which the cards have been stacked in that order
Yes, but the probability is much higher than your comment seems to suggest. IIRC, when computerized card games first started up, some people familiar with those games IRL thought the computer was cheating, since they were dealt hands with different frequencies than occurred IRL - of course, the computer's shuffle was close enough to random distribution that the more likely explanation was that real shuffled cards resulted in less varied patterns.
If you shuffle perfectly, it's extremely likely nobody has ever gotten that combination of cards in that order before. I'm on mobile so I don't feel like linking but check out VSauce's most recent video to see just how huge 52! is.
[deleted] · 1 points · Posted at 19:16:26 on February 14, 2016 · (Permalink)
The overall metabolic rate has been argued as the underlying factor that links life spans with heart rate. In the paper, the authors conclude that there is no significant correlation.
If you add "all numbers from 1 - Infinity" which I can only presume means "the natural numbers" then this is a false statement. No matter how you arrange the terms, the series diverges to infinity.
Also, there are plenty of convergent sequences that also don't have this property.
What he should have said is "given an infinite sequence of numbers whose series converges but does not converge absolutely, and given any real number r, the sequence can be rearranged such that the sum is r."
For this to work, your sequence of numbers needs to have infinitely many positive numbers and infinitely many negative numbers.
Ahhhh, that makes more sense. I imagine that's exactly what he said. This was around 2 years ago and I always thought it was along the lines of what I posted and wondered how that made sense. I just assumed he knew much more then I did.
I'll show myself out.
F-0X · 15 points · Posted at 22:04:27 on February 13, 2016 · (Permalink)
481x462 · 1 points · Posted at 02:27:10 on February 15, 2016 · (Permalink)
Yea. I think.
I could do it easily if I just slip in terms of +a -a that would cancel each other out, and have the sum converge to a.
Without those sneaked in, but using the type of summation that says 1 - 1 + 1 - 1 + 1... = 0.5, I could arrange the sum to equal any real number.
Edit: the reason adding every number from 1 to infinity in a different order will give you the same answer is because it doesn't matter what gets added first, i was trying to give an example
Second edit: in my defense i failed high school algebra. I'm not good at math. Sorry i was wrong
Yes but what I'm saying is that if you change the order of the number while going to infinity the answers will be different. Yours are the same. It doesn't work with a set amount of numbers. It's something to do with limits and summation series.
Edit: Don't worry bud. My wording made me wrong too. Lets just quietly leave and leave the math to the math people.
That isn't what he said, he said it will give you different answers if you change the order.
anthli · 8 points · Posted at 04:30:00 on February 14, 2016 · (Permalink)
Mentally squaring any number with 5 in the ones digit.
Take the 5 and square it to get 25.
Take the rest of the number (excluding the 5 in the ones digit) and multiplying it by itself plus 1.
Put the product in front of the 25 you got from step 1 and that's the square of the original number.
Example: 65. 52 = 25. Then, take the 6 and multiply it by itself plus 1, so 6 * (6 + 1) = 6 * 7 = 42. Take the 42 and put it in front of 25, resulting in 4225 = 652.
[deleted] · 269 points · Posted at 22:10:33 on February 13, 2016 · (Permalink)
Well, look into my eyes and it's easy to see, 1 and 1 makes 2, 2 and 1 makes 3. It was destiny.
Probably more of a trick than a fact, but most numbers 2 digits or larger, revert back to 9 in just a few steps by adding them together then subtracting the result from the original number. No idea why this works. Sometimes an additional step is required.
It's a variation on the "casting out 9s" trick, which I learned as a way to check whether a number is divisible by 9 (or 3): add all the digits together, if the sum has multiple digits do it again, and if the final result is 9 the original was a multiple of 9; if the final result is 3,6,9 the original was a multiple of 3. In general the final result has the same remainder when divided by 9 as the original number did.
To see why this works, think of the number 7154 as 7000 + 100 + 50 + 4, that is, consider each digit's value separately. Now think about what happens if you have a number like 7000 and remove the last 0: you've removed a 10*700, and added 1*700, or in other words, you've subtracted 9*700. Whatever the digit is, 9*X00 is a multiple of 9. So if you lop off all the trailing zeroes, you've subtracted a multiple of 9. Meaning the remaining number has the same residue (remainder) mod 9 as the original. That residue is kept when you add up the digits, and also when you repeat the process until you are left with a single digit.
In your trick, the first time you do the subtraction, you subtract [a multiple of 9 plus a residue equal to the original number's residue] from your number, leaving you with a number with no residue, that is, it's guaranteed to be a multiple of 9. After that you're just subtracting more multiples of 9 until you reach a single-digit multiple of 9, which can only be 0 or 9.
This also explains why 9 is special for tricks like this. It's one less than our number base, and when you lop off a zero, you're involving the number base.
If you start with the number 41, and add 2, then 4, then 6, then 8, etc., to obtain the sequence 41, 43, 47, 53, 61, etc., then the first 40 numbers in this sequence are all prime numbers.
Source: mathematician guy in the 90s PC game Rama (based on the Arthur C. Clarke book).
I believe the source is even older. The Polish mathematician Stanislaw Ulam was doodling in the 1960s, and came up with his famous spiral. I think the idea of starting at 41 is a derivative of his work.
EDIT: I am wrong! Wow, learn something new everyday. Wikipedia says...
In a passage from his 1956 novel The City and the Stars, author Arthur C. Clarke describes the prime spiral seven years before it was discovered by Ulam. Clarke did not notice the pattern revealed by the prime spiral because he never actually performed the experiment.
Holy smokes, has no one taken the best one yet, or at least the one with the best source? I imagine someone has but I can't find it with ctrl-f in the top 200 comments.
ii (sqrt(-1) to the power of sqrt(-1), to be clear) is about 0.208.
The Banach-Tarski paradox. It states that you can take a mathematical spheres, cut it into a finite number of pieces, and with a finite number of rotations, assemble two spheres identical to the first. Not half as small, not similar. Two spheres identical to the first. This means you can make an infinite number of mathematical spheres from only one sphere. The reason for this is that, unlike a physical sphere, a mathematical sphere is an infinitely dense set of points. When you assemble the two daughter spheres, each is half as dense as the first. However, since the first sphere is infinitely dense, the resulting spheres are ∞/2 dense, which is still ∞. Thus, the daughter spheres are identical to the parent sphere.
"A stronger form of the theorem implies that given any two "reasonable" solid objects (such as a small ball and a huge ball), either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox"."
Here's an algebra trick i learned in middle school.
x = 1 , y = 1
x = y
xy = y2
xy - x2 = y2 - x2
next you factor both sides.
x (y-x) = (y+x) (y-x)
then you cancel out the common factors on both sides.
x (y-x) = (y+x) (y-x)
x = y+x
1 = 2
Tada!
The trick is that when you cancel out (y-x) from both sides, you are actually dividing both sides by y-x (which is equal to zero). This is an easy-ish way to show somebody why you aren't allowed to divide by zero.
[deleted] · 28 points · Posted at 21:39:23 on February 13, 2016 · (Permalink)
9+10=19. Not 21, you fucking idiots. Let that meme stay in 2015 where it belongs.
If you have a conditionally convergent series (that is, a series which converges but the sum of the absolute values of the terms diverges), then you can rearrange the terms to make it converge to any real number.
For example, the series 1–1/2+1/3–1/4+... converges to ln(2), but by rearranging the terms it can be made to converge to 1,000,000.
heap42 · 9 points · Posted at 23:17:08 on February 13, 2016 · (Permalink)*
There are some... one is probably, Gödels Incompleteness Theorem... Even though i dont understand it, its still awesome.
EDIT: I understand what the theorem states and I undetand the implications, i just dont understand or rather i cannot follow Gödels Proof itself. The enitire thing with his Numbering etc... it just is to much for me... maybe at a later point in time.
[deleted] · 7 points · Posted at 05:45:59 on February 14, 2016 · (Permalink)
I'll give it a quick shot.
A formal logic consists of a set of strings. Theorems, for lack of a better word. Mathematics is then about deciding whether each of these strings is true or false.
Given a finite set of axioms (strings which are assigned a truth value to start) and laws of inference (which allow us to extract a truth value from another strings truth value). We'd like to be able to say the following.
for all strings x, x can never be proven to be both true and false.
for all strings x, x can always be proven to be either true or false.
For this would mean that Mathematics is never in vain.
We'd like to, but for any formal logic which is sufficiently complex to allow you to enumerate the theorems of the logic itself (which is much less complex than you'd think), it is impossible.
The proof is a lot more detailed than this, but the result is worth knowing on its own.
heap42 · 1 points · Posted at 15:30:47 on February 14, 2016 · (Permalink)
yea i understand... but can you proof it, thats what i have trouble with... it makes sense, and i understand what it says... but i wouldnt be able to prove it to you.
I came looking for this answer and found it at the bottom of the page. :( My lay understanding is that it says that in any logical system (capable of expressing arithmetic) there will be statements/theorems/conjectures you can make but never prove true or false. His proof essentially starts with the statement "this statement is unprovable" and then uses math to prove its true. Badass math there. Again, that's my lay understating.
In the book "Pi in the Sky" (a fun overview of math history) the author points out that if you define a religion as a belief system where there are things you simply have to accept on faith because you can't prove them true or false them mathematics is a religion and the only one that can actual prove it's a religion with rigorous logic.
I was mostly writing it for others. I've toyed with the proof. My vague hand-waving sense is that the Godel numbering thing lead to a proof by paradox similar to the proof there is no largest prime. I never understood how his numbering system discerned between valid statements and gibberish of symbols, or even if it is required for the proof.
That's a 7 minute video describing the formula and what it is (and it describes it better than I'll ever be able to). Essentially it's a bitmap (106 x 17 pixels) that will eventually display every possible sequence of pixelated images when given the correct starting 'y' coordinate.
[deleted] · 1 points · Posted at 03:24:15 on February 14, 2016 · (Permalink)
Somewhere on the earth, there are two points which are diametrically opposed (ie, exactly opposite of each other) that have the same temperature and air pressure. This is the three-dimensional case of the Borsuk-Ulam Theorem. The really interesting part is that while real-valued functions are typically the realm of the branch of math known as analysis, it is easier prove this theorem using topology, a very different branch of math.
Imagine you had a timer that counted down 52! seconds. How long would that be?
Let's say you stood on the equator. Every billion years, you take one step foreward. Once you made it around completely, you take one drop out of the Pacific Ocean. You continue doing this untill the pacific is empty. When the pacific is empty, you put one piece of paper on the ground. You refill the ocean and repeat this process untill the stack of paper reaches the sun.
And that would have barely made a dent in the time.
You would have to repeat this process 3,000 times to even come close to 52! seconds.
Edit: another cool math fact!
You take a standard piece of paper and you rip it in half and stack it, making a stance that is two pieces tall.
You do this again... 49 times.
The stack is now (paper)x250 pieces of paper thick.
To where would that reach? The roof, maybe? A story or two? A skyscraper? The clouds? The moon? Nope. It would reach to the sun.
This reminds me of this from "The Shepherd Boy" by the Brothers Grimm:
The King said, "The third question is, how many seconds of time are there in eternity?" Then said the shepherd boy, "In Lower Pomerania is the Diamond Mountain, which is two miles and a half high, two miles and a half wide, and two miles and a half in depth; every hundred years a little bird comes and sharpens its beak on it, and when the whole mountain is worn away by this, then the first second of eternity will be over."
You're not just adding a new sheet every time, you're doubling the stack. So it would look like this;
Number of tears
thickness of stack (in paper sheets)
0
1
1
2
2
4
3
8
4
16
5
32
6
64
7
128
8
256
9
512
10
1024
...
...
20
1048576
...
...
30
1073741824
...
...
40
1099511627776
...
...
50
1125899906842624
So, by doubling a single piece of paper 50 times you end up with a stack that is 1 quadrillion pieces of paper thick, which could reach the sun with ease.
grawies · 225 points · Posted at 20:56:34 on February 13, 2016 · (Permalink)
I like how this reads as "0 factorial is 1" with my mathematics glasses on but "0 does not equal 1" with the programmer glasses - and both statements are true! :)
dj0 · 19 points · Posted at 02:36:14 on February 14, 2016 · (Permalink)
And 1=0! is like an absurd statement with an exclamation mark at the end to show it's not true
lw9k · 4 points · Posted at 08:14:54 on February 14, 2016 · (Permalink)
It's also a surprised person with a bowtie and an arrow on his head
What I'm interested in knowing is what you thought of first. I'm working on degrees in math and computer science so I'm in sort of the same boat as you but for whatever reason I think I'll always consider the mathematical angle first.
grawies · 3 points · Posted at 13:48:49 on February 14, 2016 · (Permalink)
I like the explanation that relates factorials to permutations. How many ways can arrange two objects? 2! = 2. How many ways can you arrange no objects? 0! = 1
F-0X · 22 points · Posted at 22:01:13 on February 13, 2016 · (Permalink)
It's a definition if you are lazy.
It is a result if you define n! to be the number of bijections from a set of cardinality n to itself.
I agree it's not an interesting result, but it's not just a definition.
By definition of a function (i.e., as a subset of a cartesian product) we are guaranteed a function from the empty set (which of course has cardinality 0) to any other set, the empty function. Consequently, there is one map from the empty set to itself; thus 0!=1.
From an Algebraian's point of view it makes sense that the empty product is equal to the neutral element of multiplication (and the empty sum is equal to the neutral element of addition) and since 0! is equal to the empty product thus it is equal to 1.
It is more intuitive if you think that there is only one way to choose nothing.
zeta12ti · 10 points · Posted at 15:44:43 on February 14, 2016 · (Permalink)
I'd like to nominate Yoneda's Lemma. To really understand it, you're going to need some background. So here goes...
Categories
A category is a way to organize structures in mathematics. Essentially a structure is represented by an "object" or "point" and a connection between two structures is represented by a "morphism" or "arrow" between the two objects.
For example, the category of sets has as objects sets (such as the collection of natural numbers {0,1,2,3,4,...} or {Hillary, Bernie, Donald, Ted}). The arrows between sets are functions. For example, there is a function {Hillary, Bernie, Donald, Ted} -> {0,1,2,3,4,...} taking each person to their age in years: Hillary -> 68, Bernie -> 74, Donald -> 69, Ted -> 45.
More generally, between any two sets S and T, there is a set of functions denoted Hom(S, T) from S to T.1 In fact this holds for all categories: for any two objects x and y, there is a collection of morphisms Hom(x, y) from x to y.2
Generally speaking, the categories used most frequently used in math are "sets with structure" as objects and "structure preserving functions" as morphisms. For example, consider the category of magmas. A magma is a set with a way of multiplying two elements together to get a third element. For example, the real numbers with their standard multiplication form a magma. A morphism between to magmas M and N is a function f from the set M to the set N such that for a and b in M, f(a*b) = f(a)*f(b).
However, categories are much more general than just sets with structure. The arrows could be something completely unrelated to functions. The set of natural numbers can be made into a category by making there be an arrow from a to b precisely when a ≤ b.
Now we're ready for the formal definition of a category. A category C is a collection of objects ob(C). For any two objects x and y, there is a collection Hom(x,y), called the morphisms from x to y. Additionally, we have a way to compose compatible morphisms. What this means is that we can take a morphism f from y to z and a morphism g from x to y and compose them to get a morphism f∘g from x to z.
This operation of composition has to satisfy
Associativity: for any three morphisms f, g and h such that (f∘g)∘h makes sense, (f∘g)∘h=f∘(g∘h).
Existence of identity: for every object x, there exists a morphism in Hom(x,x) called idₓ, such that for any morphism from x to y, f∘idₓ = f and for any morphism g from y to x, idₓ∘g = g.3
It's now possible to check that the category of sets and the category of natural numbers really do satisfy these properties. For natural numbers, this essentially follows from transitivity (a≤b and b≤c implies a≤c) and reflexivity (a≤a).
From now on I'll just work with arbitrary categories satisfying these properties. If you're really interested, it helps a ton to get familiar with the standard examples. If you aren't interested, just think of this as some crazy abstract math that falls way on the right in this picture.
Visualizing Categories
As I mentioned before, objects and morphisms in a category are sometimes called points and arrows. This refers to a standard way of visualizing a category, or some fragment of a category. For example, this image is a way of visualizing the composition of arrows. Whenever we have a picture like this, we say it commutes if we can compose along any path and get the same morphism either way. The example commutes because f∘g=f∘g. We'll get more technical commutative diagrams below when we talk about natural transformations.
Functors
The natural kind of morphism between two categories is called a functor. A functor is required to preserve all the structure of a category. Specifically, a functor F:C->D is a function on objects Ob(C) -> Ob(D) and morphisms Hom(x,y) -> Hom(F(x), F(y)). F must preserve identies: F(idₓ) must be the identity for F(x).3 F must also preserve composition: whenever f∘g is defined, F(f∘g) = F(f)∘F(g).
I mentioned before that lots of categories contain sets with structure. Every category like this has whats called a "forgetful functor" to the category of sets. This functor takes every set with structure to the underlying set and every structure preserving function to the underlying function between sets.
We've already met the most important example of a functor: the Hom functor. Let C be a category and let a be an object in C. Using Hom, we get a functor Hom(a, -):C->SET (the category of sets). We already know what Hom(a, b) is (the set of morphisms from a to b), so we know what Hom(a, -) does to objects. What about morphisms? Let f:b -> c be a morphism in C. Hom(a, f) ought to be a function from Hom(a,b) to Hom(a,c), so given g:a->b, and f, how can we get a morphism from a to c? The answer is composition: [Hom(a, f)](g) is defined to be f∘g. You can check that this really does define a functor, since Hom(a, id) maps g to id∘g = g, so it's the identity function. Hom(a, f∘h) maps g to (f∘h)∘g=f∘(h∘g) = [Hom(a, f)](h∘g)=[Hom(a, f)]([Hom(a, h)](g)), so Hom(a, f∘h) = Hom(a, f)∘Hom(a, h).
Hom has two variables, so we can ask what happens when we have an object c and look at Hom(-, c). It turns out that this is also a functor, but somehow reversed. Hom(f∘g, c) = Hom(g, c)∘Hom(f, c), rather than the other way around. such a thing is called a contravariant functor. Equivalently, we can reverse the composition in the original category to get the category Cop. Cop has the same objects and morphisms as C, but the direction of every arrow is reversed. Composition is also reversed: f ∘op g in Cop is defined to be g∘f in C. Hom(-, c) turns out to be a functor from Cop to SET, since Hom(f ∘op g, c)=Hom(f∘g, c)=Hom(f, c)∘Hom(g, c), so the order ends up the way we want it.
Natural Transformations
Functors themselves are an object in a certain category. For categories C and D, we can for the functor category [C, D] which has a objects functors from C to D and as morphisms natural transformations. For functors F and G from C to D, a natural transformation α:F -> G is a collection of morphisms αₐ: F(a) -> G(a) for every object a in C. A natural transformation is required to satisfy the naturality condition: for every morphism f: a -> b, G(f)∘α = α∘F(f) (where the first α is the morphism F(a) -> G(a) and the second is the morphism F(b) -> G(b)). This picture is the vizualization of this (for functors Φ and Ψ and natural transformation η).
Naturality occurs all over in mathematics. For example, Adjoint functors and the Tensor-Hom Adjunction
. Other examples are the isomorphism from a finite-dimensional vector space into its double dual and the idea that two functors are the "same" even if they're literally different (natural isomorphism).
The Yoneda Lemma
Finally you have the terminology to understand the Yoneda lemma. The statement is simple: Let F:Cop -> Set be a functor and let c be an object in C. There is a one to one correspondence between elements of the set F(c) and natural transformations from Hom(-, c) to F. Moreover, this correspondence is natural in the variable c. That's it. The cool part is how many different applications this has.
Cayley's Theorem
Every group can be realized as a subgroup of a group of permutations. A group is a way of organizing the symmetries of something (in particular, every object x in a category has a group of automorphisms Hom(x,x).4). This follows from Yoneda's lemma by considering a group as a category with one object x and letting Hom(x,x) be your group.
Isbell Duality
I won't claim to understand this fully, but Yoneda's lemma the reason that Isbell Duality works. Isbell duality is a huge statement of the duality between algebra and geometry.
Representable Functors
Sometimes a functor is naturally isomorphic to a functor like Hom(c, -). Using the Yoneda lemma, we can show that if c exists, it's unique up to isomorphism.
Yoneda Embedding
Any category C can be embedded into the category [Cop, Set] via c -> Hom(-, c). The Yoneda lemma implies that this embedding preserves essential properties of C. However, [Cop, Set] is generally much "nicer" than C. For example, it's complete and cocomplete.
An example of the Yoneda embedding is the embedding of the rational numbers into the (extended) real numbers. Similarly to our natural numbers example above, the rational numbers can be made into a category. [Cop, Set] happens to be isomorphic to the reals plus infinity and -infinity. Completeness gives us all the nice properties of the reals.
Further reading
Since I'm running out of space, check out here and here for some other cools stuff.
1 Hom here stands for homomorphism, which is also where the word morphism come from.
2 When this collection is actually a set for any two objects x and y, the category is called locally small. See here for the reason we can't just assume this.
3 Why does Reddit not support subscripts globally? Any for that matter, why
does Unicode not have subscripts for every letter (notably missing a subscript 'y')?
4 Actually just the isomorphisms from x to itself. A morphism is an isomorphism if it has an inverse.
TL;DR: Yoneda's Lemma is a simple fact that has some profound consequences.
The majority of what I wrote isn't directly related to Yoneda's Lemma, but is required to understand the language of the statement.
(It's like how if you didn't understand multiplication and decimal notation, 11111111*11111111 = 123456787654321 wouldn't make any sense, but once you understand, you can easily check it).
When any 3 digit number where all the digits are the same(111, 222, 333) is divided by the sum of the digits, the quotient is always 37.
Haus42 · 4 points · Posted at 01:53:48 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Four_color_theorem : roughly that on any 2D map, there's a way to code the "countries" with 4 colors, so that no two adjacent countries have the same color. It took almost 140 years to be proven, and it was the first major theorem to be proven using computer assistance.
Spent 6 months writing a dissertation on this at university - the paper mathematically proved that it could be done with 5 and then concluded by saying "hey it could be done with 4 but it's too hard so deal with it"
Can't remember where I saw this, but the expression "(12 + 144 + 20 + 3 * sqrt(4)) / 7 + (5 * 11) = 81 + 0" is a limerick:
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
Swate- · 1 points · Posted at 13:37:59 on February 14, 2016 · (Permalink)
Oh man I love this one.
mykeuk · 5 points · Posted at 15:09:56 on February 14, 2016 · (Permalink)
Take three random, different numbers. Now you have a 3 digit number. Now reverse the number so now you have two 3 digit numbers, one the reverse of the other.
Subtract the smaller from the larger.
Now you have a new number. Again, reverse it to make a new number, one the reverse of the other.
Add the two together.
Your answer is 1,089.
Example:
831 makes 138. So 831-138 = 693.
693 + 396 = 1,089
You can use this for a magic trick. Either write down the number 1,089 or get a book, go to page 10 and find the word that's 8 lines down and 9 words in and write that down. Then get 3 people to pick 3 separate numbers and use patter to make it sound like their choices are all completely random. Then, when the answer is 1,089 get them to check your prediction or check the book, then check what you'd written down.
iPreemo · 40 points · Posted at 19:07:52 on February 13, 2016 · (Permalink)
Tangent is slope...not all that cool but it's the first thing that popped into my mind.
hayberry · 14 points · Posted at 22:37:04 on February 13, 2016 · (Permalink)
I think the first time you achieve a crystal clear understanding of derivatives and the basics of calculus is just the most amazing feeling
I took a precalculus class last year, and didn't get a thing. Started taking calc this year and WOOOOSH it was so cool to see everything I've learned all throughout school fall into place as a kind of mathematics.
ngwoo · 2 points · Posted at 00:43:23 on February 14, 2016 · (Permalink)
Calculus is super easy to explain and understand until you start getting pesky numbers involved
Or if this is what you meant, copying form wikipedia, the Opp/Adj Tan function is "ratio of the length of the opposite side to the length of the adjacent side: so called because it can be represented as a line segment tangent to the circle":
That doesn't make any sense, though. At pi/4 rad the tangent line would have a slope of -1, the secant line would have a slope of 1. Tangent is the slope of the hypotenuse, which isn't tangent to a circle.
You can see it as purely the slope of the angle going from pi/2 to 3pi/2 (which makes the original gif make more sense), but the actual relation is that the tangent function maps the length of a line tangent to a circle at an angle. Take a look at this gif:
Look at the red tangent line. As you move around the circle, the angle of the hypotenuse line creates a triangle with the red tangent line, and the length of the red line side of that triangle is the length that is plotted onto the tangent graph at its angle. For example, at pi/4, if you extend the hypotenuse to make a triangle with the red tangent line, the length of the right red side of that triangle would be 1, which is tan(pi/4). Because of right triangle properties, the length of this length actually ends up being equal to the angle of the tan angle. Here's a video that goes over the trig:
I'm aware of the all of this, but the slope of a tangent line isn't what's being output by the tangent function, it's just related in a somewhat convoluted way. Trust me, all of this "clicked" for me years ago. I understand everything there is to understand about tangent lines and the tan(x) function. All I was saying is that when he said "tangent is slope", your comment about the feeling of finally understanding derivatives wasn't really relevant when he was talking about the tangent function outputting the slope of the hypotenuse. Your comment lead me to believe that you thought he meant tangent lines touching functions.
It's not convoluted, it's the definition of the tangent function, and a fundamental part of why trigonometry was invented as a tool for understanding astronomical relationships, namely, distances.
My interpretation of what he was saying is that a tangent line is just the slope of a line at that point, which is the same as a derivative, hence my comment about calculus. You're the one who brought up the tangent function which, again, is still about a tangent line, hence why it's called the tangent function. It wasn't named just to confuse people.
I didn't bring up the tangent function, he did. The parent/root comment of all this. tan(x) means input angle, output slope. That's what he was saying when he said "tangent is slope." That's what he was commenting about. Your calculus/derivative comment wasn't relevant. I said you were thinking of tangent lines, which although they are undeniably connected at a very intricate level with the tangent function, they are not interchangeable meanings of the word tangent. In his comment, "tangent is slope" is implicitly saying that the tangent function gives you the slope of the line. There's no other meaning behind the word "tangent" given the context provided by his comment, that could possibly make sense; the only thing you've commented that has provided any relevance to what you've been saying is "my interpretation of what he was saying..."
Only after you explained yourself was there any relevance in what you were saying at first.
And yes, it is convoluted. It's the same thing as, for example, the sine integral function. You can show a function that waves up and down, with precise outputs given precise inputs. You can go on and on about the applications in engineering, and for years just tell people to use a calculator to do calculations for Si(x). You can develop entire fields of study on that function, and still not bother with the origins of its name. You see, it's called the sine-integral function not because of all of these millions of definitions for the word "integral" not just in math, but in english, not because of all of these millions of definitions of the word "sine" again, within ENGLISH, but because the function is defined as the area from 0-input under the function y=sin(x)/x, which in purely mathematical terms is y=integral(0,x)[sine(t)/t]dt, aka integral[sin(x)/x]. You have to go out of your way in order to connect its name with the origin of its name. Therefore it's convoluted. Yes, it has a very good reason to be called the sine integral function, but the only way to explain to someone exactly why it's the specific words "sine integral" and not literally anything else is through a convoluted explanation. Which is exactly why the tangent function has an exclusively convoluted connection to the other definitions of the word "tangent" that we all know and love. It took you 3 comments to explain it to someone who already knew it, because you continued to convince yourself that it needed further explanation. How does that not seem convoluted to you?
hayberry · 1 points · Posted at 05:14:11 on February 14, 2016 · (Permalink)*
He said, and I quote, "Tangent is slope". No mention of the tangent function.
But it doesn't matter, because both the tan function and tangent lines are slope--tangent line is the slope of the graph at that point, the tan function is derived from the tangent line to a circle at an angle of a circle at that point. I don't see how someone who understands "everything there is to understand about tangent lines and the tan(x) function" isn't getting that.
Convoluted: "extremely complex and difficult to follow." Perhaps for some, but that doesn't change the fact that it's the definition of the tangent function. Just because its actual usage and derivation is more complicated than the formula they teach you in middle school doesn't make it something else. Opp/Adj is just easier to digest for children, but that does not change what the function actually represents.
[deleted] · 1 points · Posted at 06:45:44 on February 14, 2016 · (Permalink)
Yes! I remember the first time I understand the concept of a derivative. I know exactly the feeling you're talking about.
Makes sense, considering tan X = (opposite / adjacent) and slope is (change in Y/change in X) and if you simply imagine a right triangle, the opposite side length = the change in Y, and the adjacent side length = the change in X
My first calculus professor demonstrated this for our class, but I've since forgotten the actual equation;
A simple variation of the sine wave can be used the determine the exact number of hours of daylight in each day during the year, and the derivative of this equation shows why, at some times during the year, you can tell that the number of hours of daylight is changing, and you can't at other times (rate of change).
Pretty simple, nothing mind-blowing, but although I've always enjoyed math that was the first time I really appreciated calculus!
loozid · 1 points · Posted at 08:18:42 on February 14, 2016 · (Permalink)
Every curve is smaller segments of line put together, proven by the rate of change. I always found that fascinating as well. It makes me picture zooming into a point on a graph and how to define a graph and the visualization of data, and the infinite amounts of points from which you can acquire the average rate of change, and makes one question what a line is, if it has ever existed in nature, idk makes me think of that.
The left side seems like a simple enough pattern, but equals a quarter the ratio of a circle's circumference and diameter.
tl;dr Proof: the Taylor series and the inverse tangent
[deleted] · 4 points · Posted at 02:51:08 on February 14, 2016 · (Permalink)
The natural number e (2.71828....) can be obtained by the infinite sum 1/(n!) for n = 0 -> infinity.
Waniou · 2 points · Posted at 06:16:20 on February 14, 2016 · (Permalink)
That's not as cool as why that's the case.
We know that ex is a function made so that the derivative is ex . So how can we make that sort of a function?
Well, we know that the derivative of x2 is 2x, x3 is 3x2 and, in general, the derivative of xn is nxn-1 .
So, we basically just make a function where, if you differentiate each term, you get the previous one. So we start with 1, because the derivative of 1 is 0. The next term will be x, because its derivative is 1. Then we need x2 / 2. The derivative of x2 again is 2x, so we get 2x/2 = x. Again, the derivative of x3 is 3x2 so we need to divide our x2 / 2 by 3 so that it'll differentiate into it. In other words, x3 / 2*3 = x3 / 6 = x3 / 3!
From here, it's pretty easy to show that, to get the previous term in the equation when you differentiate, you just have xn / n!, and in other words, you get an infinite sum, xn / n! for n = 0 -> infinity. Or, in other words, ex = x0 / 0! (Or 1) + x1 / 1! (Or x) + x2 / 2! + ... + xn / n! + ... forever. If you differentiate each term in that, you always get the previous one.
And, of course, to get the actual natural number, 2.71828, you just let x = 1 and obviously get 1/(n!).
[deleted] · 1 points · Posted at 17:54:24 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 05:49:55 on February 15, 2016 · (Permalink)
You can get as picky as you wan't with the definitions, but the reason e is commonly referred to as "the natural number" is because it is the base of the natural logarithm.
[deleted] · 1 points · Posted at 11:37:54 on February 15, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 15:52:13 on February 15, 2016 · (Permalink)
I respectfully accept your insult. Note, I am not a mathematician, but I have had my fair share of math as an aerospace engineering PhD.
[deleted] · 3 points · Posted at 04:57:36 on February 14, 2016 · (Permalink)
[deleted]
dedcupid · -1 points · Posted at 05:21:09 on February 14, 2016 · (Permalink)
Its a joke, but still math related so ill throw it in here.
What does the middle initial of Benoit B. Mandelbrot stand for? Benoit B. Mandelbrot.
Dyne4R · 5 points · Posted at 14:42:23 on February 14, 2016 · (Permalink)
It's a basic one, but you can quickly tell if any number is divisible by three by adding the digits together. If the resulting number is divisible by three, then the original number is also divisible.
5,146,752 is divisible by three (5+1+4+6+7+5+2=30)
802,465,367,987,236,592 is not.
ck2839 · 1 points · Posted at 14:45:09 on February 14, 2016 · (Permalink)
This always weird me out. It's like God's fucking with us, because that's man-made (English!) notation, and the people who invented the notation didn't have those basically randomly-assigned holiday dates in mind when they invented it.
Eh, I think of it as Bible Code/pareidolia/confirmation bias type shit. You're always gonna notice the weird coincidences more than the 363 other days that don't mean anything.
[deleted] · 13 points · Posted at 00:46:44 on February 14, 2016 · (Permalink)
I was just reading about the Bible Code 363 days ago! That's so crazy!
eudamme · 1 points · Posted at 00:50:46 on February 14, 2016 · (Permalink)
Physics major here ( had to take my fair share of math). Not really, the only reason to use different bases is when it makes computation easier. But most mathematicians don't even work with numbers anyways... Mostly variables. We use base ten because for one reason or another it allows our brains to comprehend bigger numbers. I may be wrong though so if an actual math wiz sees this, please correct me.
Edit - we could probably Google this but I'm too lazy
The joke here is that Octal 31 (which abbreviated looks like October 31st, Halloween) is equal to Decimal 25 (which abbreviated looks like December 25th, Christmas).
[deleted] · 22 points · Posted at 03:00:07 on February 14, 2016 · (Permalink)
Why was 6 afraid of 7?
Cuz 7 8 9.
dmo012 · 14 points · Posted at 05:07:01 on February 14, 2016 · (Permalink)
Cause 7 is a registered six offender
-WPD- · 3 points · Posted at 07:03:05 on February 14, 2016 · (Permalink)
Six hasn't been the same since he left Vietnam. Every time he closes his eyes, he's sees Charlie hiding in the darkness of the forest. Not that you could ever see those bastards, mind you. They were fast and they knew their way around the jungle. He remembers the looks on the boy's faces when they walked into that village and... oh Jesus. He shouldn't think about that now. Sometimes he still hears Tex's slow southern drawl. He remembers the smell of Brooklyn's cigarettes. He always had a pack of Luckys. But the boys are gone now... he knows that. It's--it's just that he forgets sometimes. And sometimes the way that seven looks at him... it makes him think. Sets him on edge. And he feels like he's back there... In the jungle... In the darkness.
With 23 people in a room, there is a greater than 50% chance that two people have the same birthday. Tested this last night with 22 people, and we found out two people has the same birthday on November 10th!
KKMX · 2 points · Posted at 01:19:36 on February 14, 2016 · (Permalink)
[deleted] · 1 points · Posted at 02:47:56 on February 14, 2016 · (Permalink)
That's a surprisingly small amount of people.
Add to that that there are more and less favorable months for getting pregnant [citationneeded]
(from a social viewpoint; relations tend to form during summers, settle down during winters)
Assuming that the decimal of Pi extends infinitely, probability states that there has to be a length of digits that corresponds to the data forming a .jpeg of you making out with a polar bear.
No need to assume, the decimal of Pi does extend infinitely, it is proven irrational. It's digits do not terminate or repeat. What is not proven is whether Pi is a normal number or not (though it is conjectured). If Pi is normal, then the idea in your comment is true.
So which irrational numbers are normal vs, um, Abby normal? Is e normal? The golden ratio?
[deleted] · 6 points · Posted at 02:45:45 on February 14, 2016 · (Permalink)
Actually we do not know this yet. It is possible that every possible sequence of digits can be found in pi's expansion, but it's also possible that this is not true. An unanswered question, and if it's false then it's also interesting: What would be special about the sequences that do or don't appear in pi's expansion?
As an example of a decimal extension that that extends forever without repeating but does NOT include every possible sequence:
0.101001000100001000001...
Obvious pattern, but the sequence of digits never repeats itself in totality. Nothing but ones and zeros to be had, however.
GokuMoto · -1 points · Posted at 13:18:05 on February 14, 2016 · (Permalink)
I want to encode the number 1415926535897932384626 in pi. It can be described as the cut of decimal digits 0 through 21 of pi. Your statement is true in that pi is longer than the excerpt I'm encoding, but if pi is known and constant between two computers, that long number can be encoded using just a label for pi and the start/end points of the desired cut.
One of the applications of the Theorema Egregrium is a proof that a 2D model of a 3D object (such as the Earth) cannot simultaneously preserve both angle and area which is why on standard 2D maps Antartica becomes enormous
That the pine cone pattern follows fibonacci numbers.
zk3033 · 3 points · Posted at 01:48:55 on February 14, 2016 · (Permalink)
Generating functions
We all know the coefficients to (x+y)n give us binomials, or rather combinatorically "ways to pick n items from two piles." Of course, the y pile could be empty, so (x+1)n becomes ways to pick an item out of n total.
Similarly, (x+y+z)n coefficients give ways to pick n items out of 3 piles. Say if we want 8 items: 2 x's, 1 y, 5 z's; just expand out the expression to the 8th power, and look at the term x2 y z5 and the coefficient is the answer.
Generating functions is a way to use the power algebra to solve combinatorial problems.
it can be expanded to things as simple as "how many ways to assemble a bike from 4 handles, 6 frames, 3 front wheels, and 2 back wheels." Or even applied to recursive functions, famously the Fibonacci.
ksugama · 3 points · Posted at 03:05:28 on February 14, 2016 · (Permalink)
1/998001 spits out all the three digit integers from 0 to 999 EXCEPT 998. So it goes 1/998001 = 0.000001002003004 and so on until ...996997999 and then it restarts
There is a numberphile video explaining why this is and why it skips 998...
Every time you randomly shuffle a deck of playing cards you have created a sequence that has likely never existed, nor will ever existi again, in the entire history of the universe.
If you multiply a 2 digit number by 11, say 36-- if you add the 2 numbers-- 3 and 6, and place that sum between them-- you have the correct number. 11 X 42 is 462, because 4 + 2 = 6.
Dad2DnA · 2 points · Posted at 04:49:49 on February 14, 2016 · (Permalink)
Reading these comments made my head hurt. Low IQ confirmed.
c3534l · 3 points · Posted at 04:58:11 on February 14, 2016 · (Permalink)*
Probably not as interesting as the others in this thread, but here are some things that kind of blew me away when I first learned about them:
Kuratowski's Theorem says if you draw a graph in two dimension, you know it can only be drawn with the lines crossing if it contains a subgraph that is K5 or the Utility Graph. That is, there's basically only two ways to draw a graph that cannot be untangled, save adding unnecessary tails and extra little nodes in there.
I forget the name of the theorem and I'm having trouble finding it online, but I also found it fascinating that we have a formula that tells us exactly how many un-disentanglable graphs there are in every dimension of space, but that really doesn't give us the least bit of clue as how to find what those graphs are. Like, you could say with absolute certainty that there are exactly 6 necessarily-crossing graphs in 19-dimensional space (I'm making those numbers up), but if someone asked you to draw one, you'd have no idea where to start.
I also like that Shannon's Source Coding Theorem gives us a hard limit as to how much data can be compressed and it's a great way of dispelling a lot of flim-flam in data compression by people who are sure they've developed an amazing new compression algorithm that cannot exist.
If you flip a coin bunch of times the probability of getting HHT is higher than the probability of getting HTT. (an explanation).
edit: can't figure out how subscript works on reddit
If you take the curve y = 1/x and create a solid body from it by revolving it around the x-axis from x=1 to x=infinity, you will get a solid with strange properties.
The volume of this shape is pi, yet the surface area is infinite. Thus, you could machine this solid from a relatively reasonable block of metal, but no amount of paint in the world could cover its entire surface.
dmo012 · 3 points · Posted at 05:10:17 on February 14, 2016 · (Permalink)
The Big Bang would have measured in the Richter scale as a 40.0 earthquake.
But, since the Richter scale increases exponentially, that means the Big Bang was 1040 times more powerful than a 10.0 earthquake.
Two twins,both 20 years old. One of them socks away $200/month, every month for 6 years. Hypothetically making 10%. At age 26 the first twin stops investing and the second one starts. The second one invests in the same investment , $200/month as his brother from age 26 to 65. At 65 who has more money?? Answer ...its a tie....how much $2 000 000. Don't ask me for the proof Ive done it more times then i can count. This was shown to us in our Economics class in high school. It was meant to prove that you should always invest for the long term in quality high dividend paying companies and not chase the hot stocks. Also to realize the as young students we have the greatest thing going for us........TIME. well back to my margaritas.
Here's a good one for all the accountants out there or other people who have to add numbers from time to time:
Let's say you add up a bunch of numbers and you expect a certain result and there's a difference. Usually you would now spend a lot of time looking for the cause of that difference by going through the numbers one by one.
Here's the catch: when the difference you have is divisible by 9, the cause of your difference is that you mixed up two figures in your calculation.
Example:
123+456+789 = correct result: 1368
Say by mistake you mixed up two figures in the last one (123+456+879) = wrong result: 1458
The difference between 1368 and 1458=90 (divisible by 9)
Here's where it really gets cool: it even works, when you mix up two figures who are not next to each other.
123+456+987=1566 -> difference = 198 (divisible by 9)
Saved my ass SOO many times....
Damoss · 3 points · Posted at 10:07:25 on February 14, 2016 · (Permalink)
Not a fact but:
Choose a number between 1 and 10.
Multiply that number by 9.
With your new number, add the numbers in that number together,
e.g. 11 = 1 + 1.
Take 5 from your new number.
Find the letter of the alphabet that corresponds to your new number.
e.g. a = 1, b = 2
Think of a country beginning with that letter.
Take the second letter of that country and think of a mammal beginning with that letter.
If you have a pizza with a radius of z and a depth of a, the volume of said pizza is pi*z*z*a.
Cpianti · 3 points · Posted at 12:52:31 on February 14, 2016 · (Permalink)
For some who has little to no grasp on mathematics outside of the badics, this is all at once the most fascinating and confusing thread I have ever read
barcodez · 3 points · Posted at 13:15:42 on February 14, 2016 · (Permalink)*
eiπ + 1 = 0
e is Euler's number, the base of natural logarithms,
i is the imaginary unit, which satisfies i2 = −1, and
π is pi, the ratio of the circumference of a circle to its diameter.
If you randomly shuffle a deck of cards (or anything really), what's the average number of cards that will be at the exact same spots as they were before?
Turns out it's 1. Doesnt even matter how many cards you started with.
Oooo, been so long. As in limit as x approches zero as in Does Not Exist?
lol, I hate you.
Edit: I graphed it and remember now. Negative Infinity. You bastard, nice one.
[deleted] · 2 points · Posted at 01:48:02 on February 14, 2016 · (Permalink)
If you take 1/x where x>=1 and rotate it in three dimensional space about the x-axis the resulting surface has infinite surface area but finite volume. That is to say you could fill it with a finite amount of paint, but you could never have enough paint to cover its exterior. This surface is known as the Gabriel's Horn or Torricelli's trumpet.
Not necessarily arbitrary. There are certain methods of coming to those answers.
1+2+4+8+16+32...=S
+
-2×(1+2+4+8+16+32...)=-2S
1+(2-2)+(4-4)+(8-8)...=-S
S=-1
jaynay1 · 3 points · Posted at 22:14:44 on February 13, 2016 · (Permalink)*
There are methods of coming to those answers. There are different methods that yield different answers. That's where the arbitrariness comes in if you want to claim equality. Well, that, plus there not typically being a definition for a divergent infinite sum.
You know, I never thought of different methods leading to different sums. Do you have some examples or explanations?
jaynay1 · 1 points · Posted at 22:25:56 on February 13, 2016 · (Permalink)
Well, the first one I came to involved an error on my part involving forgetting that one of the 1's doesn't cancel, so I'm not sure that actually does happen.
bigb1 · 2 points · Posted at 06:58:05 on February 14, 2016 · (Permalink)*
s = 1+2+4+8.....
2s = 2+4+8..... = s-1
2s = s-1 ; -s
s = -1
There are many ways to assign values to infinite sums that normally go to infinity. As a bonus, those methods give the right answer for sums that do give a finite value. Two of the most popular ones (Ramanujan summation and Riemann Zeta analytic continuation) give -1/12 as the answer for 1+2+3... . In some contexts in string theory and various other parts of physics, you get infinite sums that sometimes go off to infinity; in those cases, using the other methods can give you a sensible result. However, it is not the actual sum; it's just a way to assign a value to a series. In other cases, it lines up with infinite summation, but they are not the same thing.
Terence Tao has an excellent blog post describing that the analytic continuation method of "summing" this series is the same as looking at asymptotic data for a sum where each entry "n" is replaced by "n times a smooth cutoff function". He also goes on to explain why the "values" of the series that you get, while meaningful for an individual series, tend to conflict with the "values" of other divergent series, because they are computing asymptotics of a different order.
Infinite sums usually don't work. For example, 1+2+3+4... is infinite - not a number. You can use various special methods to fix that though. 1/2+1/4+1/8+1/16.. is 1; even when you use the special methods, they can still give the value "1" for the series without adding it up. The techniques also give you numbers for other series that don't usually work. Two common techniques both assign -1/12 to the series 1+2+3... . That doesn't mean that the sum is -1/12; it just means that it can be helpful in physics to treat it like it is. It can tell physicists that there's a hidden "hey, you need to use the Ramanujan sum here" in a formula rather than a regular sum. For working series, there isn't a difference; for series that shoot off to infinity, regular adding doesn't work but Ramanujan sums do.
So why don't we just call Ramanujan sums "adding"? Because there are several different methods that give values to normally divergent series. Frequently they conflict with each other. 1+2+3+4... is assigned -1/12 by two methods though.
Numbers don't "tend" to anything; they don't move.
It's exactly 1.
If you were talking about 1/2 + 1/4 + 1/8 + ... + 1/2n, with a finite amount of terms, then you could say that as n goes to infinity, that series approaches 1. But in the case of the single sum 1/2 + 1/4 + 1/8 + ..., nothing "changes".
The video shows that if you arrange a specific infinite set of numbers, you can arrange it in a way so that it appears to sum to -1/12. This is useful when talking about comparing different infinite sums. BUT, 1+2+3+4... = infinity
If you use the arbitrary method of summation that takes place on the real line. There are infinitely many different ways to assign values to infinite sums, and convergence on the real line is not special in any way.
Technically, we should use explicit limits for any infinite series, because adding together an infinite number of things is meaningless without explicitly stating how you're assigning values.
1+2+4+8+16+... = -1 in2-adicconvergence
[deleted] · 2 points · Posted at 08:13:14 on February 14, 2016 · (Permalink)
I'm not going to argue with an r/math regular in askreddit. (unless we fight over whether Zp means Z/pZ or the p-adic integers)
No you're not. If you were talking to an actual mathematician they would have told you that the LIMIT of the series that you defined approaches -1/12. There is no = there. Nobody who knows what they are talking about would have said =.
That's not the issue at all. Using an = sign for a series already implies taking a limit of some kind. Even taking this account, there are serious problems with claiming
1 + 2 + 3 + 4 + . . . = -1/12
from a mathematical standpoint. On the other hand, the number -1/12 is the result of a regularized sum, which is a whole other beast entirely.
It seems if you take the area under the curve but above the x axis to the right and subtract it from the area to the left -1/12 is what you are left with.
muffley · 1 points · Posted at 01:04:25 on February 14, 2016 · (Permalink)
If you walk in one direction for 1 foot, then 2 more feet, then 3 more feet, etc. at infinity you will be 1 inch behind where you started.
At the same time, without first establishing what you mean by a series, why are you allowed to take the averages and claim it is "equal" to the value of the series.
The scenario you are describing is called Cesaro summation and is different from standard summation (among many other possibilities).
1 - 1 + 1 - 1 + ... is not equal to 1/2
However, the series is Cesaro summable and its Cesaro sum is 1/2.
This is the best one here because it's so simple but so mind blowing
slaerdx · 8 points · Posted at 03:13:30 on February 14, 2016 · (Permalink)
All positive integer powers of 26 (except for 0 and 1) end in the number 76. Example:
262 = 676
263 = 17576
264 = 456976
and so on
narbris · 3 points · Posted at 06:20:51 on February 14, 2016 · (Permalink)
3762 = 141376
3763 = 53157376
3764 = 19987173376
and so on
hayberry · 4 points · Posted at 22:18:56 on February 13, 2016 · (Permalink)*
2147483647, 231 -1, is a pretty cool number. It's the largest integer you can have on a 32-bit machine, which is why it's the highest score before things get wonky on a lot of old video games. It's also a prime, and the primeness of it was proven in a letter from Euler to Bernoulli. It's actually one of 49 known Mersenne primes, and one of four known double-Mersenne primes, both of which are tied to a bunch of other mathematical conjectures and used to derive other special numbers. As a programmer and general math nerd it holds a special place in my heart. (:
Not sure if it's my fav, but I'm surprised no one has posted about Gabriel's Horn yet. It's a surface that has finite volume but infinite surface area. So you can fill with paint, but cannot paint it.
devishe · 4 points · Posted at 21:00:46 on February 13, 2016 · (Permalink)
I know I'm way late, but I always liked this explanation of the difference between a million and a billion:
One million seconds is eleven and a half days..
One billion seconds is 31 and a half years.
You can derive pi from a toothpick and some parallel lines which are drawn twice the length of the toothpick apart from each other. The probability that the toothpick will land on a line approaches 2/pi as the number of trials tends to infinity.
The strange thing about this is that pi is defined as the ratio of a circle's circumference to its diameter, which seems to have absolutely nothing to do with toothpick tossing.
Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.
If you could hang a hammock with both lines being perfectly level with no sag (this is impossible, but stick with me), the force on the lines (and whatever they are attached to) would be infinite.
This is why you need to know how to hang a hammock properly, or you can pull down walls.
That the infinite sum: 1/12 + 1/22 + 1/32 + 1/42 + ... = pi2 /6
It's not the fact that the sum converges which is cool, it's the fact that such a seemingly simple sum converges to a value which is expressed in terms of pi. This is known as the Basel problem https://en.wikipedia.org/wiki/Basel_problem
Reptile is short for Repeating Tile. It means a shape that can be divided up into smaller versions of itself. Lobster and Snake are two polyiamonds – shapes created by arranging equilateral triangles side to side. Lobster looks like a lobster claw, two of them can be joined together to make a parallelogram, which can be tiled into a lobster shape. So it's a reptile. Trying to match up the ends of a snake however always results in an overlap, so it's not a reptile.
This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, the factorization would not be unique, as, for example, 2 = 2×1 = 2×1×1 = ...
Sharynm · 2 points · Posted at 03:30:52 on February 14, 2016 · (Permalink)
That 9x 6-10 is a reverse of the numbers of 9x 1-5.
9x1=9
9x2=18
9x3=27
9x4=36
9x5=45
9x6=54 (reverse 9x5)
9x7=63 (reverse 9x4)
9x8=72 (reverse 9x3)
9x9=81 (reverse 9x2)
9x10=90 (reverse 9x1)
[deleted] · 2 points · Posted at 03:41:12 on February 14, 2016 · (Permalink)*
If you take any number and double it or half it, then take the result and add numbers together repeatedly until you condense it into one number, it will follow a predictable pattern of 1,2,4,8,7,5 or 3,6, or repeating 9s.
For instance:
1
1*2 = 2
2*2 = 4
4*2 = 8
8*2 = 16 , 1+6 = 7
16*2 = 32, 3+2 = 5
32*2 = 64, 6+4 = 10 , 1+0 = 1
64*2 = 128, 1+2+8 = 11, 1+1 = 2... and so on
or 1 = 1
1/2 = 0.5, 0+5=5
0.5/2 = 0.25, 0+2+5 = 7
0.25/2 = 0.125 , 0+1+2+5 = 8
0.125/2 = 0.0625, 6+2+5 =13 , 1+3 = 4
0.0625/2 = 0.03125,= 3+1+2+5 = 11 , 1+1 = 2 .. and so on in the opposite direction
Do you want to know if a number is divisible by 3? Add up the digits.
For instance, 144. 1 + 4 + 4 = 9 which is divisible by 3. Therefore 144 is divisible by 3.
jfffj · 1 points · Posted at 10:24:44 on February 14, 2016 · (Permalink)
There's several of those.
If adding up all the digits is divisible by 9 then the whole number is divisible by 9.
Etc for powers of 3.
If the last digit is divisible by 2, then the whole number is divisible by 2.
If the last 2 digits are divisible by 4, then the whole number is divisible by 4.
If the last 3 digits are divisible by 8, then the whole number is divisible by 8.
Etc. for powers of 2.
But my favourite: If you add up alternate digits, i.e. digits 1,3,5,... and digits 2,4,6,... and those two sums are the same, then the whole number is divisible by 11. Example:
132 is divisible by 11 (1+2 = 3)
4369356585 is divisible by 11 (4+6+3+6+8 = 3+9+5+5+5)
I know I'm super late, but to square numbers whose ones digit is 5, excluding 5 itself, suppose the number before it is X. For example, 105. X here is 10. Then, take (X)(X+1) then put it right beside 25. So in this case, 11×10= 110, put that beside 25, the answer is 11025. Works with any number whose (X)(X+1) you can mentally calculate, if you wanna do it without a calculator
The curvature of a closed orientable surface tells you how many handles it has. This is essentially the Gauss-Bonnet theorem. Chern-Weil theory is a generalization of this idea, that curvature of a space tells you important geometric and topological information. Famous physicist Edward Witten developed Chern-Simons theory, a branch of topological quantum field theory, using these ideas. Interestingly, mathematician James Harris Simons, who discovered/invented the Chern-Simons form alongside S. S. Chern, later founded an investment firm and is now worth $14 billion.
If the digits of any number add up to a multiple of 3, then the number itself is a multiple of 3.
Example:
Take the number 171.
1+7+1=9.
9 is a multiple of 3.
So 171 is also a multiple of 3 (57*3=171).
greenzr · 2 points · Posted at 03:56:29 on February 14, 2016 · (Permalink)
I know this is true for 9, but I didn't know for 3.
It's an easy way to square up a room. From an inside corner measure 3' out on Wall 1. From the same corner measure 4' on Wall 2. Measure from point 1 to point 2 and it should be 5'. If you are under 5' your corner is acute and your wall will need to be pushed away from the room, if obtuse then need to bring wall into room.
The answer of any number multiplied by 9 can always be added together to equal 9. For example 9x3=27, 2+7=9. Or a more intense example 9x523=4707, 4+7+7=18 then 1+8=9. Definitely black magic involved here.
There are propositions which are undecidable: it's impossible to systematically answer yes or no. For example, there is no way in general to decide if two real numbers are equal.
The circumfrence of the equater divided by the number of days in a year, divided again by the number of degrees in a circle, divided again by 1000 is exactly 1 foot.
1729 is the smallest positive integer that can be expressed as the sum of two cubes in two different ways, 13 + 123 and 93 + 103 . The digits also add up to 19 and when you divide it by 19 the answer is 91.
Didn't see this one on here and I find it pretty amazing. People used their own bodies to create the imperial system (Inches, feet, yards, mile, and whatever else).
1000 paces make up a mile. We call 1/8 of a mile a furlong (660 feet). 660 X 12 (inches in a foot) = 7920. There are 7920 miles if you measure the diameter of the Earth from the Tropic of Capricorn to the Tropic of Cancer. So the inch is relative to the furlong as the mile is to the Earths diameter. We are modeled after the Earth. 7920 is also a multiple of 72 which is significant, for that explanation you'll have to get into sacred geometry.
One of the most influential mathematicians of all time, Évariste Galois, did all of his work by the age of 20 when he died in a duel resulting from a dispute over a lady friend.
[deleted] · 2 points · Posted at 05:23:38 on February 14, 2016 · (Permalink)
[deleted]
Vortico · 2 points · Posted at 06:14:58 on February 14, 2016 · (Permalink)
1 is also the product of primes (exactly 0 of them)!
I learned if you want to calculate the amount of water flowing down a river (Discharge). You calculate the cross sectional area of the river and multiply it by the rivers velocity. That's the basic idea of it.
Yasrynn · 2 points · Posted at 06:02:24 on February 14, 2016 · (Permalink)
There are many levels of infinity, some larger than others.
Reala27 · 2 points · Posted at 06:02:58 on February 14, 2016 · (Permalink)*
Base conversion between numbers an be done by dividing by the target number by the target base as represented in the current base, and encoding the integer remainders until you get a 0 for the quotient. For example, converting decimal to binary (base 2). Let's take, say.... 19.
19/2 = 9 with remainder of 1. Encode the 1.
9/2 = 4 remainder 1
4/2 = 2 remainder 0
2/2 = 1 remainder 0
1/2 = 0 remainder 1
10011(base 2) = 19(base 10)
Not convinced? Fine. Let's try... base 20(base 7) to base 9 (12 in base 7 unless I can't count, which is possible)
20(7)/12(7) = 1 remainder 5
1(7)/12(7) = 0 remainder 1
20(base 7) in base 9 = 15 according to Wolfram Alpha.
Reala27 · 1 points · Posted at 06:08:26 on February 14, 2016 · (Permalink)
Also a fun function that I just know exists is the Weierstrass set. https://en.wikipedia.org/wiki/Weierstrass_function This function is continuous everywhere but differentiable nowhere. It's a fractal that changes direction at literally every point, so you cannot possibly take its derivative.
Grahm's number is so large that it is larger than the observable universe. It is used in a problem about hypercubes, a theoretical shape. It something I will probably never be able to wrap my head around.
[deleted] · 2 points · Posted at 06:22:07 on February 14, 2016 · (Permalink)
A dozen, a gross and a score.
Plus three times the square root of four.
Divided by seven.
Plus nine times eleven
Equals nine squared and not a bit more.
If you a shuffle a 52 deck of cards, it's almost certain that what you're holding is the only time that order of cards has ever existed. If you were to create a new permutation every second since the moment the universe began (13.8 billion years ago), you would still be creating new permutations today, and for millions and millions of years to come. There are more ways to arrange the deck of cards than there are atoms on Earth. The number of possible arrangements is 52 factorial (52!) which is 8.065x1067.
Written out, this is: 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.
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.
You know multiplication is commutative, as in 3 * 2 = 2 * 3
It means that percentages are commutative too : 32% of 50 (hard to compute mentally) is 50% of 32 (easy, 16).
Because obviously (x/100) * y = (x * y) / 100 = x * (y / 100)
filiona · 2 points · Posted at 08:48:08 on February 14, 2016 · (Permalink)
If you mulitply all real numbers (except for zero) you get -1.
That's because every number has an inverse (eg. 2 has 1/2, 3 has 1/3, pi has 1/pi and so on) and those pairs cancel each other to 1.
-1 is the only number that is its own inverse, so it cant be cancelled to 1.
Also works for complex numbers.
BenBro · 2 points · Posted at 08:48:45 on February 14, 2016 · (Permalink)
I tried to read this thread drunk. It hasn't gone well.
This thread just reminds me of how little I actually remember from Math. A co worker of mine solves calc problems on his lunch break while he eats and I read reddit and watch people play video games on twitch......
My understanding of primes is simplistic - I thought that the definition "divides evenly only by itself and 1" would include 1. I can see that it works for 7 & 11 and cant be bothered to remember or square any higher primes!
Drased · 2 points · Posted at 10:08:41 on February 14, 2016 · (Permalink)
Late to the party, as always, but:
This guy has proven that Pythagorean trigonometric identity is wrong, which was the main subject of his PhD. He teaches at my University, and still only has master's degree - because comission decided not to give him his title, despite not being able to find any mistakes in his work. The unofficial reason is that did this because otherwise a lot of modern math would be rendered wrong as well.
Legend says that mr Pietraszko (his name) decided not to shave until comission accepts his work and finally gives him his PhD. That was quite a few years ago, as you might have noticed :)
Ok I'm not sure if anyone's posted this yet or not, but Pi is actually fucking amazing. Since it is non-repeating yet infinite, every single digit, every single number combination - it's somewhere in Pi.
If you converted it into ASCII text, it would tell the story of your life.
Convert it into a BITMAP, and you would see your life played out.
Really interesting, but if I tried to calculate all that, my computer would most likely blow up.
MacLife
gindc · 1 points · Posted at 15:19:02 on February 14, 2016 · (Permalink)
every single number combination - it's somewhere in Pi.
Pi is irrational. But that doesn't mean it contains every number combination.
eiπ -1 =0
e, a completely irrational number.
π, another irrational number.
i, a number that doesn't actually exist.
Put them together and take 1 it equals 0. To me that's almost proof of a god
Aturom · 2 points · Posted at 11:04:16 on February 14, 2016 · (Permalink)
Me plus no one equals a pretty bummed out Valentine's day
[deleted] · 2 points · Posted at 11:06:41 on February 14, 2016 · (Permalink)
e pi*i +1 =0. Eulers identity. Bear with me And just look at the equation. You have pi, the ratio of the circumfrence of a circle to its diameter; 3.1415927 etc. You have "e ", Eulers Constant, which is arguably as important as pi and describes fundamental growth in nature and mathematics. Of course you have 1, the beginning step of all mathematics, and 0 which is a fairly new understanding but an equally mind boggling concept.
Before I get to i , remember that e and pi are not only what are called irrational numbers, they are in fact transcendental numbers. Which means not only can you not describe them with ratios, you cant describe them as solutions to a polynomial with easy numbers. Whats more, integers like 0 and 1 are infinitely rare. For every integer there are uncountably many transcendental numbers. So if you put all the numbers into a hat and pulled one the chance you get an integer like 0 or 1, or even a number you can understand like 1/2, is literally 0. There is no chance of it hapoening in the same sense that there is no chance of you winning every raffle, lottery, game that has every taken place or will ever take place.
Then you have i, the imaginary number, the square root of -1. This was the number that allowed us to describe algebra thoroughly.
So Now you have the 5 fundamental thoughts of mathematics: fundamental growth, roundness, unity, nothingness, and the imaginary number. Two of these numbers are transcendental and would probably produce at least an irrational number. Two of these are integers and would probably produce an integer. But when you combine ALL FIVE THOUGHTS, the formula is so neat that all you need is those 5 thoughts.
in some sense the formula couldnt be anything else, in another sense the probability of the formula existing is 0. Its pretty neat. Check it out! Eulers identity.
Pohatan · 2 points · Posted at 12:58:34 on February 14, 2016 · (Permalink)
A litte late to the party, but the most non-intuitive mathematical result I know of is that if you add up all the natural numbers (i.e 1+2+3+4+...), the answer to the sum is -1/12. The result is even used in string theory (if i remember correctly).
toysjoe · 2 points · Posted at 13:13:44 on February 14, 2016 · (Permalink)
You can keep adding the digits of a long number to see if it's divisible by 3.
Take for example 111,111,111,111 is divisible by 3 because
1+1+1+1+1+1+1+1+1+1+1+1=12
1+2=3
3/3 is 1
So 111,111,111,111 is divisible by 3.
Jayco86 · 1 points · Posted at 13:19:17 on February 14, 2016 · (Permalink)
With certain fractions (e.g. 1/3), it's impossible to give the true decimal value. As such, you're merely approximating these numbers, rather than giving their true sum.
Not really true. It's impossible to give the decimal value of certain fractions. Your fact is more the sum of 2 approximations to make a new approximation
phrazel · 2 points · Posted at 13:49:17 on February 14, 2016 · (Permalink)
can prove that there exist two irrationals A and B such that A to the power of B is rational without actually having to know what A and B are. Consider the identity:
(sqrt(2)sqrt(2))sqrt(2) = 2
Now, let A = sqrt(2)sqrt(2) and B = sqrt(2). If A is irrational, then A and B are the two irrationals and the proposition is proven.
If, however, A is rational, then A’ = B’ = sqrt(2) are such that A’ ^ B’ = A = rational, and the proposition is again proven, since sqrt(2) is irrational.
Forget what this is called, but I thought it was interesting, it's been done on Mythbusters too.
There are 3 doors but only 1 of them has the prize behind it. You must first pick a door. But before it is opened, 1 of the 2 doors you did not pick is opened to reveal that nothing is behind it and it would have been an incorrect choice.
Now you're given an option
A. Do you open the door you initially picked?
or
B. Do you open the other door that was not yet opened?
At first thought, this might seem pointless because you would think you have a 50% chance of guessing the correct door...but you would be wrong.
The choice that is more likely to be correct is B.
When you make your first pick, there is a 1/3 or 33.3% chance that you've already chosen the correct door, but there is a 2/3 or 66.6% chance that one of the other two doors has the prize. When one of the two unchosen doors is revealed to be incorrect, the odds do not change. The door you initially picked is not all of a sudden more likely to be correct just because one of the incorrect options got taken away, and on that same point, the other two doors that were more likely to contain the prize now only have one option, still at 2/3 chance.
It's weird and it's cool. On Mythbusters they did a large sample size (hundreds of people) and the data came back that people who chose option B. were right more often than people who chose option A.
Some people like me didn't know about it and some people aren't so quick to trust it because it sounds wrong at first, testing it like that helps people understand it easier.
ck2839 · 1 points · Posted at 14:49:04 on February 14, 2016 · (Permalink)
If you switch doors, then you win if and only if you previously chose the wrong door (which has probability 2/3). So it's quite intuitive.
If the universe was a goggleplex light years acroos, as you travel you would hit a region of space where some one there not just looks like you but is a complete carbon copy of you. Mole for mole, hair for hair and DNA for DNA. There would be no distinguishable difference at all. Even down to your scars.
the atom arrangements of the volume of space you occupy can only be so much regardless of the staggering number. I think it's 10 to the power of 100 to the power of 86 or something like that. And a Google plex is 10 to the power of 100 to the power of 100. So you'll hit a point where things just duplicate.
Inverse square law. Pretty fascinating. Doubling the distance will halve the power of light, sound etc. It's obviously a lot more elaborate than that of course, but worth looking up.
I recently learned that the number of possible shuffles of a deck of cards is so large, that it is likely that every shuffle of any deck of cards, since the invention of cards, is probably unique (despite the number of decks and shuffles happening all the time).
Gauss once said of this,"If you can't appreciate its beauty in first glance, you can never become a mathematician".
Seriously this one equation contains all the major mathematical constants from different fields.
e= Euler's Number, basis of Natural Logarithms and used in Calculus.
i=square root of -1(Complex Numbers)
pi= Needs no introduction.
1 and 0
NowC204 · 1 points · Posted at 21:52:10 on February 22, 2016 · (Permalink)
Don't worry, someone did mention it. And thanks for your explanations
An algorithm was written to construct a series of theoretical books. The books contain the letters A through Z, spaces, commas, and periods in every permutation possible.
These "books" contain: everything that has ever been written with those characters, everything that WILL ever be written with those characters, the exact date and time each of us were born, the exact date and time each of us will die. Your entire life can be found on pages inside books in this digital library (kind of...).
[deleted] · 3 points · Posted at 02:51:45 on February 14, 2016 · (Permalink)
[deleted]
prmcd16 · 2 points · Posted at 03:05:30 on February 14, 2016 · (Permalink)
source? sounds interesting.
Waniou · 2 points · Posted at 06:05:50 on February 14, 2016 · (Permalink)
I think he's referring to how Maxwell used his four equations (That is, not all known physics equations) to demonstrate that light is an electromagnetic wave.
This is a really sketchy statement for me. Can we get a source?
Waniou · 1 points · Posted at 06:07:01 on February 14, 2016 · (Permalink)
He's... almost right. I think he's referring to how Maxwell used his four equations to demonstrate that light is an electromagnetic field.
Waniou · 1 points · Posted at 06:05:20 on February 14, 2016 · (Permalink)
Err... not quite. I think what you're referring to is Maxwell's equations. That's not "all known physics equations", it's four specific equations that describe how electric and magnetic fields work. Two of these equations show that a changing electric field will generate a magnetic field, and a changing magnetic field will generate an electric field. Since generating a magnetic field is changing a magnetic field, this generates a new electric field, which generates a magnetic field and so on. For the most part, the new fields are progressively weaker until they become trivially weak and basically disappear. What Maxwell demonstrated that, if you have a wave moving at a specific speed, you could get a self sustaining electromagnetic wave. That is, a changing magnetic field that generates an electric field that's strong enough to create an identical magnetic field and it carries on, effectively forever. By plugging this into the four original equations, he got the speed of the wave and found it to be the speed of light, and this was some of the original evidence that light was an electromagnetic wave.
The theorem says "any continuous map from the n-sphere to Euclidean n-space". "n-sphere" can be a little confusing, because n refers to the dimension of the surface of the sphere. So a 1-sphere is a circle, and a 2-sphere is the surface of a ball.
Temperature is a 1-dimensional value. As is Humidity. So taken separately, you have 2 different continuous functions from S2 to R1. I can simply define a new function f(p)=(T(p),H(p)) which is a continuous function from S2 to R2, so the theorem says there is a pair of points p and q on the surface of the earth where f(p)=f(q) and p=-q.
More of an observation than anything, but 2 is the only number that you can add to itself, multiply by itself, and square by itself and still get the same result- 4
If you have two people in a room, there's a 1/365 chance they share the same birthday. Pretty obvious.
Well, what if you have four people in a room? Turns out it's not 3/365, but actually about 1/61! Why? Well, now each person has about a 3/365 chance of sharing the birthday with someone else in the room, right? So you'd think it'd be three times more likely. But there are more possible pairs now, so the odds go up more.
With two people, there is only one possible pair. But with three people, there are 3 possible pairs. And with 4, there are 6 possible pairs. With 5 people, there are 10 possible pairs. With 6 people, 15 possible pairs. By the time we get to 23, there are 253 possible pairs of people, each with a 1/365 chance of sharing a birthday.
As you add more people, you not only increase the chances that a single individual person in the room shares a birthday with someone else in the room, but you also increase the number of chances by having more people.
WildxYak · 2 points · Posted at 21:10:02 on February 13, 2016 · (Permalink)*
This table can be helpful for some to help understand it.
This explanation is incorrect. Your last line has the right idea; each new person increases the chances of every other person sharing a birthday with someone.
1 person having a unique birthday is certain: 365/365
A second person having a unique birthday is true on 364/365 days
A third person having a unique birthday is true on 363/365 days
etc.
The probability of an nth person having a unique birthday is (365 - n)/365 assuming (n-1) people have already been established with unique birthdays. To find the total probability of n people with unique birthdays, you find the chances of 1 unique birthday * the chances of a second * the chances of a third * ... * the chances of an nth:
(365 * 364 * 363 * ... * [365 - n]) / (365n)
That top number can also be expressed as a quotient of factorials
Meaning the chances of n people having unique birthdays is
[365! / (365 - n)!] / 365n
or in its final form:
P(n) = 365! / [(365 - n)! * 365n]
The probability of at least 2 of n people having a birthday is 1 - P(n) because when it is NOT true that everyone has a unique birthday, then it is true that at least 2 people share a birthday.
1 - P(n) > 0.5 at n=23
The graph of this new function is slightly different from the one implied by your description of pairings and 1/365 chances.
It's relative to statistics and some applied mathematics. IIRC at 70 people the percentage is about 90%. Sorry for no sauce, I don't have any time currently, but hopefully another kind redditor can help out
regdayrF · 1 points · Posted at 21:08:18 on February 13, 2016 · (Permalink)*
Assumption: Each day of the year is as likely to be a birtday as another day. Every birthday of the people in the room are independent to each other.
AC = No person has birthday on the same day
A = At least 2 persons have birthday on the same day
P(A) = 1 - P(AC ) = 1-(365!/(36523 *342!))
Small reminder: 365!/342! = 365 * 364 * ... * 343
( This is the amount of possibilities, that are out there for 23 different birthdays, now you just have to divide it by 36523, which is the amount of possibilities for the experiment. )
It follows the same principle as the possibility for one specific number on a dice to appear. P(B) = 1/6 --> P(BC ) = 1 - P(B) = 5/6. B being the event for one specific number to appear. BC being the event for this specific number not to appear. You have 6 numbers in total, and each number represents one possibilities. In this case 6 ~ 36523 and 5 ~ 365!/342!
user725 · 1 points · Posted at 01:01:16 on February 14, 2016 · (Permalink)
It helps if you look at is as 2 of them will have the same birthday, it's not just with your birthday.
My son was seven or eight years old when he discovered this:
We were going over the "cheats" for divisibility (e.g. an integer is divisible by five if it ends in 0 or 5).
The "is divisible by three" heuristic was giving him trouble. Traditionally, you add up all the digits of an integer as if they were in the one's place, and if the resulting sum is divisible by three, then the original number was as well.
For example 9132 is divisible by 3 because 9+1+3+2 = 15, and 15 is divisible by 3.
When we showed him a few examples, he said "but you don't have to add them ALL up. Just add the ones that aren't already multiples of three." And then he did just that for each of the examples we'd been working with.
Same example: 9132 is divisible by 3 because 1 + 2 = 3, and 3 is obviously divisible by 3. I tried dozens of numbers, and it blew me away: it worked for every one.
I'd never seen that in any text book, and I couldn't find any reference to that method on the internet. So I found the proof for the traditional method and dicked around with it until I could show that, sure enough, you only have to add digits 1,4,7,2,5 and 8 (0+1, 3+1, 6+1, 3-1, 6-1, 9-1) to determine divisible-by-three.
I was completely freaked out. My pre-teen kid was able to intuitively grasp a mathematical fact that no person (as far as I could tell with the research material available to me at the time) had ever figured out.
That is definitely great intuition for a 7/8 year old. Hopefully your proof gave you an intuitive sense for why this is true. For anyone else that is wondering:
When a value is divisible by 3 (this works for any other value) adding another value that is also divisible by 3 will yield a sum that is still divisible by 3.
Ex. 9 + 12 = 21. All these terms are divisible by 3.
Why is this relevant?
When considering an integer, you can separate the digits into two sets, those divisible by 3 ,set X = (0,3,6,9) and those that are not set Y= (1,2,4,5,7,8). If all the digits in set Y add up to a number divisible by 3, then adding any number of digits from set X would adhere to the principle stated above (adding two numbers divisible by 3). That is why one only needs to consider the digits from set Y.
Ex. Is 6319572628301 divisible by 3?
Splitting the digits into the two sets, we have:
6,3,9,6,3,0
1,5,7,2,2,8,1
Adding up the terms in the second set:
1+5+7+2+2+8+1 = 36
This is divisible by 3. Then, as all the terms, 6,3,9,6,3,0, are divisible by 3, the sum of the terms is divisible by 3 (the sum is 27), and adding that to 36 is 63, also divisible by 3. It was unnecessary to consider the terms: 6,3,9,6,3,0.
I stand corrected. More man made than natural. It is, as they say, pleasing to the eye though.
acatcus · 1 points · Posted at 23:12:40 on February 14, 2016 · (Permalink)
It's a mistake a lot of people, including me, fall for. It's a romantic notion. But if you study maths you find it's about structure and concepts, rather than magic properties of numbers. The whole golden ratio madness is not really meaningful, not to mention 99% of the logarithmic spirals claimed to be golden spirals in nature do not fit the ratio at all. It's a lot more meaningful and useful to study logarithmic spirals themselves and how they can be generated, rather than any specific ratio. Sure the golden ratio has many interesting properties, but it's not magic. Just interesting
gsuthi · 2 points · Posted at 21:26:30 on February 13, 2016 · (Permalink)
That one ∞ can be bigger than another (but don't shoot me, this is what I remember my maths teacher telling me about a couple years ago). It goes something like this:
So say you count from 1 onwards - 1, 2, 3, 4... etc. forever, that's an infinite amount of numbers.
Now do the same, but do it, and go up in 2s. So 2, 4, 6, 8 etc. You'll also be counting infinitely.
However, (and this is the slightly confusing bit for me) as much as they are both infinite, the second set of numbers contains half as many numbers as the first, making the first infinite bigger than the other.
EDIT: I had to look this up because I'm not great at explaining it, but here's a link - https://youtu.be/A-QoutHCu4o
Your two examples are of the same class of infinity. You can easily show a 1 to 1 mapping between the 2 sets by multiplying the 1st set by 2 to get the 2nd set.
You can't find such a mapping between real numbers and integers though, so real numbers are in fact in a different class of infinity than integers.
gsuthi · 1 points · Posted at 22:12:09 on February 13, 2016 · (Permalink)
Ah right I see, I knew I messed something up, thank you!
You could just say all the numbers between 1 and 2 and all the numbers between 1 and 3
481x462 · 1 points · Posted at 22:49:09 on February 13, 2016 · (Permalink)
The two infinities you described are the same size, we call it countably infinite. As the source you linked says, if you can pair them off with no leftovers, then they're the same size. And if they can be mapped to the natural numbers, can be listed, then they are countably infinite, like in Hilbert's Hotel.
"Some infinities are bigger", the bigger infinity is uncountable, where there can be no system by which we could count the number of elements without missing any. Real numbers are uncountable, like your link shows any list of real numbers will be missing the specially constructed one. And similarly, these uncountable infinities are the same size if they can be mapped to each other, your link shows the real interval [0,1] mapped to [0,2], but can also be mapped to the entire real number line, and also to 2D space and more with Hilbert's curves.
The formula for the force of gravity (in non-relativistic situations) is:
F = GmM/r2
In this equation, the number 2 is exact. It's not 2.01, or 1.99. It's not 2.00001 or 1.99999. As far as we have experimentally tested, the force of gravity is related to exactly the inverse square of the distance between two objects.
[deleted] · 2 points · Posted at 03:43:51 on February 14, 2016 · (Permalink)
Works for more than 2 digit numbers, too. Just add the first and second/second and third/third and fourth etc. digits, put them in the order you calculated between the first and last digit. Just remember to carry the tens.
For instance 11 x 11238654 becomes (1)2-3-5-11-14-11-9(4) which is 123625194.
cszlo · 1 points · Posted at 03:58:41 on February 14, 2016 · (Permalink)
11*99=1089 :(
I think it breaks after 90, but still very cool!
[deleted] · 2 points · Posted at 04:26:52 on February 14, 2016 · (Permalink)
It breaks any time the two digits add up to more than 9.
[deleted] · 2 points · Posted at 05:55:59 on February 14, 2016 · (Permalink)
5318008 upside down on a calculator spells BOOBIES.
Utming · 2 points · Posted at 07:05:46 on February 14, 2016 · (Permalink)
There are an infinite amount of numbers between 1 and 2, and an infinite number between 2 and 3... so between 1 and 3 there are infinite, but twice as many...
I think you have your units confused. A cubic meter of water weighs a metric ton. A cubic yard doesn't come out to anything even, its about .841 US tons.
[deleted] · 1 points · Posted at 15:20:37 on February 14, 2016 · (Permalink)
This is one of many reasons people like to use metric.
In my school system we had math olympics. Which I first competed in in high school, then later on in college served as a proctor. Which doesn't mean I have anything to brag about, it just lets me sound like an anal pedant on threads like this.
Also, how many quarts in a dozen, asked orally, stumps a lot of people, most of whom claim there aren't any.
In a dozen what? In a dozen quarts? 12. But the question doesn't tell you that, so you can't answer it. A quart is a unit of measure and a dozen is a number.
12 units. But answering the question requires converting the units to quarts. So if you asked, "how many quarts in a dozen gallons?" the answer would be 48.
You never said you had 12 quarts. You said you had 12. I don't understand how you can read my last comment and not understand your mistake, so I'll just let this end here.
It works grammatically, because a lot of things are implied/assumed in English grammar. I'm better at this than you [are]. He dances like an elephant [dances]. How many quarts are in a dozen [quarts]?
I'm so sad. English is a nondeterministic grammar. Unlike a computer language which is not. Reality. The more you know...WHY are you slapping me?
o_shrub · 6 points · Posted at 19:27:13 on February 13, 2016 · (Permalink)
Maybe technically not mathematical, but the gold thing is astonishing. A 14" cube of gold weighing a ton? I figured you must have had it wrong. Nope, you're right....
I like that too. But, are you Arab? Gold is much more impressive, to me, than Petrol. Though they are somewhat synonymous, I'll agree. Black gold, Texas tea. And tons beat the living dogsnot out of kg as far as impressive goes, dontcha think?
There's a number for the number of numbers there are (Aleph-Null), and, because it is a number, you can do numbery things to it. As such, there is a number that is two times Aleph-Null (Aleph-One), which is exactly twice as large, even though both are infinitely large.
As such, there is a number that is two times Aleph-Null (Aleph-One), which is exactly twice as large, even though both are infinitely large.
Woooooah. This is way, way wrong.
Yes, the cardinal numbers are numbers. Yes, you can do arithmetic (numbery things) to them. But no, 2*aleph-null is not aleph-one.
In fact, due to the way cardinal arithemtic is defined, aleph-null*aleph-null = aleph-null.
No mathematician would ever say one infinite cardinal is "x times as big" as another. That's nonsense.
If you want to get "bigger" using only cardinals up to aleph-null and arithemtic, you have to use exponentiation. Of course, the problem now is even mathematicians don't agree how big 2aleph-null actually is. Aside from a few weird known restirctions, basically all we know is that it's bigger than aleph-null. It could be aleph-one. It could be aleph-two. It could be aleph-aleph-null.
Sorry. I'm a novice at mathematics (still in high school), and I read something similar to that on Wikipedia a few weeks ago -- I guess my memory contorted what I had read over time. I'd like to learn more about the cardinals, but there may be some math I'm missing out on. Do you know of a place where I could learn more about them?
Honestly, if you truly want to learn about the cardinals, so that you have more than a tenuous grasp of "the rules" of arithmetic (because really, the arithmetic is only a tiny fraction of their utility), I would say wait until you've gone through calculus.
You can learn about them now, but their construction is extremely formal and rigorous, and it can be daunting for someone without a strong mathematical aptitude (it can be daunting for those with a strong aptitude). I would say start with a good intro to proofs book (personally recommend Transition to Advanced Mathematics), because you absolutely need the training and logical tools developed to make any headway. Once that's done, Hrbacek and Jech's "Introduction to Set Theory" is the where it's at.
[deleted] · 1 points · Posted at 16:59:55 on February 14, 2016 · (Permalink)
Gentle is fine, and yes, a really motivated high schooler could probably teach themselves lots of things. But it's not so easy to dive right in when you lack the experience of manipulating proofs. There are very basic logical tools that many people don't pick up until Calculus, or even later, like what contraposition is, or how and why PMI works.
Why? There are solutions that don't involve horizontal movements, I opened up ms paint and played around for 10 seconds at most in order to figure that out. Surely you must have figured those out.
You know if you rearrange a deck of cards, chances are you'll arrange it into an order that's never occurred before. Because, of course, there's 52! cards in a deck.
You know how big 52! is? Fucking huge.
So I've got two buddies; Carl and Erin. Now, Carl has in his hands a deck of cards. He really likes shuffling cards so he's going to do just that. Carl shuffles those cards so well that he rearranges them into a new order... every second. Every single second the cards have an entirely new arrangement.
Meanwhile, Erin is a bit of an adventurer so he starts by standing next to Carl on the equator. He then takes a single step forward... every billion years. Once Erin's circled the Earth (roughly 44million steps) he removes a single 0.5ml drop of water from the Pacific Ocean before walking around the equator again, one step every billion years. Now, when Erin has completely drained the Pacific Ocean, by removing a single drop every circumnavigation of the Earth, by taking a step every billion years... he places a single sheet of paper on the ground and refills the Pacific Ocean. He then continues his slow journey until the Pacific Ocean is empty once more, and then places a second sheet of paper on top of the first.
When this stack of paper reaches the fucking Sun... Carl is only a third of the way through shuffling every combination of cards.
Once you've had one to fifteen, you don't need each "eighty one, eighty two" etc anymore since you've already proven there is no A's in one to nine.
Chrenen · 1 points · Posted at 01:46:31 on February 14, 2016 · (Permalink)
Baker's Dozen?
[deleted] · 1 points · Posted at 14:49:32 on February 14, 2016 · (Permalink)
I think the name of that number is one hundred one. You wouldn't say ten and four when talking about fourteen, the and is a colloquially added filler word
tepori · 1 points · Posted at 21:52:48 on February 13, 2016 · (Permalink)
A number can be expressed in any base. For example, 126 in base 10 is 100 + 20 + 6 (multiples of powers of ten), or in base 2 is 64 + 32 + 16 + 8 + 4 + 2 (all powers of two).
We all know this in this thread, this is not the interesting part yet...
Observe that the required property is that places, when "full", must roll to the next higher place when incremented. In other words, working in bases are the simplest way to guarantee that when, say, 4 places of a base 10 number are maxed out, as in 9999, incrementing by 1 can be represented by a single value in the next place and zeroing out the rest: 10000.
It turns out bases are not the only way to assign places. For instance, it so happens that 22! + 1! is one less than 3!. And:
55! + 44! + 33! + 22! + 11!
is one less than 6!.
This means that you can use factorial as a radix if you want, provided that the digit in each place is only allowed to go as high as the factorial associated with the place.
So the way to count in this factorial radix is:
factorial = conversion calculation = decimal
0 = 00! = 0
10 = 11! + 00! = 1
100 = 12! + 01! + 00! = 2
110 = 12! + 11! + 00! = 3
200 = 22! + 01! + 00! = 4
210 = 22! + 11! + 00! = 5
1000 = 13! + 02! + 01! + 0*0! = 6
1010 = …
1100
1110
1200
1210
2000
2010
2100
2110
2200
2210
3000
3010
3100
3110
3200
3210
10000
10010
… etc …
Starting from the smallest place at the right and going left, instead of the 1s place, 10s place, 100s place (in base 10), there's the 0! place, the 1! place, the 2! place, the 3! place.
The largest digit allowed in the 3! place is 3. The largest digit allowed in the 6! place is 6.
wsci · 1 points · Posted at 22:06:10 on February 13, 2016 · (Permalink)
When working in base n, the digital root of any multiple of n-1 will always be n-1.
In base 5:
1 × 4 = 4
2 × 4 = 13; 1+3 = 4
12 × 4 = 103; 1+0+3 = 4
20413 × 4 = 133212; 1+3+3+2+1+2 = 22; 2+2 = 4
Changed wording for clarity
zsfy · 1 points · Posted at 22:10:13 on February 13, 2016 · (Permalink)
There are 62,000 miles of blood vessels in the human body – laid end to end they would circle the earth 2.5 times
At over 2000 kilometers long, The Great Barrier Reef is the largest living structure on Earth
A thimbleful of a neutron star would weigh over 100 million tons
If you take a bunch of consecutive nimbers and see how many times they can be divided evenly by 2 its makes a pattern within a pattern within a pattern continuously.
Euler's Equation (Identity): ei*pi + 1 = 0. Not only is this equation incredibly useful, especially in complex arithmetic, there is a kind of beauty to it as well. It includes many important numbers such as e, i, pi, the additive identity 0, and the multiplicative identity 0.
3 men go to a restaurant, the bill is $30 so they paid $10 each.
They then complain to the waiter saying it was too expensive so he speaks to the manager.
Manager says give them a $5 refund, so the waiter gets 5 x $1 bills from the cash register and keeps $2 for himself as they never left a tip and gives them $1 each refund.
They originally paid 3 x $10 = $30
They got a $1 refund each meaning they each paid $9 and the waiter kept $2.
3 x $9 = $27 + $2 = $29, where is the missing dollar.
[deleted] · 1 points · Posted at 23:45:37 on February 13, 2016 · (Permalink)
Will someone please explain how this works and a similar example? This has been bothering me for quite some time.
[deleted] · 1 points · Posted at 23:48:00 on February 13, 2016 · (Permalink)
That's the same as 240/243. Any repeating decimal is going to be represented by a ratio of whole numbers A/B, so it just happens that 240 and 243 do the trick here.
Similarly, the pattern .123123123123... turns out to be 41/333.
[deleted] · 1 points · Posted at 14:46:42 on February 14, 2016 · (Permalink)
You can't simplify that fraction further, since 80 and 81 don't have any prime factors in common. But if you want the decimal representation, you can compute it by using long division.
Here is a trick that I learned to quickly multiply 11 by any two digit number. Add the two digits together and place the sum in the middle. Take 11x11 for example. 1+1=2, so the answer is 121.
11x12 = 132
11x13 = 143
11x35 = 385
If the sum is a two digit number, add the tens place of the sum to the hundreds place of the answer. Let's use 11x55 as an example. 5+5=10, so the answer is 605.
Apparently any whole number you multiply by nine will do this. For example:
9x11=99, 9+9=18, 1+8=9
9x51=459, 4+5+9=18, 1+8=9
9x7289=65601, 6+5+6+0+1=18, 1+8=9
9x5864271=52778439, 5+2+7+7+8+4+3+9=45, 4+5=9
I've been playing with this on a calculator since I saw this thread and it always happens. I'm not very good with math, so if someone knows that this is wrong please say so.
When you add nine to a number, you could say you are adding ten and subtracting one. In base-10, this means that every time you take one from the digit in the ones place, you add one to the digit in the tens place. It's trivial.
The ratio between miles and kilometres is close to the ratio of numbers in the Fibonacci sequence. This means that 8 miles is almost equal to 13 kilometres. This is quite practical but you'll never need it.
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 possible outcomes when shuffling a standard deck of cards.
lyds7 · 1 points · Posted at 23:11:50 on February 13, 2016 · (Permalink)
These are way over my head! I was happy with ... you can find out if a number is divisible by 3 by adding the digits together and if the answer is in the 3x tables it is!
Background: there are multiple infinities. There are so many infinities, even, that none of the infinities is "infinite enough" to describe how many infinities there are.
Assuming the axiom of choice (most people do), we can order all the infinities. In particular, the "first infinity" is the size of the set of natural (counting) numbers. Many people believe the "second infinity" is the size of the set of real numbers.
So these infinities are ordered, and like computer scientists, they are indexed by 0 (the natural numbers are the "zeroth" infinity, instead of the "first").
The coolest part to me: there are infinities so big that they describe their own position in the ordering: that is to say, there is an infinite number k such that k is the "kth" infinity.
There are actually infinitely many infinities with this property.
While I see that you are joking, it is important it note that in my post, when I say "infinities" I am referring to infinite cardinal numbers.
We don't call any of these "infinity", because that would be weird: they are all infinite, none of them is "the" infinity.
However, for any particular infinite cardinal k, k+1 is not a cardinal number, it is an ordinal number with the same cardinality as k.
Further, neither of the infinite cardinals I mentioned in my post (aleph-null and aleph-one) have this property. Aleph-null is the "zeroth" infinite cardinal, not the "aleph-nullth" infinite cardinal, etc.
Between any two real numbers there are an infinite number of irrational numbers. And between those same two real numbers there are an infinite number of rational numbers. But if you threw a dart at this number line, the likelihood that your dart will land on an irrational number is 100%
[deleted] · 1 points · Posted at 23:23:15 on February 13, 2016 · (Permalink)*
This reddit account has been removed.
georgeo · 1 points · Posted at 23:25:57 on February 13, 2016 · (Permalink)
the integer roots of 1 are evenly spaced on the circumference a unit radius circle on the complex plane and from that Euler's identity e{i \pi} + 1 = 0
Zeno's Paradox- distance is infinite. Because to get from point A to point B, you have to go 1/2 the way, then 1/4, then 1/8, goes to infinity, and it turns out all motion is just an illusion.
I hope you stopped finding it strange. Look how the digits line up in the two added numbers. They all make tens. Same with the two subtracted numbers; all tens.
The harmonic series diverges to infinity, unless you remove all the fractions with a nine in them, in which case it converges on about 23.
sulump5 · 1 points · Posted at 23:57:52 on February 13, 2016 · (Permalink)
Take any 3 or more digit number that isn't the same digits, then rearrange them. Subtract the lower value of that rearrangement from the higher value. Your answer will always be divisible by 9.
Example: 345. Rearrange that to 534. Since 345 is smaller than 534, you would do 534 - 345, which gives you 189. 189 is divisible by 9. Works everytime :)
Learned this from VSauce: 52! (52 factorial), aka the number of possible shufflings that a deck of cards can have is a really big number. Like REALLY big. It's extremely likely two card decks with true shufflings have never had the same order. If you truly shuffle a deck of cards it's overwhelmingly likely that's the first time it's ever been in that order. Here's an example of how big 52! is:
If you started a timer counting down by seconds from 52! then began to walk around the world one step at a time, with 1 billion years in between each step
then once you made it all the way around the world you took a drop of water our of the Pacific Ocean, and kept walking around the earth, stopping to take a drop of water every time you complete a trip around the Earth with one billion years between steps
then once you emptied the Pacific, you placed a piece of paper on the ground and refilled the ocean and by this whole process you made a stack of papers
by the time that stack reached the sun you would be 1/3000 of the way to 0 on your clock...
If you take avogadros # and divide it by the golden ratio and multiply it by the derivative of force delta (dark matter fu / dark energy eu) then the girl you're desperately hitting on at the bar still won't suck your dick.
Arditwm · 1 points · Posted at 00:02:11 on February 14, 2016 · (Permalink)
If you assign a letter to the numbers in π (pi), so for example 1 will be a, 2 will be b and so on. You will have converted the sequence of numbers into a bunch of random letters.
c.adaeibfecei.....
But since π in infinite and random, at some point those letters will make up words, sentences, and much more. If you (theoretically) search for long enough, you will find your life story in the digits of π, from start...to finish.
Take any number like 586 and count them. So it would be 5+8+6 = 19 do it again 1+9=10. 10 is not in the multiplication table of 3 so 586 can not be defined by 3.
Edit: sorry English is not my first language.
The product of any single digit multiplied by nine has the 10's digit one less than the multiplied number with the one's digit 9 minus the ten's digit number.
Ex: 7*9=63 7-1=6 9-6=3
This always helped me get through the nines multiplication tables in grade school.
If you take any number two digits or more, rearrange the digits, and subtract them, the answer will always be divisible my nine. Also if you add all the digits of the new number, that new number will also be dividable by nine.
ei*π+1=0
Euler's identity combines the concepts of imaginary numbers, irrational/rational numbers, and zero into one concise equation. It was named the most beautiful mathematical equation ever conceived.
Order of operations is unclear in sentence form. I came up with 2+3+5+7+11+13+17=58, and 58[2]=3364. Then I tried 4+9+25+49+121+169+289. Much better. On a side note, ((6+6+6)+(6+6+6))*(6+6+6)+(6+6+6)=666, and 1+2+3+...36=666.
This not only works for every real number, it works if n=cookie. If you have 10 cookies and take away 1 cookie, you have 9 cookies. This is Sesame Street-level math, except they say C is for cookie.
“The best number is 73…. 73 is the twenty-first prime number. Its mirror, 37, is the twelfth and its mirror, 21, is the product of multiplying (hang on to your hats) 7 and 3…. In binary, 73 is a palindrome: 1-0-0-1-0-0-1, which backwards is 1-0-0-1-0-0-1.”
This goes for pretty much any function such that all functions in the complex region are unbounded, except for a constant function. It is known as Louiville's theorem and has some catches.
That a circle is has a infinite number of sides all with the length of 0
Thaufas · 1 points · Posted at 00:29:46 on February 14, 2016 · (Permalink)
Limit of (1 + 1/n)n as n->∞ = e = 2.7128...
boozin_ · 1 points · Posted at 00:34:10 on February 14, 2016 · (Permalink)
The kelvin and Rankine temperature scales are defined so that absolute zero is 0 kelvin (K) or 0 degrees Rankine (°R). The Celsius and Fahrenheit scales are defined so that absolute zero is −273.15 °C or −459.67 °F. At this stage the pressure of the particles is zero.
2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 is not prime, since 30031 = 59*509. This is the smallest counterexample. If this trick always did produce a new prime number, it wouldn't be such a big deal when the next largest prime number is discovered.
Graham's number is (was?) the largest number to be used in a proof. To express it basically required a new form of notation known as Knuth's up-arrow noation
ixfd64 · 1 points · Posted at 00:51:36 on February 14, 2016 · (Permalink)
Far larger numbers have since appeared in serious mathematics, such as TREE(3) and SCG(13).
That there's a theorem where the most likely case of a event is twice as likely as the second most like, three times more likely than the third, fourth for the fourth. This applies to almost all languages, colors in paintings, and many other scenarios.
If you lay down a rope around the equator so that it is stretched taut, and then add 1 metre to its length, now if you pull the rope up from every point it will come up to a height of 16 cm above the ground. This is a property of all spheres and is irrespective of the radius
Depending on your perspective, this is also the definition of ex!
ctaie · 1 points · Posted at 00:57:12 on February 14, 2016 · (Permalink)
If you add all the digits up in a given number and their sum is divisible by three, then the original number is also divisible by three.
jmwbb · 1 points · Posted at 00:58:23 on February 14, 2016 · (Permalink)
There's quite a few!
There are infinitely many natural numbers, integers, rational numbers, real numbers... but these infinite are of different sizes. Natural numbers are "countably infinite", which is by definition; a set with as many things in it as their are natural numbers are countable. The reals on the other hand are uncountable, their size is called the cardinality of the continuum.
What's interesting is the integers and even the rationals are countable. The integers are countable because I can put them in a sequence like this: 0, 1, -1, 2, -2... and in this way I get one integer for every natural number.
The rationals are trickier, but they're all a/b for some integers a and b. So what I can do is make a 2d grid and then draw a spiraling line outward hitting every point I'm the grid, skipping over all the points that represent things like 2/4 and 3/9 since those can be reduced, and in this way I show a natural number exists for each rational.
But I can go further and look at the definable real numbers; numbers that can be defined. Let's pretend they're being defined in English, they'll actually be defined in first order logic or something but the principle is the same. I order all the definitions alphabetically and in this way I show that the definable numbers are countable. Therefore most real numbers can't actually be defined.
Pick 5 consecutive positive integers. Their product is divisible by 120, always.
Think of a number between 1 and 10.
It's 7, isn't it?
Fact: I will guess correctly at least some of the time probably
dangil · 1 points · Posted at 01:00:00 on February 14, 2016 · (Permalink)
So the Fibonacci sequence is cool but what's cooler is if you reduce the multi-digit numbers to a "single number representation" the pattern repeats endlessly. Basically its 1 1 2 3 5 8 13 21 34 55 89 144 233 etc. you take the multi digit numbers and add the digits together until you get a single digit number; so 13=4 21=3 34=7 etc. Now the pattern becomes 1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9 (and now repeats) 1 1 2 3 5 8 4 3 7.....etc.
ixfd64 · 1 points · Posted at 01:04:40 on February 14, 2016 · (Permalink)
You can use modular arithmetic to check for the divisibility of extremely large numbers, even those that are way beyond computing limits.
Gabriel's Horn is my favorite. There is a theoretical shape that has a finite volume and infinite surface area. That means a paint can in this shape could not hold enough paint to coat the interior of itself. Paradox!
ixfd64 · 1 points · Posted at 01:05:41 on February 14, 2016 · (Permalink)
The fascinating truth behind Euclid's Fifth Postulate. You see, Euclid had 5 axioms and 5 postulates which formed the basis of the study of geometry. The axioms and 4 of the postulates were really straight-forward. Stuff like "Two things each being equal to a third thing also must be equal".
But the Fifth Postulate was sort of, well, weird. From wikipedia:
"If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles"
This did not seem like something that couldnt be derived from the other basics. So for thousands of years, the best mathematicians tried to prove this fact from the other 5 axioms and 4 postulates. And they just couldn't do it.
Well, finally in the 19th century, people finally realized the truth that there WAS no inherent contradiction which could be reached by not assuming the fifth postulate was true. In other words, Non-Euclidean geometry was a real thing, and an internally consistent system.
So.. Euclid was either so brilliant that he intuitively knew that his system of geometry was just one of many others, or else he was just too embarrassed that he could not prove his fifth postulate from the others to ever give more commentary on the subject. Or a little of both.
There are no 'floating point errors' (as in loss of precision), when using actual fractions, only when they are converted to decimals for binary ALU operations.
Hmm, well, I always thought it interesting how you could get the answer in any multiplication of 9 by adding the two numbers together to get the answer.
It's hard to explain so
9x1=9
9x2=18 1+8=9
9x3=27 2+7=9
9x4=36 3+6=9
9x5=45 4+5=9
and so on. And it was also interesting that the answers would always add or subtract 1 as the multiplication got higher.
9
18
27
36
It was pretty cool to see a pattern in the number 9, but that really hasn't helped much, but you could also apply the same principle in learning your multiplication chart for any number with a little bit of work.
Really weird fact: The Liouville numbers are, as a subset of the reals, measure 0 (i.e. "small," for some definition of small), and their complement (the set of everything that isn't them, in the reals) is meagre (i.e., 'small,' for a different definition of small).
So the reals can be divided into two sets, both of which are "small."
There is a cone known as Gabriel's horn that has a finite volume but infinite surface area. That means that it is possible to fill the cone with paint, but there isn't enough paint in the world to paint the inner walls of the horn.
Gabriel's Horn is what results when you revolve the function 1/x about the X-axis. What you'll find is that it has infinite surface area, but finite volume.
So imagine you have a paint can with infinitely thin walls. You can fill this thing all the way to the top, over flowing even. But when you dump out all the paint, you'll find that there's not enough paint in the universe to completely cover the inside.
9*2 is 18. First digit is -1 from the original number, second digit is the number needed to get 10 if added to the original number. Goes for any number 2-9
Take the list of odd numbers 1,3,5,7,9, . . . Start with 0 and add the numbers in the list one at a time. At each step you have a perfect square. I wish I knew why this works.
Simple. To go from a 2x2 to a 3x3 square, add 2 along the top, 2 along the side, and 1 in the corner. 2+2+1=5. Add 3 and 3 along the top and side, and one in the corner. 3+3+1=7. This is best illustrated with Skittles or M&Ms.
[deleted] · 1 points · Posted at 01:27:00 on February 14, 2016 · (Permalink)
Non-eucledian geometry is some weird abstract stuff. It has a lot to deal with how you define a line. On a plane or in a space like we are used to dealing with, lines are "straight" but if you look at the actual universe, most "lines" are actually curved space
Duality between lines and points in projective geometry: any theorem still holds true if you replace if you make the following substitutions:
"points" instead of "lines" and vice versa
"lies on" instead of "passes through" and vice versa
"intersect" instead of "join" and vice versa.
Duality in general appears a lot in mathematics. Duality between vectors and functionals in linear algebra. Duality between vertices and faces in combinatorial topology. Duality between conjugate complex numbers. Etcetera.
Take the square of something and add the root number and the next number in sequence to get the square of the next number.
IE 4*4=16
16+4+5=25
25+5+6=36
Figured this pattern out on my own when I was younger. I was proud I did. Don't know who was the first person to do it tho. Can't imagine I was the first.
No worries. Good to know that it has an official title and formula attached to it tho. Never once thought it was something I came up with. Too many math geniuses came before me to have missed a pretty simple pattern.
[deleted] · 1 points · Posted at 01:30:02 on February 14, 2016 · (Permalink)
If you choose a number completely at random (from the set of all real numbers) there is 0% chance that it will be a whole number. (I think it's actually rational number, not just whole, but not completely sure).
Mysta02 · 1 points · Posted at 01:31:37 on February 14, 2016 · (Permalink)
Multiplying any number by 11 is REALLY easy, even in your head.
Separate the digits, add each side-by-side sets of digits together (carrying if necessary), then delete each enclosed starting digit (not the end ones).
That's language, not math. "Even" in this context means "divisible by two". I made up the word "threeven", and defined it as "divisible by three". Three is the only threeven prime there is.
When I would take calculator and count, multiple or divide numbers I see by their diagonal, width or lenght I would get some funny numbers. And, uhm, yeah Fibonacci.
The golden ratio is literally everywhere in nature. It's the building block for earth
amatava · 1 points · Posted at 01:36:03 on February 14, 2016 · (Permalink)
I once heard that no electron can spin at the same rate of speed and temperature as any other electron, meaning anything that affects one informs all electrons in the Universe.
Any know if that's true?
akustix · 1 points · Posted at 01:36:13 on February 14, 2016 · (Permalink)
ei*pi + 1 = 0
The relationship between the five most important numbers all summed up in one tidy expression.
If you take any multi-digit number and add all its individual digits up, adding together the digits of any sums with 2+ digits in any order you choose, adding all digits together until you get down to one single digit sum, it will always be the same number. Doesn't matter which ones you add in which order, will always end up as the same single digit. Example:
13579
9+7=16
1+6=7
7+5=12
12+3=15
15+1=16
1+6=7
Mix it up in any way you want, adding the two digits of a sum or not, and it will always be 7.
This is the basis behind the ancient pseudoscience of numerology. What you did is called "casting out the nines". You see how you added 9+7 and the 9 disappeared? The 1+3+5 went the same way.
Because it is spherical and not a flat plane, any triangle drawn on the surface of the earth has more than 180 degrees as the sum of its angles.
MrLKK · 1 points · Posted at 01:37:35 on February 14, 2016 · (Permalink)
Gabriel's Horn blew my mind in Calc II. If you take f(x) = 1/x and create a concave funnel like thing (or a horn) by rotating that graph over the x-axis from x=0 to x = infinity you create an object (Gabriel's Horn) that has an infinite surface area, but a finite volume.
MrLKK · 1 points · Posted at 01:53:20 on February 14, 2016 · (Permalink)
With calculus you can make a horn-like 3D object that extends to infinity with an infinite surface area and finite volume. You can fill it with paint, but you'll never have enough paint to paint the outside
Oh, I see. Sort of. It's basically infinitely tall? Like, super narrow, I'd guess?
MrLKK · 1 points · Posted at 02:58:32 on February 14, 2016 · (Permalink)
Yeah, it's on its side, but it's the same idea. It's kinda shaped like a bugle
mces97 · 1 points · Posted at 01:37:41 on February 14, 2016 · (Permalink)
I don't know if all this is true, but when I was taking physics in college my professor was talking about the Pythagorean theorem. A squared + B squared = C squared. So here's the thing. The square root of 2 is an irrational number, but if you have two sides of a right triangle equal to 1 (whatever unit), then the hypotenuse has a definite length. He said the guy who figured that out was burnt at the stake.
A factorial (denoted by "!") is evaluated as n! = (n)(n-1)(n-2)...(1). So for example 5! = (5)(4)(3)(2)(1) = 120. Factorials are often applied in probability to describe combinations and choices, hence, you pretty much only see n! when n is some integer.
However, as it turns out you can take factorials of fractions as well.
(1/2)! = sqrt(pi)/2
This is a result of the gamma function, which is an integral that generalizes factorials for any real number n.
[deleted] · 1 points · Posted at 01:39:12 on February 14, 2016 · (Permalink)
If you take 1/x where x>=1 and rotate it in three dimensional space about the x-axis the resulting surface has infinite surface area but finite volume. That is to say you could fill it with a finite amount of paint, but you could never have enough paint to cover its exterior. This surface is known as the Gabriel's Horn or Torricelli's trumpet.
Whorrox · 1 points · Posted at 01:39:17 on February 14, 2016 · (Permalink)
There is a number, called Graham's number that can't be defined in any terms of writing the digits, as even if every single digit was an atom, there aren't enough atoms in the universe to encompass it. The number is so large that it must be written using series and special notation. To give some reference, if you took the earth as it stands, ground it up into sand, took that sand and then expanded them each to the size of the universe, then took those universes and completely filled them with lead, and took the weight of all of those universes, the weight in pounds would be less than Graham's number by a significant amount.
Comalol · 1 points · Posted at 01:42:46 on February 14, 2016 · (Permalink)
My area code (563) is one of three known Wilson primes under 20 billion. The other two are 5 and 13.
To multiply any single digit and 9, hold up all 10 fingers and then put down the finger you want to multiply with 9. The fingers still standing to the left is the tens position, fingers to the right in singles position.
Really only useful in 2nd grade or so, but that one has stuck with me.
ceraith · 1 points · Posted at 01:45:24 on February 14, 2016 · (Permalink)
You can create 2 identical spheres from one sphere that is also identical to the 2 new spheres
If you take a wire in the shape of a cycloid, place two beads anywhere on its length, and release them simultaneously, they will reach the bottom at the same time.
Maybe someone could answer a question for me. Why does BEDMAS work? Like what are the logical steps to it? I mean i know what it is but I still don't really get why that's the proper way to do an equation.
It's not some kind of mathematical fact, it's just how we write our equations. 2 + 5 * 3 is ambiguous, so we DEFINE it to mean 2 + (5 * 3). We could just as easily use BEASMD or any other ordering, we'd just have to write some of our equations a little differently.
It's like how the symbol "4" doesn't objectively mean the fourth number, it's just how we choose to represent that concept.
The number 1 actually has 2 values.
1 divided by 3 =.333 repeating
.333 repeating multiplied by 3 = .999 repeating therefore the number 1 simultaneously has the value of 1 and .999 repeating.
loozid · 1 points · Posted at 08:22:32 on February 14, 2016 · (Permalink)
wat
soxdye9 · 1 points · Posted at 01:52:03 on February 14, 2016 · (Permalink)
Kind of late to the thread but the number 6174 is very unique in that when ever you take any 4 digit number (i.e. 1254) and arrange the number from high to low (5421) then subtract the numbers from low to high (1245), you'll get some number then repeat the pattern with the new number (this case 4176), which then you get (7641-1467=6174). You will always end the pattern at the number 6174. This only works when one of the four numbers is different from the rest (1111 doesn't work but 1110 does.)
Any number that is divisible by 3, the sum of its digits will by divisible by 3. This is true with 9. If the number is also even, it is divisible by 6. Base 10 system.
Charles Babbage designed the first computer in the work. The Difference Engine was the first mechanical calculator, And it could tabulate polynomial functions.
I did the calculations on this once (can't remember if I used googol or googolplex) but if stored as .doc you would need a pile of 64-gigabyte microsd cards the size of 180 million~ pyramids of Giza to store the number. I lost the calculations during a computer reset, wish I could say for certain which it was
That Euler discovered or invented so many mathematical formulas and equations that they had to start naming them after the second person to discover them so that they all weren't named after Euler.
If you cut a ball into a finite number of parts (at least five), and reassemble it in a different way by only translating and rotating the pieces, you will end up with two balls. The Banach–Tarski paradox.
For every prime number greater than or equal to 5, one less than its square is divisible by 24.
Short proof:
Say x is prime. In the sequence x-1, x, x+1, at least one of those numbers must be divisible by 3. It can't be x, because otherwise x wouldn't be prime. Additionally, we know that one of x-1 and x+1 is divible by 2 and the other is divisible by 4, because every other consecutive even number is divisible by 4 and those are two consecutive even numbers, because x must be odd for it to be prime.
So that means (x-1)(x+1) must be divisible by 2 x 3 x 4, which is 24, since factors of the multicants are also factors of the product.
(x-1)(x+1) = x2 - x + x -1 = x2 -1, which is 1 less than the square of x, which as we said at the start is any prime number greater than or equal to 5.
Simpson's paradox, or the Yule–Simpson effect, is a paradox in probability and statistics, in which a trend appears in different groups of data but disappears or reverses when these groups are combined.
Here's one of my favorite examples:
A real-life example is provided by Ken Ross[15] and involves the batting average of two baseball players, Derek Jeter and David Justice, during the years 1995 and 1996:
Name
1995
1996
Combined
Derek Jeter
12/48 (.250)
183/582 (.314)
195/630 (.310)
David Justice
104/411 (.253)
45/140 (.321)
149/551 (.270)
David Justice had a higher batting average than Derek Jeter in both 1995 and 1996, but when you combine both seasons Jeter's batting average is much higher. In this instance it's mostly due to the very small sample size for Jeter in 1995, and small sample for Justice in 1996.
AH_MLP · 1 points · Posted at 01:59:59 on February 14, 2016 · (Permalink)
Airth · 1 points · Posted at 02:00:16 on February 14, 2016 · (Permalink)
Multiplication by 11. If it's two digits, you can just add the two digits and put the result in the middle. tho, you have to carry over when its greater than 10. Example: 25 x 11 : 2 + 5 = 7, 275.
When you shuffle playing cards it is most likely the first time that any deck EVER has been ordered that way. And it will continue to be a unique order for billions and billions and billions of years from now.
Ive always been fascinated with Fibonacci Numbers. For those unfamiliar, you start at zero, then count to one. At this point you add the two together to get 0+1=1. Now add the new number to the previous, 1+1=2, then 2+1=3 and so on. It should look like this:
0, 1, 1, 2, 3, 5, 8, 13, 21.......
Interestingly enough, these sequences can also be found in nature. Fascinating stuff!
Current secure encryption for things like your banking information or any time that you use your credit card online uses 2 extremely large prime numbers (In the billions or trillions or bigger) to form a key that are then multiplied together into something called a semi-prime. That semi-prime is then the public key that you use to encrypt your credit card information when buying something or your username and password when logging in somewhere. Because it is so difficult to discover the exact 2 prime numbers that created the semi-prime it is completely safe to send your information online using this encryption. (As long as you don't have a virus or anything on your computer)
To put how difficult it is to guess the 2 numbers that created the semi-prime, it would take all of the computers in the world longer than the length of the current age of the universe to crack the code. Its cool because something that we use every day is just math.
[deleted] · 1 points · Posted at 02:04:54 on February 14, 2016 · (Permalink)
Often this fact is abused in nutcase documentaries you can find on youtube. But overlook this and it's still amazing. Seriously, tomorrow go outside and stare really close at the center of a flower. Mindblowing.
Projective space is like space where you can get to infinity.
Think of it like a sphere. If you start at the center, you can go in a straight line to the boundary, and if you try to go further, you end up starting to go back to where you started... you went in a circle while going in a straight line.. Moreover, when you get to the boundary, you're on two opposite points of the sphere's boundary... at the same time.
Formally, real projective space RPn is Sn/~, where v ~ -v on the boundary, and Sn is the n-dimensional sphere (well, ball, it's a solid).
More interestingly, when n = 1, we have the one-dimensional version, the projective line, which is just a line with the ends glued together: a circle! Also, the space of rotation in 3D, known as SO3, looks exactly like RP3!
Source: I study mathematics.
ceazah · 1 points · Posted at 02:06:37 on February 14, 2016 · (Permalink)
80,085 spells boobs on a calculator
pclack · 1 points · Posted at 02:07:23 on February 14, 2016 · (Permalink)
ei pi = -1
Otherwise known as eulers formula. I just think it's cool that an identity containing the most famous irrational numbers is equal to something so simple as -1.
rhgla · 1 points · Posted at 02:07:32 on February 14, 2016 · (Permalink)
That I sucked at math in school and excel at my job, which is heavily based upon a requirement to be skilled at math.
I find it interesting what is actually not known by mathematicians. For example, nobody knows if every even number >2 can be written as the sum of two primes, and yet nobody has found a counterexample. Also, do you know the popular claim that Shakespeare's plays are encoded in the digits of pi? That hasn't been proven either.
If the difference in the balance of your till is divisible by 9 you transposed a number:
[DEFINITION of 'Transposition Error'
A simple error of data entry. Transposition errors occur when two digits that are either individual or part of a larger sequence of numbers are reversed (transposed) when posting a transaction. Although this error is small and unintentional, it can result in huge financial losses or errors in some instances.
BREAKING DOWN 'Transposition Error'
When two adjacent numbers are transposed, the resulting mathematical error will always be divisible by 9 (e.g. (72-27)/9 = 5). Bank tellers can use this rule to quickly find their errors in many cases. Transposition errors also occur in accounting firms, brokerages and all other areas of finance.](http://www.investopedia.com/terms/t/transposition-error.asp#ixzz406Vx8xwx )
True for 1-4. 5 was a circle below a line, later opened on one side and attached to the line, left in to distinguish it from a circle above the line, which meant 10. 6 was a circle (representing a hand) with one finger up for 5+1.t 9 was 10 with one finger down to subtract 1. The circle with three fingers up morphed into the modern 8, and the circle disappeared from the 7, probably to distinguish it from 5 and 6.
Graham's number is famously the largest number that is used in a serious mathematical proof. It is so large that if you were to write each digit in one planck volume, the smallest volume physically possible, you wouldn't be able to fit it within the observable universe. Not only that, but jumping off of /u/PlasmicDynamite's comment, you still couldn't fit it in the observable universe even if you attempted to write it using tetrations. And if you're thinking that means that means that it's larger than the number of Planck volumes, you're wrong. It means that the number has over 4 x 1085digits. If the scale of the universe is unfathomable to you, Graham's number is sure to be as well.
And moreover, since its discovery, it has actually been dethroned as the largest useful number in mathematics a few times.
There's different sizes to infinity and it's relatively easy to prove and see. I wont outline the proof now because I'm in a cab and my girlfriend is pissed I'm on my phone but check out cantor's snake or google countable
/uncountable infinity. Very cool and powerful concept that actually comes up a lot.
Basically, in the history of human kind, a deck of cards has never been shuffled the same way twice. If all the possibilities were seconds, you could stand at the equator, and wait ONE BILLION years to take ONE step. Then wait another BILLION. Keep doing this, until you've gotten all the way around the globe. Then remove 1 drop of water from the ocean. Now, start over again. By the time the pacific ocean is dry, you haven't even made a dent in the number. The video explains it so much better, but you'll never look at a deck of cards the same way again.
[deleted] · 1 points · Posted at 02:13:33 on February 14, 2016 · (Permalink)
When launching an object away from another object, the theoretical distance of the gravitational field is infinity. However, you can launch it far enough for it not to be attracted any longer. That distance is infinity, and yet by the definition of infinity, still infinitely far away from infinity.
Any integer to the 5th power has the same last digit as the original number.
[deleted] · 1 points · Posted at 02:14:56 on February 14, 2016 · (Permalink)
I would like to post my answer as a video, because all the mathematical facts I know are thanks to Square One and the Children's Television Workshop. <3
"The story you're about to see is a fib, but it's short."
The rule of 72 is a shortcut to estimate the number of years required to double your money at a given annual rate of return. The rule states that you divide the rate, expressed as a percentage, into 72
The sum of a positive numbers from 1 to infinity is -1/4.
[deleted] · 1 points · Posted at 02:17:56 on February 14, 2016 · (Permalink)*
Gabriel's Horn is a geometric shape with finite volume but infinite surface area. If you wanted to paint the horn, you could paint the inside with a finite amount of paint, but no matter what, all the paint in the world wouldn't be enough to paint the outside.
Ipsoka · 1 points · Posted at 02:18:15 on February 14, 2016 · (Permalink)
That 1+2+3+4+5+6+... = - 1/2
dyfx · 1 points · Posted at 02:18:18 on February 14, 2016 · (Permalink)
When sending messages, if each letter has over a 50% chance of being received correctly, then there is way to encode the messages before sending so that the receiver can decode the messages with basically 100% accuracy AND the encoded message is very short. Shannon's Theorem
Every next square can be found in order of increasing odd numbers added to the previous square.. Hard to explain in words but 12 is 1, 22 is 4 which is 1+3, 32 is 9 which is 4+5, 44 is 16 which is 9+7... I think thats pretty cool
This pattern works even as you proceed into cubes and beyond power progression. Here is the example for cubes. Fourth (and later) progressions require use of lesser powers broken down similarly.
43=64
53=125
125-64=61
(52)+(42)+(4*5)=61
63=216
73=343
343-216=127
(62)+(72)+(6*7)=127
dsahai · 1 points · Posted at 02:18:38 on February 14, 2016 · (Permalink)
Well given that it's valentine's day and what not, type this into Google:
sqrt(cos(x))cos(300x)+sqrt(abs(x))-0.7)(4-x*x)0.01, sqrt(6-x2), -sqrt(6-x2) from -4.5 to 4.5
The limit of the volume of a d-dimensional unit box as d goes to infinity is 1. The limit of the volume of a d-dimensional unit ball as d goes to infinity is 0 though.
ajax2k9 · 1 points · Posted at 02:21:21 on February 14, 2016 · (Permalink)
Also that if you add a number's digits and that sum is divisible by 3, the number itself is divisible by 3
You have six dots, with three in one row and three in the other. If you try to draw a line from each dot and connect it to all others (so each dot has three lines coming from it), it's impossible to do so without any line intersecting the other. This is provable with Euler's Graph Theory
Keep going, if a number is divisible by nine, it's digits summed together will be divisible by nine. Similarly, if a number is divisible by 3, it's digits are divisible by 3. Give it a try:)
123 is divisible by 3. 567 is divisible by 9.
[deleted] · 1 points · Posted at 02:23:14 on February 14, 2016 · (Permalink)
Here's something to think about: Every time you shuffle a deck of cards, you make history.
Shuffle a deck of cards once per second. Every billion years, take one step. Every time you walk around the world, take a sip from the ocean. Everytime you drain the ocean, put a single piece of paper on the ground. Once the stack of paper touches the Sun, you have only done 1/3000 of the shuffles the deck could have.
(I think that's correct. Someone please correct me if I messed that up)
A few years ago, I had him as a professor at University of California, San Diego in a Computer Science class. He was awesome!
He casually slid in that there was a number named after him, and I thought he was joking that there coincidentally was a number that shared his last name. I looked it up later; I was wrong.
eix = cosx + isinx. Don't know what it is about Euler's formula, but seeing how these completely unrelated functions come together like this for the first time in my diff eq class made me realize how awesome math is
If you take the distance from the mouth of a winding river to its tail, the ratio of that distance against a straight line from mouth to tail is approximately 3.14
Pythagoreas was net necessarily a person. He was worshiped by a cult called the pythagoreans. They attributed much work to him, evidence of his actual existence is questionable.
Awe really? I remember being told about the beach scene, some soldier or something killed him while he was drawing tribgles on a beach. Well there goes one of my "old person rambling speech no young child wants to hear"
It is possible to roll out a piece of dough such that it has a finite volume, but infinite surface area (gabriels horn).
It is possible to cut a soccer ball into small pieces, and rearrange them so that the end product is two soccerballs of the same size as the one which you started with (tarskis paradox)
The first is approachable (understandable, really) if you are familiar with some calculus. The second has to do with complex set theory and topology
Duo34 · 1 points · Posted at 02:28:55 on February 14, 2016 · (Permalink)
It is possible to prove that a solution to a problem exists, and prove we will never know what it is.
That if you say the quadratic formula to the jack in the box beat it works perfectly.
X equals negative b plus or minus the square root b squared minus 4 ac all over 2 a
Wish I could remember the expression.. maybe it was 1/x2.. something where if you were to spin it into a horn-like shape it would hold a finite volume but have infinite surface area (or vice versa).
The area under the curve of 1/x from x=1 to x= infinity gives you an infinite area.
If you take that area and wrap it around the x-axis the volume is pi.
11 times any 2-digit number (xy) equals the tens digit (x) followed by the sum of the the tens digit and the units digit (x+y) followed by the units digit (y).
e.g. 11 x 13 = 1 (1+3) 3...143.
Gets a little trickier when the sum of x+y is a 2-digit number...you just have to carry the "1" to the tens digit (x).
I'm a little late for this, but it has to be the mathematical probabilty of shuffling the same deck as anyone else (in the same order) in the history of mankind. Meaning each time you shuffle a deck of 52 cards, it's most likely the first time in history this deck in this order has been shuffled.
The number of possibilities is 52!, which is 52 factorial, meaning 52x51x50x49x48... All the way to 1. This number is astronomical.
To illustrate how big it is, imagine this:
If every star in our galaxy has a trillion planets, and each planets had a trillion people living on them, and every single of them had a trillion deck of cards. If Somehow, they could all shuffle each pack a thousand times a SECOND, and that since the big bang, just today we would start seeing the same combinations twice.
73 is the 21st prime number. It's mirror, 37, is the 12th, and it's mirror, 21, is the product of multiplying 7 and 3. In binary, 73 is a palindrome, 1001001. Backwards thats 1001001, exactly the same.
slshGAHH · 1 points · Posted at 02:37:12 on February 14, 2016 · (Permalink)*
If you're a party of two or more people, then there exist at least two people with the same number of friends. Assuming that if Amy is friends with Brad then Brad is friends with Amy.
This video on how to theoretically turn a sphere inside out really messed with my head! Very well done though, it was interesting and entertaining to watch, even if I didn't fully understand it.
you can take apart a solid sphere in only 4 pieces, and using only rigid movements and rotations in 3-d space, you can rearrange them in to 2 spheres identical to the original.
according to math, you can create matter.
this the banack-tarski theorem and relies on the axiom of choice.
A simple trick I always used when multiplying a double digit number with 11 is to use the first digit of the double digit number as the begging digit of the answer, second digit of the answer was both digits added together, and the last digit of the answer being the last digit of the orignial double digit number.
If you square each number sequentially, the difference grows sequentially by odd numbers. 1² is 1. 2² is 4. 3² is 9. 4²=16, 5²=25, 6²=36. So 1² (1) and 2² (4), is a difference of 3. Then the next (2² and 3²) is a difference of 5. 3² (9) and 4² (16) is a difference of seven. 4 (16) and 5 (25) is 9. And each growth of odd number is also made by adding the original number. Hope this makes sense. Try larger numbers for more mind bogglingness.
The ones place is a palindrome. Also, the tens place goes up by 1 more each time you pass a nine. As in, it goes up by 0 each increment until 9, then it goes up by 1s until 49, then it goes up by 2s until 169, ect...
To find the half of any fraction, merely double the bottom number. Half of 1/4 is 1/8. Half of 8/16 is 8/32, etc.
[deleted] · 1 points · Posted at 02:41:18 on February 14, 2016 · (Permalink)
God this thread makes me feel stupid
[deleted] · 1 points · Posted at 02:41:23 on February 14, 2016 · (Permalink)
The mathematical object termed "Gabriel's Horn" is an object that has an infinite surface area and finite volume. The shape can be created by ploting y = 1/x for x >= 1. Revolve this curve about the x-axis and the swept path creates the 3-d object. Interestingly enough, you create a shape that mathematically has infinite surface area yet finite volume. In terms of trying to paint such an object, you would theoretically never be able to paint the outside of the object, however you could fill it up with paint.
If you watched static on a 42" TV @ 30 fps, and each pixel was a star in the universe.
It would take 11,000 earth lifetimes or 50,000,000,000,000 years sitting in front of the TV to see every star.
[deleted] · 1 points · Posted at 02:43:39 on February 14, 2016 · (Permalink)
Not so much a fact as a musing, but combination locks should be called permutation locks.
If they truly were combination locks, then a lock that is opened by 30-17-23 would also open with 30-17-23, 17-30-23, 17-23-30, 23-30-17, and 23-17-30.
Take three circles with three different radii. Taking two at a time, look at their outer tangent lines. The intersection of each pair of outer tangent lines forms a point. There are three such points (one for each pair of circles). Those points are colinear.
12345679 x 3 = 37037037
12345679 x 6 = 74074074
12345679 x 9 = 111111111
...
basically 12345679 times any number that's a multiple of 3 creates a pattern.
the greatest common divisor of any two numbers is the smallest linear combination of the numbers. linear combination meaning ax + by = c. example 16 and 12. 16(1) + 12(-1) = 4. the greatest common divisor of 12 and 16 is 4. this true for any two numbers.
vassah · 1 points · Posted at 02:45:36 on February 14, 2016 · (Permalink)
The Borsuk-Ulam theorem is a cool one to think about. Any continuous way of setting a sphere of any given dimension into Euclidean space of the same dimension must assign two antipodal points the same place in Euclidean space.
If you think about this in terms of temperature on the Earth, or any two continuously varying real quantities on the Earth's surface, you'll see that there have to be two opposite points having the same value, etc.
Israe12 · 1 points · Posted at 02:46:30 on February 14, 2016 · (Permalink)
1/(1-x-x2 ) = 1+x+2x2 +3x3 +5x4 +8x6 +...
If you let x= 1/10, you get 100/89. This explains why this works. By choosing x = 1/100, you get 10000/9899. In general, if you take x=1/10n, you get the Fibonacci's spaced out farther and farther.
aerohk · 1 points · Posted at 02:46:35 on February 14, 2016 · (Permalink)
The answer to life the universe and everything is 42.
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.
the number of counting numbers (1, 2, 3...) is equal to the number of integers (...-2, -1, 0, 1, 2...) is equal to the number of rational numbers. (...-1/1, 0, 1/1...). but the set of real numbers is bigger than all of them.
[deleted] · 1 points · Posted at 02:48:42 on February 14, 2016 · (Permalink)
Using calculus, you can create a hypothetical 3d shape with a finite volume but infinite surface area.
iregret · 1 points · Posted at 02:49:24 on February 14, 2016 · (Permalink)
Numbers don't actually exist. Matter of fact, math doesn't exist. You can't show me a number. You can't show me a triangle. You can only show me a representation. Math is an absolute truth.
Je7pax · 1 points · Posted at 02:51:11 on February 14, 2016 · (Permalink)
I learned this in middle school.
Large multiplied by 11 can be easily figured out by doing this:
34 * 11
* Take the 34 and split it into 3 and 4
* Add them together and you put the sum in the middle, the 3 in the front and the 4 as the last number
* 3+4 = 7
* 374
If the sum of the two numbers is above 10 (IE: 85 * 11) you do the following
11 * 85
* 8 + 5 = 13
* Take the 1 and add it to the 8
* 935
If you take the graph of 1/x for x>=1, then rotate the curve 360 degrees around the x axis, the shape produced has an infinite surface area but a finite volume.
It's called Gabriel's Horn and I find it pretty interesting.
take any number, count the number of letters it takes to spell that number. repeat with the count being your new number. eventually, every number will become 4.
16 = sixteen, 7 letters
7 = seven, 5 letters
5 = five, 4 letters
4 = four, 4 letters
Benford's Law. There is an uneven frequency distribution of leading digits in most sets of natural data. It's a useful tool for identifying naively fabricated data.
Something I realized one day while on a train is that when increasing the base of a squared exponent by one, the next value is the sum of the previous base and the next base added to the previous exponential value. For example: 12=1, 22=4, 1+2+1=4. 42=16, 52=25, 4+5+16=25. IDK if i explained this well but this just is something i realized one day and it's helped me with odd exponents. IDK if the principle or anything similar applies to any exponent power above the squared power.
If a number added up equals a number divisible by 3 it is in itself divisible by 3...
Start with 729 for example:
729
7+2+9 = 18
729÷3=243
243 = 9
243÷3=81
Breaks down all the way to 1...
730
7+3=10
730÷3= 243.3.... number is not divisible by 3.
This is the only thing I remember from middle school.
I always liked
sin 0 = sqrt(0)/2,
sin pi/6 = sqrt(1)/2,
sin pi/4 = sqrt(2)/2,
sin pi/3 = sqrt(3)/2,
sin pi/2 = sqrt(4)/2
prmcd16 · 1 points · Posted at 02:58:25 on February 14, 2016 · (Permalink)*
I've always (since I learned about it) been a fan of the Euler identity for relating three things that a lot of people probably don't fully understand to each other and giving a result that every preschooler can count to. (If you don't feel like clicking the link, TL;DC: the Euler identity states that ei*pi+1=0)
Edit: another favorite is that there only need to be 23 people in a room for there to be a >50% probability that two of them share a birthday.
All maps are 4- colorable. Meaning, you can color any mandala in any hipster adult coloring book using only the crayons Pomegranate, Sandstone, Cirrhosis and Labrador, and not have any Pomegranate sections touching each other.
Wampxz · 1 points · Posted at 02:59:13 on February 14, 2016 · (Permalink)
a little interesting thing i found myself while doing a math homework is that √(x . 4x) = 2x
Example: √(2 . 8) = 4 , √(128 . 512) = 256
I really can't think of any practical use for it in any case, nor is it mind blowing, but i find it quite neat
Uhdoyle · 1 points · Posted at 02:59:37 on February 14, 2016 · (Permalink)
That whole "sum of all natural numbers = -1/12" thing. Blew my mind. I think it's still broken.
A group of students attend a frat party. At the door, someone takes all of their hats. The hat-taker becomes drunk by the end of the night, and randomly hands out hats to the group members. What is the probability that no person in the group receives their own hat back?
As the size of the group grows, that probability approaches 1/e.
Imagine any closed path, say trip from Finland to Spain to Turkey and back, take any measure that changes seamlessly, say temperature, choose any point on the path and check the measure. It's guaranteed that somewhere down the line there will be an other point with that exact measure, if the point you chose wasn't the highest or lowest peak of the measure
VSG28 · 1 points · Posted at 03:00:37 on February 14, 2016 · (Permalink)
There's an actual song with the lyrics "sin2 theta + cos2 theta = 1"
Athrul · 1 points · Posted at 03:00:42 on February 14, 2016 · (Permalink)
Four is the only number whose has the same amount of letters in its name as its corresponding number value
lurgi · 1 points · Posted at 03:05:21 on February 14, 2016 · (Permalink)
Between any two irrational numbers there is a rational number. Between any two rational numbers there is an irrational number. Yet there are more irrational numbers than rational numbers.
Euclid's fifth postulate made math much more interesting, but even though he knew something was different about it, it took many more years to get nonstandard everything.
Some infinities are bigger than others. Or the fact that theoretically you can split an object into 6 equal parts, combine them into two separate objects, both the exact same size as the original
A photon is beyond time. If you were to magically see from a photons perspective, the moment you departed the sun and the moment you hit Neil degrade Tyron's face would be the same moment without any time passing.
"The square root of 69 is 8-something" -Aubrey graham
[deleted] · 1 points · Posted at 03:10:59 on February 14, 2016 · (Permalink)
ei pi = - 1
koghrun · 1 points · Posted at 03:10:59 on February 14, 2016 · (Permalink)
Some friends and I discovered this in high school. For any triangle inscribed in a circle the number of degrees of any angle is equal to half the number of degrees along the circle between the two other points.
For triangle ABC inscribed in a circle: the number of degrees of angle A is equal to half the number of degrees along the circle between B and C.
On mobile otherwise would do the proper syntax. But basically 5 universal constants independently discovered are all related. Some extrapolate this as the god theorom as it just is too perfect. Certainly gives credit to the "universal theory of everything" in mathematics which is the holy grail today.
It was never surprising to me that there are an infinite number of prime numbers... But what IS interesting to me is that there are an infinite number of "prime pairs" - cases where n and n+2 are both prime.
Fourier wanted to prove this, but they didn't even have the terminology to describe what Carleson proved.
For non-math people, here is what it says. Take pretty much any function. Anything you could think of really. Then there it can be represented as an infinite series. If you throw a dart at the number line, the probability that the series converges at the point you hit is precisely 1. However, there are still points for which the series does not converge. But how could the dart not hit those? Take a course in measure theory.
Euler's Identity. It says the e to the power of (i*pi) equals -1. A number raised to the power of an imaginary numbed is somehow a real number. Blows my mind.
If you shuffle a deck of cards ten times it's probable that you have ordered the cards in a way that has never been done before... 52! Is a very large number.
In my math textbook, I came across the problem ABCD * 4 = DCBA. This problem intrigued me and a few hours later I constructed a formula to find all the possible 4 digit reversible numbers.
A = all natural numbers, 1<=A<=9
D = 10-A
B = A-1
C = D-1
ABCD*(D/A) = DCBA
Probably not that great but I thought it was interesting.
If you had a one in a million chance of winning a lottery ticket, and you bought a million lottery tickets. The probability that you have won is just 63.2%.
[deleted] · 1 points · Posted at 03:16:29 on February 14, 2016 · (Permalink)
6.0429639023813999128 is the highest number you can get too on a calculator, just 9.999999999E99, found it on my schools scientific calculators in middle school.
lank3y · 1 points · Posted at 03:34:47 on February 14, 2016 · (Permalink)
You just need a better calculator. Try a HP calculator that uses RPN and the upper limits are much much higher.
Math exists. We aren't really creating anything "new". Not since we came up with imaginary numbers. Since that point, we've just been discovering properties of numbers. All the complicated, calculus and weird theorms and shit? That's just...there. Its part of numbers.
one, two, three, four, five... Everything is already there, we're just discovering it.
I don't even think we made anything new with imaginary numbers either. The way we write them is new I guess, but they exist in nature. Like for AC current you need a system like imaginary numbers to represent the phase of the current
My teacher in high school showed us a really cool trick when you're multiplying two numbers together. For instance take 99×99. 99 is 1 away from 100, so 1+1 is 2. 100 - 2 = 98. Then 1 × 1 = 1, or 01. So 99 × 99 = 9801.
I think it works all the way down to 51 and there's a way to do the numbers below that but I can't quite remember
[deleted] · 1 points · Posted at 03:19:31 on February 14, 2016 · (Permalink)
Ask me for the statistics of the likelyhood of an event happening in the future.
CHTCB · 1 points · Posted at 03:20:51 on February 14, 2016 · (Permalink)
when will i get laid?
[deleted] · 1 points · Posted at 03:22:34 on February 14, 2016 · (Permalink)
It has to be the likelyhood of an event happening. It can't pinpoint a date but if you ask, "will I get laid over a certain time period" I can give you the likelyhood of it happening over that period of time.
CHTCB · 1 points · Posted at 03:34:14 on February 14, 2016 · (Permalink)
will i get laid tomorrow?
[deleted] · 1 points · Posted at 03:51:19 on February 14, 2016 · (Permalink)
There's a 50% chance you get laid tomorrow
lank3y · 1 points · Posted at 03:33:50 on February 14, 2016 · (Permalink)
soon.
However expressed in geological time the entire history of mankind is a blink in time. So "soon" is really relative.
sjryan · 1 points · Posted at 03:19:45 on February 14, 2016 · (Permalink)
There are hierarchies of infinity. For example, suppose that the universe is infinite and one out of every trillion atoms is the element gold. Then the number of atoms in the universe is infinite, then so is the number of gold atoms.
Likewise, suppose that we presume that one out of a hundred planets in the universe is earthlike, and that one out of a hundred of those planets has intelligent life. In an infinite universe, we might initially think there's infinite room because there are infinite planets. But the ratio works out to one hundred planets for every intelligent species. Draw the interstellar boundaries carefully, or there will be a lot of territorial wars.
For every n integer, there are an infinite number of rational numbers between n and n+1. Yet there are also an infinite number of integers! So we could say that there isn't just an infinity of rational numbers, there's an infinity of infinity of rational numbers.
I know it's a taylor series, I just don't have any intuitive understanding of how this equates to pi.
lank3y · 2 points · Posted at 04:01:15 on February 14, 2016 · (Permalink)
Let me be less of a jerk here if I can. You know that a taylor series can be a fairly good approxiamation to a function at a given value x. Let's say that we want a taylor approxiamation to tan(x) or even the inverse function arctan(x). If we both agree that arctan(1) = 0.7853981633974483096... then what we have here is arctan(1) = pi/4. Now just miltiply by four and you get pi. Consider that angles are calculated in radians around a cirlce and that a circle is a full 2 x pi radians. Then pi/2 would be the same as 90 degrees and pi/4 would be the same as 45 degrees. Visualize a right angle triangle inside a circle and it gets real clear real fast that the tangent of that angle is just 1. Anyways, a taylor polynomial expression with infinite terms will be just exactly what you posted. Multiply by four and you get pi. Easy?
lank3y · 1 points · Posted at 03:50:43 on February 14, 2016 · (Permalink)
taedrin · 1 points · Posted at 03:21:14 on February 14, 2016 · (Permalink)
The maximum number of moves needed to solve ANY (legal) configuration of the Rubik's Cube is 20. This is called "God's Number". This fact was not discovered until 2010.
"Irrational numbers" do not have an exact value: they have an endless set of digits to the right of the decimal point.
Pi, approximately 3.14159 ... Is irrational, and so is "e", which appears very often in mathematics; its value is about 2.718 ... (the three dots mean "and so on").
i is often the symbol for the square root of -1; it's called an "imaginary" number because in elementary algebra, negative numbers can't have square roots.
So: three numbers with apparently no common features. But there is an equation called "Euler's identity" which says that
e ^ (i * pi) = -1;
Read aloud, this says "e raised to the power of i times pi equals -1".
I was astonished when I first read this, and more so when I could prove it mathematically.
Just because a number has an endless amount of decimals doesn't mean it hasn't got an exact value (whatever that's supposed to mean). Pi, e, sqrt(2), etc. do have exact values. As do rational numbers with endless decimal expansions such as 1/3.
lank3y · 1 points · Posted at 03:31:47 on February 14, 2016 · (Permalink)
My birthdy represented by 4 numbers divided by 2 is my sisters birthday. My birthday is April 3rd 1996 so 4396, and my sisters is February 1st 1998 which is 2198
[deleted] · 1 points · Posted at 03:24:39 on February 14, 2016 · (Permalink)
[deleted]
lank3y · 1 points · Posted at 03:30:15 on February 14, 2016 · (Permalink)
prove it .. however you need to post a youtube video of you doing the recital .. no need for much in the video but you do need to recite the digits in a video. Also, yes, that is geeky and cool. In my world it is.
To help with multiplying single digits by nine, put up all ten of your fingers and put which number you're multiplying by nine. The remaining fingers on the left are your tens and the remaining on the right are your ones.
Pretty much nothing compared to everyone else's, but it blew my mind in third grade.
I don't know if anyone already said this one, but I couldn't find it:
You can multiply
15 x 15,
25 x 25,
35 x 35
and so forth quickly. Any double digit number that ends in 5 by itself quickly by taking the first digit multiplying it by itself plus one and putting 25 on the end. For example:
45 x 45
4 x 5 = 20
Tack 25 on the end is 2025
45 x 45 = 2025.
Another example to solidify:
85 x 85
8 x 9 = 72
85 x 85 = 7225
Works for 15 multiplied by itself up to 95. This one is easy to teach to kids and gets them excited about learning their multiplication facts.
I'm a little late to the party, but if you had a circle the size of the observable universe, and you wanted to compute its circumference with an accuracy equal to the size of a proton, the number of digits of pi that you'd need is only 43.
Either mathematicians are totally crazy for trying to find more and more digits of pi, or they're planning ahead for a time when the survival of humanity will depend on the ability to construct extremely large, accurate circles.
[deleted] · 1 points · Posted at 03:27:49 on February 14, 2016 · (Permalink)
I fell like the internet is the only place math can be "cool".
The pythagorean theorem works for arbitrary dimensional objects. Suppose I have n-dimensional space, and in that space I make a k-dimensional parallelogram. If I project that parallelogram onto one of the k-dimensional coordinate planes i n-dimensional space, that projection has a k-dimensional area. If you sum the squares of all of the k-dimensional areas of these k-dimensional projections and then take the square root, you get the k-dimensional area of the original parallelogram.
If a differential forms is closed, meaning its derivative is zero, then it must be exact, meaning that it is the derivative of some other differential form. However, this is only true on a space with no holes. If you poke a single hole in space, then there is one equivalence class of forms which is closed but not exact. This form is essentially the electric field of a point charge.
[deleted] · 1 points · Posted at 03:31:24 on February 14, 2016 · (Permalink)
The most efficient base for expressing numbers is 3 (actually, you need at least e numbers, since e is about 2.7..., you need to round up to 3). And Donald Knuth has written balanced ternary "the prettiest number system of all".
I cannot confirm this, but I know I've read it from more than a couple sources, but it may (or may not) be true that the number "Googol" (a 10100) is SO large that there's not even estimated to be a googol atoms in the ENTIRE universe. I think the estimate is somewhere around 1067 atoms; but, I'm sure I'm off by a few orders of magnitude....
Eleven Plus Two is an anagram of One Plus Twelve, and they both equal thirteen.
[deleted] · 1 points · Posted at 03:35:17 on February 14, 2016 · (Permalink)
[deleted]
kerry63 · 1 points · Posted at 03:45:12 on February 14, 2016 · (Permalink)
I learned this in 5th grade, but with a slightly different approach. I was taught to take 25 x 25 and raise one of the numbers to a 3 and cross multiply. So 3 x 2 = 6 and then add 25 since it was the same numbers.
If you wanted to multiply 25 x 35 you would raise the higher of the two. So it would be 4 x 2 and since the two were different you would add 75. Therefore 25 x 35 would be 875.
jeffl97 · 1 points · Posted at 03:36:50 on February 14, 2016 · (Permalink)
One time I was just messing around with numbers and I found out this interesting thing with 9's. For instance
9 X 8 = 72.
If you put a 9 after the number you're multiplying by, and then subtract it from the addition of 9 to that same number you'll get the right answer. Ie: 89 - 17 = 72.
100 X 9 = 900 or 1009 - 109 = 900
12 X 9 = 108 or 129 - 21 = 108.
145 X 9 = 1305 or 1459 - 154 = 1305 etc.
[deleted] · 1 points · Posted at 03:37:20 on February 14, 2016 · (Permalink)
I like the way cones can be sliced up to reveal hyperbolas, parabolas, circles, ellipses, lines, or a single point.
When I was in the 8th grade I noticed that consecutive squares equal the sum of consecutive odd integers. It's simple but somehow surprisingly impressive.
Due to the Infinite Probability Theorem, you can put in laundry into your dryer and there is a chance that it will come out perfectly folded. Though there's a 100% chance my mom folds it if it doesn't.
Multiplication by 11. For a two digit number, add the two digits and stick it in the middle.
So for 43 x 11: 4+3=7, 437
62 x 11: 6+2=8, 682
84 x 11: 8+4 =12. The tens digit carries over into the next column, giving us 924
You can take this on to higher digit numbers, too. Triple digit multiplied by 11, add the left and middle, the right and middle, and stick those numbers between the first and last digit.
123 x 11: 1+2=3, 2+3=5, therefore 1353
438 x 11: 4+3=7, 3+8=11 (tens carry over), therefore 4818
You can actually keep going - with a number of any size, just add the first and second, the second and third, etc. etc., then put those digits in the order you calculated them between the first and last digits.
Gabriel's Horn. Basically, if you take the improper integral from 1 to infinity of the graph of 1/x and rotate it about the x-axis, you get a shape with an infinite surface area but a finite volume.
4Sken · 1 points · Posted at 03:44:17 on February 14, 2016 · (Permalink)
(753+951)-852=852
Also works backwards;
(159+357)-258=258
Here's a fun one that you've probably heard before, but never seen a simple explanation for. There are an infinite number of infinities that are all different sizes.
To be formal, there are really an infinite number of infinite sets, which all have different cardinality. If you're unfamiliar, cardinality is just the word we use to describe how many elements are in a set, like {banana, apple, pear} is composed of the elements: banana and apple and pear. We say that set has cardinality 3. Now here's the fun part. There are naturally sets with infinite cardinality. Like the natural numbers, N. N is {1,2,3,4...so on}. We say N is countably infinite. Sets larger than N are not countably infinite. This generally comes across as weird, cause intuition tells us that infinity is infinity right. Well the most interesting parts of math are where intuition fails and the truth has to be hunted down.
Enter the power set denoted P (S) where S is a set. The power set returns the set of all subsets of S. A subset is exactly what it sounds like, it's a set made up only of elements in S. For finite sets it goes like this.
S={1,2,3}
P (S)={(1,2,3), (1,2), (1,3), (2,3), (1), (2),(3), and the empty set, which has no elements}
Now the power set has a neat property for set S, P (S) will have greater cardinality than S. And that's all she wrote. The dominoes are starting to fall like a house of cards, checkmate. Take the set N, we've discussed it, it has infinite cardinality. P (N) has greater cardinality than N. P (P (N))has even greater cardinality than that. Every time you apply the power set to your infinite set, the result has greater cardinality and is still infinite. And from here we have an infinite set of different infinities.
folding a piece of 42 times gets you to the moon.
103 times becomes as wide as the universe.
goofy91 · 1 points · Posted at 03:51:57 on February 14, 2016 · (Permalink)*
Graham's number is a number so large that its ordinary digital representation cannot be contained in the observable universe (assuming that each digit occupies one Planck volume, i.e. the smallest measurable space). Also, its last rightmost decimal digit is 7.
The sum of odd numbers gives you the list of perfect squares.
1= 1
+3=4
+5=9
+7=16
Etc
remi19 · 1 points · Posted at 03:53:54 on February 14, 2016 · (Permalink)
Federman points out in his book, the God particle, that 137:
"contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck's constant). Scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of Planck’s constant may be, will all come up with 137, because it is a pure number. Lederman recalled that Richard Feynman had even suggested that all physicists put a sign in their offices with the number 137 to remind them of just how much they don’t know.
snaky69 · 1 points · Posted at 03:53:55 on February 14, 2016 · (Permalink)
41 is the beginning of a long sequence of prime numbers, where you add consecutive even numbers.
41, 43, 47, 53, 61, 71, 83, ... and many more are all prime. I think the chain is broken around 650.
meodd8 · 1 points · Posted at 03:54:34 on February 14, 2016 · (Permalink)
Infinity of an imaginary number actually has a real value.
Vortico · 1 points · Posted at 07:23:47 on February 14, 2016 · (Permalink)
If you curcumscribe (draw a circle around, touching the corners of, but not intersecting) a perfect hexagon, the radius of the circle is the side length of the hexagon.
Hold your hands up in front of you and whatever you're multiplying 9 by, put that finger down and you have your answer.
E.g 9x3, you put down your 3rd finger from the left, so you now have 2 fingers on the left, and 7 fingers on the right, so those are your digits, 2 and 7 - 27.
I'm going to reverse your question on you. You tell me the mathmatical fact. ~ Three people check into a motel. The manager says that will be $30. Each person hands over $10 and the manager tells them they have room 123 for the night. They go to their room and about an hour later the manager says "damn the rooms are $25 tonight". He calles in the bellboy and gives him $5 to return to the people in room 123. On the way the bellboy thinks to himself "$5 is near impossible to divide amongst 3 people so I will keep $2 and give them each $1." That's what he does and the people thank him. "Thanks" Now each person paid $9, for a total of $27 and the bellboy has $2 for a total of $29 but they paid $30. So where is the missing $1 ?
OK, here is the coolest mathematical fact I know of. If you counted one dollar every second for a $1 million it would take you roughly 11 days. Doable. If you did that with $1 billion it would take you roughly 37 years. Nopeble.
There's no such thing as a "knot" in four dimensional space. That is, no matter how you arrange loop of string in four dimensional space, it can be untied completely by pulling on it. However, there is a way to "knot" a sphere in four dimensional space.
Vortico · 1 points · Posted at 07:07:58 on February 14, 2016 · (Permalink)
For those interested, a 2-knot is an embedding of S2 into R4 (or S4 ), and their behavior is even more eccentric than classical knots, which are themselves surprisingly difficult to classify.
Lots of number theory on here, which is very cool, but if we think of cool as extremely counterintuitive, I am always reminded of the woefully incorrect statement that is repeated by intelligent but mathematically disinclined individuals: "you can't prove a negative."
That idea of course has no basis in fact. Any statement can be thought of as a negative of its own negative (for example "2+2 equals 4" can be thought of as "2+2 doesn't not equal 4", but that's just to demonstrate that there is nothing uniquely special about a "negative").
I understand that by "proving a negative", most people mean "proving that something does not exist." That is admittedly hard, because one must consider all the possible ways that something can exist and disprove each one of them. Sometimes the mathematics works out so that such a thing is possible.
More interestingly, one of the most significant cases of "proving a negative" in mathematics is the proof that while a polynomial of the 2nd, 3rd and 4th degree can be solved in a deterministic way, polynomials of 5th degree or more cannot be solved. This was proved by Evariste Galois. Furthermore and far more interestingly, it was based on writings that he developed throughout his 20-year lifetime, the last of which were written late at night on the 30th of May 1832, the night before he was to die in a duel over a woman. Part of his last writings was a plea that his works were extremely significant and should be reviewed by famous mathematicians of the time.
Of course, he was right, and the branch of mathematics that he invented (all by the age of 20 mind you) is one of the few that is still studied to this day.
Your head physically can not store enough information in your head to process graham's number (the largest number ever used in a proof). This is because a black hole the size of your head can't even store that much information.
There's a law which states that in the numerical representation of many things such as the constants of nature, lengths of rivers, heights of buildings or even tax returns, the leading digit is more likely to be a small number. Benford's Law.
Not really a fact, but relevant because Valentines Day. Put r=a(1-cos(theta)) into a graphing calculator (in polar mode). Hand that calculator to your crush/SO/whatever. You're welcome.
Also, there are functions like the Weierstrass function that are continuous everywhere, but differentiable nowhere. Because fuck logic
SPQC · 1 points · Posted at 04:03:33 on February 14, 2016 · (Permalink)
All the numbers from 1 to 100 add up to 5050.
dittbub · 1 points · Posted at 04:03:43 on February 14, 2016 · (Permalink)
0.999... Is exactly equal to 1
mallad · 1 points · Posted at 04:03:51 on February 14, 2016 · (Permalink)
In English, four is the magic number.
If you spell out any number and count the number of letters in it, then continue that pattern until the number doesn't change, you always land on four.
For example, ten is 3 letters. Three is 5 letters. Five is 4 letters. Four is 4 letters because four is the magic number.
It's a fun little game to play with people who don't know it - tell them to name any number, then count the letters in your head and tell them the results. IE - "ten is three, three is five, five is four and four's the magic number" and then have them try another number until they figure out the rule.
If you add 1234567890+1234567890 and keep pressing equals on the calculator, you get 11,111,111,010 22,222,222,020 33,333,333,030 44,444,444,040 55,555,555,050 66,666,666,060 77,777,777,070 88,888,888,080 99,999,999,090 eventually
I just thought it was cool when 5th grade self found that out by myself.
Sinkaix · 1 points · Posted at 04:04:36 on February 14, 2016 · (Permalink)
How 0.999999 = 1
0.99999 = X
9.99999 = 10X
9.00000 = 9X
1.00000 = X
[deleted] · 1 points · Posted at 04:04:48 on February 14, 2016 · (Permalink)
Every compact orientable 2-manifold (surface) of genus (# of holes in surface) g>=1 is homeomorphic (can be deformed into) the connected sum of g tori.
[deleted] · 1 points · Posted at 04:06:02 on February 14, 2016 · (Permalink)
3* 0,33 = 1
won
[deleted] · 1 points · Posted at 04:06:14 on February 14, 2016 · (Permalink)
ei*pi=-1
For real.
em3am · 1 points · Posted at 04:06:17 on February 14, 2016 · (Permalink)
If we try and communicate with extra-terrestrial aliens by using umber systems, are we prepared if their number system is based on e. It is the basis of many, many, many natural phenomena?
You have 23 random people in a room.
More than 50% of the time, two of them will share a birth date (month and day, not year)
70 people in a room? 99.9% chance that at least two of them share a birthdate.
If someone gave Jesus Christ $1000 every 15 minutes from the day he was born until today, he still wouldn't have as much money as Bill Gates. $1000 x 4 x 24 x 365.25 x 2016 = $70.6B. Bill Gates net worth = $79.2B
Loyheta · 1 points · Posted at 04:09:49 on February 14, 2016 · (Permalink)
A square number plus the square root plus the square root plus 1 equals the next square number. I have no idea how else to explain it. I was just sitting in geometry freshman year in High School and figured out the pattern. I've never read this pattern or seen it anywhere so its kind of fun figuring this stuff out on your own.
22 = 4
2+3+4 = 9
32 = 9
3+4 = 7
9+7 = 16
42 = 16
Another example maybe easier to understand?
62 = 36
6+7+36 = 49
72 = 49
I guess the equation would be X2 + 2X+1 = (X + 1)2
Imagine square numbers as actually squares on a grid. So, 4 is this:
1
2
3
4
and 9 looks like this:
1
2
3
4
5
6
7
8
9
As you can see, to go from 4 to 9, you have to add 5 square units. Two on the side and three on the bottom, or some combination thereof. Imagine going from 9 to 16, and you'll see you need to add 4 on one side and 5 on the other.
There have to be an infinite number of prime numbers. Why?
Because if there were a finite number of them, you could multiple them all together, add 1, and get a new prime number that wasn't part of the original count.
Here is the ELI5 comment where I first saw this and it exploded my brain. (Props to /u/Chel_of_the_sea)
There is a proof of the infinitude of primes that goes something like:
pi/4 = (3/4)(5/4)(7/8)(11/12)(13/12)(17/16)(19/20)... etc where the numerators of the product are prime numbers and the denominators are the nearest multiple of 4 to the numerator. It equals exactly pi/4, which is kind of interesting.
Any sufficiently strong formal system (e.g., arithmetic) is incomplete, if it is consistent. Basically, Godel proved that there are some mathematical truths which are unproveable.
Conditionally convergent infinite series (series which converge when the terms alternate in sign, but are divergent when each term is made positive) can have the order of summation rearranged so that they are equal to any number.
e.g. the series 1 + 1/2 + 1/3 + 1/4 + ... is divergent.
The series 1 - 1/2 + 1/3 - 1/4 + ... converges to log(2) = 0.693...
However if we rearrange the exact same set of numbers:
1 - 1/2 -1/4 + 1/3 - 1/6 -1/8 + 1/5 - 1/10 -1/12 +...
But we can group together the first two numbers out of each group of 3:
= 1 - 1/2 -1/4 + 1/3 - 1/6 -1/8 + 1/5 - 1/10 - 1/12 +...
= 1/2 -1/4 + 1/6 -1/8 + 1/10 - 1/12 +...
= 1/2*(1 - 1/2 + 1/3 -1/4 + 1/5 - 1/6 +...)
= log(2)/2
Half the sum of the first ordering (!)
[deleted] · 1 points · Posted at 04:11:54 on February 14, 2016 · (Permalink)
Hold up ten fingers. For 2 * 9 put down your second finger from the left. You're left with 1 finger up on the left and 8 fingers up on the right (18).
5 x 9 up down your fifth finger from the left. You're left with 4 on the left side and 5 on the right (45).
FowD9 · 1 points · Posted at 04:12:44 on February 14, 2016 · (Permalink)*
a googol is already a pretty hard to understand large number: 10100 that's 1 followed by 100 zeros.
A googolplex is almost incomprehensible with how big it actually is: 10googol or 1010100. that's 1 followed by a googol zeros
just to attempt to put it into perspective, if the universe were 1010100 meters long there would be EXACT clones of you.
to further explain this, say in a 1x1 meter cube, there is a finite number of possibilities in which particles (electrons/protons) can be arranged. and while you might think that the number of combinations particles can be arranged in a 1x1 meter cube is almost uncomprehensible. there will be so many instances of that 1x1 meter cube in a googolplex meter long universe, that there will be multiple EXACT copies of that 1x1 meter cube.
so, if you're standing in that 10x10 meter cube, with particles aligned in a specific way that make you, you. A googolplex meter universe is so large, that there will be multiple copies of you in that universe
another example on just how ridiculously large this number is, if you were to take every single particle (electrons/protons, smaller than atoms, it's what atoms are made of) in the observable universe and use those particles to each represent a zero. you wouldn't have enough zeros to write out the number for googolplex (1010100 )
One of mine is that 10/81 is 0.123456790123456790..... which can be written as 1/10 + 2/102 + 3/103 ... + 8/108 .... + n/10n most people assume that the 8/108 term isn't part of the sequence because there is no 8 in 10/81 but this is just the 1 carried over from the 10/10n is 10/1010 = 1/109 which can be easily added to 9/109 to make 10/109 = 1/108 which adds to 8/108 making it 9/108
0.1234567
0.00000008
0.000000009
0.0000000010
0.00000000011
which makes the digit 8 not appear in the decimal despite being in the squence
Sorry for shit format don't often post but nothing like some maths to get me going
If you need to multiply any double-digit by 11, just add those two numbers together and stick the middle number in the middle... So, 11 x XY = X(X+Y)Y; or 11 x 23 = 253!
The sum of ALL positive integers equals -1/12. There is a great numberphile video on this and it's absolute none sense but apparently mathematically accurate.
The golden ratio is a good approximation of the conversion factor between miles and kilometers. This makes the Fibonacci sequence also a good approximation when converting between miles and kilometers (e.g., 8 miles is approximately 13 kilometers).
MrMi10s · 1 points · Posted at 04:17:42 on February 14, 2016 · (Permalink)
This is going to get buried but it's super useful.
If you want to divide a number by 5, first multiply it by 2 and then divide it by 10.
For example we have 37.
37x2=74
74÷10=7.4
7.4 × 5 = 35
Posta92 · 1 points · Posted at 04:18:09 on February 14, 2016 · (Permalink)
In a room of just 23 people there’s a 50-50 chance of two people having the same birthday.
I found a cool pattern linking Pascal's and Euler's triangles, and exponents. I hadn't even heard of Euler's Triangle when I found it. First, overlay Pascal's Triangle with Euler's Triangle, rotated 60° with the peak resting on the second column (the consecutive integers). Multiply each number in Euler's by the corresponding number in Pascal's. Add the numbers in Euler's rows. Example: place the top 1 (Euler) over 5 (Pascal). The next row (11) covers (10 15). Multiply by 1, add them to get 25. Two consecutive triangle numbers make a square; not the cool part. The next row (1 4 1) covers (10 20 35). Multiply to get 10+80+35, or 125. Likewise, (1 11 11 1) over (5 15 35 70) yields 5+165+385+70, or 625. It worked with every number I tried, but I have no idea how to prove that it's always true.
[deleted] · 1 points · Posted at 04:20:18 on February 14, 2016 · (Permalink)
This is more of a science fact than a math fact, but there are over 80 trillion possible DNA combinations as a result of two human gametes creating a fertilized egg.
That's what my genetics professor at ASU said anyway.
Graham's number is too big to grasp and would cause your head to collapse into a black hole
AresIII · 1 points · Posted at 04:21:40 on February 14, 2016 · (Permalink)
The Golden Ratio
The Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form, it looks like this:
a/b = (a+b)/a = 1.6180339887498948420 …
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
You can prove mathematically that given infinite time, a drunk ant is guaranteed to visit the same Cartesian coordinates (X, Y) more than once, but a drunk bird is not guaranteed to hit the same coordinates (X, Y, Z) more than once.
"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?"
The answer to this question is that Yes, it certainly is to my advantage to switch my choice. :)
Indeed, nearly 1,000 people with PhDs got the answer to this question/problem wrong. :(
Any whole number that that is evenly divisble by 3, when reversed, is still evenly divisible by 3.
Don't know what principle it is, who first figured it out, or what it's good for. All I know is that I figured it out one day when I looked at the thermostate at work and had a bit of an apple to the head moment.
I believe it also applies to the number 9.
If anyone knows about this, or if I'm actually totally wrong, comment please.
4011 · 1 points · Posted at 04:32:50 on February 14, 2016 · (Permalink)
Any time the sum of digits in a number add up to 3, it will be divisible by 3. So that means that 234, 342, 432, etc. will all be divisible by 3. And if the number is even, it's also divisible by 6.
The sum of the digits of all multiples of 9 add up to 9 or one of its multiples (which in turn add up to 9). It's possible to know if a number is evenly divisible by 9 by adding the digits up (and then adding the digits of the sum up) and seeing if you get 9.
[deleted] · 1 points · Posted at 04:30:38 on February 14, 2016 · (Permalink)
A father dies leaving instructions that his 17 camels are to be split up between his 3 sons as follows -
half the camels are to go to the eldest son
a third of the camels are to go to the middle son
and a ninth of the camels are to go to the youngest son
Failing to think of a way of carrying out their father's wishes, they decided to seek help. So they sent a message across the desert to their uncle, who though poor was considered to be wise.
A month later, up rode their uncle on his grotty old camel. After he'd had a rest and something to eat, they explained their problem to him.
"Tell you what", he said, "I'll lend you my camel, then you'll have 18, and you should be able to divide them up without difficulty."
So the eldest son chose his 9 camels from the flock, the middle son chose his 6 camels, and the youngest son chose his 2 camels. Uncle then got back on his camel (which no-one had chosen because it was old and grotty) and rode back home across the desert (no doubt muttering to himself about the failings of the younger generation).
I will never need to know it for anything I ever do in real life, and yet for some reason I'm required to take algebra (which I loathe and can't do) for my degree! Yay! Such a cool math fact.
Vortico · 2 points · Posted at 06:56:41 on February 14, 2016 · (Permalink)
I am a mathematician but empathize with you. I was required to take a few literature, philosophy, psychology, history, and economics classes in college, and while they were fun at times, I feel my time could have better been spent on courses directly related to my specialization.
e is the natural growth rate of things: ~ 2.71828 It's fundamental in chemistry, finance, statistics, you name it. It's part of how the world works.
i is equivalent to √-1, the fundamental imaginary number. A place holder you could say, for a thing that doesn't exist along the standard real number line.
π = 3.14159... You know, pi. Everyone likes pi. Has to do with circles and stuff.
Three numbers fundamental to our core understanding, two irrational, one imaginary, seemingly unrelated and from three different branches of math. Except that...
eiπ = -1
Whoa.
romxza · 1 points · Posted at 04:38:40 on February 14, 2016 · (Permalink)
Allow me to nitpick lol. That is a common misconception... e isn't the "natural growth rate of things". ekx is how we write growth rates when the growth rate is proportional to the current value, i.e. "exponential growth". But k here can stand for any rational number, so in effect the growth is ax for some rational number a. Using base e as a base of the exponent is just convenient because the constant of proportionality in the growth rate of ex is precisely one.
jdylopa · 1 points · Posted at 04:32:38 on February 14, 2016 · (Permalink)
I'm very late to the party, so not many people will see this, but here goes:
Not all "infinities" are equal, but there are the same amount of integers (whole numbers both positive and negative) as there are natural numbers (whole numbers starting at 0 or 1 depending on the book). This goes for a lot of things (for instance, the set of all integers also has the same amount of numbers as the set of all even numbers, or the set of all rational numbers...infinite cardinality can be a weird thing).
[deleted] · 1 points · Posted at 04:33:23 on February 14, 2016 · (Permalink)
The 9 times table trick, it's pretty hard to explain
9x1=9
9x2=18 9-1=8 add the 1 to the 10 digit
9*3= 27 8-1=7 add the 1 to the 2 and you get 3
one of the fundamental "proofs" in quantum field theory, you can show that the sum of all positive integers (1+2+3+4+5...) is -1/12. It's insane: https://www.youtube.com/watch?v=w-I6XTVZXww
The number sets we know today were created on the basis of an empty set. Such as:
Let 0 denote the empty set then:
1 = {0}
2 = {{0},0} and so on.
Our numbers were created from nothing, much like everything else we know and love.
Mine is a bit of a word problem.
This is a mathematical equation that proves that girls are evil.
Several variables in this equation.
G=Girls
T=Time
M=Money
E=Evil
Girls require time and money.
G= T×M
Everyone knows time is money
T=M
G= M×M or M2
Money is the root of all Evil
M= square root (E)
Square both sides.
M2 = E
If G=M2
Then G=E
Girls must be evil.
Rick0r · 1 points · Posted at 04:39:46 on February 14, 2016 · (Permalink)
as numbers guy and, coincidentally, an accountant, bookkeeper is the only word with 3 consecutive duplicate letters. Not very "mathematical" but it might help you out in jeopardy.
ythl · 1 points · Posted at 04:41:09 on February 14, 2016 · (Permalink)
One of the consequences of the second law of thermodynamics is that a certain amount of energy is necessary to represent information. To record a single bit by changing the state of a system requires an amount of energy no less than kT, where T is the absolute temperature of the system and k is the Boltzman constant. (Stick with me; the physics lesson is almost over.)
Given that k = 1.38×10-16 erg/°Kelvin, and that the ambient temperature of the universe is 3.2°Kelvin, an ideal computer running at 3.2°K would consume 4.4×10-16 ergs every time it set or cleared a bit. To run a computer any colder than the cosmic background radiation would require extra energy to run a heat pump.
Now, the annual energy output of our sun is about 1.21×1041 ergs. This is enough to power about 2.7×1056 single bit changes on our ideal computer; enough state changes to put a 187-bit counter through all its values. If we built a Dyson sphere around the sun and captured all its energy for 32 years, without any loss, we could power a computer to count up to 2192. Of course, it wouldn't have the energy left over to perform any useful calculations with this counter.
But that's just one star, and a measly one at that. A typical supernova releases something like 1051 ergs. (About a hundred times as much energy would be released in the form of neutrinos, but let them go for now.) If all of this energy could be channeled into a single orgy of computation, a 219-bit counter could be cycled through all of its states.
These numbers have nothing to do with the technology of the devices; they are the maximums that thermodynamics will allow. And they strongly imply that brute-force attacks against 256-bit keys will be infeasible until computers are built from something other than matter and occupy something other than space.
Isturma · 1 points · Posted at 04:42:01 on February 14, 2016 · (Permalink)
I owe Day [9] for teaching me this exists, but I've learned more about it since then - Graham's number. It's the largest possible number to a simple theorem, but it's so impossibly large that it has more digits than there are stars in the observable universe.
The proof is ridiculously easy, even if the statement is true, I find it very hard to wrap my head around this simple fact. There are infinite number of primes, no matter how many of them you find, you will keep finding them
The smallest infinity is the set of whole numbers going upwards forever. It's called accountable infinity. The set of all real numbers (the number line) is bigger than that. You can make even larger infinities by combining infinite sets in a certain way. It's called a power set. All of this was first discovered by Cantor. He went insane after discovering it because mathematicians during his time didn't accept it, even though he had solid proof of what he was saying. There is a way of determining the relative size of different sets (finite or infinite). You can say that two sets are the same size if you can make a 1 to 1 correspondence between all the elements of the two sets and there are none left over. One is larger than the other if there are some elements left over in the larger set after you have accounted for all the elements in the smaller set.
There are so many different permutations (orderings) a 52 card playing deck that a) it's extremely unlikely that a sufficiently shuffled deck has ever resulted in the same one in human history and b) they out number the stars in the observable universe.
You know they say that 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%, AT BEST, at beat me. Then you add Kurt Angle to the mix, your chances of winning drastic go down. See the 3 way, at Sacrifice, you got a 33 1/3 chance of winning, but I, I got a 66 and 2/3 chance of winning, because Kurt Angle KNOWS he can't beat me and he's not even gonna try!
So Samoa Joe, you take your 33 1/3 chance, minus my 25% chance and you got an 8 1/3 chance of winning at Sacrifice. But then you take my 75% chance of winning, if we was to go one on one, and then add 66 2/3 per cents, I got 141 2/3 chance of winning at Sacrifice. See Joe, the numbers don't lie, and they spell disaster for you at Sacrifice.
He was nominated for a Fields Medal for his work in probability theory.
Not the coolest but pretty neat. The 9 times tables are pretty easy to remember. If you're wondering if your answer is right, just add up the answer's digits and if you get 9 or a number divisible by 9 then you're probably on the right track.
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)
...
9 x 37 = 333 (3 + 3 + 3 = 9)
...
9 x 237 = 2,133 (2 + 1 + 3 + 3 = 9)
...
9 x 3586 = 32,274 (3 + 2 + 2 + 7 + 4 = 18; 18 is divisible by 9)
Nine is also pretty cool when dividing!
9 / 9 = 1
8 / 9 = 0.8888_
7 / 9 = 0.7777_
6 / 9 = 0.6666_
I'm sure you see what I'm getting at.
Here's one more cool "9 fact". If you multiply anything by a number which each digit is 9 the answer is very simple.
9 x 999 = 8991 (9 x 9 = 81, add the 2 remaining 9s in the middle of the 81)
7 x 999,999 = 6,999,993 (7 x 9 = 63, add the 5 remaining 9s in the middle of the 63)
4 x 999,999,999,999,999 = 3,999,999,999,999,996 (4 x 9 = 36, add the 14 remaining 9s in the middle of the 36)
I believe that part only works until 10 though. For instance:
21 x 9,999 = 209,979 (21 x 9 = 189; same procedure doesn't work)
I always thought it was interesting that pi is calculated to such extreme precision as the infinite sum (from n=0) of 4*(-1)n /(2n+1). Learned it in AP Calc, still fascinated by it. Also, makes integration and summation a whole lot easier than if we didn't have a pi constant.
[deleted] · 1 points · Posted at 04:53:34 on February 14, 2016 · (Permalink)
There is no largest number expressible in nine words because it would be smaller than the largest number expressible in nine words plus one.
ksiyoto · 1 points · Posted at 04:53:39 on February 14, 2016 · (Permalink)
If you have two fractions with different denominators, and you want to find a fraction in between the two, you can just add the numerators together and the denominators together.
Example: 5/7 and 64/73---> 69/80 would be in between those two.
I'm pretty late so I bet this will get buried, but I think it's cool how the different between subsequent perfect squares can be modeled by the equation 3+2n.
For example, diff of 1 and 4 is 3
4 and 9 is 5
9 and 16 is 7
And so on and so forth... Idk maybe that a widely known thing but it's just something I realized awhile back
The derivative of ex = ex. I don't feel like typing out the proof for it because I'm on mobile (also why the formatting is weird) but it's super cool that the derivative, which observes the slope of a functuon, is itself. So, if you were to map out the change in the slope of it, you would just graph it again. This blew my mind when I first learned it.
11:15, restate my assumptions: 1. Mathematics is the language of nature. 2. Everything around us can be represented and understood through numbers. 3. If you graph these numbers, patterns emerge. Therefore: There are patterns everywhere in nature.
Russian hand method to multiply 9 by [1-9]. Put out your hands so you see all 10 fingers. To multiply 9 by 2 put down your ring finger on your left hand (basically count from the left counting each finger as 1 spot). To the left of the ring finger is one finger so the 10's place is one. To the right of the downed finger are eight fingers to the 1's place is 8. 9 * 2 = 18. For 9 x 7 put out your hands and count your fingers from the left until you reach the 7th one (the right index finger). Put that finger down. To the left of the downed finger are 6 fingers so the 10's spot is 6. To the right of the downed finger are 3 fingers so the 1's spot is 3. 9 * 7 = 63.
Vortico · 1 points · Posted at 06:35:51 on February 14, 2016 · (Permalink)
Well, it's a natural extension of repeated multiplication of the first n whole numbers. 1 is the multiplicative identity, so an empty product should definitely be 1 by convention. This makes computing binomials and stuff a lot cleaner.
I'm not sure if this counts as math but there's a common misconception that cycling anything that can only yield 2 possible answers an even number of times will always result in a 50/50 draw, when in reality there's just as much of a chance for the results to be 100/0 or 60/40 as for the latter.
An extraordinarily large amount of people I ask about this seem to think that statistics such as those are set in stone.
crusoe · 1 points · Posted at 05:36:11 on February 14, 2016 · (Permalink)
Right. But the chance ifa sequence diverging more and more from average as it co tinues becomes less and likely. Regression to the mean.
True. But no matter how you look at it, flipping a coin 10 times doesn't guarantee 5 heads and 5 tails. Then again, statistics rarely guarantee anything.
Vortico · 1 points · Posted at 06:31:44 on February 14, 2016 · (Permalink)
What do you mean? There are transfinite sequences, but when you hear the word "sequences" you usually mean a countably long list, which are all the same size.
I mean that an infinite sequence of whole numbers will be larger than an infinite sequence of odd numbers, but theyre still both infinite
Vortico · 1 points · Posted at 18:43:39 on February 14, 2016 · (Permalink)
The two sequences you gave are actually the same size since there is a bijection between the whole numbers and odd numbers. To me, this is perhaps more bizarre than infinite sequences having different sizes.
Vortico · 1 points · Posted at 20:29:08 on February 14, 2016 · (Permalink)
You can only put a finite number of elements between your first ellipsis. Otherwise, since all elements in a sequence have an index, what index would the second 1 be? (It must be an integer.) Since there is a one-to-one association between the elements in a sequence and their index, all sequences have the same number of elements as the set of positive integers.
Vortico · 1 points · Posted at 00:17:45 on February 15, 2016 · (Permalink)
I wasn't either. You've given a sequence that you claim to be larger than the sequence of positive integers, by stating that there are an infinite number of elements, and then 1, 3, 5, etc. You can't do that as explained above, so your sequence is ill-defined.
[deleted] · 1 points · Posted at 05:07:30 on February 14, 2016 · (Permalink)
The Banach-Tarski Paradox.
Simply put: given any object, you can take something out of that object, and still have the original with something left over. Vsauce did a really cool video on it a while back.
crusoe · 1 points · Posted at 05:34:40 on February 14, 2016 · (Permalink)
This only works for infinitely fine sets. Real matter is made of atoms so you can't use this to duplicate matter...
if you sum all the numbers to 10000 you get 50005000
every time you add a zero add a zero :)
matadata · 1 points · Posted at 05:08:13 on February 14, 2016 · (Permalink)*
Everything travels through space-time at the speed of c (299 792 458 m/s), yet quantum mechanics allows 2 particles to instantly react to each other from any distance.
I remember hearing you experience something that is "One in a million" type experience once every 3 months on average.
_Psyki · 1 points · Posted at 05:09:31 on February 14, 2016 · (Permalink)
Fermat's Last Theorem, one of the most famous problems in maths that took hundreds of years to solve, was one of many scribblings in a textbook by French Mathematician Pierre de Fermat. He proposed his theorem not long before he died, along with a line to the effect of "I have a wonderful proof, but I do not have enough space to write it down". I like to think that he never even thought that he had proven his conjecture and was just an early troll.
10028ar · 1 points · Posted at 05:09:42 on February 14, 2016 · (Permalink)
ex.: 69.. 6+9=15.. 1+5=6.. 15-6=9.
or
77. 7+7=14.. 1+4=5.. 14-5=9.
Pure Magic.
kajorge · 1 points · Posted at 05:11:06 on February 14, 2016 · (Permalink)
Here's one I learned recently:
Take a number, say 6, and find both its square and its cube and concatenate them (put them together). So we have 62 = 36, 63 = 216 so our result is 36216. This number has one 1, one 2, one 3, and two 6's.
How many numbers are there that when you do this operation, your result has all the numbers 0 through 9 repeated only once?
Multiples of 9, when added together, make 9.
Example:
81(8+1)
72(7+2)
36(3+6)...
You might be thinking"what about triple digits?", well...
108(1+0+8)
144(1+4+4)
126(1+2+6)...
And so on. Pretty cool! Is there a name for this kind of phenomenon?
spelling of parallel is easy to remember if you use 112 = 121
_Psyki · 1 points · Posted at 05:13:04 on February 14, 2016 · (Permalink)
Even if we were to write each digit down on a single (separate) atom, there still would not be enough atoms in the universe to write down a googolplex.
Benford's law. Naturally occurring numbers are more likely to begin with smaller digits than larger digits. For example, if you were to measure the length of a random river, there would be about a 30% chance the leading digit of your measurement would be a 1, and less than a 5% chance that it would be a 9. However, in order for the law to work numbers must be from some type of distribution that crosses many orders of magnitude (1,10,100,1000, etc.), so people's height in feet or meters wouldn't work, but height in millimeters would. Additionally, the numbers cant be normally distributed, such as IQ scores. (normal distributions have a symmetric bell shaped curve, in which the peak is equal to the median, mode, and average.) And this law is also used as evidence for fraudulent behavior.
Zeno's paradox. Basically says that, if you were to half the distance between you and a wall in front of you an infinite amount of times, you'd never reach the wall, thanks to numbers being infinite. The wiki article explains it much more eloquently.
Some infinities are bigger than other infinities. There are an infinite infinities also.
pound30 · 1 points · Posted at 05:16:56 on February 14, 2016 · (Permalink)
I must not be that smart but I guess multiplying 11 by any double digits you add the double digits and put it in the middle. If its over 10 you carry the one.
ex: 11 x 23 = 253
crusoe · 2 points · Posted at 05:30:44 on February 14, 2016 · (Permalink)
Not if they are parallel. Or in 3 dimensions. Now if you mean non euclidean space, then in spaces with positive curvature even parallel lines will cross.
pound30 · 1 points · Posted at 05:38:44 on February 14, 2016 · (Permalink)
Well I was going to bring that up but I thought it could be somewhat confusing.
In the 9 times table if you write it out as follows the numbers on either side of the answers runs consecutively from top to bottom and back up again 0-9 then 0-9 again
9x1= 09
9x2= 18
9x3= 27
9x4= 36
9x5= 45
9x6= 54
9x7= 63
9x8= 72
9x9= 83
9x10=90
Gabriel's Horn. A true mathematical paradox--structure with infinite surface area and finite volume--and something those with only a basic understanding of calculus and understand. https://en.wikipedia.org/wiki/Gabriel%27s_Horn
This may be more physics-based than mathematical, but I've found it pretty interesting that nature itself will use the hyperbolic cosine function to naturally minimize the gravitational potential energy. These are called catenaries and can be seen by resting a string that is fixed at both ends. It can also be seen if you take two rings dipped into bubble soap, put them together, then slowly pull them away as the soap film creates the hyperbolic cosine. :)
Tera_GX · 1 points · Posted at 05:24:59 on February 14, 2016 · (Permalink)
The basic multiplication table for 9 inverses itself halfway through. As in 18 (9×2) is reverse of 81 (9×9). It also increments the first digit by +1 and the second digit by -1. So easy to understand nines.
Vortico · 1 points · Posted at 07:51:25 on February 14, 2016 · (Permalink)
Right, 4 is the lowest dimension in which an embedding exists.
HCPwny · 1 points · Posted at 05:29:07 on February 14, 2016 · (Permalink)
If you take an infinite number of numbers, and then remove all of the even numbers, you would still have an infinite number of numbers.
It's why the idea of infinite universes is so overstated. Just because an infinite number of universes could potentially exist, not every possible variation necessarily has to exist.
Benjo_ · 1 points · Posted at 05:30:45 on February 14, 2016 · (Permalink)
If you differentiate the volume of a sphere formula you get the surface area formula. Similarly, if you differentiate the area of the circle formula you get the circumference formula
Vortico · 1 points · Posted at 06:10:27 on February 14, 2016 · (Permalink)
You can also integrate sqrt(1 - A(z)2) from -1 to 1 where A(z) is the area of a circle to get the volume of a sphere. Continue doing this with A(z) being the "n-volume" of the previous step to get the volume of an n-sphere.
Raffix · 1 points · Posted at 05:31:30 on February 14, 2016 · (Permalink)*
Find any 4 consecutive integers.
Multiply the smallest with the biggest and you'll always get the multiple of the other two minus 2.
4 * 7 = (5 * 6) - 2
9 * 12 = (10 * 11) - 2
2865 * 2868 = (2866 * 2867) - 2
This works with ANY 4 consecutive integers even the biggest integers you can think of or with negative integers, even with zero (-2, -1, 0, 1 -> [-2 * 1] = [-1 * 0] - 2). This little trick helped me remember that 6 * 9 = 54 and 7 * 8 = 56 which I always confused in my multiple tables as a kid.
you can have a line with a length of one with a point on that line that divides the line segment into two parts and the ratio of the smaller part to bigger part is equal to ratio smaller part to both parts added together. Meet PHi http://www.goldennumber.net/
That mathematicians can simply say "but if we simply do this, like this instead" or " if we cheat a bit" to explain/prove theories and no one will call them out on that bullshit. This happens in mathematics too often and people are hailed as a genius when they do. If you can't prove or disprove a mathematical equation without changing the equation to get the answer you want, you didn't prove shit.
Tupper's self-referential formula.
Basically its a function that writes itself once graphed. It's k units high on the y-axis, which represents a 543 digit number.
A bagel cannot have everything on it. The bagel can have all the cream cheese, tomatoes, burnt tires, flowers, broken glass, Schrodinger’s Cat, oil fires, Miss Universe, the concept of hope, Whitey Bulger, and on and on until everything definable in the universe but it cannot also be on itself.
Science, as an exploration, has a destructive nature. New science will replace and disprove previous science. Mathematics is eternal and purely additive. If it's ever mathematically true, it's always true.
This squaring trick just kinda popped in my head a couple years ago.
So, say you know one square (in this example I'll use 12) but you don't know the square above it (in this case 13). So, to figure it out with addition we take 122 (144) add 12 (our original number) then 13 (our next number) which'll give us 169. Which just so happens to be 132 .
And, this of course can be done in a sequence.
169 + 13 +14 = 196 = 142
196 + 14 + 15 = 225 = 15 2
225 + 15 + 16 = 256 = 162
Etc.
If you add up the digits of the number that's being multiplied by 11 and stick it in the middle of said numbers, you'll get the answer.
Examples:
11x23
2+3=5 So...
11x23= 253
elkazay · 1 points · Posted at 05:53:28 on February 14, 2016 · (Permalink)
9-2 = 0.0123456789 or something like that
eric_ja · 1 points · Posted at 05:54:13 on February 14, 2016 · (Permalink)
Not only can we make up a number, i, and define it to be a square root of -1, we need not stop there. We can actually create any number of additional square roots of -1, that are not i or -i. And we need not stop there, either, we can actually create any number of square roots of positive 1, besides 1 and -1. And the resulting algebra, a Clifford algebra is not only sane, but it is actually useful for geometry and physics.
I think Gabriel's Horn paradox is pretty cool. I would describe it to y'all but that would take a while and Wikipedia does a way better job. So here is the link https://en.wikipedia.org/wiki/Gabriel%27s_Horn .
TLDR It is a Theoretical shape that has infinite surface area and a finite volume.
The volume of a hypersphere of diameter n approaches zero as the dimensionality of the sphere approaches infinity.
The volume of a hypercube of width n approaches infinity as the dimensionality of the cube approaches infinity.
This means that if you embed a hypersphere of dimension n inside a hypercube of the same dimension, as you increase the size of n the sphere takes up less and less volume within the cube. The limit of this is an infinite dimension representation where the sphere takes up no room inside the infinitely voluminous cube while having a diameter the same size as the width of the cube.
If you add a number and the sum is divisible by 3, then the original number is also divisible by 3. Ex. The sum of the numbers in 1476 are 18. Since 18 is divisible by 3 than so is 1476. 1476/3=491
x mod 9 = the sum of the digits in x and if x > 10, then those digits added together until x is < 10.
Unless is comes out to zero then the digits add to 9.
Example:
429 MOD 9 = 6 because 4 + 2 + 9 = 15 and 1 + 5 = 6
111 MOD 9 = 3
81 MOD 9 = 0 but the sum is 9
77 MOD 9 = 5 because 7 + 7 = 14 and 1 + 4 = 5
You can round a decimal number to halves, thirds, etc using this formula.
round(x*n)/n
Example:
Let x be 4.3 and we want to round to the nearest 3rd so n = 3.
xn = 4.3(3) = 12.9
We round this like we normally do and get 13
Then we divide by 3 and get 4.3333...
This may seem trivial but if you needed to round to the nearest 16th or something crazy, it makes it a lot easier.
If you use a slight different formula, you can round to the nearest whole number.
round(x/n)*n
Say we wanted to round to the nearest 5th whole number.
Let x = 23.43
n = 5
x/n = 4.686
rounding we get 5
5 * n = 5 * 5 = 25
So 23.43 rounded to the nearest 5 whole number is 25.
I found this most useful for snapping objects to a grid when programming my puzzle game.
To get the numerator for 0.123232323..., take the digits prior to the point where the repetition begins (in this case, 123) and subtract from it the digits that AREN'T repeating: 123 - 1 = 122.
The denominator will have the same number of digits (3 in this case); the number of 9s will be equal to the number of repeating digits, followed by zeros. In this case, 2 digits are repeating, so two 9s followed by a zero: 990.
Recognizing this pattern helps you quickly figure out that, for example, 0.1234555555... = 11111/90000.
If you have the sum of all natural numbers to infinity, it is equal to negative 1 over 12. You are only adding positive numbers and end up with a negative.
Kinzuko · 1 points · Posted at 06:10:12 on February 14, 2016 · (Permalink)
You can draw a triangle on a sphere with nothing but right angles.
Edit: after looking through the other responses I feel really dumb x.x
Probably waaay late to the party, but the number 6174 has a very interesting property. If you take any 4 digit number where at least 2 non-equal digits, and then rearrange the digits into two numbers, one as big as it can be and one as small as it can be, and then take that difference you get a new 4 digit number. Repeat this process and you'll always end up with 6174 in less than 8 iterations.
Example: 2534. Biggest: 5432, Smallest: 2345. Difference: 5432-2345 = 3087. And repeat no more than 7 times.
Oh and when you have 6174 you're "stuck" since: 7641-1467=6174
Maybe a pretty well known one but if you want to know a number's square and you know the previous number's square you can add those two numbers together plus the previous square and find the next one.
Example:
You want to find 262
You know that 252 = 625
Add (26+25) + 625 = 676 = 262
I was just sitting in math class one day and it worked every time.
You can never see the actual edge of an image on a mirrored sphere. A sphere is a 3D representation of an exponential function so the visual 'edge' of the image is just infinitesimal refraction.
jm6492 · 1 points · Posted at 06:22:58 on February 14, 2016 · (Permalink)*
Take it a step further. If you wanted to calculate 100mph. It isn't in the sequence BUT you can add existing numbers in the sequence to get 100 and take the numbers next to those - add them up and you get km/h.
So 3+8+89 = 100. The numbers next to those numbers can be added up.
5+13+144 = 162 km/h (100 mphis actually 160KM/h but its close enough.
If you can remember that string of fibonacci sequence, you can do rather quick and get a rough equivalent between the two numbers.
The fibonacci sequence is pretty interesting in of itself and can do a number of things I'm sure I don't know about.
One cool thing I like to share is that there are more irrational numbers between 0 and 1 than there are rational numbers across the whole number line. There are some subtleties about it, but pretty cool none the less
Every even number can be expressed as the sum of two primes. There's not really a reason for this but it holds true in every example anyone has ever tested.
fanalin · 1 points · Posted at 08:19:20 on February 14, 2016 · (Permalink)
It's ei*pi+1 = 0 (Euler's identity)
Easy to remember by thinking about the unit circle. exipi follows along the unit circle with increasing x, and x=0 and x=2 you are at the 1 (e2ipi=1). For x=1, you have eipi = -1.
If you think of any two-digit number (eg, 43), add the two numbers that make it up (eg, 4+3=7) and then subtract it from the number you originally had (eg, 43-7=36), you'll get a multiple of 9.
I had a teacher do a proof that proved that 0.99 repeating was exactly equal to 1.
Growing up I always had this assumption that it was an infinitely small step away from 1 while never truly being 1.
j0hnk50 · 1 points · Posted at 06:39:25 on February 14, 2016 · (Permalink)
to find half of any fraction simply double the denominator.
quick! what is half of 7/16?
mag0802 · 1 points · Posted at 06:39:43 on February 14, 2016 · (Permalink)
The number of possible digits between 0 and 1 and 1-Infiniti are not the same. The number of digits between 0-1 is more - a term referred to as aleph infiniti.
muzau · 1 points · Posted at 06:39:44 on February 14, 2016 · (Permalink)
Given that x is equal to four,
x1 is a line 4 units long, one dimension.
x2 (x squared) is a square, each edge 4 units long. two dimensions.
x3 (x cubed) is a cube, each edge also measuring 4 units long. three dimensions.
So what happens at x4? or x100. Just the idea that math allows for these crazy unfathomable constructs to exist s mind blowing.
114 is the only square number in the Fibonacci Sequence (excluding 02 = 0 and 12 = 1), and it's the 12th number in the sequence.
tjpoe · 1 points · Posted at 06:40:58 on February 14, 2016 · (Permalink)
That due to the nature of the random and infinite length of Pi, every number you'll ever see will be in in there. Your phone number, your social security number, your birthday and your death date.
Given that the basic trigonometric functions sin(x) and cos(x) have derivatives that are cyclical in nature, computing their large-numbered derivatives is trivial.
Given f(x) = sin(x), then:
f'(x) = cos(x)
f''(x) = -sin(x)
f'''(x) = -cos(x)
f''''(x) = sin(x)
So, every nth derivative is equal to the (n-4)th derivative, with the exception of the first 3.
Stated more generally, fn (x) = fn%4 (x).
For example, the 16,000,001st derivative of sin(x) is cos(x), because 16,000,001 % 4 = 1, so we look at the first derivative.
This makes chain rule / integration by parts much easier if you have a large derivative.
There are different size sets of infinite numbers.
Edit: for instance there is an infinite amount of possible numbers between 1 and 2 but there there is a bigger infinite number set between 1 and 3 etc etc.
My face is about to fucking implode reading through these responses
geofurb · 1 points · Posted at 06:45:01 on February 14, 2016 · (Permalink)
Draw a line from 0 to 1 along the x-axis. Move each point up in the y-direction by the distance it is from the origin. You should now have a line segment from (0,0) to (1,1) along y = x
It's longer. Calculus is weird, man.
Phileap · 1 points · Posted at 06:45:09 on February 14, 2016 · (Permalink)
I forgot what it is called, but imagine you stand in front of a wall. Say you are a meter in front of it. You walk half a distance, and then half of that distance, and half of that distance and so on. You will never touch the wall.
[deleted] · 1 points · Posted at 06:45:18 on February 14, 2016 · (Permalink)
You can paint a neverending fence with less then 1 liter of paint.
The last four digits of my home number (3928) minus my mom's cell (0281) plus my dad's cell (2713) equals my sister's cell (6360).
[deleted] · 1 points · Posted at 06:47:23 on February 14, 2016 · (Permalink)*
The golden ratio (aka φ) (~ 1.618034) is embedded within itself in so many ways. Here's the most head-scratching example of this that I happened upon:
Take the Fibonacci sequence. As the sequence goes up, the difference between two successive numbers approaches the golden ratio.
So, if you took a Fibonacci number, then multiplied it by the golden ratio, you'd get an approximation of the next Fibonacci number. (For example, 610 and 987 are two consecutive Fib numbers. And (610 * φ) = ~987.0007331. Pretty good guess!).
But this approximation method starts off pretty bad. (1 * φ) = ~1.618034, which is not that close to 1. Let's skip up a few levels. (3 * φ) = ~4.854102. Hm, good guess, but the correct answer was 5.
The error gets slimmer and slimmer as the sequence goes up. So let's now look at how big the error is for every step.
Fibonacci number
Approximation based on φ
Error (Absolute Value)
1
1
1.618033989
0.6180339887
2
1.618033989
0.3819660113
3
3.236067977
0.2360679775
5
4.854101966
0.1458980338
8
8.090169944
0.09016994375
13
12.94427191
0.05572809
21
21.03444185
0.03444185375
34
33.97871376
0.02128623625
...
...
...
10946
10945.99993
0.00006610699347
17711
17711.00004
0.00004085629553
28657
28656.99997
0.00002525069795
And so on...
Now here's the kicker. What do you get when you add up all those error numbers in the third column?
1.61803398874989... !!
I studied the golden ratio for two years (albeit in high school) and still don't understand how it can be hidden so deeply within itself.
EDIT: Formatting
[deleted] · 1 points · Posted at 06:47:35 on February 14, 2016 · (Permalink)
Not a "fact" as of yet, but a substantial number of mathematicians have dedicated their careers to the proof of Goldbach's Conjecture, which has been shown to hold up to 4x1018. Extremely simple statement:
Every even integer greater than 2 can be expressed as the sum of two primes.
Kreizhn · 1 points · Posted at 07:05:29 on February 14, 2016 · (Permalink)
Probably too late, and also probably only of interest to real nerds, but the following nerd sniped myself and my colleagues the other day.
If A is any nxn matrix, there exists a homogeneous degree (n-1) polynomial p_A such that p_A(A) = exp(A). In fact, for any analytic function, such a polynomial exists.
Proof: Do it for diagonalizable using Lagrange interpolation. Use density of diagonalizable in (nxn)-matrices to extend in general. Only problem comes in that the Lagrange polynomial fails for eigenvalues of non-unit multiplicity. The fix is effectively L'Hopital's rule, though to show that this is still analytic, some work needs to be done. Form an n! cover of the (nxn)-matrices {A,lambda1,...,lambda_n} and argue from there.
I was a magician for 15 years. Shuffled cards 5 times for each trick, three card tricks per show. that's 15 shuffles per show, averaged 4 shows per week, or 60 shuffles. That means I have shuffled decks 46,800 times and I haven't even included that hundreds of thousands of times during practicing. And I haven't even come close to .001% of all the combinations.
Feeling a little late to the party, but the magical multiplication of 11 is my favorite! 11 multiplied by any two digit number NR is equal to NFR where F = N(digit) +R(digit). For example (1132=352, because N=3 and R=2 so F=N+R or F=3+2 there for 1132=352 because NFR= 3 5 2). That was harder to explain than expected.
[deleted] · 1 points · Posted at 07:18:34 on February 14, 2016 · (Permalink)
When you divide an integer 'm' by another integer 'n', the maximum number of unique decimal places after which the pattern repeats itself is n-1. For example, 1/11 is 0.090909... so the pattern repeats itself after every 2 digits and 1/7 = 0.1428571428.. which repeats itself after 6 digits. So 1/555 would have a maximum of 554 decimal places after which the sequence would repeat.
"Theoretically the sum of an entire human experience can be quantified in an algorithm. What we consider the soul is actually a direct reflection of an amalgamation of any and all available experiences, which could supposedly be quantified, assuming our experiences produce a certain brain reaction. These reactions could be mapped, copied, and made into modules."
I like to think of prime numbers as the periodic table of integers. All integers (excluding -1, 0, 1) are composed of prime numbers. Which also in itself proves that there are infinite prime numbers which is also very cool!
I understand what they mean, but I still disagree. if you extend 0.99999999 for 999,999,999,9999999999999999999 then it is still less than 1. but then that is not infinite. 1 = 1. 0.999 forever is still every so infinitesimally slightly less than one.
Give me a number between .99(repeating forever) and 1, u can't, which means it's the same number. Also .99999999999 divided by 3 = .333333333333333, and 1 divided by 3 =.333333333, plus 3/3 =1 and .99999999(RF)
A guy named George Dantzig, solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman. Learned about this in a math class in college, most impressive thing iv heard about math.
deh707 · 1 points · Posted at 07:27:17 on February 14, 2016 · (Permalink)*
You can figure out 9 x 0-10 (nine times zero through ten) with the 10 fingers on your hands.
Imagine looking at both of your hands (palms facing you, unclenched), then think of each finger in this manner:
Left thumb = 1
Left index = 2
Left middle = 3
Left ring = 4
Left pinky = 5
Right pinky = 6
Right ring = 7
Right middle = 8
Right index = 9
Right thumb = 10
For example; for 9 x 4, clench your left ring finger (4), and count how many fingers remain on the left side (3), then count how many remain on the right side (6).
The sum from k=0 to infinity of ((n-1)k * (n choose k)) = nn.
This works for all natural numbers (whole numbers) n bigger than 1.
This is an application of the binomial theorem, but I intuited it while solving a combinatorics problem and have been unable to prove it independently of the binomial theorem.
You can describe most functions (as long as they have a finite number of discontinuities) with a sum of infinite different sines and cosines. You can describe 1/x (a function that jumps from -infinite to +infinite) with a sum to infinity of sines and cosines.
Starting from 0 add each consecutive odd number, 1,3, 5 etc. These will give you the square of numbers, 12=1(0+1), 22=4(1+3), 32=9(4+5) and so on, I think
[deleted] · 1 points · Posted at 07:42:51 on February 14, 2016 · (Permalink)
Both the sun and the moon appear to be identical in size when observed from earth, despite being drastically different sizes, distances, and orientations to the planet.
Putting this here in case anyone reads it. It's a fact I like to throw to my friends more because I took the time to figure it out (and haven't seen it elsewhere, though it's not exactly easy to google, so if somebody could point me to anywhere else it's discussed that'd be awesome.) It's not exactly useful in any way I've found, so that also makes sense.
The difference between (n) and (n+1) is, obviously enough, 1.
The difference between the difference between (n)2 and (n+1)2 is 2, (22 - 12 = 3, 32 - 22 = 5, 42 - 32 = 7; 7 - 5 = 5 - 3 = 2) something that's pretty common knowledge, I'd expect.
The difference between the difference between the difference between (n)3 and (n+1)3 is 6, (23 - 13 = 7, 33 - 23 = 19, 43 - 33 = 37, 53 - 43 = 61; 19 - 7 = 12 37 - 19 = 18, 61 - 37=24; 24 - 18 = 18 - 12 = 6).
The difference between the difference between the difference between the difference between (n)4 and (n+1)4 is 24, (24 - 14 = 15, 34 - 24 = 65, 44 - 34 = 175, 54 - 44 = 369, 64 - 54 = 671; 65 - 15 = 50, 175 - 65 = 110, 369 - 175 = 194; 671 - 369 = 302; 110 - 50 = 60, 194 - 110 = 84, 302 - 194 = 108; 108 - 84 = 84 - 60 = 24.)
This sequence continues at least out through n5 and n6, though I'm obviously not showing those here as the amount of operations required to demonstrate it grows rather quickly, to give the sequence n!. This is also limited by other factors (like needing to stick to the counting numbers; as one might expect involving the negatives in sequences revolving around exponents leads to a bad time.)
Also I apologize deeply for formatting, I'm not at all used to putting up equations on reddit.
[deleted] · 1 points · Posted at 08:12:42 on February 14, 2016 · (Permalink)
This is true in general, i.e., if you take k times the differences between k-th powers, you always get a constant. And this constant is k! (k factorial), that is 1 * 2 * 3 * 4 .... * k.
This can be useful in this sense. Imagine you have a series of numbers 10, 29, 72, 151, 278, 465, 724, 1067, 1506, 2053 and you want to know if they come from a polynomial.
Well, clearly they can always come from a polynomial because given n points there is always a polynomial of degree at most n-1 that pass through those points. However one is usually interested in low degree polynomials.
So you take differences. In this case, if you take differences 3 times you obtain 12,12,12,12,12,... this tells us two things, first that this come from a cubic polynomial, the second is that the leading coefficient, the coefficient of x3 is equal to 12 / 3! = 12 / 6 = 2. So our polynomial starts with 2 * x3. Now we can subtract 2 * 13, 2 * 23 , 3 * 33, ... from our list of numbers and we are left with 8, 13, 18, 23, 28, 33, 38, 43,.. we take differences one time and we get constant 5. So we know that these numbers come from a polynomial of degree 1, with coefficient 5/1! = 5. So our polynomial starts with 2 * x3 + 5 * x and taking this away from our list of numbers we are left with a list of 3's. So we have obtained that our original list of numbers can be obtained with the formula 2 * x3 + 5 * x + 3.
0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999... infinitely repeating, is equal to 1.
I've hit load more comments a few times and still haven't seen this.
The number 41 is awesome. 41 is prime. Add 2 and you get 43, also prime. Add 4 to that and you get 47, also prime. Add 6 to that and you get 53, also prime. This sequence continues for 41 intervals.
Ok. This is just simple elementary math, but still pretty cool & helpful to kids. The sum of the numbers in the results of the 9 times table, from x2 through x9, always total 9. Additonally (teehee), the first digit in the results is always one less than the multiplier. So:
9x2=18 ... 1+8=9
9x3=27 ... 2+7=9
9x4=36 ... 3+6=9
And so on and so forth
Well, it does work for 9x1 too, but who needs that lol?
I was taught this in school as a child. I thought everyone was. But everyone I ever told this too had never heard of it. My kids thought it was magic. Needless to say, I have always had to think waaay less while multiplying by 9. Chee!
If you assume that temperatures are continuous (which you should due to the way that temperature diffuses) then you can mathematically prove that there exists a point on the earth where if you drilled a hole from it, through the earth's core and out the other side (a straight line), the temperature on both sides is the same.
puntti · 1 points · Posted at 08:03:10 on February 14, 2016 · (Permalink)
There are so many ways to arange a deck of cards (52!), that every time you scramble the deck, the cards almost certanly go into an order never seen before by any man.
I always thought it was cool that 11x11=121
so separating the 1s and putting the sum in the middle.
11x12=132
11x13=143
11x45=495
this only works until the sum is greater than 9, but when I realised this as a kid I knew God was maths.
also the old 9xsibgle digit numbers is 1 less than said number with however much is left until 9 next to it. e.g.
9x4=36
3+6=9
I realise everyone knows this, but maybe someone doesn't?
Also I suck at math and can't wrap my mind around most of these. :<
Guide to seeing if a number can be factored by most numbers 1-10
1- everything
2- even numbers
3- add the individual digits of the number until you get 3,6 or 9
4- half the number will be even
5- units digit will be 0 or 5
6 - even amd the trick of 3s works
7 - I don't know of a trick but if you do please share
8 - half of a half will be even
9- add the individual digits of the number until you get 9
10 - the units digit is 0
Some/all of these are common knowledge, but I didn't learn all of them at first.
Toover · 1 points · Posted at 08:12:15 on February 14, 2016 · (Permalink)
Question: How many numbers have the number 3 within them (e.g.: 437)?
Answer: All of them.
OK, some explanation. Obviously, some numbers do not contain a 3, such as 10 and 20. But if examine all the numbers up to 3644, you'll see that 40% of them do, in fact, contain a 3. By the time you get to 40,000, about half of the numbers will contain a 3. Before you get to four billion, 70% of the numbers will contain a 3.
The ratio does not increase smoothly. It dips and zig-zags, but grows steadily.
For the mathematically inclined, the ratio of numbers less than N that contain a 3 is something like:
0.297793 * ln(ln(N)) - 0.215225
Not an exact formula, but holds almost true into the hundreds of trillions. The point is that the ratio increases forever, albeit slowly. Eventually, all numbers contain a 3.
zzalec · 1 points · Posted at 08:20:12 on February 14, 2016 · (Permalink)
Pascal's Triangle
Biobak_ · 1 points · Posted at 08:21:24 on February 14, 2016 · (Permalink)
Late to the party, but here's my less interesting more weird fact:
Add up any digits of a multiple of 9, and you'll get a multiple of 9.
27 or 2 + 7 = 9
135... = 9
297... = 18
and so on. There's definitely some incredibly simple connection I'm missing here, though. edit: formatting
Yragary · 1 points · Posted at 08:22:29 on February 14, 2016 · (Permalink)
You can divide any repeating decimal by .999999...... And convert to a fraction. Ex) .3333333....=.333333.../.999999....=.3/.9=3/9=1/3
Another ex) .272727.....=.272727....../.999999.....= .27/.99=27/99=3/11
This can be done since .9999999......=1 and both can be proven using the sum of an infinite series.
That if you type in 58008 and flip it upside down it spells something awesome.
[deleted] · 1 points · Posted at 08:26:39 on February 14, 2016 · (Permalink)
The zipfs law, 80-20 rule will always hold.
Oleing · 1 points · Posted at 08:26:56 on February 14, 2016 · (Permalink)
According to my grade 12 math teacher the quadratic equation and bringing your calculus book to a party will get you the most women. That fact has stuck with my ever since then.
For two digit numbers:
To find the answer, separate the two digits, then take the sum of the two digits and insert it in between.
Take 43x11 for example. 4_3, 4+3 = 7, so 43x11 = 437
If you have to carry, say for example 48x11, then do 4_8, 4+8= 12, then put the 2 in the middle and carry the 1, so 48x11 = 528
For digits greater than 2 digits, the process is similar.
Take 324x11 for example. 3_ _ 4, then do 3+2 = 5, and 2+4 = 6. Thus 324x11 = 3564
Take 4317x11 as another example. 4_ _ _ 7, 4+3 = 7, 3+1 = 4, 1+7 = 8, thus 4317x11 = 47487.
nxsky · 1 points · Posted at 08:33:50 on February 14, 2016 · (Permalink)*
There are many cool things but only one that I use regularly. It involves tan, cos and sin as well as angles 30, 45, 60 and 90 degrees (although I don't use it for 90).
Draw an equilateral triangle of side length 2 and cut in half (use either side). You're left with sides 2, 1 and sqrt3. Angles 30, 60 and 90.
Draw a right angle triangle sides 1, 1 and sqrt2. You then have angles 45 and 90.
Start at the 762nd digit of pi the number 9 repeats six times. So you could recite all the numbers until the nines and say " and so on" to imply that pi was rational.
The Ancestor Paradox - where you calculate the number of your ancestors in each generation of your family tree. Two parents. Four grandparents. Eight great-grandparents. Etcetera. Keep going back about say 800 years and you have 4 billion ancestors in a single generation of your family tree. Another generation, 8 billion. Another generation, 16 billion. And that's just roughly 850 years ago.
Let alone that most of your ancestors even at this point will only be from one geographic area (say the United Kingdom, or at least just Western Europe, for example). Add in things like the Black Death that wiped out a third of Europe's population in the 1340s. There are a lot of bottlenecks involved.
Inbreeding!
BajaBlu · 1 points · Posted at 08:38:07 on February 14, 2016 · (Permalink)
That 58008 upside down reads BOOBS.
Jdrawer · 1 points · Posted at 08:38:09 on February 14, 2016 · (Permalink)
The fact that 1! = 0! and the simple proof that proves it.
Also, the German word for "factorial" is the same for "faculty."
Geometry question: If a dot is infinitely small and a line is infinitely thin, if you were to look a the start of the line in the 3rd dimension (looking down the length of the line from the end), it would be a dot, right? However, since a dot is infinitely smll, would that mean that the 3rd dimension is infinitely small, too?
If you want to know a number squared, like 13, and you know the previous or the next squared number, say we do know 12 squared, then you can add the sum of the two numbers (12+13) to the square of the lower number (144), which gives you the higher number squared (169)
It is possible to check if a number can be divided by three of you simply add all the individual digits and divide them by three. I.e. 4317 = 4 + 3 + 1 + 7 = 15. 15 can be divided by 3 and thus can 4317.
Amazingly this works on every iteration (15 = 1 + 5 = 6)
Anything divided by zero is not defined . Zero is like a joker in the pack of cards . Depends on the user how to get the most out of it . Zero is indeed like our universe : very little is known to us .
Appare · 1 points · Posted at 08:58:14 on February 14, 2016 · (Permalink)
I probably spent a total of 20 hours working on this week's physics homework. The highest grade I can get on it is an 87.5%.
Not a cool fact, but I'm bitter.
[deleted] · 1 points · Posted at 08:58:29 on February 14, 2016 · (Permalink)
Only 49 perfect numbers have been discovered (https://en.m.wikipedia.org/wiki/Perfect_number), but it is still unknown whether there are an infinite number. Also, all 49 are even, and it is still unproven whether there exists an odd perfect number.
Fredvdp · 1 points · Posted at 09:17:59 on February 14, 2016 · (Permalink)
The following is not definitely a fact, but it certainly applies to many numbers.
Take any integer above zero. If it's even, divide by two. If it's uneven, multiply by 3 and add one. If you keep repeating this, you will eventually reach 1.
e.g. 7 - 22 - 11 - 34 - 16 - 8 - 4 - 2 - 1
This has not been proven, so if you can find a number to which this doesn't apply, mathematicians will start writing about you.
one of my favorite involves dividing numbers by 9.
if 1/9 is 0.11111111...
and 2/9 is 0.2222222...
and 3/9 is 0.3333333...
and so forth, shouldn't 9/9 be 0.9999999, and not 1?
That if you add all positive integers from 1 to infinity, you end up with the answer -1/12.
Just let that soak in for a bit. Adding positive numbers only to get a negative fraction.
I guess I would say that the derivative of the sine function is the cosine function. That is, the slope of the tangent line to the sine curve is the same as the value of the cosine function.
That or the derivative of ex is... ex. It's the only function where that is true.
Can you tell that I'm taking calculus again and we just got to derivatives?
[deleted] · 1 points · Posted at 09:37:17 on February 14, 2016 · (Permalink)
There are the same number of points in the entire set of real numbers as there are between 0 and 1
All primes can be sorted into 2 categories 4n+1 and 4n-1.
Any of the p ≡ 1 (mod 4) types (which is technical way of saying 4n+1) can be written as the sum of two primes but the 4n-1 can't.
For example 3*4 +1 = 13 = 32 + 22
hesohi · 1 points · Posted at 09:38:31 on February 14, 2016 · (Permalink)
Florence Nightingale was the first person to use statistics for anything other than gambling. She wasn't the first to suggest that hospitals should be clean, but she was the first to be successful in arguing it by using numbers. She also created the prequel to the pie chart.
Something i learned and not as fancy as some of these answer:
Assume there is 3 doors, behind 2 of them are empty and 1 has a goat. Your goal is to pick the door that has a goat behind it. After you picked a door, the the host (or someone) will reveal one of the the remaining 2 doors that happened to be empty and ask you if you want to switch your decision. Question now is: what will be your chance of getting the door that has the the goat if you choose to switch door?
Most people will think they have 50% (one out of 2 doors). However, it was proven that they will have in fact 2/3 chance of picking the door that has the the goat after switch. There is a name for this paradox but I don't remember, on mobile currently
Also, most of the people who read my comment would most likely ignore the the fact that the word "the" always appear twice side by side
While mathematically true this (the monty hall problem) isn't reflected in the outcome of repeated experiment as the probability of a door being correct was set WHILE there were still three doors. It's clever mathematic bullshit.
The entropy of a black hole the size of your head carries less information then it would take to write out Graham's Number. So if you tried to write out Graham's Number in your head it would eventually have so much information that it would collapse in on itself to form a black hole.
Grug16 · 1 points · Posted at 09:41:24 on February 14, 2016 · (Permalink)
1/3 = 0.3333333...
2/3 = 0.6666666...
1/3 + 2/3 = 1.
0.3333333... + 0.6666666... = .9999999...
.9999999... = 1;
[deleted] · 1 points · Posted at 09:43:36 on February 14, 2016 · (Permalink)
Maybe not the most complicated or anything, but one of my favorites, which is weird al inspired is:
"My pancreas attracts every other pancreas in the universe, with a force, proportional, to the product of their masses, and inversely proportional, to the distance between them."
also know as:
F = G((m1*m2)/D2) (forgive me if it's off, hard to format it into reddit)
Which is the formula for gravity.
xiape · 1 points · Posted at 09:47:43 on February 14, 2016 · (Permalink)
If you have a complex function with a derivative everywhere, it must have infinitely many derivatives everywhere (entire), and must go off to infinity (unless it's completely flat)
It is possible to cut a sphere into several pieces, and then to reassemble those pieces without stretching into two identical balls w/ the same dimensions as the original.
[deleted] · 1 points · Posted at 09:49:44 on February 14, 2016 · (Permalink)
Natural logarithms and ex
The derivative of ex is ex... That's fucked up
Jca1 · 1 points · Posted at 09:51:12 on February 14, 2016 · (Permalink)
There are the same amount of natural numbers, real numbers, and complex numbers, despite the fact that real numbers contain all the natural numbers and more, and complex numbers contain all the real numbers and more
I personally think that quadratic reciprocity is one of the coolest things in mathematics; basically, if you have two primes p, q, the problems of whether or not p is a perfect square modulo q and whether q is a perfect square modulo p are related in an beautiful, symmetric way.
smithmf · 1 points · Posted at 09:52:26 on February 14, 2016 · (Permalink)
That maths works in nature too. If you measure a river as the crow flies from its source to the sea and multiply that distance by pi, you get roughly the distance of it from source to sea including all its meandering corners. This is, apparently, especially true in S. America for some reason.
The differential of the volume of a sphere = the surface area of that sphere.
Also differentiating the surface area of a circle will = the radius.
First time I heard this my mind blew.
[deleted] · 1 points · Posted at 09:55:29 on February 14, 2016 · (Permalink)
Pi can be worked out as 4*(1-1/3+1/5-1/7+1/9-...) ad infinitum. When people work out Pi in their heads this is how they do it
I always liked the model of information and probability mathematics delivers.
A friend once told me this little riddle with the caption "Mathematics is witchcraft":
A woman tells you she has two children, one of them is a girl. What is the likelihood of said woman having two daughters?
By looking through all the possible combinations of two children she can have ((boy,boy);(girl,boy);(boy,girl);(girl,girl)) and excluding (boy,boy) we can verify that the likelihood amounts to 1/3.
Now the woman tells you she has two children, one of which is a girl, and said girl is born on a monday. The probability of her having two female children now rises to 13/27.
Whilst the information on which day the girl was born seems arbitrary and not at all related to our question, it still alters our model a lot. Intuition: By stating that the girl was born on a monday, she becomes more fixed. Think about what would happen if the woman told you she had two children, with the older one being a girl. Now the probability for two girls would be 50%.
When you multiply 9 times 1,2,3,4,or 5 the numbers reverse if you multiply them by 6,7,8,9 and 10.
01x9=09 90=10x9
2x9=18 81=9x9
3x9=27 72=8x9
4x9=36 63=7x9
5x9=45 54=6x9
These numbers multiplied by 9 are not exclusive to multiplications of 10 or less but the formula stays pretty much the same. To go into it would involve me typing from or oratating from something other than a smart phone.
This will probably get buried, but it's a part of mathematics relating to step theory problems.
Let's say some dot can move to the left one unit and right one unit, and it chooses either direction with the same probability (50% chance of the left and 50% of the right), is there a theoretical guarantee that if the dot leaves it's initial point (even if after almost an infinite number of moves), that it'll return to where it starts eventually?
The answer is yes.
Now, assume there is a flat plane of points. So the dot can now move up, down, left, and right, all with equal probability again. Is the dot theoretically guaranteed to return to its starting point?
Yes it is.
Now, assume this dot is in a 3-dimensional space, where it can move left, right, up, down, above, and below itself, all with equal probability. Is the dot theoretically guaranteed to at some point return to its starting point?
No it is not!
It's pretty interesting if you're someone who takes interest in probability/statistics, or math in general!
When multiplying two-digit numbers by 11, add the digits of the "non-11" together and put the result of that in the middle of the two.
Example: 11*27 -> 2+7 = 9 -> 297.
With three-digit numbers, add the 1st and 2nd digits together and then the 2nd and 3rd digits together. Replace the 2nd digit in the three-digit number with the two numbers you got from adding the 1st and 2nd digit and the 2nd and 3rd digit.
I know that by how many ones you square, the number goes up till the amount of ones and them comes down like pyramid. F. e. 11112=1234321 or 1111112=12345654321 or 112=121
ei*Pi + 1 = 0 , where e = Euler's number and Pi = the ratio of a circle's circumference to its diameter, both are irrational numbers. i = square root of -1.
A dozen, a gross and a score,
Plus three times the square root of four,
Divided by seven,
Plus five times eleven,
Equals nine squared and not a bit more!
Z_9 · 1 points · Posted at 10:27:37 on February 14, 2016 · (Permalink)
A coffee cup and a doughnut/bagel are essentially the same thing: a solid with a one hole.
That the sum of all the positive integers (1 to infinity) is not infinity, but -1/12. Negative one twelfth. Yes.
This is obviously crazy, yet it is true. There is a not-too-insanely-difficult proof (also one that IS insanely difficult involving the Riemann zeta function). FURTHERMORE, just as many mathematical formulas have real-world application, this one does too, in String Theory for one.
I guess this implies that the sum of all the negative integers is 1/12.
J_hoff · 1 points · Posted at 10:28:28 on February 14, 2016 · (Permalink)
There are enough molecules in one breath of air that when evenly distributed around the world, each following breath of air from anyone on the planet would contain 1-2 molecules from the first breath.
If you had a teaspoonful of carbon and removed one atom per second, every second, since the dawn of the universe approximately 14 billion years ago, today you would not have even removed one millionth of the total number of carbon atoms in that teaspoonful.
Jesus. I thought I was bad at math before, but reading this thread makes me feel like I can't even comprehend...well, just about every fucking thing I'm reading.
[deleted] · 1 points · Posted at 10:31:30 on February 14, 2016 · (Permalink)
Take the imaginary number i, raise it to the imaginary power i, and you get a real (although irrational) number:
ii = e-pi/2
zangent · 1 points · Posted at 10:34:34 on February 14, 2016 · (Permalink)
Any integer with no 9s divided by an equal number of 9s makes a repeating decimal of the top number.
E.g. 1024/9999 = 0.102410241024...
Daradex · 1 points · Posted at 10:35:27 on February 14, 2016 · (Permalink)
If you add together all of the whole numbers from 1 all the way to infinity I.e 1+2+3+4+5... etc the result is -1/12. This number is also used in a lot of calculations in string theory where it's necessary to know the result of adding all of the numbers together.
A geologist I met while working abroad explained Mandelbrot and fractals occurring in nature to me when I was a little drunk and stoned sitting by a fire roasting some marshmallows. My mind imploded on itself.
[deleted] · 1 points · Posted at 10:50:36 on February 14, 2016 · (Permalink)
Every number of three or less digits that is a multiple of 37 will still be if its digits are cyclically permuted. A few examples :
37*13 = 481, 148/37 = 4
37*11 = 407, 740/37 = 20
And it works in any base !
37*15 = 483, 348/37 = F (base 16)
37*5 = 233, 323/37=6 (base 8)
Edit : got that from bash.org a long time ago (when it was still active) but I don't seem to be able to retrieve the source.
jammu · 1 points · Posted at 10:50:40 on February 14, 2016 · (Permalink)
that the number of real numbers between 1 and 2 is same as that between 1 and 3, and that the number of rational numbers between 1 and 2 though infinite is less than number of reals between 1 and 2.
Scotteo · 1 points · Posted at 10:51:50 on February 14, 2016 · (Permalink)
Add 1 to Product of 4 consecutive numbers to get a perfect square!
i.e. 1+x(x+1)(x+2)*(x+3) = (1+3x+x2 )2 , => a perfect square.
Theorem is MATHEMATICALLY applicable to all numbers, but a definition of "perfect square" requires x to have integer value.
Gladix · 1 points · Posted at 11:17:36 on February 14, 2016 · (Permalink)
Sum of all integers (1 + 2 + 3 + 4 + ...) is - 1/12 calculated with partial sums. Kinda neat when you think about it. The sum of all whole positive numbers is partial negative number.
Fenrime · 1 points · Posted at 11:18:10 on February 14, 2016 · (Permalink)
372 is divisible by 3 because 3+7+2=12 , 1+2 is divisible by 3. Just add up the numbers to find out if it's divisible by 3.
[deleted] · 1 points · Posted at 11:25:29 on February 14, 2016 · (Permalink)
calculater joke i learned in 3rd grade
A woman's boobs weighed 69 pounds,
which she though was 2, 2, 2 much.
So she went down 51st street
to see DR. X
he gave her 8 pills.....which left her....
I learnt it in primary school (uk) as there was a girl who was 13 and had size 84 books but wanted size 45 so she went to the doctor and the doctor said 0h take these tablets 2 X (times) a day and she ended up boobless
rezdm · 1 points · Posted at 11:26:00 on February 14, 2016 · (Permalink)
1 + ei*Pi = 0
[deleted] · 1 points · Posted at 11:27:15 on February 14, 2016 · (Permalink)
My favourite things:
The platonic solids.
Hexagons are the regular polygon with the highest number of sides you can tile on a plane
Triangles have the fewest number of sides possible to create a 2d polygon, making triangles the fundamental polygon. It's easy to make any other polygon out of triangles.
The number of potential chess games there are. I would try and explain it but couldn't do it justice.
sdo17yo · 1 points · Posted at 11:28:14 on February 14, 2016 · (Permalink)
From grade school, that you can do the nine times table with your ten fingers spread out on your desk.
9x1=spread out all ten fingers, hide the first finger. The answer is the remaining fingers=9.
9x2=spread out all ten fingers, hide the second finger. The answer is the amount of fingers on the left of the second finger put together with the number of fingers on the right=18.
9x3=spread out all ten fingers, hide the third finger. The answer is the amount of fingers on the left of the third finger put together with the number of fingers on the right=27.
Etc.
Ownejj · 1 points · Posted at 11:28:26 on February 14, 2016 · (Permalink)
If you keep halving your steps as you walk towards a door you will never leave the room.
Balthegor's prime (1000000000000066600000000000001) is a vaguely interesting number, a palindromic prime number that the superstitious think is significant due to the 13 0's either side of the number of the beast.
https://en.wikipedia.org/wiki/Belphegor%27s_prime
Aznreka · 1 points · Posted at 11:35:24 on February 14, 2016 · (Permalink)
If you flip 3.14 (Pi) upside horizontally and vertically it looks like the word "PIE". Feel free to write a paper on this. I'm expecting a nobel prize.
arcs · 1 points · Posted at 11:33:22 on February 14, 2016 · (Permalink)
If you do a contour integral around the pole of a complex function f(z) you will get the same answer as the first term of the Taylor approximation of said function at that point. (Times 2 pi i)
[deleted] · 1 points · Posted at 11:33:23 on February 14, 2016 · (Permalink)
The ratio of the length of and A4 sheet of paper to its breath is square root of 2.
This works for all A- papers (A0, A1, A2, A3, A4,... )
Just a simple thing: That the area of the function ex from -infinity to 0 is 1. It's infinitely growing and growing, but the sum is the finite number 1. Blew my mind, when I learned it.
johkih · 1 points · Posted at 11:35:18 on February 14, 2016 · (Permalink)
I always found it pretty cool that if the sum of the digits in a number is divisible by 3, then the whole number is divisible by three. For instance, 441231, 4+4+1+2+3+1 = 15, 1+5 = 6, 6 is divisible by three, therefore 441231 is divisible by three. Also works with 9.
Aznreka · 1 points · Posted at 11:43:27 on February 14, 2016 · (Permalink)
"Dek, el, and do." The power of twelve.
aaegler · 1 points · Posted at 11:46:02 on February 14, 2016 · (Permalink)
If you add the individual numbers of multiples of 9 they will always add up to 9, or multiples of 9 (the higher you go). Eg, 9 x 4 = 36. 3 + 6 = 9.
Mad_Jas · 1 points · Posted at 11:49:12 on February 14, 2016 · (Permalink)
All numbers divisible by 3 add up to 3, 6, 9. Despite the fact that I "discovered" this in my own little world, I'm sure I'm hundreds of years behind the curve.
Ex1) 519. 5+1+9=15; 1+5=6... therefore 519 is divisible by 3.
Ex2) 12321. 1+2+3+2+1=9; therefore divisible by 3
[deleted] · 1 points · Posted at 11:56:01 on February 14, 2016 · (Permalink)
If you add up all the positive integers, I.e. 1+2+2+4+5+... All the way up to infinity, the answer which pops out is -1/12.
The positive whole numbers add up to give a negative fraction. Have a nice day.
You're always within 20 moves of solving a Rubik's cube. Also Zeno's Paradox. Basically to go anywhere you have to get halfway there but then you have to get halfway there but then you have to get halfway there and so on and so forth. Infinity is everywhere.
Edit: Words
oighen · 1 points · Posted at 11:57:09 on February 14, 2016 · (Permalink)
Take a cup full of water, gently mix it with a spoon without touching the walls of the cup. Brower fixed point theorem says that there is at least one molecule in the exact same place it was before you mixed.
Now the weather. Someone already said that there's always at least a cyclone on Earth. A neater fact is that at any moment there are at least two antipodal points with the exact same temperature and atmospheric pressure. This is due to Borsuk-Ulam theorem.
Oh, on a useful note. Everybody knows that a three legged table can't wobble since three points define a plane. Unfortunately four legged tables often wobble. If the wobbling is due to the terrain and not to the fact that you are a cheap ass and bought a shit table and the table is square, simply turning it at most 90° will fix the wobble.
[deleted] · 1 points · Posted at 12:03:50 on February 14, 2016 · (Permalink)
a way t remember e.
There are 2 things i want you to remember about andrew jackson. He was the 7th president elected in 1828... 2.71828 he was elected twice so we'll write it twice. 2.718281828. his face was very angular... so we'll the degrees of a special traingle... 45 90 45. 2.718281828459045. the angular/triangle thing is a stretch, but he really was the 7th president and was elected twice... the first time in 1828
My favourite example of the Mean Value Theorem is this : "imagine you've just stumbled out of a pub and start to head home. You sway back and forth going in the wrong direction a heap of times. Eventually you make it home. To have made it home there was at least one time you were facing in the exact correct direction you should've headed after leaving the pub." That is how my Real Analysis lecturer explained it to us.
marktx · 1 points · Posted at 12:05:35 on February 14, 2016 · (Permalink)
the sum of all natural numbers all the way up to infinity = -1/12
In physics to move between acceleration, velocity, and position you use integrals and derivatives, but you can keep going, finding the rate of change in acceleration (jerk) and the rate of change in jerk, which is snap.
These are important to a lot of fields, most notably moving and braking systems (because jerk is what causes whiplash and other unpleasant physiological effects) and robotics (where jerk and snap not only define how fluid a motion looks but how much stress it places on mechanical joints).
But you can keep going even further! The fifth derivative is crackle, and the sixth is pop.
These have less practical use than jerk and snap, and are mostly of interest to mathematicians because the rate at which the rate of change of acceleration is changing is hardly a vital mechanical statistic.
gordo65 · 1 points · Posted at 12:09:17 on February 14, 2016 · (Permalink)
Not really as cool as most other posts, but i felt so fucking smart when I as a kid realized that 9*x would always end up with a number that could be turned into a new 9:
9*2=18 | 1+8=9
9*7=63 | 6+3=9
9*43=387 | 3+8+7=18 | 1+8=9
9x386,72=3480,48 | 3+4+8+0+4+8=27 | 2+7=9
Golmin3 · 1 points · Posted at 12:13:48 on February 14, 2016 · (Permalink)
This is a bit obscure, but, the number of "differential structures" (explanation below) for the very simple space Rn is:
1 - for n not equal to 4
uncountably infinite - for n=4
What I think is cool about that is not only that 4 dimensions is different, but how much the difference is. Also that we may well live in a 4D space.
"Differential structure" is a bit of a complicated idea, but. Imagine you want to draw a map of something. Sometimes you can do that find with a nice Euclidean drawing (eg a map of a football field, can be drawn on a 2D picture), but sometimes you can't, eg you can't draw a map of the Earth on a flat piece of paper without distorting something impossibly (eg by having the pole a line across the top).
So, you could do this by having a number of pictures (known technically as "charts"). You can do this with two charts for a sphere for instance.
A differential structure is (roughly speaking) one where you use n-dimensional charts and where the charts overlap you can convert from one chart's co-ordinate system to the other in a way that is differentiable (in the high school sense).
Obviously some ways of doing this aren't fundamentally different from others. Eg you could take two charts of the Earth and move teeny bits of one to the other in a neatly differentiable way and that would make no difference (in technical language the two systems are equivalent as differential structures).
A differential structure is one of these systems of charts where the overlaps are all nicely differentiable. For R2 (say) there's only one really distinct way of doing this. For R4 there are lots.
myztry · 1 points · Posted at 13:24:08 on February 14, 2016 · (Permalink)
We don't actually live in 3D space, as in x, y & z which are constructs for convenience replaceable by things like spherical co-ordinates. Our real existence is more akin to vectors where everything is merely direction with a magnitude.
Perhaps one day FTL travel will be achieved not by moving but by reducing the magnitude of distance ahead of the vessel while increasing the magnitude behind the vessel, in a given direction.
Binomial distribution is a favourite of mine, and while the Gambler's Fallacy (the belief that past performance is an indicator of future performance) is perfectly valid, it frequently gets mistakenly applied in conversations regarding dice rolls and slot machines.
Say you're trying to roll a 1 on a six sided dice, so you have a one in six chance of winning a roll. Anyone will tell you that the odds never improve and you are never "due" for a win. This is technically true but ignores the fact that while the odds of rolling a one remain constant per roll, the odds of finding a success in a sample of rolls do increase as the sample size gets larger.
To put it another way, if you roll one million dice, the odds of rolling a 1 are a constant 16.66% per dice, but 99.99% over the entire sample. And while continuing to roll dice will never "guarantee" you a win, the event of never rolling a win will become increasingly improbable the more dice you roll.
So gamblers, a machine is never "due" for a win, but if it has been pulled a 100 billion times and not paid out, it's either a statistical anomaly, or broken.
Well in honor of my reddit user name, one of my favorite mathematical objects is a clopen set. A open set Ais a generalization of the metric space concept of an open set, basically you can create a tiny ball around any point in the set. A closed set B is a set whose compliment--i.e. all of the space that is not in the set B--is open. A clopen set is both open and closed. Now in the metric space of real numbers, the only clopen sets are all of the real numbers and the empty set. But there are topological spaces who sets are all clopen! It's crazy.
I've posted this before and some people replied to point out how I was wrong, but here goes anyway:
The idea that 'Pi' can be represented by an infinitesimally long number of seemingly random (but obviously not 'random') digits means that, theoretically, if you assigned every number a value, say a letter or even just 1s and 0s in binary, somewhere along that infinite number of decimal places you would find the entire written works of Shakespeare, for example.
By extending the notion of functions to complex numbers, then pretty much for free you get out that a bunch of super difficult things can be integrated by performing differentiation.
My elementary school students love how in the 9x table (up to 10x9) if you add the tens digit and ones digit together you always get 9. This is how the finger trick works. For example 7x9=63, 6+3=9.
That the answer to everything in the universe is 42.
MpMerv · 1 points · Posted at 12:39:40 on February 14, 2016 · (Permalink)
I'm not too knowledgeable in math so I'm sure there are much cooler facts than this, but I think it's weird how there is no exact number to describe pi, the ratio of a circle's radius to its area. 3.14159 just goes on forever so it begs the philosophical question, do we really know the area of a circle ever?
This question and answers are so cool!! My answer seems less intelligent but I still find it interesting. The Pythagorean theorem is interesting to me. I think it is fascinating that if the hypotenuse of a right triangle were made out of steps, no matter how small the steps, at some point it changes into a straight line with a different length.
bacami47 · 1 points · Posted at 12:47:54 on February 14, 2016 · (Permalink)*
In mathematics zero stands for nothing. However, nothing cannot be represented by anything.... not even a 0
No joke. It's actually used in complex physics like string theory and the "proof" is really easy to follow. You just have to accept that 1-1+1-1+1-1+... all the way to infinity averages out to 1/2, then it's like 3 steps.
There's a surprising connection between the j-invariant, a modular function (well, its Laurent series representation, which is like a way to write down a function as an "infinite polynomial") and the Monster group. The fucking monster group. WTF? How the fuck are those two even connected??!
A math Postulate is something unproven (or so self-evident that nobody's bothered going through the trouble of proving it) and just taken for granted to be true.
0.33333333... x 3 = 1
As 1/3 x 3 = 1
And 0.333333... = 1/3
As there is no Number existing between 0.9999... and 1 it is considered the same number. I did not want to accept this the first time i heard this but finally I had to :(
If you want to know if a number is evenly divisible by 3 without a calculator, add all the digits of the number. EX: 123 1+2+3 = 6 which is divisible by three and so is 123
An infinite nuber of actions can be performed in a finite amount of time. For example: Cut a piece of paper in half in one minute. Then cut one of those halves in half in 30 seconds. A half of that in 15 seconds and so on. You will never exceed 2 minutes.
[deleted] · 1 points · Posted at 13:21:41 on February 14, 2016 · (Permalink)
conway created a way of telling if you can fill a surface with a given tile.
you know the classical question can you fill a 8x8 chess board with dominoes if u cut out 1 corner square?; what if u cut 2 opposite corner squares?; this evolved into more complicated questions, and therefore his way of finding out; it involves an algebraic way of describing the surface ; suppose that this algebraic expression of the tile is equal to the neutral element of the group we re working in ( the elements that help us describe this surfaces are in this group); if this equality implies the fact that the expression that describes the big surface is also = to e, then it can be covered in such tiles; i read this a while ago in a book and it blew my mind
Works with all numbers. I just randomly discovered it, I'm not sure if it has a name as a real fact or anything.
E.g. 13 x 13 = 169
12 x 14 = 168
Swate- · 1 points · Posted at 13:49:50 on February 14, 2016 · (Permalink)
I use this in my head all the time for multiplication. I'm not sure if this application of it has a name but it ties in to the difference of perfect squares:
(a+b)(a-b) = a2 - b2
Therefore, for your example, a=13 (the original squaring number) and b=1 (the amount of deviation either side of a).
Alright cool. Yeah the superscript triangle without a bottom symbol doesn't show up I guess. I'm on mobile as well so that may be a problem. Oh well, I understand now.
If you want to estimate the value of, say, a crowd at a foorball game, answer these two questions:
What is the smallest estimate you would believe? ... in other words, the smallest value that if someone said, "the value is [this]", you would say, "ehhhh, yeah I guess that's possible, but I don't think it cam be any lower than that
Similarly, what is the largest estimate you would believe?
... add the two values and divide by two. I feel this is better than just trying to guess a point estimate.
I also like to consider how off I feel the result is and adjust my estimate from there.
I've guessed stadium capacities to within a few hundred people. Concerts are hard to verify because you can't really get the actual number from anybody.
The point is, this method instills greater confidence in me when I need to estimate a number.
Not a mathematical truism, per se, but it's statistics... there is a variance around truth unknown. This method helps me.
Swate- · 1 points · Posted at 13:39:53 on February 14, 2016 · (Permalink)
I do something similar but I feel like a multiplication-based result yields more accuracy personally. I do my best to multiple the two answers and then square root the product.
Obviously addition is easier, and I'm just pulling at pedantic strings lol, but ye
i do not know the formula, i just know that if you take to consective numbers, lets say 4 and 5, add them up equals nine. now the squared version of 4 is 16 and 5 is twenty five, the difference between the two is nine. this works all the way up 5 plus 6, 6 plus 7, etc
sut123 · 2 points · Posted at 13:54:10 on February 14, 2016 · (Permalink)
The geometric mean of the coefficients of the continued fractions of almost every real number is Khinchin's constant (≈2.685452).
Continued fractions is a way to describe real number using integers, very different from a numeral system.
To write a number as continued fractions, you write down its integer part as the first digit and continue with the reciprocal of the rest. The integer part of THIS number is the second digit and you keep on going like that.
For example 3.14159265359... would be 3 + .14159265359..., so 3 is the first digit. The reciprocal of .14159265359... is 7.06251330592..., so 7 is the 2nd digit. The reciprocal of .06251330592... is 15.9965944095..., so 15 is the 3rd digit.
Pi can therefor be written as the integer sequence 3,7,15,1,292,1,1,1...
The geometric mean of a set of numbers is a kind of average that is different from our usual average. The arithmetic means adds n numbers and divides by n. The geometric means, on the other hand, multiplies n (positive) numbers and takes the nth root of that.
The amazing thing is, that, for almost all real numbers, the geometric mean of the digits of the continued fractions converges towards a single number, called Khinchin's constant. Obviously not ALL numbers do, it's easy to create counterexamples. The continued fractions of the number 4 is just '4' and can't converge to anything. The same is true for any rational number. Other examples of numbers that don't have this property are all roots of quadratic equations and Eulers number.
In fact, there is not a single number of interest (that means not specifically constructed for this purpose) that we know for sure has this property. Not even Khinchin's constant itself. Yet it can be proven almost all numbers do.
As one final note, we know very little about Khinchin's constant as of now. We do not even know if it is rational.
If you have a deck of card with N cards in it and you riffle it in the natural way (split it in 2 parts, insert one of the two in the other one) the entropy of the deck, how "random" it becomes, increase drastically after 3/2 Log_2(N).
It is quite flat before and after that point.
That means that you need 7 riffles to have a randomized deck of 52 cards.
It was studied by Persi Diaconis. Great guy, mathematics and magician.
When you're trying to divide a fraction by a fraction, just use the outties-over-innies method. (2/5)/(1/3) = (32)/(51) = 6/5
[deleted] · 1 points · Posted at 13:57:35 on February 14, 2016 · (Permalink)
0.9 recurring = 1
[deleted] · 1 points · Posted at 13:58:20 on February 14, 2016 · (Permalink)
The difference between the squares of two consecutive numbers is the sum of those two numbers, i figured it out during a maths test in highschool and was really chuffed with myself.
The square numbers are separated in succession by the odd numbers.
1(1) = 1
2(2) = 4
3(3) = 9
4(4) = 16
1 is separated from 4 by 3, 4 is separated from 9 by 5, 9 is separated from 16 by 7, etc. 3, 5, 7, 9, 11... Someone a little more privy to mathematics can probably whip up a cohesive equation for this.
I don't know if it is my favorite per se, but I was just explaining to my 3rd grader that 9 times any single digit number will yield a quantity with where the digit in the tens place is one digit smaller than that number and the sum of both digits will be 9. Or 9x where x is a single digit integer = a two digit answer wherein the digit in the tens place is (x-1) and the the digit in the ones place is 9 - (x-1).
jasnoc · 2 points · Posted at 14:13:10 on February 14, 2016 · (Permalink)
I'm a 4th grade teacher, read them the book "The Best of Times" by Greg Tang. I read my 4th graders this book the beginning of each year. Excellent tips for working multiplication facts 1-9.
That any number which has re-occurring decimals (at some point) can be turned into an exact fraction
[deleted] · 1 points · Posted at 14:00:58 on February 14, 2016 · (Permalink)
To determine if. a number is divisible by 11, add upthe numbers n every other digit. Then, add up the others. If they both equal the same amount, the number is divisible by 11.
For example:
121... 1+1=2, and 2=2, it's divisible by 11.
5731.. 5+3=8, and 7+1=8, it's divisible by 11 (521×11)
Infinity is as fascinating to me as how, what or why the universe was created... I became so interested in it when I heard from somewhere if a monkey had infinite time and infinite attempts, it would eventually type the entire works of Shakespeare..
In school we once had to invent a "mathematical trick". I was never good at maths so I was sure that I couldn't come up with anything clever at all. I fiddled a bit with numbers on my calculator and found a "trick" to easily find out a secret number multiplied by 99. All Information I needed to find it was the number of digits the secret number has.
So, for example, a person asks me what the number is if the sum is 2277 and the number has 2 digits the secret digit is 23. The "calculation" works like this:
SUM = 2277
SECRET = ??
Now if the secret number has two digits you take the last 2 numbers (77) and add up to them until both are 0, starting from the right e.g.
77 + 3 = 80
80 + 20 = 100
The number is 23. The simplest example is a single-digit number:
SUM = 99 (1x99)
SECRET = 1
SUM = 198 (2x99)
SECRET = 2
I hope I explained it well. People usually tent to not get it when I try to explain. You can do this with any length of secret digit length, the calculations get "harder" the more secret digits there are. Anyway, casual people are usually super impressed when you tell them you're able to find out any number they multiplied by 99 just by knowing the digits in the secret number and the end sum.
ck2839 · 1 points · Posted at 14:26:48 on February 14, 2016 · (Permalink)
Most of us know Pythagorean Theorem that states a2 + b2 = c2, where it is possible to have a,b and c as all integers. For example: 32 + 42 = 52. But did you know this fact:
an + bn ≠ cn for all a,b,c,n ≥ 3 (where a,b,c,n are all natural numbers). This is called Fermat's Last Theorem and took centuries for mathematicians to prove.
lolhawk · 1 points · Posted at 14:31:30 on February 14, 2016 · (Permalink)
You can create 2 identically-shaped potato chips from two completely different potatoes by intersecting the potatoes with each other. The outline of the intersection appears once overall - but twice on the two separate potatoes.
Pretty simple one to wrap the mind around, but there are infinitely equal amount of numbers between 0.0 and 1.0 as there are whole numbers in existence.
Not exactly a fact more of a game. Try to fill a square with pentagons, there rules are there cannot me any gaps, there must be a finite amount of polygons and the most complex rule two polygons cant share some than one side. I guess my fact is there is a solution and every polygon can be constructed with these constraints just quadrilaterals are the hardest.
∑ 1/(21+n ) [n=0 initially] for any number of iterations, the number will never be equal to or greater than 1. Basically, add up 1/2 + 1/4 + 1/8 +... the number will always be lower than 1. It's not that cool of a fact, but it's the best I've got. lol
Ainjyll · 1 points · Posted at 14:38:50 on February 14, 2016 · (Permalink)
1.618033:1 is considered by many to be the most aesthetically pleasing ratio in the world. It's also called the Golden Ratio and can be found in countless places in nature, art, architecture and other places.
It is still highly contested by experts as to whether or not this ratio is really found in nature as much as claimed, but it's still pretty damn cool to me.
sixnew2 · 1 points · Posted at 14:39:23 on February 14, 2016 · (Permalink)
paurwar · 1 points · Posted at 14:39:56 on February 14, 2016 · (Permalink)
The Fibonacci sequence is an excellent tool for making quick coversions from miles to kilometers and vice versa. E.g. if the sequence is 1, 2, 3, 5, 8, 13... 3 mi is roughly 5 km and 8 mi is roughly 13 km! This is because the golden ratio, on which the Fibonacci is based, is 1.618 and the conversion of km to mi is 1 mi = 1.609 km.
ARAR1 · 1 points · Posted at 14:40:00 on February 14, 2016 · (Permalink)
I have a question. A lot of answers in this thread have facts for repeating sequences and other numerical alignment. Would that be true if we were using a different numeral system? i.e would prime numbers be different if we were counting using a hexadecimal system?
There's different sizes of infinity. So the amount of numbers between 0 & 1 is infinite but the amount of numbers between 0 & 100 is infinite and so on, even though the difference between 0 & 100 is bigger.
You are correct, in fact the minus in -1/12 in the casimir force means that it is an attractive force.
[deleted] · 1 points · Posted at 14:46:43 on February 14, 2016 · (Permalink)
When you're squaring numbers the distance between the product of the last square and the product of the current square is always increasing by two. It goes like this:
11=1, the product being 1.
22=4, and the distance between 1 and 4 is 3.
3*3=9, and if you add 2 to the distance between the last square that makes it 5, and if you add that to the last square you get the next one, which is 9.
It's kinda obscure and I figured it out myself so idk whether or not people already know it or if it's even useful, but that's the basics of how it works.
ck2839 · 2 points · Posted at 14:54:51 on February 14, 2016 · (Permalink)
A "Crab Canon" is a piece of music that has two lines that are palindromes of one another. The piece can be played from the start or the end. Bach messed around with this and even wrote a piece of music where one player played the music normally and another flipped the sheet music upside down and played it that way. Fun stuff.
PMPG · 1 points · Posted at 14:57:00 on February 14, 2016 · (Permalink)
All the numbers that devide into a certain number are added together and make new number . All the numbers that de ide into that one add together and give you the first number.
Marsleo · 1 points · Posted at 15:07:46 on February 14, 2016 · (Permalink)*
I don't kown,but I want to say "1+1=2" is the coolest mathematical fact which I know even that had ever never been proved yet,yes,it could named Morden Goldbach conjecture I think.Our subconscious still think "1 + 1 = 2" is real cause it's the basic of other most of math theories in my opinion.
In 1920, Norway's brown proved "9 + 9".
In 1924, the German's Mach proved the "7 + 7".
In 1932, the British Mr Sterman proved "6 + 6".
In 1937, the Italian Tracy has proved that the "5 + 7", "4 + 9", "3 + 15" and "2 + 366".
In 1938, the Soviet union buchholz skarn is Bob proved that the "5 + 5".
In 1940, the Soviet union buchholz skarn is Bob proved that the "4 + 4".
In 1956, the Chinese king yuan proves the "3 + 4".Later proved that the "3 + 3" and "2 + 3".
In 1948, Hungary's proved that the "1 + c", where c is a great natural Numbers.
And the Soviet union in 1962, the Chinese Pan Cheng hole barr bain proves that the "1 + 5", China's king yuan proves the "1 + 4".
In 1965, the Soviet union by evening too cuny and small dimension noguera madoff, and Italian friend Billy proved the "1 + 3".
In 1966, China's trained Chen jingrun proved the "1 + 2".
The birthday paradox. ((364/365)((# of people(# of people - 1))/2))(-1)—1×100
That's the persentage someone in a room shares a birthday. So in a room of 30 people there's a 90% chance someone shares a birthday with someone else
Not really math per se, but there are more ways to arrange a deck of cards than there are atoms on earth. There are 80,000,000.... (+60 more 0s) unique ways to shuffle a 52 card deck.
Rule of 72 tell you how long it will take to double your money at any given fixed annual interest rate. 72/rate=years
For example: 6% interest = 72/6 = 12 years to double your money.
Or you can use the same idea to learn what rate you need in order to double your money within your time frame. 72/rate=years
12 years = 72/12 = 6% needed in order to double your money in 12 years.
I'm not exactly a math person, so this may seem obvious to some of you. I found that if you multiply a number (lets say 50 x 50) and get the result, then you take those same numbers and decrease one side by one and increase the other side by one (49 x 51), it's always one less than the first result.
50 x 50 = 2,500
49x 51 = 2,499
3,000 x 3,000 = 9,000,000
2,999 x 3,001 = 8,999,999
This is just something I found interesting. Not that it's overly useful though.
You can calculate any squared number that ends with a 5 by multiplying the number before the 5 with that same number + 1. Then multiply it by 100 and add 25. Works everytime.
Examples:
25² = (2 x 3) x 100 + 25 = 600 + 25 = 625
95² = (9 x 10) x 100 + 25 = 9000 + 25 = 9025
135² = (13 x 14) x 100 + 25 = 18200 + 25 = 18225
1475² = (147 x 148) x 100 + 25 = 2175600 + 25 = 2175625
take an odd number and square it. now take the consecutive numbers that add up to the squared odd number. these three now form a pythagorean triple.
32 = 9.
9 = 4 + 5
32 + 42 = 52.
72 = 49
49 = 24 + 25
72 +242 = 252
getbixi · 1 points · Posted at 16:07:53 on February 14, 2016 · (Permalink)
1729 it is the smallest number expressible as the sum of two cubes in two different ways.
1729 = 13 + 123 = 93 + 103
1729 is one of four positive integers which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number:
1 + 7 + 2 + 9 = 19
19 × 91 = 1729
When constructing something, you can ensure square corners by making marks
3 units of measure down one side and
4 units down the other side.
Now make sure the distance between the marks is 5 units.
To quickly square a number ending in 5:
Take the digits preceding 5 and multiply by next ascending (Natural) number, then put a 25 on the end of this. Example, square 35:
3*4=12 352 =1225
Proof: Assume, for contradiction, that there exists a non-empty set of all positive integers that are not interesting. One of them is smaller than all the others, so it is the smallest uninteresting positive integer. That's an interesting trait, making it an interesting number. But our hypothesis assumes it is uninteresting! This creates a contradiction. Therefore the set of uninteresting positive integers cannot be non-empty. So all positive integers are interesting.
Given any integer in base 10, one can easily check it's divisibility of 3 by summing up all it's digits to see whether that sum is divisible by 3 or not. For example, 53358 is divisible by 3 because 5+3+3+5+8=24, which is divisible by 3.
The reason is remarkably simple: one can write 53358 into
5x10000+3x1000+3x100+5x10+8
=5x(9999+1)+3x(999+1)+3x(99+1)+5x(9+1)+8
=[5x9999+3x999+3x99+5x9]+[5+3+3+5+8]
The number inside the first square bracket is obviously divisible by 3, so if the number inside the second square bracket(which is the sum of the digits) is also divisible by 3, then the whole number is divisible by 3.
You can apply the same idea to check for divisibility of 9.
The divisibility of 11 is a bit more complicated. To check whether an integer in base 10 is divisible by 11, you sum up it's odd and even digits separately, then you check whether their difference is divisible by 11. Example: 30624 is divisible by 11 because the odd digits add up to 3+6+4=13 and the even digits add up to 0+2=2, their difference is 11.
9x11 = 99 Digits add to 9 when you add them up
9x12 = 108 Digits add to 9
9x13 = 117 Digits add to 9
9x14 = 126 Digits add to 9
9x15 = 135 Digits add to 9
I've never been much of a math whiz, but an easy way to calculate time occurred to me only a few years ago, while writing a program.
Say it's 4:33 and you want to figure out the time 36 minutes after that. Simply add 33 and 36 to get 69, subtract 60, and add an hour (since the result is >60). Your new time is 5:09.
My teachers tried to teach me this in elementary school, but I just didn't get it in those days. It seems easy and obvious now as an adult (with pre-calculus and Calculus classes under my belt).
The commutative property of addition (rearranging the numbers will give you the same sum) does not apply to some kinds of infinite sums. Meaning if you change the order of addition in certain kinds of infinite sums, you can change the answer.
The Pigeonhole Principle. If n items are put into m containers, with n > m, then at least one container must contain more than one item. For example, if you have 13 people together, there's a guarantee that at least two of them share the same birth month.
jpconn1 · 1 points · Posted at 18:53:12 on February 14, 2016 · (Permalink)
You can quickly determine if a number is divisible by 3 by adding up the digits. If the sum of the digits is divisible by 3, then the number is divisible by 3. Example 111111 is divisible by 3.
matti77 · 1 points · Posted at 18:57:14 on February 14, 2016 · (Permalink)
I figured out that there are APPROX the same number of drops in a gallon as there are seconds in a day.
I'm a plumber, so it's helpful to get a rough estimate how much water is being wasted. 1 drip/second is about 1 gal/day wasted.
Slamming it down on the stage was a reference to another comment about how this was turning into a rap battle. Your comments were excellent, even if I'm inclined to an anti-realist position myself.
A force of projectile gas, however brief, from the Gluteus Maximus while in space will propel the offender forward. Causing a trajectory to the planetary's atmosphere which burns to ashes the offender to death. So be warned, no matter what, do not eat last weeks bean burrito while floating in space with no space suit on, dua!
jdquinn · 1 points · Posted at 21:01:15 on February 14, 2016 · (Permalink)
You can determine if any number is divisible by 3 very easily without a calculator. Remove all digits that are 3, 6 or 9, then add the remaining digits, repeat if necessary until you obtain a single-digit number. If the result is 3, 6 or 9, the original number is divisible by 3.
826479166143, remove all digits that are 3, 6 or 9:
8247114, add these digits together:
27, add these digits together (since none are 3, 6 or 9):
9. 826479166143 is divisible by 3.
A shortened way of doing this is after step 1, as soon as you have an answer that you can identify as being divisible by 3 or not, that will indicate if the input is divisible by 3.
I think limits are fascinating. It's almost a way of sneaking impossibilities through until we can deal with them. Like the definition of derivatives. We sneak h=0 through an expression in which that's undefined until it is defined. Plus, it's like we're sneaking the secant line closer and closer to being a tangent line, and we end up with the slope at a single point.
Math is really cool if you've got instructors who explain it well, which I didn't learn until college.
Basically alternating addition and subtraction, 4 in the numerators, odd numbers in the denominators.
Granted, it's not a great formula. It takes hundreds of terms before you even hit 3.14. But it's still nice to know that it can be boiled down to something that simple.
saladaz · 1 points · Posted at 21:57:30 on February 14, 2016 · (Permalink)
that einstein equations are still being proved right
oxeimon · 1 points · Posted at 22:21:45 on February 14, 2016 · (Permalink)
This all depends on how you define the notion of limits, "distance", and convergence. There is a very special notion of convergence for which this is true, but it is of course false for the usual notion of distance (obviously 1+2+3+4+... gets arbitrarily large and doesn't converge to any finite number)
EDIT: Your statement is only true in some special p-adic topology
Thank you for introducing Dr. Tadashi Tokieda to me. I don't study math, but his teaching style and passion are lessons in themselves. He reminds me of how Richard Feynman can break something down.
Koisame · 1 points · Posted at 23:40:41 on February 14, 2016 · (Permalink)
Something related has been mentioned by u/Felix_Tholomyes, but if you were to chose a real number at random you would get a so called normal number with a 100% probability. The twist being that no normal number is known to us at all.
[deleted] · 1 points · Posted at 23:54:51 on February 14, 2016 · (Permalink)
1x1, 11x11, 111x111, 1111x1111, 11111x11111, 111111x111111, 1111111x1111111, 11111111x11111111, 111111111x111111111 in a song format if you ever took chorus class with a teacher that used that method.
1 + 1 = a window. Haha nah but when I was a kid it literally blew my mind that when drawn on paper it made out to be a window, I begun to question how it ever equaled 2.
The Dubins-Schwarz theorem ( roughly stating that any martingale is actually a brownian motion ) makes me uncomfortable.
Actually all the things relating to the Brownian Motion makes me uncomfortable
lilkobi · 1 points · Posted at 18:31:03 on February 26, 2016 · (Permalink)
Someone mentioned divisible by 9 integers adding up to 9. Pretty sure this stands true for divisible-by-3 as well. If the final result is 3, 6, or 9, the value is divisible by 3.
1149 -> 1+1+4+9=15 -> 1+5=6
1149/3=383
Take a book. Any book. Now count each time a word occurs, like how many times 'the' is written, but for every word. Take the most occurring word and halve the amount of times it was in the book, thats about how many times the second most common word appeared in the book. Now take 1/3rd of the original number and you have about how many times the 3rd most common word appears. Its called the zipf mystery
Circles don't actually exist in nature they are a human idealism as no real shape can have infinite sides so if you zoom in it will always be a super large number of sides shape ... I always find this one weird
IZ3820 · 1 points · Posted at 08:21:36 on February 14, 2016 · (Permalink)
Right? Cause I been trying to work it out, ohhhhh
[deleted] · 2 points · Posted at 23:58:53 on February 13, 2016 · (Permalink)
The number 64.
Stemming from the 8x8 principle.
The genetic code by which DNA stores the genetic information consists of "codons" of three nucleotides. The functional segments of DNA which code for the transfer of genetic information are called genes. With four possible bases, the three nucleotides can give 43 = 64 different possibilities, and these combinations are used to specify the 20 different amino acids used by living organisms.
There are also 64 squares on a chess board.
There are also 32, and 64 bit operating systems.
64 is also used in a principle law of the universe; but I can't remember it off the top of my head, I'll have to look into it when I get home.
There are also other instances of the number 64 in a lot of religious documents. But I'm not going to get into that.
Powers of two are just about everywhere. If there's 64, there are usually others, too.
43 = 64
43 = 64. To post that, you have to write 4^3 = 64 , and copy-pasting doesn't play fair with exponents in reddit. :/
OTOH, yes, 64 is a quite interesting number both in recreational math and application. It's a shame that your post ended up somewhere between "80085 on a calculator" and "root of 69" posts.
motoxer · 0 points · Posted at 00:57:23 on February 14, 2016 · (Permalink)
Okay, okay, since the whole -1/12 has been handled in other comments, no that sum is not equal to -1/12. -1/12 is the result of applying a regularization process to the series 1 + 2 + 3 + . . . . that is in now way what mathematicians mean when they write the series down, but is still incredibly important.
I still approve of that. Adding a positive to a positive equals a positive, so adding positive numbers forever to a positive number will always equal a positive number.
Right. And that's why in standard summation, the sum's value is infinity -- it is a divergent series.
What the -1/12 is measuring is the growth rate of a function which measures how the sum goes to infinity when you apply smooth weights to its terms. It is absolutely not the value of the series.
prmcd16 · 1 points · Posted at 03:03:38 on February 14, 2016 · (Permalink)
Seconded.
Melba69 · 1 points · Posted at 05:22:50 on February 14, 2016 · (Permalink)
Well that makes sense. You never see 2 odd numbers of 2 even numbers when talking about numbers sequentially right? If 3 is odd and 2 is even, that makes 1 odd and 0 even.
There is a trick to seeing if any number is divisible of 9. You sum up the digits together, and if the sum of the digits is divisible by 9, then the original number is also divisible by 9. If the sum is larger than 9, check to see if the sum equals 9 for ease. (Fun fact: same trick works for multiples of 3)
Examples:
09: 9+0=9
18: 1+8=9
72: 7+2=9
99: 9+9=18 ----> 18: 1+8=9
171: 1+7+1=9
So if you take any number that is using all the numbers 0-9, you can rearrange the numbers into these pairs:
(9+0)+(8+1)+(7+2)+(6+3)+(5+4)=9+9+9+9+9
and then sum them all together (each pair equals 9 independently).
And to finish it off, 9+9+9+9+9= 5(9)=45, 45 is divisible by 9 because 4+5=9. And yes, this last step i showed was redundant because you can already see that it is divisible by 9 because i just added only 9s together.
I'm pretty sure the term root has to do with some Latin translation (mistranslation?) of the radix, the radical symbol for square root. We also have cube roots which goes against the multiplication table theory, if I'm understating you correctly. Also, what would the square root of 5 or 7 be in a multiplication table?
This is just a question of notation. It's true because you have an infinite sum on the left side that converges to 1.
kikilio · 1 points · Posted at 21:11:46 on February 13, 2016 · (Permalink)
If you dropped any object into an airless, frictionless tunnel between any two points on Earth, it would take 42 minutes for that object to reach the other side of the tunnel.
[deleted] · 1 points · Posted at 21:45:51 on February 13, 2016 · (Permalink)
From the other side at some point, wouldn't it be acting against gravity?
The sizes of infinity. Let's just talk about positive real numbers here.
1) The positive integers. You know, 1, 2, 3, 4, 5, 6, 7 et cetera
2) The positive fractions (rationals). Integers divided by integers. You know, 1/2, 2/3, 1/3, 32/33, et cetera
3) The irrational numbers. Numbers whose decimal forms never repeat (so no 1/3 = .333333~), or numbers that can't be represented by a fraction. These are numbers like pi (3.1415...), e (2.7...), e + pi, sqrt(2), et cetera.
How many numbers are in 1) ? Why, infinity, of course.
How many numbers are in 2) ? Why, infinity, of course.
How many numbers are in 3) ? Why, infinity, of course.
Ahh, but are there more numbers in 2 than 1? Are there more numbers in 2 than 3 or 3 than 2?
Let's think about it intuitively. Take any two integers. Say, 4 and 5. There's an infinitie number of fractions between them (9/2, 19/4, et cetera). But take two fractions, say 1/2 and 2/3, and there are zero integers between them. So of course, there must be more fractions than integers, right? Similarly, take any two fractions, and there are an infinite number of irrational numbers between them. Also, take any two irrational numbers, and there's an infinite number of rational numbers between them. So 2) and 3) are the same size, right?
Wrong. 1) and 2) are the same size. And 3) is larger than either.
For some context and proof that 1) and 2) are the same size:
This really annoys me. The only reason people think it's cool is because it's unintuitive... if you don't know the more general, actually useful form of the equation.
It's like saying it logically makes no sense that the derivative of 2x includes ln(2), because why would 2 be related to e? Well because that's how e is defined.
Rivers have pi! The distance traveled is roughly the distance of source to mouth as the crow flies times pi. In other words, distance traveled : distance = pi, on average.
What is seriously, seriously cool, is that with all the kerfuffle around the Numberphile video purporting to show infinity, or rather 1+2+3+4+5..., = -1/12 , it turns out that if you take all the numbers both positive and negative and graph them -1/12 pops up beautifully.
By that I mean the summing of all numbers including decimals and negative numbers. For instance ...-0.2 + -0.1 + 0 + .1 + .2 ....
If you minus the area under the graph above the x axis on the left from the one on the right you get zero leaving the sum of all numbers through to infinity at -1/12!
I consider myself not all that mathematical but this little gem has intrigued me to no end. Love it.
Why would that area be equal to the sum? Shouldn't the sum be dependent on the behavior as it gets higher, not what happens between 0 and -1?
Also, that sum is entirely unrelated to the "sum of all numbers". There is no sum of all numbers.
All I'm doing is taking the area from the left side of the graph, which is a positive number even though it represents negative numbers and taking it away from the area on the right hand side of the graph which would leave us with zero. I don't claim this is legitimate since I don't have the mathematical skills to say so. But the area left is -1/12.
Also, your sum "... + -.2 + -.1 + 0 + .1 + .2 + ... "misses an infinitely larger amount of numbers than it captures.
But the graph captures them. It doesn't matter how minute you go they will still represented in the graph, remember we are graphing sequential additions.
I agree that it's interesting, and may even be relevant. It's disengenuous to call that the sum of all natural numbers, though, for several reasons.
Perhaps, and I was at pains to point out my numerical illiteracy, but to have the Numberphile crew do their machinations and get a figure of -1/12th then to find the same number appearing when all the positive and negative sequential additions are graphed I thought was pretty bloody cool. To dismiss it as a fluke or merely interesting I felt doesn't do it justice which is why I thought it 'the most interesting fact I know'.
The Numberphile video is wrong. There's a way to make it accurate, but nearly every statement there is blatantly false. (I wrote it up elsewhere in this thread.)
Also, that is not a graph of sequential additions. That is the graph of the analytic continuation of the sum of the first n natural numbers. The "analytic continuation" is just the function that behaves nicely that happens to pass through those points. It's not the same thing as the original function. The original function doesn't say anything at all about negative numbers or non-integers!
Oh, and there is no sum of all real numbers. There is no way to define it to make sense.
Yes, it's pretty cool, and it may even be related to how they get -1/12. However, calling that area the sum of anything is simply false. unlessyougetintothedefinitionofareaunderacurve(akaintegral)incalculusandeventhenit'snotthesumbutthelimitofasum
More than happy to bow to your obviously superior grasp of mathematical nomenclature and concepts, especially since mine is so woeful.
I found the clash between the physics and the mathematical fraternities over the video really interesting and great fun for an outsider like myself.
What is obvious though is that physicists find -1/12 useful in their calculations and reflected in the real world. For it to appear visually tickled my fancy and my uneducated guess is that it will probably be found to have greater importance than it is given at the moment.
Edit: Additional thoughts.
Also, that is not a graph of sequential additions. That is the graph of the analytic continuation of the sum of the first n natural numbers. The "analytic continuation" is just the function that behaves nicely that happens to pass through those points.
The graph surely is the function of all numbers both negative and positive and of an infinite degree of minutia which must be a truer representation of infinity I would have thought.
It's not the same thing as the original function. The original function doesn't say anything at all about negative numbers or non-integers!
Which might give cause to question Numberphile's presentation but doesn't negate what I have put.
There's no clash, and we're fully aware that it has some importance (though not as much as you make it out to be). Often, the sudden appearance of -1/12 signals that there's a regularization hidden somewhere in the formula which "lets through" regular infinite series unchanged but assigns finite values to normally infinitely large sums.
Zeta regularization and Ramanujan summation are both used frequently in mathematics and physics.
Honestly, that video turned me off of Numberphile in general. If you want interesting math channels, I recommend these (none of them require any math knowledge past 6th grade; favorites bolded):
Quirkology, magic tricks based on physics and psychology.
Veritasium, interesting explanations of physics and chemistry.
Tom Scott, who visits various places around the world to point out interesting facts. Also has an entirely unrelated but still interesting series on linguistics.
Big Shredder, in case you want to know what things look like when they get thrown into a big shredder.
There's no clash, and we're fully aware that it has some importance (though not as much as you make it out to be).
Well you seem to be very dismissive of the two physicists in the Numberphile video and by extension of Ramanujan.
"Dear Sir, I am very much gratified on perusing your letter of the 8th February 1913. I was expecting a reply from you similar to the one which a Mathematics Professor at London wrote asking me to study carefully Bromwich's Infinite Series and not fall into the pitfalls of divergent series. … I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + · · · = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. …"
I do like Feynman's take on the difference between the approaches of each fraternity.
He talks about understanding the connection of the words with the real world.
I would have thought if -1/12 is useful in understanding String Theory then it is the job of physicists to use the tool if they are comfortable doing so. It is the job of mathematicians to explain why it works in the real world.
the whole thing is an over 100 year old hoax to show that you cannot use the same mathematical formula manipulation proofs on an infinite series that you would a normal equation.
as much as I hate to burst everyone's bubble, 1 + 2 + 3 + ...., = ∞
[deleted] · 1 points · Posted at 01:16:22 on February 14, 2016 · (Permalink)
If you shuffle a full deck of cards, it is extremely likely the cards have never been in the order you just put them in. Ever.
Xazrael · 1 points · Posted at 01:17:35 on February 14, 2016 · (Permalink)
There's a card trick I know that, using 21 cards, if you pick any card, and I shuffle its row into the middle of the deck, I can find your card by shuffling the deck back together 3 times - and it'll be the 8th card I draw from the top of the reshuffled deck.
The Drake equation.. N = R* • fp • ne • fl • fi • fc • L.. a probabilistic argument used to arrive at an estimate of the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.
A hexagon has the highest surface area to perimeter ratio of any shape. In layman's terms, if you have a rope of a given length and want to enclose as much space as possible with it, you should make a hexagon. This is why bees build hexagonal cells in their hives, and hexagons show up frequently in nature
Bees use hexagons because they have a high surface area AND and they tile well (like squares). When it comes to just the surface area, circles are the best. That's why bubbles are spherical (3-d version of spheres)s
I always thought it was really cool that there are infinitely more decimal numbers between 0 and 1 than there are whole numbers between 0 and infinity.
Yeah, the natural numbers are countable. However, the irrationals are uncountable. It is fascinating. You ought to consider looking into measure theory. Try reading up on the cantor set.
[deleted] · 1 points · Posted at 05:16:30 on February 14, 2016 · (Permalink)
What I got from that article is that 1+2+3+4... can be assigned the value -1/12, but using the word "sum" or "equals" is misleading. The article complains about how it was explained, not that it's wrong.
I can't remember the exact theory, but if you travel out far enough in the universe, like trillions of lightyears, the combinations of atoms start repeating and running out if combinations.
No. A real number is either rational or irrational. By definition, a real number is rational if it is the ratio of two integers, and an irrational number is a number that is not rational. 1 is rational whether you write it as 1 or as 0.9999....
There was a man years ago; I'm sorry I don't remember his name or any integral information of the sort, but he proved to 100% mathematical certainty that human kindness was purely a survival tactic. He later killed himself due to his inability to reconcile such a discovery. His findings and formulas were also completely original; void of any sources or citations whatsoever.
There are so many possible combinations of a deck of cards that if you shuffle a deck it is most likely that the arrangement you are holding has never before existed.
8.0767 arrangements of cards possible for a standard deck of 52 playing cards.
If you rearranged the deck in a new arrangement once every second since the big bang (13.8 billion years ago) you would still be making new combinations today and for millions of years to come.
Sabbaer · 1 points · Posted at 09:27:54 on February 14, 2016 · (Permalink)
1+1=2
awaqu · 1 points · Posted at 09:41:53 on February 14, 2016 · (Permalink)
0.999_ does not = 1 becuse it would take infinite time and space for it to. It only theoretically = 1.
1/3 = 0.333_
2/3 = 0.666_
3/3 = 0.999_ = 1?
This is proof that math is imperfect when forced to define either infinity or zero and thus I theorize that "fractions" are a manmade construct and reality doe snot work in fractions, but in wholes and there comes a point where there is both an indivisible quantity and a finite quantity.
I agree. Just cause people can make it seem like they equal each other by writing it out, thinking in reality the fact that 0.999... is a different number than 1. 0.999... will equal 1 - .000000......1.
[deleted] · -3 points · Posted at 23:03:47 on February 13, 2016 · (Permalink)
It is also hypothesized that mitochondria originally were independent prokaryotes that got engulfed by a larger bacteria, which then developed a symbiotic relationship!
kionih · 0 points · Posted at 20:48:12 on February 13, 2016 · (Permalink)
According to the Giant Impact Hypothesis, a Mars-sized object collided with Earth at an oblique angle, obliterating a huge section of the existing upper layers and ejecting a massive amount of material into orbit. Much of this material coalesced and became the moon as we know it.
Now....what is REALLY cool is that the moon used to be a lot closer. So much so that several billions of years ago the entire lunar cycle was on the order of hours, not days. The moons orbit has been slowing as its distance has been increasing from the Earth.
Whilst the Earth was in a semi-molten, pre-crustal period of early development, the proximity to the moon, combined with the very short orbital period meant that the tidal forces that the moon exerted on the Earth were vastly stronger and more frequent.
In effect, this means that the early moon was capable of producing a perpetual "Wave" that would be experienced across the Earth several times a day due to the effect of this tidal bulge. As the Earth's surface was still in a semi-molten state, this would have appeared to a static observer as a gigantic lava wave, circling the Earth multiple times per day.
It may not be the coolest one here. Personally I love so many of these but can we take some time to acknowledge our great lads Pythagoras and Newton. I know we learn their works in high school but just think how much this has opened up for us!!
heap42 · 1 points · Posted at 00:11:29 on February 14, 2016 · (Permalink)
Right?... I mean all these highly complicated are fucking useful and awesome and all... but sometimes i am just in awe when i think that a few thousand years ago people managed to come up with things like Pythagoras etc... and then we got days like these where we somehow managed to measure Gravity Waves and simultaneously still kill each other and hate each other and have Wars and all that shit.
sweetei · 0 points · Posted at 21:46:08 on February 13, 2016 · (Permalink)
Shuffle a deck of cards. Chances are ( by a huge degree), that no deck of cards has ever been in that exact order. There are precisely '52!' Possible arrangements for a deck of 52 cards. This number, 8.1 x 10 ^ 67, is greater than the number of stars in the known universe.
graaahh · 0 points · Posted at 22:05:27 on February 13, 2016 · (Permalink)
The number of inches in a mile is equal to the number of astronomical units in a light year to within a fraction of a percent.
Also equal to within a fraction of a percent: the volume of a sphere with a radius of one kilometer and the volume of a cube with a side length of one mile.
Euler's Equation (Identity): ei*pi + 1 = 0. Not only is this equation incredibly useful, especially in complex arithmetic, there is a kind of beauty to it as well. It includes many important numbers such as e, i, pi, the additive identity 0, and the multiplicative identity 0.
The number 6 is in wit-sec, because it knows 7 is a cannibal.
dpfw · 0 points · Posted at 22:57:56 on February 13, 2016 · (Permalink)
Take your age, divide by two, add six, subtract zero, multiply by two, subtract twelve. That's you're age.
[deleted] · 0 points · Posted at 22:59:13 on February 13, 2016 · (Permalink)*
There is a number so large, if you could think of it in terms of it's individual numerals all at once, that amount of data would cause your brain to collapse into a black hole.
That makes no sense. Black holes are caused by extreme densities (I.e. the mass of a star collapsing). Thinking about large amounts wouldn't cause your brain or anything inside your brain to increase in mass or density at all, since the brain operates by electricity.
[deleted] · 2 points · Posted at 04:28:07 on February 14, 2016 · (Permalink)*
Electricity works on the same physical properties everything else does and EVERYTHING has mass, or effects mass.
You can argue all day about what the number is, but since thoughts aren't magic, if you had enough thoughts in a confined space...Poof.
Cwmcwm · 0 points · Posted at 23:07:01 on February 13, 2016 · (Permalink)
An infinite number of engineers walk into a bar. The first one says "one beer, please". The second, "1/2 beer please". The third "1/4 beer, please". The fourth, "1/8 of a beer, please".
The bartender/mathematician replied "okay, okay two beers, comin' up".
kvlxm · 0 points · Posted at 23:08:08 on February 13, 2016 · (Permalink)
Dolly Parton weighed 69 pounds. The doctor said that was too (2) too (2) too (2) much, so he told her to take 51 of these pills, 8 times a day, and then she was...
6922251 x 8 = 55378008
Raherin · 0 points · Posted at 01:19:26 on February 14, 2016 · (Permalink)
5318008 = BOOBIES
[deleted] · 0 points · Posted at 01:21:23 on February 14, 2016 · (Permalink)
The sum of all integers (ie 1+2+3+4+5... +(n+1)... where n is any integer) is equal to -1/12. Numberphile did a simplified proof on their YouTube channel for everyone that doesn't study string theory.
The universe works on a math equation
that never even ever really even ends in the end
Infinity spirals out creation
We're on the tip of its tongue, and it is saying
We ain't sure where you stand
Supposedly, there is a theory that states that any two people in the entire world can be connected by 6 connections. Connections being people that you know. So like, I know a guy in Israel, who knows a guy in Jordan who knows a guy in Syria who knows a guy who works for Isis who knows the leader...etc. makes sense, but I'm sure there are some exceptions. But for the majority it seems plausible.
Santa Clause exists:
Let S be the statement "if S is true then Santa exists". Try to prove by assumption and see if no contradiction is reached. So assume S is true. Then the statement "If S is true then Santa exists" holds, and since S is true, then Santa exists. So far we have proven that if S is true, then Santa exists, which is the statement S.
So we know that S is true. And this is the statement "If S is true then Santa exists". So it follows that Santa exists.
The rule of 70. If you want to know roughly how long (in years) an investment will take until it doubles in value, just do 70/r (where r is the rate of return.)
I suppose this is more statistics than mathematics, but you know that saying "a million monkeys with a million typewriters will eventually create the complete works of Shakespeare"? Well, it's technically true, but people tend to underestimate just how unlikely it is of happening, by, uh, a lot. Statisticians are kind of upset by it because it gives people a poor sense of scale for both how long infinity is, and just how random events can be.
"Even if every proton in the observable universe were a monkey with a typewriter, typing from the Big Bang until the end of the universe (when protons no longer exist), they would still need a ridiculously longer time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10500 chance of success. To put it another way, for a one in a trillion chance of success, there would need to be 10360,641 universes made of atomic monkeys."
This is just for Hamlet, with a 26 character keyboard, ignoring punctuation, spacing, and capitalization.
Really late posting so no one will probably see this, but there is a relatively simple connection, for lack of a better word, between the squares of 2 numbers and the numbers themselves. I discovered this when I was in the 4th grade all by myself and was really proud of it at the time.
Take 6 and 7 for example. 62 is 36 and 72 is 49. Now if you take the original numbers and add them up you get 13, which just so happens to be the difference between the 2 squares. The formula, which I am just now making up on the spot, should be
b2 - a2 = a + b
where a and b are two positive whole numbers directly next to each other on the number line and b is the larger of the two numbers.
Not really that cool but it's cool to me because I independently thought of this at a young age.
I might be wrong, but I have tested it with a few different numbers and it seems to work for them all that I've tried it with. Can you think of any of any of the numbers that don't go with it off the top of your head?
For starters the sum S1 that he claims equals 1/2. If you gave that to any mathematician, not a single one would say it's 1/2. The answer would be DNE.
He is a mathematician though, which throws a monkeywrench in that logic. And while it's divergent, it's Cesaro sum is 1/2, and though that only makes so much sense to me, it seems plausible.
Vortico · 1 points · Posted at 18:51:45 on February 14, 2016 · (Permalink)
Right, I just wanted to be clear that in order to get the result -1/12, you have to decide on an extension of the definition of an infinite sum. You could just as easily come up with another arbitrary method which "assigns" the sum the value 17, for example. Regardless, the sum doesn't exist in the traditional sense without stating your regularization method.
Yes, understood. But, "arbitrary" is much more interesting when it actually has implications that we can demonstrate about the universe. The thing about our mathematical system is that it's abstract. Things like infinity doesn't really even make sense in a finite universe. Computation devices such as Turing machines don't even exist in a finite universe.
em3am · 0 points · Posted at 04:04:21 on February 14, 2016 · (Permalink)
The only five numbers you need: 0, 1, pi, e, and i.
I don't know quite how to word this but let's give it a shot.
If you think of a number let's use 16 as an example, and then think of everything that ads up to it. For example:
Correct, it diverges because limits approach infinity but never quite get there. If the sum were to be carried out to infinity, it would result in -1/12. Which is ridiculous, but is apparently backed up by quantum theory.
Vortico · 2 points · Posted at 20:35:32 on February 14, 2016 · (Permalink)
"Carried out to infinity" isn't rigorous. If you were to say "The zeta renormalization of the sum is -1/12" you would be correct since you're extending the definition of infinite sums, but without state this, there is no number which is a limit point of the sequence of partial sums.
MetaMD · 0 points · Posted at 04:24:07 on February 14, 2016 · (Permalink)
1+2+3+...... = -1/12
Vortico · 1 points · Posted at 07:00:46 on February 14, 2016 · (Permalink)
No, the sum diverges.
MetaMD · 1 points · Posted at 07:25:12 on February 14, 2016 · (Permalink)
It doesn't actually. You can find several rigorous proofs of this. Crazy that you would just comment like that.
Vortico · 1 points · Posted at 07:41:05 on February 14, 2016 · (Permalink)
I would agree with you if you say "The zeta regularization of the sum 1+2+3+... is -1/12", but by the traditional meaning of an infinite sum, it certainly diverges.
bla4562 · 0 points · Posted at 04:24:13 on February 14, 2016 · (Permalink)
pi never repeats
[deleted] · 0 points · Posted at 04:27:02 on February 14, 2016 · (Permalink)
[deleted]
Vortico · 1 points · Posted at 07:00:21 on February 14, 2016 · (Permalink)
Surprised that this isn't at the top: sum of all natural numbers is -1/12
ie. 1+2+3+4+5+6+...=-1/12
Edit: natural numbers not the set of real numbers.
Vortico · 1 points · Posted at 06:59:07 on February 14, 2016 · (Permalink)
No, the sum diverges.
[deleted] · 0 points · Posted at 04:28:28 on February 14, 2016 · (Permalink)
The sum of the natural numbers (positive counting numbers) is equal to -1/12.
Vortico · 1 points · Posted at 06:57:37 on February 14, 2016 · (Permalink)
No, the sum diverges.
[deleted] · 1 points · Posted at 13:46:22 on February 14, 2016 · (Permalink)
The regularized sum converges, using the Riemann zeta function. This result is extremely important in quantum physics and string theory, and also explains many observed natural phenomena, including the Casimir effect
Vortico · 1 points · Posted at 07:20:04 on February 14, 2016 · (Permalink)
I wish this video didn't exist. It confuses way more people than helps. Zeta function regularization is used in a few areas of analytic number theory, which has strong applications in QFT. However, I've only seen the method used in computation, where another more difficult method could also do the job.
Regardless, the uses of this somewhat obscure technique doesn't change the fact that by the traditional meaning of a sum, it certainly diverges.
Vortico · 1 points · Posted at 20:30:35 on February 14, 2016 · (Permalink)
Whoops, I made a small mistake. Hyperbolic spaces contain a point at infinity but there are geodesics which do not intersect. It's true about projective spaces.
Yurei2 · 0 points · Posted at 05:17:46 on February 14, 2016 · (Permalink)
Pi doesn't actually go on forever. Since there is a smallest possible small in the universe (see Plank length) and pi is an expression of a geometric length (the ratio of diameter to circumference) at the point where the distance expressed hits the plank limit pi stops. True, it technically keeps going but after that point its just irrational nonsense with no possible use or purpose.
Vortico · 1 points · Posted at 06:17:51 on February 14, 2016 · (Permalink)
The definition of pi has nothing to do with the discretization of the universe.
Yurei2 · 1 points · Posted at 06:55:45 on February 14, 2016 · (Permalink)
While true, that is also false, because if it can't exist in reality or doesn't exist in reality, it's fictional. Meaning after point X, further numbers of pi are fictional in nature.
Or in short, the laws of physics prove math is fictional stuff made up by humans and not the word of god as math lovers insist it is.
Vortico · 1 points · Posted at 07:23:14 on February 14, 2016 · (Permalink)
true = false
I can't debate this.
Yurei2 · 0 points · Posted at 12:07:36 on February 14, 2016 · (Permalink)
Welcome to the real world. Where light can be both a particle and a wave at once, certain subatomic strata can apparently spontaneously generate, and quantum superpositions prove things can exist in multiple states at once.
seran0 · 0 points · Posted at 05:19:17 on February 14, 2016 · (Permalink)
Probably the mathematical constant e.. I am not really versed enough in Math to explain it, but when I learned it, how it was found and its relevance in the universe, it kind of blew my mind.
It's the highest growth factor. In a sense that ex >= xe for any x that is a real number. If you take the limit as n goes to infinity of (1+1/n)n then you get e.
Psykerr · 0 points · Posted at 05:45:08 on February 14, 2016 · (Permalink)
Obviously. I should have added this is a college public speaking class. We were all waiting for this guy to go on with his "magic trick" but he just like stopped at that point and sat down.
The idea that two seemingly unrelated mystical irrational numbers combined with an imaginary one gives -1 is absolutely magical. A co-worker claims that this is proof of divine creation.
Actually those equalities are both wrong. Any decimal requiring repetition to infinity is an approximated by the given fraction.
It's the same as Pi not having a definite fraction. So 1/3 ~= 0.333...
and 0.333... = 333.../1000...
The thing to remember is that the decimal system is an expansion of fractions by use of exponent placeholders. So 123.456 is really just a shorthand way of writing out 1x102 + 2x101 + 3x100 + 4x10-1 + 5x10-2 + 6x10-3. A fraction is a ratio of two numbers in any given number base, and the decimal equivalent or approximation is just a way of representing that fraction in a different way. It's very possible to have a fraction that can only be represented as a fraction and not written into its decimal equivalent; in fact it happens all the time. A common misconception is that "rational" numbers are numbers that can be and are written in decimal form, but the only requirement for a number to be rational is that it can be written in "ratio" form (i.e., as a fraction of two numbers in the given base).
The summation of all whole integers from 1 to infinity is -1/12. Think about that. Adding every single number from one to infinity gives you a negative number. And a fraction.
Because Pi is an infinite number, it contains EVERYTHING represented in numbers. It holds the answer to all our questions, the fate of our futures, the code for all computing, absolutely everything... We just can't single out which part is what.
Kleenme · 0 points · Posted at 08:09:11 on February 14, 2016 · (Permalink)
It was actually a lot more complicated than just that. But I had a calculus teacher show it to the class once. This was over a decade ago, or I'd post it all up.
If you subtract the year of your birth from this year (2016), the resulting number will be your age! How freaky is that? And it gets even weirder; it works for other people's year of birth too!
When I started dating, my grandfather said this, "so...I hear you got yourself a girlfriend. Just remember, one plus one equals three." This counts, right?
Not actually known for sequences of arbitrary length, although I'm sure it's true for short sequences like those
Dinkir9 · -3 points · Posted at 21:12:02 on February 13, 2016 · (Permalink)
I fucking love mathematics so I have several...
The area under the equation: e-(x2) (thats -x2 im having trouble getting it to work right on my phone) is the square root of pi.
The ratio between consecutive fibonacci numbers approaches the golden ratio. ((1+sqrt5)/2)
The continued fraction form of e is 1:2,1,1,5,1,1,8,1,1,11,1,1,14....
e2(pi)i=1 (by changing that 2 to x its running on a cosine curve essentially)
Every single composite number can be defined as the sum of 2 prime numbers.
1-1/2+1/3-1/4+1/5-1/6.... is the ln(2) or 0.693.....
The Gamma function can be used to find the factorials of decimals... Factorials being... 8!=1×2×3×4×5×6×7×8 (see where the problem arises finding decimals?)
I've got more but I don't want to get too crazy here
Mazork · 2 points · Posted at 22:43:55 on February 13, 2016 · (Permalink)
Every single composite number can be defined as the sum of 2 prime numbers.
You're saying I'm part of the reddit hivemind because I agreed that you made a mistake? Wow, dude. Ok.
Math is all about proofs and rigor. You made a claim that something was a "mathematical fact" when it's not actually known yet. That's all.
Dinkir9 · -2 points · Posted at 06:27:17 on February 14, 2016 · (Permalink)
A lot of things aren't known yet we accept them as everyday fact. For all intents and purposes it's a fact, any,number you would care to test would work out. The only point of proving something in math is so that you can exploit it and connect it to other things in math, proving something works or doesnt work? Well that's kinda already known beforehand by the people working on this 'proof'.
Would it be better if I said "It's theorized that any composite number can be defined as the sum of two primes?" Still interesting and I thought it was cool, but you'd rather twist my words and nitpick at an individual point instead of accepting several cool little pieces of mathematical trivia. Oh and most people (such as the Reddit hivemind) would have simply accepted what I said and moved on without that guy stating that it wasn't actually a proven fucking fact. Yet it's so damn functional and practically true that it's like Einsteins Theory of Relativity, nobody knows how or why but it just works and you're gonna have to get over that, unless you want to take it up with the man himself?
You realize number theory conjectures that had been checked to ludicrously large numbers have been later proven false, right? It's not nitpicking; it's the way mathematics works, which is fundamentally different to the nature of experimental sciences.
The only reason this exchange is happening is that, when presented with a comment that your facts were not yet facts (and might not be facts!) you tried to make fun of the commenter. He/she was just trying to make a polite point.
[deleted] · -3 points · Posted at 02:34:53 on February 14, 2016 · (Permalink)
1 black person = 3/5 of a white person
[deleted] · -2 points · Posted at 23:05:46 on February 13, 2016 · (Permalink)
0 is not a perfect 0. there are no absolute values. 0 is actually 0.000000000000000000000000000000000000000000000000000000000000000000000000000001 for example.
Kevlar98 · -1 points · Posted at 20:47:16 on February 13, 2016 · (Permalink)
The collatz conjecture. Any number can get to one by dividing by two if even or multiplying by 3 and adding one if it's odd and repeating with the results.
[deleted] · 1 points · Posted at 20:58:26 on February 13, 2016 · (Permalink)
What he's saying is that sin and cos have a "fixed point" (a point where x=sin(x)) and further, that no matter what you start with, the sequence obtained by repeatedly applying sin (or cos) will always converge in that point.
If y = Sin(sin(sin(...sin(x)...))) where x is any real number
y=sin(y)
sturio · -1 points · Posted at 20:57:57 on February 13, 2016 · (Permalink)
You can cool something to absolute zero (almost) by shining lasers at it.
It works like this. Imagine there a bunch of people at the beach. These are the atoms in your substance. Now imagine them trying to walk around in the waves. The waves are the lasers beams traveling in one direction. When the people (atoms) try to walk against the waves, they slow down. However, walking in other directions doesn't really affect them at all. So the net effect is that the people keep walking slower and slower, until they have almost stopped. A similar thing happens to atoms. When they travel towards a laser beam, they see a certain energy from the laser. This energy makes them slow down. However, when they travel in different directions, they see different energy that doesn't effect them at all due to the doppler effect. The result is that the lasers only work to slow the atoms down (make things colder), but never to speed the atoms up. So if you keep the energy of the laser at the right energy, it will eventually slow the atoms down until they reach absolute zero (almost).
Late to the game, but BY FAR the most interesting mathematical fact I've ever seen is that the sum of all integers from one to infinity equals negative one twelfth, or:
1 + 2 + 3 + 4 + ... = -1/12
This has actually been proven both mathematically and in observations in quantum mechanics. It is the craziest, most unintuitive math fact I've ever seen. 60 symbols does a great video on it here:
Oh god, I think I'm gonna have a stroke responding to these for some reason. That identity isn't true; the sum used in quantum mechanics is a regularized sum and is quite different from standard summation.
RazarTuk · -1 points · Posted at 00:51:14 on February 14, 2016 · (Permalink)
1+2+3+4+5+6...= -1/12. It can be proven and it's a result that actually comes up in some experimental, empirical observations involving advanced physics. https://www.youtube.com/watch?v=w-I6XTVZXww
It appears in string theory and lots of other places in physics, but what it really shows us is that human intuition about math is very wrong, and that our understanding of even the topic of mathmatics is very limited as a human species.
When you subtract infinity from infinity, the standard rules of math break. Real Analysis, at least at the foundations, does not attempt to define infinity - infinity. The intuitive argument for that proof is... Interesting though.
There are plenty of places in math and physics where this "sum" appears, and astoundingly the math only works out if you plug in "-1/12". These occurrences are also unrelated to each other, so this is not a single "math trick", but is more of a truth of reality. It may be similar to how i (sqrt of -1) also needs to exist in mathematics even though it alone is nonsensical.
Using root(-1) is adjoining the field of real numbers with i. Kind of like when you use an (x,y) coordinate plane. Only, multiplying everything by i gives a rotation of 90 degrees on your plane. If you worked with quaternions it's similar there. It's not in the least bit nonsensical.
Saying 1+... = -1/12 < 1 defies that the characteristic of the real numbers is 0. I believe the proof works, and that it can have some meaning in some places. Though, I would need to see them myself to agree they could be on the level of the development of the complex plane.
CJamezon · 1 points · Posted at 13:04:06 on February 14, 2016 · (Permalink)*
FYI: I have a degree in Mechanical Engineering, and have been doing robotics, machine simulation, inverse kinematics, since 1990, and have written over 1,000,000 lines of code involving complex numbers. I think perhaps you need to just get over yourself, and perhaps drop the "oh no it isn't" attitude. Just a life tip for ya.
You're the kind of person who would have told Einstein "action at a distance" was not the least bit "spooky", despite knowing less about it than him...and when he corrected you, you'd call him disgruntled. You know that's precisely what just happened. Enjoy being you.
[deleted] · 1 points · Posted at 18:41:04 on February 14, 2016 · (Permalink)
The Einstein analogy was about how you would react to the word "spooky" if he made the mistake of saying it to you in social media. It wasn't about my knowledge level, and you know it. Nice try pretending not to understand what my point was. Didn't believe a word of it.
About -1/12, I don't think anyone fully understands that. Math can be somewhat counter-intuitive at times, like in Quantum Mechanics, where two contradictory things can both be true at the same time, because a physical object can be in two locations simultaneously. You know the famous quote: "If you think you understand QM, then you definitely don't understand QM." The wikipedia page on "-1/12" has a section titled "Physics" that are the primary two examples of it's use, with one being so important that it would indicate there are 26 dimensions to our reality.
1-1+1-1+1-1+1-1+1.....=1/2 (..... Means to go into infinite). Also when a person pedals a bicycle the point the tire contacts the ground is not moving. Some of the things I've learned in Calculus.
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to infinite divergent series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.
I'm not sure what you think you're accomplishing here. There is an interesting result from an obscure branch of number theory in which the equivalence I reported holds. This result turns out to have applications in physics, especially in predictive models about the real world. Thus there are both theoretical and empirical contexts in which the statement I made is "true."
Your complaints thus far are a bit like a Calculus student insisting that one must never divide by zero. In fact, l'Hopital's rule widens, though does not erase, the constraints on dividing by zero. Similarly, results about connectedness (for example) which hold for metric spaces might fail in more arcane topologies. That does not mean that you'd be justified in saying that a connected subspace is not closed and bounded (just because not every single topology has a metric).
When you insist that we must never repeat this interesting -1/12 result by Ramanujan, it says only that you aren't interested in playing with math the way that I'm playing with math. It doesn't prove me "wrong."
So to repeat, I'm not sure what you think you're accomplishing here.
Try looking it up further. It's still not right, and the actual reason why -1/12 is an important value for that (divergent to infinity) series is far more complicated.
[deleted] · -1 points · Posted at 03:03:16 on February 14, 2016 · (Permalink)
1+1=1.
Don't belive me?
Let's say you have two groups of people.. if they come together how many groups do you have?
One.
Your welcome.
*also if you think about it everyone and anyone is still only one.
nemoking · -1 points · Posted at 05:42:03 on February 14, 2016 · (Permalink)
Graham's number is so big that if the human brain had the ability to be able to understand it, it would need to be so dense that it would reach the schwarzchild radius and collapse into a black hole.
Vortico · 1 points · Posted at 05:54:37 on February 14, 2016 · (Permalink)
What do you mean "understand"? You can write down the definition, compare it with other numbers, multiply and add it to other numbers.
You know how when you think of a number like 3 or 5 you can visualize that number, immediately recognise that number of items without thinking etc etc. Thats what I mean by 'understand'. I'm no maths proffessor (just a lowly law undergrad), but I remember seeing this in a series of videos on Youtube by the channel, NumberPhile.
Vortico · 1 points · Posted at 06:26:26 on February 14, 2016 · (Permalink)
If visualizing an array of n objects is your definition of understanding a number, you definitely don't need to go as high as Graham's number. 10100 will do it (with the rough assumption that you need as least n neurons to visualize n.)
baronmad · -1 points · Posted at 05:43:23 on February 14, 2016 · (Permalink)
Fact is a bit misleading when it comes to this one.
That if you add all the positive numbers together, 1+2+3+4... all the way to infinity the answer you will get is -1/12 from nothing but positive numbers you come out with a negative number.
This is not a fact as such because in mathematics limits doesnt work on a convergent series because they dont have a limit.
1+2+3+4+... does not equal -1/12. One way of associating a value to divergent series happens to associate the value -1/12 to this series, but that does not mean that the sum of this series is -1/12.
there are infinitely many kinds of infinity. one of them is countable, all of the others are uncountable
0.000...1 is equal to 0 so that has nothing to do with infinity (and there are only countably many 0s in "0.000..." anyway. also your first list is finite
it's not quite an equality though, it's just a value that we can assign to a series even when it diverges. it doesn't really make sense to say that the sum is actually equal to -1/12.
Regularizing divergent series using a number of different methods has long been recognized as mathematically sound, and has been used in a number of useful ways in other areas of mathematics, and even in physics. This blog post by the one of the mathematicians who appears in the video links to a lot of resources, and provides a lot of explanation, for why this is not some mathematical bullshit, and why it is actually a useful and valid value to assign this sum.
I'm not saying it's bullshit, I'm just being a little bit pedantic and justifying what the other poster mentioned. We don't say that the sum is actually equal to -1/12, but rather we are assigning the value to it because it makes it easier to manage (we don't want to deal with infinity, especially in physics). Look carefully at the language used, we never actually state that the sum is equal but rather that we associate/attach this particular value with the sum. There is a quite distinct difference.
It does sort of take away from the magic of it all, but this is not an arbitrary assignment, and as you mention, has many applications in other fields.
I already did. It's in the video, which you didn't watch, where three mathematics professors from the University of Nottingham explain why this is true.
I guess you didn't read the description of the video because it clearly states "Tony Padilla and Ed Copeland are physicists at the University of Nottingham."
They're currently physicists, but Tony Padilla was formerly a professor in math, and has a BA in maths from Cambridge. You're right that Ed Copeland does not have a degree in math, but as a physicist he had to study the hell out of it nonetheless. But fine, if you'd like to split hairs, here's a video on the same subject from Edward Frenkel, a math professor at cambridge, and here's a paper by Terrance Tao, math professor at UCLA. Speaking of which, someone who is so confident in their understanding of math to doubt physics professors at Nottingham must have a pretty strong background in math. How many years have you studied it? Was it all the way through high school? Or did you need to do another year in college?
[deleted] · -2 points · Posted at 04:44:14 on February 14, 2016 · (Permalink)
You linked to a video about laptop batteries, so I'm not sure how to help you.
In any case, the series 1+2+3+4+... diverges. In other words, as you add more numbers, the sum gets larger and larger without bound. There is a way of assigning the value -1/12 to the expression "1+2+3+4+...", but that does not mean that the sum of the natural numbers is -1/12.
Ugh, I am getting seriously sick of misinformation being spouted here. Read the other comments on the other 500 times this is mentioned in the thread, talking about what this "series" means, because that identity is flat out wrong at worst, and severely misleading at best.
boom456 · -3 points · Posted at 22:12:00 on February 13, 2016 · (Permalink)
1+2+3+.... = -1/12
(or something along those lines.)
Most other things listed here I can almost wrap my head around some way or another. I cannot understand how the sum of positive integers can ever equal a negative. But apparently it's proven!
Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
The infinite sequence of triangular numbers diverges to +∞, so by definition, the infinite series 1 + 2 + 3 + 4 + ⋯ also diverges to +∞.
There are methods of associating a value to a divergent series. Some of these methods associate the value -1/12 to the series 1+2+3+4+..., but this does not mean that the series equals -1/12.
Vortico · 1 points · Posted at 07:54:23 on February 14, 2016 · (Permalink)
From the article:
In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of −1/12.
So you would be correct if you say "The zeta regularization of the sum 1+2+3+... is -1/12", but by the traditional meaning of an infinite sum, it diverges.
Vortico · 1 points · Posted at 06:00:32 on February 14, 2016 · (Permalink)
No, the sum doesn't exist. The zeta function regularization of the sum yields -1/12, but that's less surprising since the definition requires the zeta function and analytic continuation methods, which might as well pop out a simple "-1/12" from that mess.
Saved comment
Lindby · 5079 points · Posted at 06:41:30 on February 14, 2016 · (Permalink)
x% of y = y% of x
y(x/100) = x(y/100)
yx/100 = xy/100
So, in order to calculate a percentage in your head it might be easier to turn it around.
Example
What is 2% of 50? It's the same thing as 50% of 2.
JoseJimeniz · 843 points · Posted at 13:09:29 on February 14, 2016 · (Permalink)*
Cool. Let's see if I can use it to calculate sales tax on a drive thru order
Dammit.
PhilxBefore · 205 points · Posted at 13:34:35 on February 14, 2016 · (Permalink)
$1.69 for those who are wondering.
mohallor · 13 points · Posted at 14:18:59 on February 14, 2016 · (Permalink)
Wait 13² is 169, is this true of any number? Is x% of x just x²/100?
EonesDespero · 39 points · Posted at 14:28:13 on February 14, 2016 · (Permalink)
OP calculated the 13% of 13$, which you can calculate as 13*13/100.
So, yes, of course you can calculate the x% of X$ as x2 /100, because it literally how you calculate it.
How do you calculate the % of anything?
pzelenovic · 8 points · Posted at 15:00:25 on February 14, 2016 · (Permalink)
hahahahahaha
Rob_1089 · 9 points · Posted at 15:00:02 on February 14, 2016 · (Permalink)
13% of 13=13x0.13
EonesDespero · 13 points · Posted at 15:19:34 on February 14, 2016 · (Permalink)
13x0.13=13x13/100
gHx4 · 1 points · Posted at 11:13:30 on February 20, 2016 · (Permalink)
Wait, so does that imply that x*y is a quick way to estimate the result of any number * percentage?
I find division fairly hard to do mentally, but multiplication is a breeze.
EonesDespero · 2 points · Posted at 17:45:55 on February 20, 2016 · (Permalink)
A percentage is literally any number divided by 100.
You can calculate the 90% of 200 as 20090/100 or 2000.9
However, I don't see the improvemnent. Dividing or multiplying by 100 (or any power of ten for the matter) is the easiest operation besides doing it by 1.
ChenChow · 11 points · Posted at 14:30:06 on February 14, 2016 · (Permalink)
x% of x = x(x/100) = x²/100
nice!
PhilxBefore · 3 points · Posted at 14:33:25 on February 14, 2016 · (Permalink)
Yes, if the percentage and the total are equal integers.
kilkil · 2 points · Posted at 18:26:08 on February 14, 2016 · (Permalink)
Well, yeah.
Percent means "divide by hundred", so 13% of 13 is just "13 of 13 divided by 100", which is 13×13/100, which is 1.69.
ectish · 2 points · Posted at 02:38:23 on February 15, 2016 · (Permalink)
169 is 13² ...hm
[deleted] · 8 points · Posted at 13:40:45 on February 14, 2016 · (Permalink)
Hehe, 69
bigsnarf149 · 1 points · Posted at 14:53:22 on March 11, 2016 · (Permalink)
x% of x equals (x2 /100)
Thiswasoncesparta · 0 points · Posted at 21:51:00 on February 14, 2016 · (Permalink)
So x% of x is (x2)/100
[deleted] · 12 points · Posted at 14:13:45 on February 14, 2016 · (Permalink)
Did you remember to try that trick where you swap them around?
JustAnotherPanda · 2 points · Posted at 17:10:12 on February 14, 2016 · (Permalink)
Obviously you have to swap them first.
poncho531 · 3 points · Posted at 14:47:58 on February 14, 2016 · (Permalink)
What state do you live in where there's 13% sales tax? In MN we only have 7.275%.
Acid44 · 5 points · Posted at 20:37:32 on February 14, 2016 · (Permalink)
Ontario
ScottLux · 2 points · Posted at 16:34:35 on February 14, 2016 · (Permalink)
In California we only pay 8.5% in sales tax but on the flip side we also have to okay $2400+9.3% tax on all income above $50k. (There are actually even higher brackets going up to 13.3% above $1M)
[deleted] · 1 points · Posted at 21:38:46 on February 16, 2016 · (Permalink)
[deleted]
ScottLux · 1 points · Posted at 17:06:10 on February 17, 2016 · (Permalink)*
That number was just California. I pay close to 50% marginal tax rates while making about ~60% more than the median income in my county. 13.6% payroll taxes (half paid by your employer, though arguably should still be counted as a lot of people are self employed and it's money that would otherwise go in your pocket), 9.4% state income tax, 28% federal income tax
Wakkawazzalo · 1 points · Posted at 14:52:24 on February 14, 2016 · (Permalink)
13%? Ew.
guoit · 1 points · Posted at 18:51:10 on February 14, 2016 · (Permalink)
You tip at drive thru's?
_Artos_ · 1 points · Posted at 22:16:03 on February 21, 2016 · (Permalink)
He said sales tax not tip.
bestofreddit_me · 1 points · Posted at 23:18:41 on February 14, 2016 · (Permalink)
It's not that hard if you break apart these numbers.
13x13 is 13 x 10 + 13x3.
Can you do 13 x 10?
Can you do 13 x 3?
Can you add 130 + 39?
JoseJimeniz · 3 points · Posted at 00:55:07 on February 15, 2016 · (Permalink)
Thirteen is ten and three
Ten percent of thirteen is one point three.
And the other number, what was it, three. Thirteen percent of three is... I don't know.
Ten plus three times ten plus three.
Wait, what was the algorithm again?
Ten times thirteen is one hundred thirty. And then to that we have to add.... ten times..... Three times thirteen.
Oh god. Twenty... Thirty... Plus three times three.
Three times three is nine.
Nine plus... what.
It was thirteen times ten plus three times ten. So, ....
God dammit.
The integral of sine X is negative cos X.
coredumperror · 1 points · Posted at 03:26:56 on February 15, 2016 · (Permalink)
You have 13% sales tax?! I thought LA's 9.5% was bad!
JoseJimeniz · 2 points · Posted at 05:47:50 on February 15, 2016 · (Permalink)
8% "state" tax, and then 5% federal tax.
coredumperror · 1 points · Posted at 07:18:29 on February 15, 2016 · (Permalink)
Oh yuck!
BurnedOutTriton · 1 points · Posted at 14:58:28 on February 14, 2016 · (Permalink)
Found Washington state.
Erythroy · 0 points · Posted at 21:42:45 on February 14, 2016 · (Permalink)
Which is 26% of 6,5. Which is 52% of 3,25. Which is 100% of 1,675.
Bit of work, but u'll get pretty close this way.
hypervelocityvomit · 1 points · Posted at 08:11:46 on February 15, 2016 · (Permalink)
#pwned
Erythroy · 1 points · Posted at 09:25:11 on February 15, 2016 · (Permalink)
So how is this an easy way? (Yes it should've read 104%)
hypervelocityvomit · 1 points · Posted at 12:34:31 on February 15, 2016 · (Permalink)
I used the numbers I had lying around (from the halving and doubling). 1.625 is the last number of the halving / doubling steps, and .065 is the first (6.5, shifted 2 places).
I admit, "pwned" was an exaggeration.
Erythroy · 1 points · Posted at 16:00:02 on February 15, 2016 · (Permalink)
Wait, now I'm confused :D
How did you get the 4% value from the 26% (6,5) value?
hypervelocityvomit · 2 points · Posted at 11:56:31 on February 16, 2016 · (Permalink)
I was computing 104% of 1.625, so I took 1.625 as 100% of 1.625, and 6.5 as 400% of 1.625 (that was two halving steps earlier, so it was 400%). Shift that to the right 2 places and it becomes .065 (4% of 1.625).
Erythroy · 2 points · Posted at 15:56:01 on February 16, 2016 · (Permalink)
Ohh I see, thanks for clearing it up for me! :)
garblegarble12342 · 1662 points · Posted at 12:54:30 on February 14, 2016 · (Permalink)
Im going to masturbate to this.
Yes-I-Was-Drunk · 112 points · Posted at 13:28:15 on February 14, 2016 · (Permalink)
You mean mathturbate, right?
topoftheworldIAM · 45 points · Posted at 13:42:41 on February 14, 2016 · (Permalink)
said Mike Tyson
The_Bronze_Scrub · 14 points · Posted at 14:32:17 on February 14, 2016 · (Permalink)
You mean Mike Tython, right?
[deleted] · 5 points · Posted at 15:37:24 on February 14, 2016 · (Permalink)
No, it's my python.
Fourstago · 6 points · Posted at 17:40:00 on February 14, 2016 · (Permalink)
yeth
YRNhermy · 13 points · Posted at 13:36:31 on February 14, 2016 · (Permalink)
Don't forget to floss
crazycaesar · 2 points · Posted at 15:30:15 on February 14, 2016 · (Permalink)*
Oh my God.
[deleted] · 5 points · Posted at 21:19:15 on February 14, 2016 · (Permalink)
Becky look at her butt
submissivepussytits · 6 points · Posted at 13:31:29 on February 14, 2016 · (Permalink)
With your numberwang?
don_truss_tahoe · 2 points · Posted at 14:27:07 on February 14, 2016 · (Permalink)
PhD economist here. I'll join you.
Filipy · 2 points · Posted at 14:37:07 on February 14, 2016 · (Permalink)
X x Y x 1/100 this way of looking at it might help some.
The_Music · -1 points · Posted at 14:08:08 on February 14, 2016 · (Permalink)
Is it summer Reddit already?
phistomefel_smeik · 88 points · Posted at 12:54:48 on February 14, 2016 · (Permalink)
You changed my life forever.
DrPhineas · 474 points · Posted at 12:12:32 on February 14, 2016 · (Permalink)
Are you fucking kidding me? This is why I love Maths. All these years learning and learning and something so simple and useful escapes me.
Smaktat · 7 points · Posted at 14:45:20 on February 14, 2016 · (Permalink)
Gotta figure stuff like this out yourself. If you feel as if you're capable at that, then you're probably capable of much more advanced math depending on how fast you can find the patterns.
kenetha65 · 3 points · Posted at 13:49:58 on February 14, 2016 · (Permalink)
How many maths?
esuohe · 1 points · Posted at 13:54:24 on February 14, 2016 · (Permalink)
HOW CAN SHE MATHS
geetarzrkool · -2 points · Posted at 13:45:37 on February 14, 2016 · (Permalink)
You can always spot the "foreigner" when the say "Maths", plural.
Woyaboy · 30 points · Posted at 14:13:43 on February 14, 2016 · (Permalink)
What do you mean? You're the foreigner to op...
geetarzrkool · 5 points · Posted at 14:44:45 on February 14, 2016 · (Permalink)
Impossible! America, and by proxy Americans, can never be "foreigners" anywhere at any time because 'Murica.
Also, Reddit is an "American" site, so any non-Americans are "foreigners" whilst here.
JanitorMaster · 2 points · Posted at 22:20:27 on February 14, 2016 · (Permalink)
46% of reddit's users are not American.
source
geetarzrkool · -2 points · Posted at 23:02:48 on February 14, 2016 · (Permalink)
But Reddit was created by and is based out of America. It was "born" here, you might say, which means it's "American".
db0255 · 1 points · Posted at 04:53:43 on February 15, 2016 · (Permalink)
DAGNABBIT. The Internets were founded in America, by Americans, for Americans, and it's well known the center of if it is somewhere off the coast of Kansas. It's the most Americanest thing there is up there with moms, apple pie, hot dogs, blue jeans, and Budweiser beer!!!!
JanitorMaster · 3 points · Posted at 09:48:32 on February 15, 2016 · (Permalink)
If you keep the internet for yourself, we won't give you the World Wide Web!
- Switzerland
mohallor · 10 points · Posted at 14:17:43 on February 14, 2016 · (Permalink)
As an American, I find that "Maths" actually sounds quite nice and I often wish I could say it like that without receiving weird looks
geetarzrkool · 3 points · Posted at 14:43:09 on February 14, 2016 · (Permalink)
The weirdest part is that we say "mathematics" (plural) when referring to the field as a whole, but only ever use "math" (singular) when referring to a given class or branch of said field. Go figure.
Get it? Go "figure" when talking about math(s)! I'll be going now ...
w675 · 2 points · Posted at 15:20:55 on February 14, 2016 · (Permalink)
This isn't really a good way to think about it.
If you consider the term Mathematics as plural, it should be implied that there is a singular version of the same word - Mathematic. Have you ever heard anyone say the word Mathematic?
No, you haven't.
geetarzrkool · 2 points · Posted at 15:22:48 on February 14, 2016 · (Permalink)
That's my point entirely :/ The term "maths" (i.e. mathematics) is more correct, but nonetheless rarely used in America despite being so.
Reading comprehension. It's a good thing ;)
w675 · 3 points · Posted at 15:32:51 on February 14, 2016 · (Permalink)
No, you're thinking in terms of plural and singular which is incorrect in this situation. Think of my above comment as a proof by contradiction, if you will.
The word math is a shorter form of the word mathematics. The word mathematics is not a plural word, so why on earth would you carry the s to the shortened version? It's nonsensical.
Reading comprehension is definitely a great... um, thing. You should give it a shot.
geetarzrkool · 1 points · Posted at 15:50:03 on February 14, 2016 · (Permalink)
Wrong again. The term "mathematic(s)" refers to several fields/branches/disciplines that involve numbers and other quantitative values. It's not a singular practice or branch of study. As such, it's quite appropriate to use the plural form even in an abbreviated form, which is why so many people do so.
w675 · 5 points · Posted at 15:53:37 on February 14, 2016 · (Permalink)
I'll just let /u/Davis660's comment from this thread take over from here.
The_Asian_Hamster · 15 points · Posted at 14:04:32 on February 14, 2016 · (Permalink)
To them and many others you're the foreigner
geetarzrkool · 2 points · Posted at 14:45:18 on February 14, 2016 · (Permalink)
So says The_Asian_Hamster.
Sounds foreign to me...
glorioussideboob · 6 points · Posted at 15:12:54 on February 14, 2016 · (Permalink)
You can always tell the American when they act like the 'native' on a global website and call everyone else a 'foreigner'.
geetarzrkool · 4 points · Posted at 15:23:24 on February 14, 2016 · (Permalink)
So you're saying the entire planet isn't actually ours? I'm going to have to look into that.
db0255 · 1 points · Posted at 04:54:52 on February 15, 2016 · (Permalink)
Plot twist: he lives in Arkansas.
Wait a second.....
DrPhineas · 4 points · Posted at 14:29:41 on February 14, 2016 · (Permalink)
Perspective.
Also, this is another "I'm American and I'll say things a different way making everyone else's way wrong"
geetarzrkool · -1 points · Posted at 14:40:21 on February 14, 2016 · (Permalink)
I never said anything about it being right or wrong. Simply an astute and accurate observation. Insecure much?
chevymonza · -3 points · Posted at 13:56:24 on February 14, 2016 · (Permalink)
They're great at math, but terrible at language.
SadisticAvocado · 5 points · Posted at 14:29:24 on February 14, 2016 · (Permalink)
The long form is mathematics, so surely the shortened form would also be plural
Davis660 · 2 points · Posted at 14:42:06 on February 14, 2016 · (Permalink)
Speaking as a brit who says Maths, math is the correct way. "Mathematics" isn't actually a plural word, it comes from the Greek "Mathematica", in Greek an 'a' at the end of a word sometimes denotes a plural much like an 's' does in English. In this case it didn't but it was carried over between languages and so we have "Mathematics"
So "Math" is correct, but I will always say "Maths" because it's so ingrained in me.
However, the internationally agreed on spelling and pronunciation of that metal that Americans say wrong is actually "Aluminium". So you win some you lose some.
chevymonza · 2 points · Posted at 15:12:24 on February 14, 2016 · (Permalink)
I was joking actually, but it does help to know the real reason why they do this! Figures non-americans are smarter......!
Am_Sci · 1 points · Posted at 14:39:06 on February 14, 2016 · (Permalink)
"Mathematics" is not plural. I'm pretty sure it is uncountable and has no plural form. Also, nobody shortens economics to econs-- just saying.
[deleted] · 2 points · Posted at 14:54:55 on February 14, 2016 · (Permalink)
Ive never heard someone shorten it to "econ" either though
w675 · 2 points · Posted at 15:23:56 on February 14, 2016 · (Permalink)
You're probably alone in that regard.
Maasterix · 9 points · Posted at 14:18:57 on February 14, 2016 · (Permalink)
In Britain we (correctly) say maths instead of math.
chevymonza · 1 points · Posted at 15:13:28 on February 14, 2016 · (Permalink)
Well, we Americans value efficiency ;-p
Maasterix · 3 points · Posted at 15:15:59 on February 14, 2016 · (Permalink)
I can see that
chevymonza · 2 points · Posted at 15:20:13 on February 14, 2016 · (Permalink)
......in matters of spelling, I should've been more specific! Not where it matters to the environment, sheeeesh.
PhilxBefore · 1 points · Posted at 13:31:54 on February 14, 2016 · (Permalink)
Because they don't teach it correctly.
Looking at you, shitty American public school system.
charlesthechuck · 6 points · Posted at 13:57:23 on February 14, 2016 · (Permalink)
He's not american though.
PhilxBefore · -1 points · Posted at 14:30:48 on February 14, 2016 · (Permalink)
No one said he was.
[deleted] · 1 points · Posted at 19:14:50 on February 14, 2016 · (Permalink)
I hate maths, and math too.
[deleted] · -9 points · Posted at 14:09:06 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 9 points · Posted at 14:19:16 on February 14, 2016 · (Permalink)
It's only 'math' in North America. The full name of the subject is 'mathematics', not 'mathematic'.
gammadistribution · 2 points · Posted at 14:30:42 on February 14, 2016 · (Permalink)
Abbreviations don't have to be plural. They're both fine.
[deleted] · 1 points · Posted at 15:17:54 on February 14, 2016 · (Permalink)
I didn't say it was wrong, I was pointing out that 'maths' isn't wrong.
minipanda_bike · 18 points · Posted at 13:51:43 on February 14, 2016 · (Permalink)
You can also multiply the price and percentage and divide by 100 like this: 2x50/100 = 1 I find it easier to use for calculating tip. For example, if your bill rounds up to 30$ and you want to give 15% tip, for either 15% of 30$ or 30% of 15$ you will need a moment to calculate it in your head but (30x15)/100 or (3x15)/10 is pretty easy to do. You can also try with 12% of 70$, 6% of 25$, 62% of 5$ or even 13% of 13$.
pomlife · 9 points · Posted at 17:20:49 on February 14, 2016 · (Permalink)
If I needed to find 15% of $30, I'd just find 10% ($3.00), then half that ($1.50) and add them together ($4.50).
XtremeGoose · 1 points · Posted at 20:53:57 on February 14, 2016 · (Permalink)
The easiest way is often that if we have ab% of x (where ab is a 2 digit number and a is the multiple ten and b is the unit) then we have a×(x/10) + b×(x/100). Since 0 <= a,b < 10 this is not hard.
deathproof-ish · 50 points · Posted at 12:52:29 on February 14, 2016 · (Permalink)
At a restaurant my group got a 20% discount for late food.
They gave us the group check with 20% off.
We kindly asked for separate checks...
Writer said management couldn't allow that because it was a larger discount...
mvp725 · 26 points · Posted at 13:21:16 on February 14, 2016 · (Permalink)
Haha I've been the waiter in this situation where the customers think they're getting one over on us. "We've got a 10% off coupon, can you split our checks so we get 20%"
That's....that's not how that works
deathproof-ish · 14 points · Posted at 13:28:43 on February 14, 2016 · (Permalink)
They weren't pulling a fast one, they're just dumb
Drbert21 · 2 points · Posted at 13:52:19 on February 14, 2016 · (Permalink)
But you should still play along, it helps as long as they tip
Cyberhwk · 2 points · Posted at 20:59:06 on February 14, 2016 · (Permalink)
Wait, I'm confused here.
Joe, Bob, Sally, and Jane each order $25 meals:
Split the checks:
$20+$20+$20+$20 = $80
What am I missing here?
deathproof-ish · 1 points · Posted at 21:09:20 on February 14, 2016 · (Permalink)
Joe, Bob, Sally and Jane order meals of varying prices totaling up to $100 and get the discount.
20% off of 100% is $80
Joe $10 with 20% is $8 Bob $50 with 20% is $40 Jane $30 with 20% is $24 Sally $10 with 20% is $8
Total: Still 80
The percentage of a whole is equal to the same percentage of the individual parts (even if not equal).
Cyberhwk · 2 points · Posted at 21:12:51 on February 14, 2016 · (Permalink)
Oh OK, so we're agreeing. Not sure why I thought the post was saying that management was RIGHT in thinking that splitting checks was a greater discount.
deathproof-ish · 1 points · Posted at 21:14:30 on February 14, 2016 · (Permalink)
Oh yea haha no they were incredibly dim on the subject. We argued until it wasn't worth it and accepted our new 10% discounts for our individual checks.
Sorry I was just showing that even if the checks were drastically different the discount is the same as oppose to if they were split evenly.
dilligaf_huh · 13 points · Posted at 12:52:32 on February 14, 2016 · (Permalink)
Finally, something that has meaning in my life. Thank you
OMNICTIONARIAN96 · 9 points · Posted at 12:50:15 on February 14, 2016 · (Permalink)
This is an actually useful one, thanks
patmd6 · 8 points · Posted at 13:51:48 on February 14, 2016 · (Permalink)
WHAT THE HELL?!? YOURE TELLING ME I COULD HAVE BEEN DOING THIS THE WHOLE DAMN TIME?!?
[deleted] · 28 points · Posted at 12:57:11 on February 14, 2016 · (Permalink)
At first thought % was modulus and got really confused.
Syrrim · 2 points · Posted at 21:55:23 on February 14, 2016 · (Permalink)
I was really intrigued, and momentarily thought Id broken RSA.
[deleted] · 1 points · Posted at 22:04:03 on February 14, 2016 · (Permalink)
Yeah I was like whoa this is way over my head till I realized it was a percent.
[deleted] · 1 points · Posted at 10:31:10 on February 16, 2016 · (Permalink)
Found the programmer
[deleted] · 17 points · Posted at 12:55:38 on February 14, 2016 · (Permalink)
Dude, I'm almost crying this is so awesome.
192873982 · 16 points · Posted at 13:22:50 on February 14, 2016 · (Permalink)
Or in other words: multiplication is commutative...
w675 · 5 points · Posted at 15:27:36 on February 14, 2016 · (Permalink)
Apparently a lot of people struggle to see the forest for the trees.
thefisherman1961 · 14 points · Posted at 13:23:30 on February 14, 2016 · (Permalink)
I'm an engineer and I never noticed this. Brilliant.
Apparatjik · 4 points · Posted at 13:29:01 on February 14, 2016 · (Permalink)
You think they would have taught me this in school. Thank you for this actually useful info!
badbackjack · 10 points · Posted at 13:55:10 on February 14, 2016 · (Permalink)
This is bullshit! I have a minor in math. This doesn't mean I'm an expert, but I'm better at math than most people I know. And I've never heard of this simple, perfect fact. That is a crime.
w675 · 3 points · Posted at 15:28:39 on February 14, 2016 · (Permalink)
If you've heard about the commutative property when dealing with multiplication, then you've heard of this fact.
Scranda1 · 4 points · Posted at 14:29:50 on February 14, 2016 · (Permalink)
Wow. So does this work every time?
[deleted] · 1 points · Posted at 15:30:05 on February 14, 2016 · (Permalink)
Yes.
mshafer1988 · 1 points · Posted at 22:39:53 on February 26, 2016 · (Permalink)
60% of the time, it works everytime.
[deleted] · 2 points · Posted at 13:56:13 on February 14, 2016 · (Permalink)
Hay! You could just multiply the two numbers together and divide by 100! You math nerds are so handy!
vinbia · 2 points · Posted at 13:20:08 on February 14, 2016 · (Permalink)
mind blown
youropinionman420 · 1 points · Posted at 13:49:51 on February 14, 2016 · (Permalink)
Incredible
unionjunk · 1 points · Posted at 13:52:33 on February 14, 2016 · (Permalink)
Holy shit you're right!
zombiefingerz · 1 points · Posted at 13:53:56 on February 14, 2016 · (Permalink)
I love you.
WutangCND · 1 points · Posted at 14:06:07 on February 14, 2016 · (Permalink)
Mind blown.
----_____---- · 1 points · Posted at 14:06:54 on February 14, 2016 · (Permalink)
This is the first useful one I've seen - thanks
kassabz · 1 points · Posted at 14:08:29 on February 14, 2016 · (Permalink)
Oh god I feel like I discovered the mystery of the universe!
MrChittles · 1 points · Posted at 14:11:23 on February 14, 2016 · (Permalink)
....holy shit
SpadoCochi · 1 points · Posted at 14:26:50 on February 14, 2016 · (Permalink)
I had this worked out in my mind already but had never put it into words, or even realized I was doing it.
What an amazing acknowledgement.
randomguy186 · 1 points · Posted at 14:29:03 on February 14, 2016 · (Permalink)
This is a simple application of the fact that xy=yx.
Dandelion_33 · 1 points · Posted at 14:29:09 on February 14, 2016 · (Permalink)
2% of 50 is 4, 50% of 2 is 1. It doesn't work
DrPhineas · 2 points · Posted at 14:32:45 on February 14, 2016 · (Permalink)
2% of 50 is 1
Dandelion_33 · 1 points · Posted at 14:38:47 on February 14, 2016 · (Permalink)
Whoops sorry, forget i even said anything
[deleted] · 1 points · Posted at 14:31:25 on February 14, 2016 · (Permalink)
That's the commutative property of multiplication right there.
CAPS_LOCK_OR_DIE · 1 points · Posted at 14:34:15 on February 14, 2016 · (Permalink)
I read this and was a little skeptical, but then tried it and I think I'm dead.
LeBastun · 1 points · Posted at 14:40:50 on February 14, 2016 · (Permalink)
So you mean 35% of 75.99 is same as 75.99% of 35?
Yeah, math is still too complicated for me!
Lindby · 1 points · Posted at 14:48:09 on February 14, 2016 · (Permalink)
Of course it wont be useful every time. But on occasion it's helpful.
Doggysoft · 1 points · Posted at 15:02:17 on February 14, 2016 · (Permalink)
Grenaaaaade!
Mind-blown.
[deleted] · 1 points · Posted at 15:29:52 on February 14, 2016 · (Permalink)
This is fucking insane. Like I keep thinking to myself this can't work out.
8% of 75
75% of 8
creampieguy49 · 1 points · Posted at 15:42:09 on February 14, 2016 · (Permalink)
I really needed this yesterday during my SAT test ;(
[deleted] · 1 points · Posted at 16:12:19 on February 14, 2016 · (Permalink)
God bless you
iwantbeta · 1 points · Posted at 16:15:55 on February 14, 2016 · (Permalink)
holy fucking shit.
[deleted] · 1 points · Posted at 16:18:25 on February 14, 2016 · (Permalink)
How the fuck did I not know that.
db0255 · 1 points · Posted at 04:44:39 on February 15, 2016 · (Permalink)
Now THIS is a life pro tip. What's a 20% tip on a $75 meal?
Quantization · 1 points · Posted at 02:20:35 on February 16, 2016 · (Permalink)
1% of 200 = 2
200% of 1 = 2
Sheeeeeeeeeeeeeeeeeit
KevansMcGurgen · 1 points · Posted at 10:39:23 on February 18, 2016 · (Permalink)
You fucking hero.
Lanza21 · 1 points · Posted at 17:24:49 on February 22, 2016 · (Permalink)
I'm a theoretical physicist and I never thought of this...
Unsurepooper · 1 points · Posted at 15:00:43 on March 6, 2016 · (Permalink)
I use this all the time, regular people think it's witchcraft
LuckyGreenLizard · 1 points · Posted at 09:20:32 on March 12, 2016 · (Permalink)
Holy shit.
Coinkidinks · 1 points · Posted at 19:09:24 on April 5, 2016 · (Permalink)
Can someone prove why this works?
SeanRK1994 · 1 points · Posted at 13:27:40 on February 14, 2016 · (Permalink)
As a programmer, I read that first line as
"The remainder of x/y is equal to the remainder or y/x"
grasmanek94 · -2 points · Posted at 13:04:38 on February 14, 2016 · (Permalink)*
While this is a nice fact, and surely makes it sometimes easier... unfortunately try 7% of 193. :) but hey - 50% of 2 is indeed easier than 2% of 50!
Edit: For the people which think that this won't work on 7% of 193 (ofcourse it will!)... do it from your head without the assistance of calculators in any form or shape.
nukem2k5 · 10 points · Posted at 13:18:04 on February 14, 2016 · (Permalink)
Well it's fairly easy either way, unless you need an exact number. 193% ~= 200%, so 2x7=14, but you know the number is actually a little less (by 7% of 7, which is a little less than 0.7 (i.e. 10% of 7). So roughly 13.5?
DrPhineas · 2 points · Posted at 14:34:07 on February 14, 2016 · (Permalink)
Only 0.01 off. More than acceptable margin of error for most practical applications.
[deleted] · 4 points · Posted at 13:17:11 on February 14, 2016 · (Permalink)
Huh? 7% of 193 and 193% of 7 both equal 13.51. Unless I'm misunderstanding what you mean.
edible_starling · 2 points · Posted at 13:18:51 on February 14, 2016 · (Permalink)
He saying switching it around doesn't make it any easier like the 2% of 50 one does.
[deleted] · 1 points · Posted at 13:29:29 on February 14, 2016 · (Permalink)
Ok that makes sense.
smusashi · 2 points · Posted at 13:18:40 on February 14, 2016 · (Permalink)
This still works for me. 193% of 7 = Just under double of 7 = 13.51.
letsbeefriends · 1 points · Posted at 13:22:16 on February 14, 2016 · (Permalink)
Well 7% of 193 is 13.51 and 193% of 7 (7 x 1.93) is 13.51 so I still think it's pretty neat.
lgpicture · 1 points · Posted at 13:18:49 on February 14, 2016 · (Permalink)
Still the same:
7/100x193=13.51
193/100x7=13.51
dendaddy · 0 points · Posted at 13:36:10 on February 14, 2016 · (Permalink)
So 20% of $37.50 should be 37.5% of 20 ? All I know is if I do that the waitress is going to get a bad tip.
naratcis · 0 points · Posted at 13:36:11 on February 14, 2016 · (Permalink)
This isnt as helpful as it sounds. Calculating those easy examples can also be done without this trick and much effort in the traditional way. When it comes to something like 13% of 77, that formula would make you calculate 77% of 13. Not very useful.
zazu2006 · -5 points · Posted at 13:14:15 on February 14, 2016 · (Permalink)
If by cool you mean like one of the most basic properties of math...
siliconloser · 1705 points · Posted at 01:17:40 on February 14, 2016 · (Permalink)
If you have a rope long enough to wrap exactly around the equator of the Earth, you only need to add 6.3 meters of rope for for it to be able to hover 1 meter off the ground.
jerkandletjerk · 246 points · Posted at 07:44:17 on February 14, 2016 · (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)!
UrsulaMajor · 122 points · Posted at 13:55:05 on February 14, 2016 · (Permalink)
It also applies to a bottle cap
arguablytrue · 2 points · Posted at 14:49:27 on February 14, 2016 · (Permalink)
Does it apply to Ursula Major?
mynameiscass1us · 14 points · Posted at 00:11:26 on February 15, 2016 · (Permalink)
Are you talking about the villain in The Little Mermaid?
gregsting · 10 points · Posted at 14:03:31 on February 14, 2016 · (Permalink)
Same goes for a ping pong ball, the radius is not relevant
[deleted] · 7 points · Posted at 16:58:50 on February 14, 2016 · (Permalink)
Instructions unclear, dick stuck in sun.
Silverskeejee · 5 points · Posted at 15:24:18 on February 23, 2016 · (Permalink)
This is the point where that blew my mind. That and someone else commenting that the different is basically 2*pi meters. >.o
RootLocus · 3 points · Posted at 10:17:15 on March 9, 2016 · (Permalink)
Or a tennis ball.
quasielvis · -8 points · Posted at 12:44:03 on February 14, 2016 · (Permalink)
I think that's implied.
[deleted] · 6 points · Posted at 15:56:39 on February 14, 2016 · (Permalink)
[deleted]
TeddyTedBear · 4 points · Posted at 18:05:55 on February 14, 2016 · (Permalink)
It's actually very simple :) the formula for circumference is 2pi*r which, for a (increase in) radius of 1 meter, equals about 6.3 meters.
corin26 · 316 points · Posted at 03:53:10 on February 14, 2016 · (Permalink)
explain
ithinkiamopenminded · 531 points · Posted at 04:09:29 on February 14, 2016 · (Permalink)
Radius of the Earth = 6.3674447*106 meters
Radius of the Earth + 1 meter = 6.3674447*106 +1 meters
Circumference = 2pi radius
Circumference of the earth = 4.0007835 × 107
Circumference of the earth + 1 meter = 4.0007841 × 107
Difference between the two: 6 meters
Dellanetor · 358 points · Posted at 07:07:00 on February 14, 2016 · (Permalink)
Also more simply put 1×2×pi = 6.28...
Auctoritate · 188 points · Posted at 07:21:06 on February 14, 2016 · (Permalink)
And even more simply put, 2×pi.
HolyGarbage · 316 points · Posted at 07:36:56 on February 14, 2016 · (Permalink)
And even more simply put, tau.
Siiw · 230 points · Posted at 10:40:19 on February 14, 2016 · (Permalink)
And "tau" is Norwegian for "rope".
MightyButtonMasher · 145 points · Posted at 10:54:46 on February 14, 2016 · (Permalink)
Just like the rope, we've come tau*radius!
MattOnYourScreen · 17 points · Posted at 13:04:01 on February 14, 2016 · (Permalink)
I feel like this whole comment chain was setting you up for that
[deleted] · 7 points · Posted at 14:17:01 on February 14, 2016 · (Permalink)
rad.
MightyButtonMasher · 3 points · Posted at 14:31:32 on February 14, 2016 · (Permalink)
to which degree?
square--one · 27 points · Posted at 11:03:24 on February 14, 2016 · (Permalink)
Checkmate, atheists.
karma3000 · 9 points · Posted at 11:28:09 on February 14, 2016 · (Permalink)
Mind = blown
fiftyseven · 9 points · Posted at 11:33:07 on February 14, 2016 · (Permalink)
how neat is that
[deleted] · 4 points · Posted at 11:34:48 on February 14, 2016 · (Permalink)
so neat
stephanplus · 2 points · Posted at 13:12:23 on February 14, 2016 · (Permalink)
German too
[deleted] · 2 points · Posted at 13:22:22 on February 14, 2016 · (Permalink)
...We've come full circle, eh?
(sorry this was a bad pun)
Ballnuts2 · 1 points · Posted at 14:41:46 on February 14, 2016 · (Permalink)
really?! now that's frikkin neat
dj_destroyer · 3 points · Posted at 07:52:18 on February 14, 2016 · (Permalink)
Blueberry pi is crack.
beniceorbevice · 1 points · Posted at 10:00:56 on February 14, 2016 · (Permalink)
Who's motorcycle is this?
Fhaarkas · 2 points · Posted at 12:09:22 on February 14, 2016 · (Permalink)
Jesus Marie it's a chopper!
dj_destroyer · 1 points · Posted at 15:27:17 on February 14, 2016 · (Permalink)
Whose chopper is this?
beniceorbevice · 1 points · Posted at 19:05:35 on February 14, 2016 · (Permalink)
It's jerry's
Agurk · 2 points · Posted at 11:00:09 on February 14, 2016 · (Permalink)
Funny thing is "tau" means "rope" in norwegian.
wiggaroo · 1 points · Posted at 12:20:57 on February 14, 2016 · (Permalink)
And tau sounds like tow... and tow trucks pull things... with ropes...
Kryptof · 7 points · Posted at 07:22:39 on February 14, 2016 · (Permalink)
And even MORE simply put,
crabbix · 6 points · Posted at 07:32:59 on February 14, 2016 · (Permalink)
Simply,
[deleted] · 5 points · Posted at 07:37:44 on February 14, 2016 · (Permalink)
[deleted]
isthisdutch · 4 points · Posted at 08:50:17 on February 14, 2016 · (Permalink)
Now I finally understand the problem. Thank you!
cnet15 · 1 points · Posted at 07:49:19 on February 14, 2016 · (Permalink)
Smply
The_Ineffable_One · 1 points · Posted at 13:48:44 on February 14, 2016 · (Permalink)
This is considerably more elegant.
singham · 1 points · Posted at 14:11:30 on February 14, 2016 · (Permalink)
That is irrespective of initial radius. Now this is more interesting.
shook_one · 55 points · Posted at 08:11:27 on February 14, 2016 · (Permalink)
but how do you make it hover?
Timothy_Claypole · 10 points · Posted at 10:27:45 on February 14, 2016 · (Permalink)
Maths
Atario · 9 points · Posted at 10:51:23 on February 14, 2016 · (Permalink)
Spin it like it's a wheel.
danmickla · 4 points · Posted at 18:51:34 on February 14, 2016 · (Permalink)
Magnets
torokunai · 1 points · Posted at 00:34:53 on February 15, 2016 · (Permalink)
One guy in Ecuador and one guy in Indonesia holding it up
ectish · 1 points · Posted at 02:46:47 on February 15, 2016 · (Permalink)
With unlimited resources? 72 hours.
r/AskReddit/comments/45t24t/you_have_three_days_to_create_total_chaos_on/
Uberzwerg · 9 points · Posted at 08:52:50 on February 14, 2016 · (Permalink)
why using exponential factors like 106 if you are still using every digit?
6.3674447*106 m instead of just 6367444.7 m?
OriginalEmanresu · 3 points · Posted at 13:56:58 on February 14, 2016 · (Permalink)
Scientific notation is usually used in situations like that to make sure the ready can quickly identify the magnitude of the number, and so it can be more easily rounded later on.
Really, its just a matter if convention
Lighterlow · 4 points · Posted at 11:05:06 on February 14, 2016 · (Permalink)
I think you can cut the *107 if you are going to write all the digits anyway
blackNstoned · 3 points · Posted at 08:44:43 on February 14, 2016 · (Permalink)
makes sense. like when you deal with numbers in the 107 range and addition of 1 will make very insignificant change to the actual calculations of that number compared to the number
Ragingbeast · 2 points · Posted at 07:37:01 on February 14, 2016 · (Permalink)
ELI5
Treats · 2 points · Posted at 09:47:28 on February 14, 2016 · (Permalink)
But how does that make it hover?
SirSoliloquy · 2 points · Posted at 08:07:09 on February 14, 2016 · (Permalink)
Wouldn't work though.
convoy465 · 3 points · Posted at 08:12:32 on February 14, 2016 · (Permalink)
If it were an unbreakable unbendable solid then it would, then you could give it an infinite amount of momentum in a direction and have it decapitate everyone on earth! it's flawlesss!!!
SirSoliloquy · 4 points · Posted at 08:19:31 on February 14, 2016 · (Permalink)
You have a strange definition of "rope."
NSGDX1 · 1 points · Posted at 08:20:46 on February 14, 2016 · (Permalink)
You won't be able to add the 6.3m piece in the end then. If it were a normal rope then some X part of the rop will not be in contact and it will travel like a wave forever, even without infinite momentum.
Also, you won't be able to give the ring that much momentum so it moves. And since gravity isn't same everywhere it would bend(or start vibrating at least).
convoy465 · 3 points · Posted at 08:24:30 on February 14, 2016 · (Permalink)
I was assuming it was just created floating 1 meter above the ground.
NSGDX1 · 1 points · Posted at 08:25:43 on February 14, 2016 · (Permalink)
Yeah, it can't
kogasapls · 3 points · Posted at 08:38:26 on February 14, 2016 · (Permalink)
Pretty much every assumption about this scenario is physically impossible, but this is all irrelevant. None of the issues you're raising contribute to or detract from the concept that appears confusing.
NSGDX1 · 1 points · Posted at 08:43:11 on February 14, 2016 · (Permalink)
Kogasa pls
t-- · 1 points · Posted at 10:45:23 on February 14, 2016 · (Permalink)
only if you use gravity waves
gregsting · 1 points · Posted at 13:58:39 on February 14, 2016 · (Permalink)
The radius is irrelevant : Circumference of earth=2pi×r Circumference of earth + 1m= 2pi×(r+1)=(2pi×r)+2pi
Wathever r is, the difference is 2pi = 6,28m
Dick_Beaterson · 1 points · Posted at 08:37:12 on February 14, 2016 · (Permalink)
thats adding one meter in length, its not adding enough length to hover 1 meter.
[deleted] · 6 points · Posted at 07:32:51 on February 14, 2016 · (Permalink)
circumference=pi * radius (squared)
dc= 2pi * dr
That means for any circle, an increase in radius of X requires a circumference increase of 2pix. It's unrelated to the current size of the radius.
zacker150 · 2 points · Posted at 20:04:13 on February 14, 2016 · (Permalink)
You mean 2 *pi *r
[deleted] · 1 points · Posted at 21:15:34 on February 14, 2016 · (Permalink)*
Derp. Can't believe no one else noticed that yet. I was sitting there trying to remember chain rule and I thought if c=pi r2 then dc would = 2 pi r dr and couldn't figure out why that wasn't lining up..that's because that's the formula for area haha..I was tired and drunk when I wrote that.
t-- · 1 points · Posted at 10:43:50 on February 14, 2016 · (Permalink)
I think he means the magic of how its going to hover 1 meter off the ground.
I'm assuming it has something to do with gravity waves.
SCombinator · 1 points · Posted at 12:11:19 on February 14, 2016 · (Permalink)
The ratio of Diameter to Circumference is a fixed ratio of 1 : pi. So to increase the diameter by 2 meters (1 meter off each side) you need to increase the circumference by 2pi.
BroskeySmiter · 1 points · Posted at 17:43:18 on February 14, 2016 · (Permalink)
No
XtremeGoose · 1 points · Posted at 21:38:58 on February 14, 2016 · (Permalink)
Better maths:
On ground: c_0 = 2πr
1m off ground: c_1 = 2π(r + 1)
Difference: ∆c = 2π(r + 1) - 2πr = 2π(r + 1 - r) = 2π = ~6.3 m.
Hence you can see ∆c does not depend on r.
[deleted] · 1 points · Posted at 09:37:09 on February 16, 2016 · (Permalink)
EXPLAIN!
buggaz · 44 points · Posted at 07:32:16 on February 14, 2016 · (Permalink)
I added the 6 meters. What now? It is definitely not hovering.
addandsubtract · 37 points · Posted at 07:55:32 on February 14, 2016 · (Permalink)
Spin it.
NewbornMuse · 3 points · Posted at 14:02:39 on February 14, 2016 · (Permalink)
Really fast.
----_____---- · 3 points · Posted at 14:07:50 on February 14, 2016 · (Permalink)
Bop it.
gaussjordanbaby · 9 points · Posted at 05:58:55 on February 14, 2016 · (Permalink)
This is a good one.
swimmerhair · 11 points · Posted at 07:02:26 on February 14, 2016 · (Permalink)
Anyone notice how that number (6.3) is almost exactly 2*pi?
hutcho66 · 36 points · Posted at 07:17:06 on February 14, 2016 · (Permalink)
It is exactly. He rounded it.
Mermbone · 3 points · Posted at 07:40:39 on February 14, 2016 · (Permalink)
still not getting this at all.
[deleted] · -2 points · Posted at 08:56:27 on February 14, 2016 · (Permalink)
[deleted]
monkeyjay · 5 points · Posted at 09:41:17 on February 14, 2016 · (Permalink)
Yea the relatively small amount of length added to add 1 meter around the whole earth seems surprising. Of course to add 1 meter more radius around a tennis ball or the sun you'd add 6.3 metres of rope. Or if you could rope the whole milky way just add 6.3 more metres to give a metre more space around the whole thing.. . Etcetc
gregsting · 2 points · Posted at 13:57:55 on February 14, 2016 · (Permalink)
Circumference of earth=2pi×r Circumference of earth + 1m= 2pi×(r+1)=(2pi×r)+2pi
Wathever r is, the difference is 2pi = 6,28m
[deleted] · 1 points · Posted at 08:57:24 on February 14, 2016 · (Permalink)
kek
shwenny · 3 points · Posted at 09:10:16 on February 14, 2016 · (Permalink)
This works for any size sphere, not just the earth
siliconloser · 1 points · Posted at 14:54:46 on February 14, 2016 · (Permalink)
True, but when you use the Earth as your example it makes it seem more interesting.
Ucantalas · 2 points · Posted at 08:00:27 on February 14, 2016 · (Permalink)
...I wanna get a lot of rope and see this in action.
Fuck you Saturn, we made out OWN ring!
kbtrpm · 2 points · Posted at 13:59:46 on February 14, 2016 · (Permalink)
Likewise, if you have a rope long enough to wrap exactly around a tennis ball, you only need to add 6.3 meters of rope to be able to hover 1 meter off the surface of the tennis ball.
[deleted] · 1 points · Posted at 08:08:25 on February 14, 2016 · (Permalink)
[deleted]
siliconloser · 1 points · Posted at 14:50:31 on February 14, 2016 · (Permalink)
You got me! It stays.
jrm2007 · 1 points · Posted at 08:39:40 on February 14, 2016 · (Permalink)
Wow, this is my favorite one also. I would guess even someone good at math would initially surprised by this.
RoadtoVR_Ben · 1 points · Posted at 09:11:59 on February 14, 2016 · (Permalink)
Someone math this please.
TheMonoTM · 1 points · Posted at 09:32:21 on February 14, 2016 · (Permalink)
Are you telling me the secret to levitation is 6.3m of rope?
[deleted] · 1 points · Posted at 11:55:09 on February 14, 2016 · (Permalink)
Actually 6.28m
AxelvonBremen · 1 points · Posted at 09:36:05 on February 14, 2016 · (Permalink)
I find it so fascinating that the distance never changes, even when you tie it around a football.
chieftraplord · 1 points · Posted at 10:20:46 on February 14, 2016 · (Permalink)
Could you ELI5?
-duvide- · 1 points · Posted at 10:27:40 on February 14, 2016 · (Permalink)
I think it takes more than extra rope to make rope float, but I see what you're saying.
JooJoona · 1 points · Posted at 11:21:12 on February 14, 2016 · (Permalink)
Or the Sun... or anything for that matter.
10dfez · 1 points · Posted at 11:25:15 on February 14, 2016 · (Permalink)
I'm too hungover to check if this is true. So is it?
Turtle_78 · 3 points · Posted at 13:13:02 on February 14, 2016 · (Permalink)
A circle of radius 1m has a circumference of 2pi metres. 2pi is approximately equal to 6.3. If the radius is increased by 1m, the circumference is increased by about 6.3m.
Folamh3 · 1 points · Posted at 11:43:32 on February 14, 2016 · (Permalink)
I'm sure this makes sense, but I'm having a hard time believing it.
FallosLudo · 1 points · Posted at 12:17:41 on February 14, 2016 · (Permalink)
Wat?
crazyfreak316 · 1 points · Posted at 12:25:53 on February 14, 2016 · (Permalink)
This is true for all spheres, whether its sun or earth or pluto.
hulminator · 1 points · Posted at 12:25:58 on February 14, 2016 · (Permalink)
Just experienced this today tightening my motorcycle chain. Small movement of the sprocket immediately takes all the slack out of the chain.
jasonsbest · 1 points · Posted at 12:33:18 on February 14, 2016 · (Permalink)
There's a better one for imperial units. How much more rope would you need to raise a rope 6 inches off the ground? πft.
bigd0g · 1 points · Posted at 12:59:52 on February 14, 2016 · (Permalink)
But the earth is an ellipsoid, not a spheroid.
abshekke · 1 points · Posted at 17:03:51 on February 14, 2016 · (Permalink)
you need to be sent some gold man you opened my brain
siliconloser · 1 points · Posted at 17:21:12 on February 14, 2016 · (Permalink)
It's really simple geometry, it just seems so cool when you apply it on the scale of the Earth- or any other planet really
abshekke · 1 points · Posted at 17:53:11 on February 15, 2016 · (Permalink)
Your first comment makes geometry a lot more interesting and exciting. Simple formula can be used for such gigantic questions :D
Crixomix · 1 points · Posted at 16:55:24 on February 18, 2016 · (Permalink)
Basically the idea here is that adding circumference to anything is a LINEAR task that only cares about the percentage of the curve you're wrapping around and how much bigger you want to go. It could be around a beach ball or a curve down interstate 70.
almightySapling · 0 points · Posted at 07:17:50 on February 14, 2016 · (Permalink)
And my students always complain that differentials aren't useful.
Poindexter234 · 0 points · Posted at 09:59:21 on February 14, 2016 · (Permalink)
Assuming the earth is a perfect sphere? Or with mountains and oceans and the lumpiness?
[deleted] · -14 points · Posted at 04:09:40 on February 14, 2016 · (Permalink)*
[deleted]
pineconez · 7 points · Posted at 05:21:59 on February 14, 2016 · (Permalink)
A Dyson sphere is not stable. Neither is a ringworld.
kabas · 3 points · Posted at 06:30:59 on February 14, 2016 · (Permalink)
so we cant build a dyson sphere in real life?
seldomsmith · 4 points · Posted at 06:35:30 on February 14, 2016 · (Permalink)
Is that the ball in the dyson vacuum?
Pdubs2_0 · 4 points · Posted at 06:44:41 on February 14, 2016 · (Permalink)
Yes, but it's also a the name given to a mega structure that totally surrounds a celestial body. Usually a star, but in this case the Earth.
seldomsmith · 4 points · Posted at 06:47:50 on February 14, 2016 · (Permalink)
Pretty much the same thing.
Pdubs2_0 · 3 points · Posted at 06:49:47 on February 14, 2016 · (Permalink)
¯\_(ツ)_/¯ Basically
kabas · 1 points · Posted at 07:52:05 on February 14, 2016 · (Permalink)
no, it is to completely encircle a sun with a sphere, with solar panels, for lots of energy.
ItsJustMeJerk · 3 points · Posted at 06:55:29 on February 14, 2016 · (Permalink)
I've heard the idea of a Dyson swarm could be plausible. But I guess that isn't related to what we're talking about...
confusedThespian · 3 points · Posted at 06:58:14 on February 14, 2016 · (Permalink)
My understanding is that Dyson's original vision more closely resembles a swarm than a sphere, anyway. Is that incorrect?
pineconez · 1 points · Posted at 07:44:03 on February 14, 2016 · (Permalink)
No, it's absolutely correct. The idea of a solid sphere is a result of Science Fiction Writers Having No Sense of Scale.
Pdubs2_0 · 2 points · Posted at 06:43:02 on February 14, 2016 · (Permalink)
How is the Dyson sphere not more stable than a ring? Wouldn't gravity be a nonfactor in the sphere? In the case of a ring, if it was only slightly off center the ring would come crashing down. But if the Dyson sphere were off center it wouldn't start accelerating towards the planet.
irrationalskeptic · 2 points · Posted at 07:34:27 on February 14, 2016 · (Permalink)
It would, but at a slightly lesser rate because the average distance changes less(iirc the acceleration would be 2/3 that of a ringworld). Rigid Dyson spheres have unstable orbits, but if there were some sort of mesh that countered for collisions it could be stable
Pdubs2_0 · 1 points · Posted at 07:48:14 on February 14, 2016 · (Permalink)
Can someone math this? I really wanna know how this all works out now. I'm now invested in know how this all works for sure. I thought I knew but now I'm just learning more new things.
ultronthedestroyer · 1 points · Posted at 08:09:48 on February 14, 2016 · (Permalink)
Both the shell theorem and equivalently Gauss' law prove that no acceleration due to gravity would be present inside a Dyson shell due to the shell itself.
It's the same reason the electric field inside a conducting ball is zero.
ultronthedestroyer · 1 points · Posted at 08:07:44 on February 14, 2016 · (Permalink)
Inside a Dyson sphere (a uniform shell), there is 0 acceleration due to gravity from the shell no matter where you are inside the shell.
This is a consequence of Gauss' law.
irrationalskeptic · 1 points · Posted at 08:24:23 on February 14, 2016 · (Permalink)
You're very right about Gauss' law, but it's only true for a point mass/sphere in the center, no? Earth is an oblate spherical but the sun is almost perfectly spherical, so this matters more for ringworld than Dyson spheres. In any case, even if it isn't unstable it also isn't stable. Imagine a meteor crashing into it or solar pressure gradually pushing it. Gravity will have a net zero effect on it so it won't correct and will still crash. Good catch though
ultronthedestroyer · 1 points · Posted at 18:03:24 on February 14, 2016 · (Permalink)
Nope! That's the neat thing about it. For a spherical shell, the potential is constant inside. Therefore there is zero gradient of the field, and consequently there is zero force due to gravity (or electrical charge) inside from the shell no matter where you are.
Now there may be other things inside the shell, such as other people, or a star, or whatever, and you will have gravitational attraction to those things, but not to the shell itself.
irrationalskeptic · 1 points · Posted at 19:03:10 on February 14, 2016 · (Permalink)
That's really elegant. Does it only work with inverse square forces?
ultronthedestroyer · 1 points · Posted at 23:33:55 on February 14, 2016 · (Permalink)
Fantastic question! Yes, it only applies to inverse square laws like gravity and electrostatics.
verifiy · 1623 points · Posted at 21:40:32 on February 13, 2016 · (Permalink)
You know the quadratic formula? Well there is also one for 3rd order polynomials and another on for 4th order polynomials. however, there isn't one for any higher order polynomials, and there can't be.
Nettius2 · 1310 points · Posted at 02:34:47 on February 14, 2016 · (Permalink)
And those formulas are DISGUSTING.
pikaras · 1177 points · Posted at 05:08:56 on February 14, 2016 · (Permalink)*
For those who didn't know, the equasions 3rd order polynomials ax3 + bx2 + cx + d = x =
{q + [q2 + (r-p2 )3 ]1/2 }1/3 + {q - [q2 + (r-p2 )3 ]1/2 }1/3 + p
where
p = -b/(3a), q = p3 + (bc-3ad)/(6a2 ), r = c/(3a)
Edit: For those wondering how horrifying the fourth root one is, here's a link (It's way too complex for me to type)
from_the_sidelines · 2264 points · Posted at 06:12:01 on February 14, 2016 · (Permalink)*
what the fucking fuck is all of this mess
Edit: was super drunk when I posted this. Still stand by it.
ZombyTed · 1606 points · Posted at 06:14:46 on February 14, 2016 · (Permalink)
It's like somebody dumped a bucket of variables on the floor, and blamed it on the intern.
[deleted] · 50 points · Posted at 06:27:41 on February 14, 2016 · (Permalink)
I have only one upvote to give, but know that I chuckled almost-silently to myself for 70 seconds and my wife looked at me like I'm nuts.
(though that happens a lot)
bh2005 · 8 points · Posted at 07:15:31 on February 14, 2016 · (Permalink)
You must be an intern
thundergonian · 9 points · Posted at 06:30:18 on February 14, 2016 · (Permalink)
No, it's just Chipotle serving Alphabet Soup.
mrhaisch · 2 points · Posted at 06:43:39 on February 14, 2016 · (Permalink)
Won't give you food poisoning though
pukevines2 · 2 points · Posted at 07:21:13 on February 14, 2016 · (Permalink)
But at least it's free.
Froz1984 · 3 points · Posted at 09:30:56 on February 14, 2016 · (Permalink)
Oh, there is an equation (or polynomial, can't remember) related to prime numbers that uses all of the alphabet.
Niruz · 3 points · Posted at 09:51:53 on February 14, 2016 · (Permalink)
A bucket of variables.. My sides.
bliow · 487 points · Posted at 06:29:57 on February 14, 2016 · (Permalink)
If you think that's bad... here's the general solution for ax4 + bx3 + cx2 + dx + e = 0
https://upload.wikimedia.org/wikipedia/commons/9/99/Quartic_Formula.svg
ReignDance · 574 points · Posted at 06:56:54 on February 14, 2016 · (Permalink)
.svg for savage.
gabouls1234 · 8 points · Posted at 10:19:31 on February 14, 2016 · (Permalink)
svg4life
rafalfreeman · 2 points · Posted at 13:34:15 on February 14, 2016 · (Permalink)
.SaVaGes
autoit · -3 points · Posted at 08:36:58 on February 14, 2016 · (Permalink)
funny have an upvote
ReignDance · 1 points · Posted at 00:40:20 on February 15, 2016 · (Permalink)
Thanks, have one back. It really looks like you needed one.
GaryV83 · 151 points · Posted at 06:48:10 on February 14, 2016 · (Permalink)
IT'S SO FUCKING BIG IT DOESN'T FIT ON MY GODDAMN SCREEN!!!!
#SingleScreenPeasantry
gHx4 · 13 points · Posted at 06:58:42 on February 14, 2016 · (Permalink)
Zoom 25% Alrighty then, time to bust out my...
second screen
coolshades
EDIT: Well then, I need another screen. Apparently I need another 300 pixels
[deleted] · 8 points · Posted at 11:02:04 on February 14, 2016 · (Permalink)
Can confirm, have third screen: http://i.imgur.com/4fAtcG3.jpg
holybuttwipe · 1 points · Posted at 22:35:48 on February 21, 2016 · (Permalink)
What DE is that?
[deleted] · 2 points · Posted at 22:46:38 on February 21, 2016 · (Permalink)
XFCE with the Arc-darker theme and Numix Circle icons.
holybuttwipe · 1 points · Posted at 22:52:16 on February 21, 2016 · (Permalink)
Awesome. Thanks
AuroraHalsey · 1 points · Posted at 00:12:05 on February 15, 2016 · (Permalink)
Got it all on one screen!
http://puu.sh/n8crZ/490129742b.png
4k ftw.
gHx4 · 1 points · Posted at 11:10:52 on February 20, 2016 · (Permalink)
Late to the punch, but it's a good thing you've got 4K because I'm always straining to find the new tab I wanted to read next
HolyGarbage · 7 points · Posted at 07:49:29 on February 14, 2016 · (Permalink)
I spread it out in all its glory over my three screens. It was beautiful, just letting you know.
Edit: It actually didn't fit even on three screens on default zoom level... wth.
david2278 · 6 points · Posted at 12:21:29 on February 14, 2016 · (Permalink)
Got it to fit http://i.imgur.com/aWV9tgs.png
GaryV83 · 1 points · Posted at 18:32:27 on February 14, 2016 · (Permalink)
You're the first. Bravo!
niborc · 3 points · Posted at 09:46:48 on February 14, 2016 · (Permalink)
Don't worry, it is so big it doesn't even fit on my 2 screens... Even when I zoom out as much as Firefox allows...
dont_wear_a_C · 6 points · Posted at 07:55:30 on February 14, 2016 · (Permalink)
are we still doing phrasing?
po43292 · 2 points · Posted at 10:41:44 on February 14, 2016 · (Permalink)
Nah, write it out on paper. With a pen.
bilde2910 · 2 points · Posted at 11:52:03 on February 14, 2016 · (Permalink)
I can just barely not fit it on my 4K screen at 25% zoom. I need like five more pixels for that.
poncho531 · 2 points · Posted at 14:51:37 on February 14, 2016 · (Permalink)
I zoomed out all the way (25%) and it still won't fit.
zanderkerbal · 2 points · Posted at 22:47:54 on February 14, 2016 · (Permalink)
Same. After I zoomed out all the way.
waffanculo · 8 points · Posted at 06:48:21 on February 14, 2016 · (Permalink)
If the moon was one pixel...
Isord · 6 points · Posted at 06:49:48 on February 14, 2016 · (Permalink)
That link gave me PTSD.
midoman111 · 5 points · Posted at 07:47:38 on February 14, 2016 · (Permalink)
Suddenly, I don't feel so bad about having to know the quadratic formula.
aeschenkarnos · 3 points · Posted at 06:44:12 on February 14, 2016 · (Permalink)
I wonder if there's some alternative conception for it, that presents it in an extremely simple way.
bliow · 11 points · Posted at 06:52:27 on February 14, 2016 · (Permalink)
There are patterns to it. You define some intermediate quantities based on a, b, c, d, and e, and use them to make the overall formula simpler to express. You'll see this at https://en.wikipedia.org/wiki/Quartic_function#General_formula_for_roots - there is an initial formula for the four roots x1, x2, x3, x4 that is not too much worse than the quadratic formula. But then you notice it's not defined just in terms of a through e, there are this weird S and p and q you don't remember seeing. And the definitions of S, p, and q end up having more complexity... but there are these recurring patterns that they label as Delta_0 (delta is the triangle on that page) and Delta_1 and Q.
That's also the trick used by /u/pikaras above to write the cubic in less space.
F1RST_WORLD_PROBLEMS · 3 points · Posted at 07:00:23 on February 14, 2016 · (Permalink)
I was wondering why you didn't just type it out for us, then I clicked the link. My god, that is too much.
hypervelocityvomit · 1 points · Posted at 09:16:00 on February 15, 2016 · (Permalink)
The direct formulas are bad, not only due to their length, but also because you'd have to recompute certain quantities over and over. If you break them down, things get better.
It gets better if you precompute quantities like
2b3 - 9abc + 27c2 + 27a2 d - 72bd, which appears 12 times per equation.
Call it s and the value within most of the roots simplify to
-4(b2 - 3ac + 12d)3 + s2 ; if that's negative, there are no r values.
There are only 3 places where the 4 "r" formulas are different, and these are different signs. The next step is to compute the still somewhat big terms which are the same, and finally to piece them together using the different signs. If you do that, g is the part starting with 1/2 and about one third of the formula, h is about the middle third, and j is the rightmost 1/4 of the formula, and the final step is:
r1 = -a/4 - g - 1/2 sqrt(h-j),
r2 = -a/4 - g + 1/2 sqrt(h-j),
r3 = -a/4 + g - 1/2 sqrt(h+j),
r4 = -a/4 + g + 1/2 sqrt(h+j).
Also, you check if h<j, because r1 and r2 don't exist if it is.
HesSoZazzy · 2 points · Posted at 07:21:52 on February 14, 2016 · (Permalink)
ok how the HELL does someone come up with that? There are variables in the solution that aren't in the equation it solves. I've always loved math, or at least the idea of it. It's beautiful. But I can't understand a damned thing and it drives me crazy. I feel like there's a key and if I were to just find it, it would all make sense.
bliow · 5 points · Posted at 07:40:07 on February 14, 2016 · (Permalink)
which? r1, r2, r3, and r4 are just names for the 4 different solutions.
I kind of mentioned variables in a short-form solution that don't appear in the longer solution here: https://www.reddit.com/r/AskReddit/comments/45m1zl/whats_the_coolest_mathematical_fact_you_know_of/czzcbif
not just one key. infinitely many. each key unlocks a different door. behind this door are other doors and the reward for opening a door is that you see more locked doors before you. (you are in a maze of twisty little passages, all alike?)
[deleted] · 1 points · Posted at 09:52:58 on February 14, 2016 · (Permalink)
Indeed. You can call them x1, x2, x3 and x4 if you prefer.
garblegarble12342 · 1 points · Posted at 12:26:01 on February 14, 2016 · (Permalink)
A lot of math is just writing shit in a different way. The guy who writes it in the right different way discovers something new.
[deleted] · 2 points · Posted at 09:51:13 on February 14, 2016 · (Permalink)
It's beautiful. Thanks for sharing.
uberduck · 2 points · Posted at 10:19:41 on February 14, 2016 · (Permalink)
It's not too bad.... Wait there's scrolling to the right?!
Lukasv · 1 points · Posted at 07:12:03 on February 14, 2016 · (Permalink)
Holy fuck
Doom-Slayer · 1 points · Posted at 07:12:12 on February 14, 2016 · (Permalink)
The fucking scrollbars have their own scrollbars its so big
Blade2277 · 1 points · Posted at 09:06:07 on February 14, 2016 · (Permalink)
What do each of the r's mean?
hypervelocityvomit · 1 points · Posted at 08:45:51 on February 15, 2016 · (Permalink)
The r's are the 4 solutions.
If there are fewer solutions, you'll end up with roots of negative numbers, so some of the r's won't compute, or possibly with some roots = 0, so in the edge cases, some r's will come out equal.
yodigitty · 1 points · Posted at 09:18:36 on February 14, 2016 · (Permalink)
We did this in one of my advanced high school math classes.. so fucking awful.
butler1233 · 1 points · Posted at 12:06:16 on February 14, 2016 · (Permalink)
What the fuck high school did you go to to subject you to this torture?
yodigitty · 1 points · Posted at 19:42:20 on February 14, 2016 · (Permalink)
Believe it or not, my high school was out in the middle of nowhere, pretty much. Literally, looking around in a 360° angle, all you see is corn.. it was awful.
marcopennekamp · 1 points · Posted at 10:01:48 on February 14, 2016 · (Permalink)
Looks like something that should be implemented in a program, so that we can burn all other occurrences of this formula before it reproduces.
graywolfe42 · 1 points · Posted at 10:07:58 on February 14, 2016 · (Permalink)
I stared at this image on my phone for a solid minute thinking "this isn't all that bad" before realizing my phone screen was only showing like the first fifth of it.
RAFCRA · 1 points · Posted at 10:26:37 on February 14, 2016 · (Permalink)
can i just ask why does this stuff matter? like what does it get used for?
garblegarble12342 · 3 points · Posted at 12:26:50 on February 14, 2016 · (Permalink)
Math people use it to masturbate.
bliow · 1 points · Posted at 10:10:26 on February 15, 2016 · (Permalink)
Mostly it just gets waved around like "look how awful this is". And usually it is served up as a side dish to the main mindfuck, which is "oh by the way, the higher order polynomials, starting with quintics x5, are LITERALLY IMPOSSIBLE to write down formulas for" not because the formulas would be too big to be practical, but because they can't exist at all, which is a complete mindfuck and requires a fair bit of study to really understand.
It is used for several things according to wikipedia, but giving a laundry list of how it's used is sort of answering the question wrong. The real answer is more like, lots of things result in polynomials (like the quadratic or the quartic), and so solving these equations where the highest term is x4 tells us things about how polynomials work in general (and those are really everywhere).
Also there are powerful ways of calculating the answers to within many decimal places without touching that god-awful formula.
UsablePizza · 1 points · Posted at 10:30:43 on February 14, 2016 · (Permalink)
I tried using that formula in a graphics assignment to draw a torus. (a doughnut like shape).
It was viewable from one side and didn't have a shadow... I checked it even like 5 times. Needless to say, I learned that they are horrible pieces of work.
Colopty · 1 points · Posted at 12:38:26 on February 14, 2016 · (Permalink)
But why? D:
Junkeregge · 1 points · Posted at 14:01:00 on February 14, 2016 · (Permalink)
Are you telling me there once was a guy on Earth who had nothing better to do with his life that that?
bliow · 2 points · Posted at 09:58:12 on February 15, 2016 · (Permalink)
They hadn't invented reddit yet.
bootshick · 1 points · Posted at 02:24:52 on February 15, 2016 · (Permalink)
Holy mother of God
LunaTehNox · 1 points · Posted at 23:52:07 on April 6, 2016 · (Permalink)
Now I don't have eyes anymore
flamingboard · -1 points · Posted at 09:35:37 on February 14, 2016 · (Permalink)
I'm so glad autism exists to figure this stuff out.
[deleted] · 2 points · Posted at 07:20:36 on February 14, 2016 · (Permalink)
[deleted]
oldLoginWasRealName · 2 points · Posted at 10:25:39 on February 14, 2016 · (Permalink)
Close: you've got it confused with The distance equation/pythagorean theorem: a2 + b2 = c2. That one is nice, and can keep going forever (into time travel or extra spacial dimensions or whatever (read Flatland if you want that to make sense; it's just 100 pages and very accessible)). You just add a variable: a2 + b2 + c2 ...= z2 where a through y are how far you went in directions a through y, and z is the total distance.
These fuckers are to find a curve's roots (zeros, places where the curve touches/crosses the x axis). The one everyone learned is if x is squared plus some shit, the next if its cubed, errand you can't do it if it's x5.
Source: am math major, want to get rid of shit online math homework
[deleted] · 1 points · Posted at 06:37:21 on February 14, 2016 · (Permalink)
"who made this big mess?"
3Lonely5Me · 1 points · Posted at 08:27:38 on February 14, 2016 · (Permalink)
I live for this mess.
martinluther3107 · 1 points · Posted at 09:46:44 on February 14, 2016 · (Permalink)
I am proud I actually know this one!
EnkoNeko · 1 points · Posted at 09:58:08 on February 14, 2016 · (Permalink)
^ What was going through my head.
DreadNinja · 1 points · Posted at 11:04:06 on February 14, 2016 · (Permalink)
It's actually quite easy! 12th grade stuff.
moyno85 · 1 points · Posted at 11:19:20 on February 14, 2016 · (Permalink)
this is giving me intense anxiety
itisike · 1 points · Posted at 12:27:10 on February 14, 2016 · (Permalink)
Get a copy of journey through genius. It has a chapter on how these were discovered, very readable.
Slabbo · 1 points · Posted at 13:54:26 on February 14, 2016 · (Permalink)
Splitting the bill at a restaurant with my cheap friends.
BlueKlay · 1 points · Posted at 14:58:08 on February 14, 2016 · (Permalink)
I think that's the new way they're teaching division in elementary school.
gr770 · 1 points · Posted at 17:45:21 on February 14, 2016 · (Permalink)
Bitch please:
https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html
[deleted] · -3 points · Posted at 06:51:38 on February 14, 2016 · (Permalink)
It's just basic math.
BlackDS · 16 points · Posted at 05:54:42 on February 14, 2016 · (Permalink)
Mother of God...
ITouchMyselfAtNight · 15 points · Posted at 06:30:38 on February 14, 2016 · (Permalink)
I can't believe I missed this as the logical continuation of the quadratic formula. It seems so obvious now.
unrighteous_bison · 13 points · Posted at 07:03:33 on February 14, 2016 · (Permalink)
as an engineer, that looks delightful. no wronskians, laplace transforms, or other bullshit. just a simple formula that can be programmed by most any programming language in a few minutes.
jwaldo · 7 points · Posted at 06:52:28 on February 14, 2016 · (Permalink)
When I was young, I was horrified by math. When I was in high school, my teachers taught me to appreciate and respect it. Now though I realize I was right to fear math, that the fear comes from the innate knowledge that equations like this lurk all around us...
rawling · 7 points · Posted at 08:18:29 on February 14, 2016 · (Permalink)
Not a good start there?
God_Damnit_Nappa · 7 points · Posted at 07:04:48 on February 14, 2016 · (Permalink)
(╯°□°)╯︵ ┻ ━┻
GratefulGrape · 6 points · Posted at 09:13:18 on February 14, 2016 · (Permalink)
Calm down, bro. You snapped the bench in half.
lejialus · 5 points · Posted at 07:11:44 on February 14, 2016 · (Permalink)
Now make arrange it into a nifty little song for me.
BestPseudonym · 3 points · Posted at 06:45:34 on February 14, 2016 · (Permalink)
Wheres the formula for fourth order polynomials?
eternally-curious · 4 points · Posted at 07:03:13 on February 14, 2016 · (Permalink)
Here.
pikaras · 2 points · Posted at 07:05:30 on February 14, 2016 · (Permalink)
I never bothered to memorize that one. It's a fucking monster
factsbotherme · 1 points · Posted at 06:59:58 on February 14, 2016 · (Permalink)
Its too complex to even write down.
Dent18 · 2 points · Posted at 07:53:50 on February 14, 2016 · (Permalink)
Fuck that just use wolfram alpha
pikaras · 2 points · Posted at 08:04:50 on February 14, 2016 · (Permalink)
I'm starting my career in HRM. I'll never even need to know to wolfram alpha that thing but I still know it because im a nerd
FlatJoe · 2 points · Posted at 09:05:34 on February 14, 2016 · (Permalink)
"For those who didn't know" pffff what kind of worthless ignoramus doesn't know this basic concept.
pikaras · 1 points · Posted at 09:40:05 on February 14, 2016 · (Permalink)
Because a lot of people in the math community do know and this post is not for them? (and there are a lot of math nerds in this thread)
khaotickk · 2 points · Posted at 09:51:29 on February 14, 2016 · (Permalink)
Woah there take it easy Satan, I can only process a few letters at a time
suckmypenisfukmygoat · 1 points · Posted at 06:48:38 on February 14, 2016 · (Permalink)
Is it weird that I kinda wanna work that out just cuz?
whale_oilbeef_hooked · 1 points · Posted at 07:09:16 on February 14, 2016 · (Permalink)
yes, I know some of these words.
MrLime11 · 1 points · Posted at 08:24:25 on February 14, 2016 · (Permalink)
Filthy.
PrepaidSniper · 1 points · Posted at 09:53:41 on February 14, 2016 · (Permalink)
The guy just pissed on us
[deleted] · 1 points · Posted at 10:10:02 on February 14, 2016 · (Permalink)
Did someone prove these just to show that they can or is there any advantage to using these rather than solving higher order polynomials numerically (like a normal person)?
pikaras · 1 points · Posted at 19:22:45 on February 14, 2016 · (Permalink)
There used to be math competitions and one of the challenges would would be to factor fourth order polynomials without rational roots. In the 16th century, someone figured it out but kept it secret so he could keep winning. (At least that's the story my math teacher told us)
[deleted] · 1 points · Posted at 19:51:03 on February 14, 2016 · (Permalink)
Haha brilliant. Thanks for that
[deleted] · 1 points · Posted at 10:11:00 on February 14, 2016 · (Permalink)
Mathematician here. Cannot confirm, I've never felt the need to use it. Besides, there's no fucking way I'm going to check that.
LinkerZz · 1 points · Posted at 10:21:02 on February 14, 2016 · (Permalink)
Seriously, how can someone possibly figure this out? I mean, how the hell did they reach this formula for the first time?
pikaras · 1 points · Posted at 19:21:18 on February 14, 2016 · (Permalink)
It's a pretty simple extension of the quadratic formula. I assume the only hard part would be figuring out what q r and p were
-duvide- · 1 points · Posted at 10:25:27 on February 14, 2016 · (Permalink)
Couldn't they just say this formula will give all four solutions instead of writing it four times?
bsmfaktor · 1 points · Posted at 10:29:40 on February 14, 2016 · (Permalink)
Kill me now
[deleted] · 1 points · Posted at 10:58:47 on February 14, 2016 · (Permalink)
In Germany this formula is called the midnight's formula. I think now I know why
crazilackey · 1 points · Posted at 11:33:34 on February 14, 2016 · (Permalink)
And people wonder why I hate math?!? 2+2 is to complex for me!
Diels_Alder · 1 points · Posted at 11:43:47 on February 14, 2016 · (Permalink)
Nope.
Keenbean248 · 1 points · Posted at 11:59:40 on February 14, 2016 · (Permalink)
My first thought on that quartic formula was "it's not that bad." Then I kept scrolling...
PonyBaron · 1 points · Posted at 12:09:55 on February 14, 2016 · (Permalink)
Ahn complex polynom formulas. At college I'd always try what is my favorite curiosity to reduce them.
If the sum of the coeficients are equal to 0 the number 1 is a roots. Like X2+2x-3=0 1+2-3=0 1 is a root Find the root of a big polynom and divide it to make a smaller one.
Gotta miss my diferencial equations classes, soo many math tricks to resolve integers and shit
Ps: Sorry if there is any math-word wrong not a native speaker
A_favorite_rug · 1 points · Posted at 12:50:13 on February 14, 2016 · (Permalink)
Nope. Fuck that. I'll stick with quadratic formula I was taught.
Those variables, man.
Sage2050 · 1 points · Posted at 13:30:32 on February 14, 2016 · (Permalink)
What's the rationale for not simply writing in the substitutions in the equation?
pikaras · 1 points · Posted at 19:17:36 on February 14, 2016 · (Permalink)
What?
grohlier · 1 points · Posted at 14:36:26 on February 14, 2016 · (Permalink)
I'm just sitting over here going, "Negative Beeeeeeeeeeee Negative Beeeeeeeeeeeeeeeee.... plus-or-minus the squareroot, plus-or-minus the squareroot..."
erisawesome · 1 points · Posted at 16:28:10 on February 14, 2016 · (Permalink)
Synthetic division it is!
tsavoy004 · 1 points · Posted at 19:00:05 on February 14, 2016 · (Permalink)
I would love to see someone type the fourth root one
UberDuDrop · 1 points · Posted at 19:08:22 on February 17, 2016 · (Permalink)
This is a Great Old One in the form of a fucking mathematical equation.
Kallisti13 · 1 points · Posted at 04:28:13 on February 20, 2016 · (Permalink)
Wtf.
Novastra · 1 points · Posted at 06:23:08 on February 14, 2016 · (Permalink)
Yep, that is DISGUSTING
VelvetHorse · 1 points · Posted at 06:29:04 on February 14, 2016 · (Permalink)
Fuck this bullshit.
[deleted] · 0 points · Posted at 07:12:57 on February 14, 2016 · (Permalink)
As a high school dropout I look at this with Peter Griffin face.
AvantAveGarde · 8 points · Posted at 05:57:08 on February 14, 2016 · (Permalink)
Mathematicians HATE THIS
allora_fair · 5 points · Posted at 10:08:38 on February 14, 2016 · (Permalink)
In my maths class, we decided to see if we could track down those formulas after the teacher alerted us to their existence.
We were wildly impressed with the one for cubics, and the class entreated me to copy it down.
Next, we found the one for quartics. There were shocked mutters, horrified gasps, and my pen dropped from my hands.
reddit__scrub · 1 points · Posted at 06:24:42 on February 14, 2016 · (Permalink)
But its beautiful that you can make a computer do it for you
abaddamn · 1 points · Posted at 07:32:35 on February 14, 2016 · (Permalink)
And those polynominals can be reduced to a Pascal Triangle and from there we get the Fibonacci series. WTF
novvesyn · 1 points · Posted at 08:44:22 on February 14, 2016 · (Permalink)
Thank god for Viete's formula.
charlesthechuck · 1 points · Posted at 14:04:04 on February 14, 2016 · (Permalink)
Which one is that?
novvesyn · 1 points · Posted at 17:14:05 on February 14, 2016 · (Permalink)
The one that relates the sum of products of the roots of the polynomial to its coefficients. In quadratics (ax2 + bx + c) that is b = -(x1+x2)/a c = x1*x2/a
Spamakin · 1 points · Posted at 14:22:43 on February 14, 2016 · (Permalink)
I tried watching the Khan Academy video on how to calculate these formulas in your head. It's quite neat, but confusing as all hell
[deleted] · 1 points · Posted at 15:32:15 on February 14, 2016 · (Permalink)
Thats why you just copy them into your calculator and pray that the prof doesnt care. or make a phony RAM clear program
jax_the_champ · 50 points · Posted at 05:47:18 on February 14, 2016 · (Permalink)
Why can't there?
[deleted] · 97 points · Posted at 06:33:18 on February 14, 2016 · (Permalink)*
Understanding why is the final result of a year-long graduate-level mathematics course I am currently trying to slog through. It has to do with miniature algebra-things called Galois Groups, and whether they are what's called "solvable". In assuming that there could be a generalized solution to the quintic, you can likely generate a contradiction.
Ph0X · 15 points · Posted at 22:05:18 on February 15, 2016 · (Permalink)
Fun factoid (you might've been told by your teacher).
Galois, who basically started that whole sub branch of mathematics, died at the age of 20 in a duel for a girls love.
He developed a whole branch of math before the age of 20... can you imagine what kind of things he would've achieved if he had lived to 40-50?
[deleted] · 14 points · Posted at 23:10:58 on February 15, 2016 · (Permalink)
Not only that, but he had it mostly in his head and stayed up all night before the duel, scribbling it out for posterity's sake. May have contributed to being slow on the draw.
Joined in attempts at revolution, died for "love", solidified an entire branch of mathematics, and still didn't live out his potential. Here I am at 25 and I can't not masturbate.
Bobius · 43 points · Posted at 08:23:47 on February 14, 2016 · (Permalink)
Or an 8 week course at Cambridge!
At week 4 our lecturer said something along the lines of "and this is where I'd stop if this were any other university."
Timothy_Claypole · 27 points · Posted at 10:19:55 on February 14, 2016 · (Permalink)
Why is this downvoted? Cambridge undergrad maths includes Galois Theory. This is part of postgrad maths elsewhere. Frankly I say good on them for having the highest standards, but also it might fry my brain if I attempted it.
DrPhineas · 12 points · Posted at 11:38:38 on February 14, 2016 · (Permalink)
People don't like that he went to a better University than they did
boonamobile · 25 points · Posted at 12:39:35 on February 14, 2016 · (Permalink)
More that he's pretentious about it
DrPhineas · 7 points · Posted at 12:55:32 on February 14, 2016 · (Permalink)
Ahh, you're right. I didn't see that last line.
Log2 · 4 points · Posted at 23:15:50 on February 14, 2016 · (Permalink)
Mostly because it is not as uncommon as he makes it sound. Personally, I've never met anyone that graduated in pure math that didn't study Galois theory.
StannisBa · 5 points · Posted at 23:42:50 on February 14, 2016 · (Permalink)
Where is he pretentious?
Log2 · 3 points · Posted at 23:14:27 on February 14, 2016 · (Permalink)
I had Galois theory as a part of an algebra course, and this was in Brazil. I'm pretty sure that Galois theory is a standard undergrad subject to cover in any math undergrad course in any decent university.
Homomorphism · 3 points · Posted at 07:51:50 on February 15, 2016 · (Permalink)
Galois theory is a common upper-level undergraduate elective.
Completeness_Axiom · 1 points · Posted at 12:14:57 on February 14, 2016 · (Permalink)
False. (Optional) Final year module on BSc at Warwick.
Timothy_Claypole · 2 points · Posted at 12:27:13 on February 14, 2016 · (Permalink)
Well, yeah and maybe at Oxford too. Obviously at a top uni for maths (like Warwick) it's not unexpected, I didn't say "elsewhere" to mean "everywhere else".
[deleted] · 3 points · Posted at 18:17:35 on February 14, 2016 · (Permalink)
The year-long course at my university is the full elementary abstract algebra sequence: One quarter each of groups, rings, and fields. It culminates at the end of the year with Galois theory. If you want to assert that students are raised in eight weeks' time from group axioms to the proof of the general non-solvability of the quintic, then I would be very impressed.
Bobius · 1 points · Posted at 18:19:38 on February 14, 2016 · (Permalink)
Groups was an 8 week 1st year course for us, GRM (groups, Rings and Modules) was 8 weeks of 2nd year, Galois Theory was 8 weeks of 3rd year.
[deleted] · 3 points · Posted at 18:29:00 on February 14, 2016 · (Permalink)
Then our algebra sequences are identical up to isomorphism.
[deleted] · 1 points · Posted at 20:04:31 on February 14, 2016 · (Permalink)
Or one term of a frosh course at Caltech!
Those poor frosh, polynomials suck. Algebra used to seem cool, but it's got nothing on topology and logic
harlows_monkeys · 2 points · Posted at 20:38:10 on February 14, 2016 · (Permalink)
There are no freshman courses at Caltech that include Galois theory.
Galois theory is covered in the third term of Ma 5, which is a sophomore course for math majors (and anything from sophomore to senior for people who are not math majors who want to take introductory abstract algebra for fun).
Ma 5 has no prerequisites so in theory one might be able to take it as a freshman, but in practice that would be very hard to arrange because freshman at Caltech have a full schedule of required core courses. It would be hard to get one's advisor to approve taking Ma 5 as a freshman. Furthermore, since freshman are not expected to be in Ma 5 there is no attempt to schedule it to avoid conflicting with required freshman courses, further reducing the chances that one could convince one's advisor to allow one to take it.
[deleted] · 1 points · Posted at 21:07:48 on February 14, 2016 · (Permalink)*
Most people I know in Ma5 are frosh. Every math major I can think of that I know, besides those that switched into math after frosh year, took Ma5 as a frosh. Take that for what you will, it's possible my sample is weirdly skewed, but I don't think so.
But independent of my sample, it's absolutely not hard to get an adviser to let you do that
Homomorphism · 0 points · Posted at 08:20:37 on February 15, 2016 · (Permalink)
It's perfectly possible to cover Galois theory in eight weeks if you already know group and ring theory, which I assume is the case.
WyclefJean · 2 points · Posted at 21:10:56 on February 14, 2016 · (Permalink)
Ah yes, I know some of these words
almightySapling · 16 points · Posted at 06:33:41 on February 14, 2016 · (Permalink)
The proof of this fact is very involved, but essentially it ties the solutions of polynomials to the ability to decompose a certain group into a chain of groups whose factors are all abelian.
Needs_No_Convincing · 17 points · Posted at 07:14:52 on February 14, 2016 · (Permalink)
Totally.
mifbifgiggle · 6 points · Posted at 07:43:07 on February 14, 2016 · (Permalink)
Relevant username
das_hansl · 12 points · Posted at 10:22:32 on February 14, 2016 · (Permalink)*
It's very complicated. In general, roots of polynomials are exchangeable. If one has the polynomial x2 - 2 = 0, it is has two solutions, sqrt(2) and -sqrt(2). If one would would swap sqrt(2) and -sqrt(2), nobody would notice this, because the only connection to the numbers that you already had, is through the polynomial x2 - 2 = 0. Since x is squared in the polynomial, the sign disappears.
As a general rule, you can see from the way in which solutions can be exchanged, what is the polynomial that defines them.
If you have a general 5-th degree polynomial, then its solutions are exchangeable by all permutations of 5 numbers. If you want a closed form for these solutions, you need to show that they can also be obtained through a sequence of simple roots, which are polynomials of a restricted form xp - c = 0. It has been shown that, using only such polynomials, one can never get the full permutation group of five objects. Essentially, the solutions of a polynomial xp - c can be exchanged only in a circular way.
Note that I simplified quite a lot. The general theory is called 'Galois Theory'.
Kered13 · 4 points · Posted at 14:31:32 on February 14, 2016 · (Permalink)
While it's by no means a complete proof, that's a remarkably simple and intuitive (for the nature of the problem) sketch! I spent several hours reading the Wikipedia article on Galois theory a couple weeks ago trying to get the vaguest grasp of how the proof went and got nowhere.
randomharun · 2 points · Posted at 12:12:19 on February 14, 2016 · (Permalink)
Is there any significance as to WHY 5th order polynomials aren't solvable? As in, why can 4th order polynomials be solved when 5th order can't? What changes in mathematics that this suddenly doesn't work anymore? From my very basic understanding I had assumed that most mathematics "just scale". As in "if it's possible to do something in previous instances, with more thought, it should be possible to do in other instances".
Also I'm a bit confused: Has it been proven that 5th order polynomials are impossible to solve generally? Or has it been proven that you can't generally solve quintic functions but some are solvable?
Is this the kind of thing where there's a hard limit to the maths or is this the kind of point in time where we would need another (yet unthought of) conceptualisation of mathematics and numbers in order to solve the problem? Like how we needed irrational numbers to explain sqrt(2) or imaginary numbers to have negative roots?
Sorry for the long text but these questions have been in my uneducated mind for quite some time.
das_hansl · 3 points · Posted at 13:07:24 on February 14, 2016 · (Permalink)*
The general 5th order polynomial is unsolvabe: There is no closed formula, using only radicals, that solves Ax5 + Bx4 + Cx3 + Dx2 + Ex + F = 0.
Some concrete 5th order polynomials are unsolvable, e.g. x5 - 6x + 3 = 0. Others have trivial solutions, e.g. (x-3)(x+2)(x-1)(x+8)(x+5) = 0.
The roots of a 4-th degree polynomial can be permuted in 24 ways. It is a smaller group, and it is still simple enough to be composable into a sequence of cyclic groups. The reasons are a bit technical, but it is still possible.
It is clear that all polynomials have solutions in the complex plane, it is just that some of these solutions cannot be expressed using clean radicals.
randomharun · 1 points · Posted at 13:39:25 on February 14, 2016 · (Permalink)
I understood this a little bit, so thank you!
I still don't see why it would be necessary to "only use radicals" in order to get a closed formula but that's probably me not knowing enough.
das_hansl · 1 points · Posted at 13:43:32 on February 14, 2016 · (Permalink)
That's just a matter of mathematical elegance. Radicals are kind of nice because they represent the solutions of the simplest possible polynomials. Of course in applications, one can always solve the equation numerically.
appropriate-username · 1 points · Posted at 14:39:30 on February 14, 2016 · (Permalink)
Wolframalpha found approximate solutions:
http://www.wolframalpha.com/input/?i=x%5E5+-+6x+%2B+3+%3D+0
testaa · 1 points · Posted at 14:09:34 on June 16, 2016 · (Permalink)
really nice brief explanation, thanks
thebigbadben · 1 points · Posted at 13:51:23 on February 14, 2016 · (Permalink)
The term to google for that rabbit hole is the "Abel-Ruffini theorem".
blebaford · 34 points · Posted at 02:36:39 on February 14, 2016 · (Permalink)
I really need to revisit that proof. When I took abstract algebra it was the last thing we covered, and I think I understood it like 75%, but now I'm back to being baffled.
[deleted] · 13 points · Posted at 02:50:57 on February 14, 2016 · (Permalink)
You'll Galois-nt to review that for certain...
TwoFiveOnes · 8 points · Posted at 04:15:43 on February 14, 2016 · (Permalink)
Pleaaaasee don't oomg that was wretched
blebaford · -3 points · Posted at 05:19:43 on February 14, 2016 · (Permalink)
you did not just make that pun that was SAVAGE
DaGranitePooPooYouDo · 2 points · Posted at 10:41:51 on February 14, 2016 · (Permalink)
You know what's purple and commutes?
An Abelian grape.
[deleted] · 2 points · Posted at 18:12:54 on February 14, 2016 · (Permalink)
My friend (He's an algebraist) proposed to his gf. She said she wanted a really nice ring. So he got her a field.
Ultima_RatioRegum · 3 points · Posted at 08:20:29 on February 14, 2016 · (Permalink)
Check out the book Fearless Symmetry by Ash and Gross. It's the only book I've ever read that clearly explains Galois theory (and a pretty good outline of the proof of Fermat's Last Theorem) in a way that doesn't require graduate-level abstract algebra.
[deleted] · 15 points · Posted at 02:56:49 on February 14, 2016 · (Permalink)
It's funny that in my country we learn the quadratic formula as the Bhaskara formula (after its discoverer), but that doesn't seem to be the case in the US.
Waniou · 13 points · Posted at 05:59:06 on February 14, 2016 · (Permalink)
My maths teacher taught it to me as "big grunter" because he thought it was big and grunty.
I had a very strange maths teacher.
Voxel_Brony · 1 points · Posted at 01:22:35 on February 15, 2016 · (Permalink)
No, that's sounds normal for a math teacher. My geometry teacher always referred to circles as hellagons.
Waniou · 1 points · Posted at 01:27:04 on February 15, 2016 · (Permalink)
He also made several bad jokes, some of which, I legitimately don't know how he never got fired for. These included "Did you hear about the two bad apples? Too bad!" and "If ice gives you icicles, what do tests give you?"
mechroneal · 3 points · Posted at 10:37:41 on February 14, 2016 · (Permalink)*
I just started watching this documentary on Netflix, called Maths. One of the things they talk about is there are indications that this universal truth of "a2 + b2 = C2" had been discovered, or at least brush up against by several people/cultures over time, because they are fundamental laws, regardless of counting systems, etc.
They also mentioned that Pythagoras believed reality was directly made of whole numbers and ratios. When Hippasus pointed out that the number which represents the length of a hypotenuse in a right triangle whose sides have length of 1 basically breaks this idea (the square root of 2 is an irrational number), the follower was killed.
db0255 · 2 points · Posted at 10:48:35 on February 14, 2016 · (Permalink)
The pythagorean theorem comes up a lot in the Ancient world before Pythagoras. There were civilizations that understood and used it. The PROOF of the general equation, however, didnt come about until Pythagoras.
[deleted] · 2 points · Posted at 06:41:44 on February 14, 2016 · (Permalink)
This may not be why, but there is a respectably large movement in US math to allot what are considered "useful" names to concepts, rather than naming them after the mathematicians or anything else colorful. I get it in some cases, but there's a few folks who don't even want to call things "pathological" because it's supposedly biasing.
ghostabdi · 5 points · Posted at 02:51:23 on February 14, 2016 · (Permalink)
That is weird. It's known as the Abel–Ruffini theorem. https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem
SunriseSurprise · 5 points · Posted at 06:02:01 on February 14, 2016 · (Permalink)
I like how the Wiki linked in one of the replies puts it as I think this is the big wtf:
clopensets · 2 points · Posted at 12:09:20 on February 14, 2016 · (Permalink)
OMG this. I love Galois Theory. Also I really like mathematical results--how would I put it--that before being versed in the field may seem rather arbitrary. Like this, there are linear, quadratic, cubic, and quartic formulas, but no other power. Why? We develop a theory that can reduce certain field theory to group theory problems. The properties of symetry groups can then be used to prove that there is no higher power formula. I'm glossing a little bit, but I really enjoy these sorts of results.
Lord_Skellig · 2 points · Posted at 22:43:05 on February 14, 2016 · (Permalink)
Does this not prove that P =/= NP? You're saying there is no algorithm for finding the roots of a 5th order polynomial, so it is not in P, however given the roots it is trivial to check that they are correct, so it is in NP.
BT_Uytya · 2 points · Posted at 08:16:17 on February 16, 2016 · (Permalink)
No.
This result shows that you can't in general describe the solution for polynomial equation in a way that is significantly better than decimal expansion.
If roots are given as (potentially infinite) decimal expansion, then it takes an infinite amount of time to check that the answer fits.
jerkandletjerk · 1 points · Posted at 07:40:54 on February 14, 2016 · (Permalink)
and there's a beautiful piece of history for 3rd order polynomial roots.
LigerZerOJaegaer · 1 points · Posted at 12:46:21 on February 14, 2016 · (Permalink)
why cant there be?
don_truss_tahoe · 1 points · Posted at 14:31:13 on February 14, 2016 · (Permalink)
Not sure can't is the right word. Using a series of approximation formulae and expansions, we can get a 5th order equation + o(.) where o(.) just denotes a negligible component.
[deleted] · 1 points · Posted at 04:30:07 on February 15, 2016 · (Permalink)
Almost only counts in horseshoes and compact spaces!
don_truss_tahoe · 1 points · Posted at 05:28:13 on February 15, 2016 · (Permalink)
Almost surely
chironon · 1 points · Posted at 15:27:03 on February 14, 2016 · (Permalink)
Do you know why there are no such formula for the 5th order? I've not been able find a good initiative explanation of why. It seems a bit like saying there's no solution to x2 = -1, but its turned out to be pretty useful just define i := √-1
The-Night-Forumer · 1 points · Posted at 17:24:23 on February 14, 2016 · (Permalink)
Why can't there be?
Fahsan3KBattery · 1 points · Posted at 21:18:04 on February 14, 2016 · (Permalink)
Furthermore Galois discovered this and the formulas for quartics and solveable quintics the night before he died. He stayed up all night writing down everything he was working on and things that just occurred to him into a letter which he posted to a friend and then went straight off to fight a duel at dawn. He lost the duel and was killed.
ggeoff · 1 points · Posted at 21:59:52 on February 14, 2016 · (Permalink)
Is there an eli5 proof for why there can't be?
ectish · 1 points · Posted at 02:42:20 on February 15, 2016 · (Permalink)
The quadratic formula can be sung to the tune of Gilligan's Island and also to Pop Goes the Weasel.
Spiralofourdiv · 1 points · Posted at 17:02:41 on February 16, 2016 · (Permalink)
See Galois Theory
Maker_Wolf · 1 points · Posted at 07:44:42 on February 14, 2016 · (Permalink)
Why can't there be?
It makes sense that the equation would be exponentially more complicated, but why impossible?
omniron · 0 points · Posted at 07:08:49 on February 14, 2016 · (Permalink)
Completely mind boggling there isn't a formula for 4th order... Never knew this until recently. So counterintuitive... Our universe is magic.
rngisforfailures · 5520 points · Posted at 19:18:19 on February 13, 2016 · (Permalink)*
The guy that proved the existence of irrational numbers was murdered for his finding.
Edit: The Google cached version
Edit 2: Original link is now HTTP instead of HTTPS
Edit 3: Gilded, thank you!
TheRealSteve72 · 3121 points · Posted at 23:54:28 on February 13, 2016 · (Permalink)*
I never picked up that "irrational" means "cannot be a ratio".
Neat.
EDIT: As a bunch of people below noted, ratio OF INTEGERS.
Still neat.
FPSdouglass · 781 points · Posted at 00:59:37 on February 14, 2016 · (Permalink)
But pi is irrational and the ratio between the diameter and the circumference of a circle.. Hmm
Archack · 151 points · Posted at 03:54:00 on February 14, 2016 · (Permalink)
Can't tell if you're being sarcastic, but irrational numbers cannot be expressed as a ratio of INTEGERS.
neurohero · 3 points · Posted at 09:33:35 on February 14, 2016 · (Permalink)
I was always taught that pi is 22/7. Is that incorrect?
MakuWasTaken · 64 points · Posted at 09:35:03 on February 14, 2016 · (Permalink)
Yes, that's incorrect.
UmbrellaCorp1961 · 29 points · Posted at 09:48:58 on February 14, 2016 · (Permalink)
Yes. Incorrect. But a fairly close approximation.
Jonno_FTW · 15 points · Posted at 09:49:55 on February 14, 2016 · (Permalink)
It's an approximation that's easy to do on a calculator.
[deleted] · 5 points · Posted at 10:47:46 on February 14, 2016 · (Permalink)*
[deleted]
onemessageyo · 3 points · Posted at 12:42:53 on February 14, 2016 · (Permalink)
There's a lot more digits so it's not really accurate, just accurate enough. In my first year of college we had to use 3.1415 or the professor would mark it.
Shady-McGrady · 1 points · Posted at 16:21:25 on February 14, 2016 · (Permalink)
Would?
pomlife · 3 points · Posted at 17:24:59 on February 14, 2016 · (Permalink)
Yes, that's a word. Your point?
AskYouEverything · 2 points · Posted at 17:39:50 on February 25, 2016 · (Permalink)
point?
regular-normal-guy · 1 points · Posted at 19:29:40 on February 14, 2016 · (Permalink)*
Whether it's "accurate enough" depends entirely on what you plan on doing with the results.
High school math: accurate enough. Wood working: probably accurate enough. Fine machining: probably accurate enough. Astrophysics: not even close to close enough.
DataWhale · -1 points · Posted at 12:19:14 on February 14, 2016 · (Permalink)
Sometimes you do math with fractions though.
Archack · 3 points · Posted at 15:49:09 on February 14, 2016 · (Permalink)
Pi is approximately 22/7, just like it's approximately 3.14. If the diameter of a circle is rational, then the circumference must be irrational, and vice versa. Or they both could be irrational. Cool stuff!
Chrome_Panda_Gaucho · 1 points · Posted at 13:12:31 on February 16, 2016 · (Permalink)
Pi can be calculated by doing the following infinite series. (4/1) - (4/3)+(4/5)-(4/7)+(4/9)...
Chrome_Panda_Gaucho · 2 points · Posted at 13:12:10 on February 16, 2016 · (Permalink)
Pi can be calculated by doing the following infinite series. (4/1) - (4/3)+(4/5)-(4/7)+(4/9)...
But you can see you never reach a finite value
neurohero · 1 points · Posted at 14:32:22 on February 16, 2016 · (Permalink)
I suppose, when I was first taught it when I was 12, the teacher didn't want to complicate matters.
The funny thing is that I've now taken maths up to second year university, using pi many many times in many many calculations but have never had the occasion to question that original piece of misinformation.
weinerschnitzelboy · 0 points · Posted at 10:38:16 on February 14, 2016 · (Permalink)
Wat?! I mean if you plug it into a calculator you'll see its just wrong.
Chrome_Panda_Gaucho · 1 points · Posted at 13:11:17 on February 16, 2016 · (Permalink)*
Pi can be calculated by doing the following series. Pi can be calculated by doing the following infinite series. (4/1) - (4/3)+(4/5)-(4/7)+(4/9)...
You keep doing that indefinitely, it doesn't mean you cant express it as a ratio of integers, it's that there is no pattern of integers than can difine the number in a finite solution
gratz · 110 points · Posted at 01:05:55 on February 14, 2016 · (Permalink)
Somebody please explain this to me
[deleted] · 398 points · Posted at 01:17:39 on February 14, 2016 · (Permalink)*
irrational = cannot be a whole number ratio - that is, cannot represented as a fraction of two integers, like 1/2 or 53/26. You can't write pi as a fraction* because a circle with a whole-number radius doesn't have a rational circumference.
* a fraction of two rational numbers, anyway. Technically, pi can be written as a continued fraction, or something like π/1 like /u/Autumn_Thunder pointed out.
Edit: Apparently I have no fucking idea what I'm doing. Just scroll down for a better analysis.
[deleted] · 264 points · Posted at 05:22:38 on February 14, 2016 · (Permalink)
Circular Reasoning!
almightySapling · 111 points · Posted at 06:11:36 on February 14, 2016 · (Permalink)
I am laughing waaaaaay too hard at this.
SadGhoster87 · 4 points · Posted at 07:05:12 on February 14, 2016 · (Permalink)
You win. You win the thread. Pack up and go home, this guy did a mucho bueno job.
Autumn_Thunder · 48 points · Posted at 03:54:48 on February 14, 2016 · (Permalink)
http://www.smbc-comics.com/?id=2208
[deleted] · 30 points · Posted at 04:05:38 on February 14, 2016 · (Permalink)
...true. I guess it would be more correct to say:
Edited original comment to fix.
[deleted] · 23 points · Posted at 04:58:44 on February 14, 2016 · (Permalink)
[deleted]
klod42 · 0 points · Posted at 10:53:52 on February 14, 2016 · (Permalink)
But then Pi is rational, because pi/1 is a fraction of two rational numbers.
coolirisme · -6 points · Posted at 08:00:52 on February 14, 2016 · (Permalink)
You can definitely write pi as a fraction of two whole numbers but those whole numbers will be infinitely long.
3.1416..... = 31416..../10000....
MCBeathoven · 6 points · Posted at 09:01:43 on February 14, 2016 · (Permalink)*
But infinitely
longlarge (i.e. infinitely long before the decimal point) numbers aren't rational.JulitoCG · 2 points · Posted at 10:02:52 on February 14, 2016 · (Permalink)
Unless they repeat, that is
MCBeathoven · 1 points · Posted at 12:57:41 on February 14, 2016 · (Permalink)
Yes, if they repeat after the decimal point. If they repeat infinitely before the decimal point they aren't rational anymore.
JulitoCG · 1 points · Posted at 17:01:34 on February 14, 2016 · (Permalink)
Touché, this is why I shouldn't talk math at 6am while on Molly lol I miss things like that. Well played!
GodlessPerson · 1 points · Posted at 12:02:41 on February 14, 2016 · (Permalink)
Depends. 1/3 is infinitely long but it is rational.
MCBeathoven · 2 points · Posted at 12:58:44 on February 14, 2016 · (Permalink)
Yes, I meant infinitely long before the decimal point. Edited my comment.
udbluehens · 1 points · Posted at 14:09:26 on February 14, 2016 · (Permalink)
1 and 3 are integers...
GodlessPerson · 3 points · Posted at 14:30:05 on February 14, 2016 · (Permalink)
But their output is infinitely long and still is rational.
udbluehens · 1 points · Posted at 15:37:14 on February 14, 2016 · (Permalink)
The definition of rational is you can represent the number as the division of two integers. It being infinitely long doesnt matter at all
GodlessPerson · 2 points · Posted at 15:49:28 on February 14, 2016 · (Permalink)*
I know that. That was exactly my point. The guy above my first comment was the one who got it wrong.
olorin_aiwendil · 6 points · Posted at 09:05:05 on February 14, 2016 · (Permalink)
A number a is rational iff there exists two finite integers b and c such that a=b/c
Happy?
noblesavagery · 0 points · Posted at 08:59:12 on February 14, 2016 · (Permalink)
..woah
Sorathez · 3 points · Posted at 07:06:24 on February 14, 2016 · (Permalink)
But this is circular. Your definition implies that a rational number is a number that can be expressed as a fraction with two rational numbers, and you can't use a word to define itself in this way.
However all rational numbers can be expressed as fractions with two integers, which renders this step unnecessary
casino_r0yale · 1 points · Posted at 08:06:40 on February 14, 2016 · (Permalink)
I mostly agree, but you (and very many other people) make it sound like it's always bad to use a word in its definition. Sometimes a recursive definition is the only way to define something.
crazy_clown_cart · 1 points · Posted at 08:55:33 on February 14, 2016 · (Permalink)
Well you can't leave me hanging like that. Examples?
MCBeathoven · 1 points · Posted at 09:05:46 on February 14, 2016 · (Permalink)
n factorial is n multiplied by the factorial of n-1 and 0 factorial is 1.
The first two Fibonacci numbers are 1 and the others are the sum of the two previous Fibonacci numbers.
crazy_clown_cart · 1 points · Posted at 03:27:49 on February 15, 2016 · (Permalink)
The factorial can clearly be defined iteratively. But for the Fibonacci numbers, very true.
casino_r0yale · 1 points · Posted at 16:40:20 on February 14, 2016 · (Permalink)
A list is an element and a list, where the smallest list is the empty list. A tree is a node and a list of trees (the roots of its children). An addition expression is a pair of smaller addition expressions that we will later add.
crazy_clown_cart · 1 points · Posted at 03:25:46 on February 15, 2016 · (Permalink)
Well, I'm not sure if these really support your point. A list isn't what you're describing - a list is just an ordered collection of elements. What you're describing is how we actually implement a linked list, which can still be thought of iteratively (a collection of nodes, each of which points to the next). A tree can be defined mathematically as a minimally connected graph, etc. But I see what you're saying. Recursive definitions can be very useful.
casino_r0yale · 1 points · Posted at 16:14:16 on February 15, 2016 · (Permalink)
I wasn't trying to define the mathematical notion of either tree or list, because minimally connected graph isn't exactly a good definition either ;) I was defining and naming the recursive structure in one go. Like you said, though, the goal was to provide an intuition about the concept.
crazy_clown_cart · 1 points · Posted at 23:02:36 on February 15, 2016 · (Permalink)
How so?
casino_r0yale · 1 points · Posted at 01:20:06 on February 16, 2016 · (Permalink)
A tree is a directed acyclic graph where each node has exactly one parent. This is why it is useful to think of trees as recursive structures. A minimally connected graph can form an X shape where to sources point to a convergence node, which jumps out to 2 sinks, and so you may not be able apply the exact same algorithm across each node.
crazy_clown_cart · 1 points · Posted at 05:27:50 on February 16, 2016 · (Permalink)
Hmm, I see. I would consider that more of a specific type of tree, I guess a rooted tree. I remember learning DAGs as a different structure. But I'm not sure.
casino_r0yale · 1 points · Posted at 05:31:46 on February 16, 2016 · (Permalink)
Yes, all trees are DAGs, not all DAGs are trees.
BriansRottingCorpse · 12 points · Posted at 04:18:54 on February 14, 2016 · (Permalink)
π/1
Forwardslash
[deleted] · 9 points · Posted at 04:32:54 on February 14, 2016 · (Permalink)
This is why I shouldn't post late at night.
scarymonkey11622 · 1 points · Posted at 05:13:41 on February 14, 2016 · (Permalink)
So why is sqrt(3)/3 rational but 1/sqrt(3) is irrational?
NC-Lurker · 2 points · Posted at 08:31:44 on February 14, 2016 · (Permalink)
It's not. Sqrt(3) is irrational, and multiplying or dividing an irrational by a rational (3) always gives an irrational number as a result.
TheRealPizza · 1 points · Posted at 05:15:48 on February 14, 2016 · (Permalink)
Math noob here, isn't pi 22/7?
carolinallday17 · 2 points · Posted at 05:21:17 on February 14, 2016 · (Permalink)
That's a good approximation, good to two decimal places, but it's different after that. Furthermore, 22/7 repeats while pi does not.
Ltbsd · 2 points · Posted at 09:05:40 on February 14, 2016 · (Permalink)
Fool's Pi!
-Futurama
lickmyspaghetti · 1 points · Posted at 07:30:16 on February 14, 2016 · (Permalink)
So... you're telling me 22/7 won't give me pie? My whole life was a lie
DJRIPPED · 1 points · Posted at 08:49:23 on February 14, 2016 · (Permalink)
-/u/carolinallday17
rngisforfailures · 28 points · Posted at 01:12:41 on February 14, 2016 · (Permalink)*
All this means is that at most one of the circumference or diameter is a natural number.
Edit: As splergel pointed out, integer is more correct than natural number, when defining rational numbers.
Edit 2: As klod42 pointed out, radius and circumference are both non-negative, so I feel smart for changing it back to how it was originally.
[deleted] · 29 points · Posted at 01:56:31 on February 14, 2016 · (Permalink)
What it actually means is that the definition posted above is wrong. An irrational number is one that cannot be written as a ratio between two integers. And if the radius (or circumference) of a circle is an integer, it follows from the definition of pi that the other one isn't. So there's no contradiction.
UlyssesSKrunk · 3 points · Posted at 06:36:02 on February 14, 2016 · (Permalink)
More generally it means an irrational number is one that cannot be written as the ratio of 2 numbers where neither is irrational since you can always turn a rational number into an integer.
GrammatonYHWH · -4 points · Posted at 06:26:14 on February 14, 2016 · (Permalink)
Yup, just means that the circumference of any circle is also irrational.
packman1988 · 1 points · Posted at 23:14:28 on February 14, 2016 · (Permalink)*
I think I see what you're saying, that even if the circumference was an integer, the ratio would still be 2 irrational numbers.
Unfortunately that's not what defines an irrational number. Just because 1 ratio is only irrational numbers does not mean there is no ratio which includes only integers (and integers all have the same rational value [integer]/1)
minimim · 2 points · Posted at 04:29:10 on February 14, 2016 · (Permalink)
How do you get negative measurements?
klod42 · 2 points · Posted at 10:56:04 on February 14, 2016 · (Permalink)
How is integer more correct? Circumference and diameter have to be positive. If anything, natural number is more precise.
rngisforfailures · 2 points · Posted at 19:18:39 on February 14, 2016 · (Permalink)
You are right. The way I phrased it initially, I said a non-natural number, where non-integer would have been more correct.
I was staring directly at the definition of rational number, and the way I was looking at it, considered any negative fraction as not a rational number, which was wrong.
We just don't have to worry about it negative numbers for this case.
LetMeLickYourCervix · 13 points · Posted at 01:10:37 on February 14, 2016 · (Permalink)
My brain is wrinkling
jeexbit · 17 points · Posted at 04:01:02 on February 14, 2016 · (Permalink)
that means it's working...
flexmuzik · 10 points · Posted at 02:55:26 on February 14, 2016 · (Permalink)
What he said is slightly wrong. Irrational means 'cannot be a ratio of two integers'. You cannot possibly find a circle whose diameter and circumference are perfectly integer values (not that is makes sense for natural measurements to have such precise values, but anyway..)
ImAStupidFace · 3 points · Posted at 07:20:01 on February 14, 2016 · (Permalink)
Well, I just found a circle that has an integer diameter and circumference. It's 0.
xerk · 1 points · Posted at 09:26:43 on February 14, 2016 · (Permalink)
https://www.reddit.com/r/math/comments/wi1rv/can_a_circle_have_a_radius_of_zero_can_a_point_be/c5dhw26
kohbo · 9 points · Posted at 01:16:25 on February 14, 2016 · (Permalink)
I'm no mathematician, but the pi normally used is rounded for simplicity. The constant pi is never ending and can't be expressed as a ratio of two whole numbers.
https://en.m.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
http://math.stackexchange.com/questions/1179600/why-is-pi-considered-irrational-if-it-can-be-expressed-as-ratio-of-circumference
The answer on stack exchange gives a good way to think about it. Since pi is a never ending number how would you ever express pi in terms of 314159265.../1000000000.... (you can't!)
bobby8375 · 16 points · Posted at 01:23:16 on February 14, 2016 · (Permalink)
The other answers have it actually, though I think you learned something by doing some research here. A rational number means a ratio of two numbers, but specifically the ratio of two integers (where the denominator is not zero). Pi is geometrically defined as the ratio of the circumference and diameter of the circle, but both of these cannot simultaneously be integers.
philly_fan_in_chi · 7 points · Posted at 02:27:09 on February 14, 2016 · (Permalink)
Slightly OT: not only is pi irrational, but it is also transcendental, meaning it can never be a zero for a polynomial with rational coefficients. Proving this finally resolved the "squaring the circle" problem of antiquity.
ilovelsdsowhat · 1 points · Posted at 04:02:03 on February 14, 2016 · (Permalink)
That proved you could not square the circle, right?
philly_fan_in_chi · 3 points · Posted at 04:08:56 on February 14, 2016 · (Permalink)
Correct. Squaring the circle means that you would need to construct a line of length proportional to pi, using just straight edge and compass, which is impossible if pi can never be the result of an algebraic equation.
seantme · 1 points · Posted at 07:22:26 on February 14, 2016 · (Permalink)
22/7 is awfully close
bommerangstick · 1 points · Posted at 03:39:36 on February 14, 2016 · (Permalink)
Being pedantic (although when isn't maths pedantic), 1/3 is a never ending number. It can't be expressed by xyz.../100... yet it is definitely rational. It's a stronger thing to say that it has to be a decimal that doesn't repeat to infinity. Whether it is a never ending number is not really useful either, and even 1/10 could be written as a repeating decimal, although it would be a trivial one.
Ltbsd · 1 points · Posted at 09:11:15 on February 14, 2016 · (Permalink)
1 and 3 are both integers already, so "1/3" is a ratio of integers --> rational number
bommerangstick · 1 points · Posted at 10:28:22 on February 14, 2016 · (Permalink)
I never said it wasn't.
Edit: In fact I actually said it was.
Ltbsd · 2 points · Posted at 14:43:37 on February 14, 2016 · (Permalink)
I must've missed something in your comment earlier, my bad.
MattieShoes · 9 points · Posted at 02:04:15 on February 14, 2016 · (Permalink)*
Anything you can write as a fraction is a rational number. EDIT: using integers
A fraction is essentially a ratio.
Rational numbers "end" (terminate and result in endless zeroes, like 1/8 is 0.12500000...), or they repeat (like 1/3 is 0.3333333...). Even numbers like 1/97 repeat eventually (it's a 96 digit sequence).
Numbers which cannot be expressed as a fraction are irrational numbers. Things like pi, e, sqrt(2), the golden ratio, and so on. You can make up fractions that are really CLOSE to the right value (22/7 famously for pi, etc) but you can't make a fraction that's exactly right.
jimmery · 2 points · Posted at 05:34:30 on February 14, 2016 · (Permalink)
thanks, this is the best ELI5 explanation here
NC-Lurker · 2 points · Posted at 08:36:36 on February 14, 2016 · (Permalink)
It's not, because it's incorrect (mainly the first line). You can write irrational numbers as fractions, if you use other irrational numbers. An obvious example would be sqrt(2) = 2/sqrt(2). Or Pi=Pi/1.
One actual definition of rational numbers is "any number that can be written as a fraction of two integers".
ssaallttyy · 1 points · Posted at 08:21:18 on February 14, 2016 · (Permalink)
This is a good way to explain it, but not entirely true. pi/1 is a fraction, but pi is not a rational number.
MattieShoes · 1 points · Posted at 13:02:12 on February 14, 2016 · (Permalink)
Fair enough :-) a whole number fraction
ionyx · 1 points · Posted at 09:18:21 on February 14, 2016 · (Permalink)
this cleared up so much for me. thanks
cabothief · 3 points · Posted at 04:27:22 on February 14, 2016 · (Permalink)
Relevant
stevekochscience · 2 points · Posted at 04:34:51 on February 14, 2016 · (Permalink)
Ha! This guy believes in circles! (But thank you and parent comment for cool thoughts. I hadn't realized ratio either. Only took me four decades.)
IWanted0xcdcdcdcd · 2 points · Posted at 05:35:59 on February 14, 2016 · (Permalink)
COINCIDENCE OR ALIENS!?!?!?!?!
Circumference of a circle is also irrational.
RogueRaven17 · 2 points · Posted at 06:02:09 on February 14, 2016 · (Permalink)
Hmm...sounds like someone's gonna get murdered...
karzbobeans · 2 points · Posted at 06:24:52 on February 14, 2016 · (Permalink)
Hey he's onto something! Murder him!!!
Wheres_The_Pepsi · 2 points · Posted at 07:14:50 on February 14, 2016 · (Permalink)
THE PLOT THICKENS
itisike · 2 points · Posted at 12:12:58 on February 14, 2016 · (Permalink)
Cause circles aren't real. Go ilerminaty
Blayblee · 2 points · Posted at 12:27:31 on February 14, 2016 · (Permalink)
Angrily writes '/u/FPSdouglass' in little black book
Fragninja · 1 points · Posted at 04:52:22 on February 14, 2016 · (Permalink)
Well then what the fuck is going on here?
rishinator · 1 points · Posted at 04:56:10 on February 14, 2016 · (Permalink)
pi is not irrational, it is transcendental.
LightlySaltedPeanuts · 1 points · Posted at 04:57:43 on February 14, 2016 · (Permalink)
But if the diameter of a circle is a rational number, then the circumference will be irrational because you are multiplying a rational number by an irrational one, so pi is not a ratio of two rational numbers
mkap26 · 1 points · Posted at 05:05:08 on February 14, 2016 · (Permalink)
But those are variables, not constants. Pi cannot be expressed as the ratio of any 2 constant values.
iflylikewilma · 1 points · Posted at 05:13:09 on February 14, 2016 · (Permalink)
What the that make my girlfriend?
Daggertrout · 1 points · Posted at 05:17:38 on February 14, 2016 · (Permalink)
This is how you get murdered by the Addluminati.
guimontag · 1 points · Posted at 05:17:45 on February 14, 2016 · (Permalink)
Cannot be a ratio of integers
slice_of_pi · 1 points · Posted at 05:27:42 on February 14, 2016 · (Permalink)
Hey, now.
[deleted] · 1 points · Posted at 05:28:56 on February 14, 2016 · (Permalink)
Pi is a ratio of variables, not fixed integers.
jam1garner · 1 points · Posted at 05:38:36 on February 14, 2016 · (Permalink)
As in "cannot be the ratio of two rational numbers" for example, with a radius of 2 you have a circumference of 4 Pi an irrational number. A rational number could be defined as "can be described as the ratio of two other rational numbers"
nighthawk454 · 1 points · Posted at 05:52:02 on February 14, 2016 · (Permalink)
The context being that the (rough) definition for a rational number is a ratio of two real numbers.
So irrational means "not a ratio", and the context adds "of two real numbers".
[deleted] · 1 points · Posted at 05:53:16 on February 14, 2016 · (Permalink)
Cannot be the ratio of two integers. There was a bit missing.
sexiestbuttcheek · 1 points · Posted at 05:54:42 on February 14, 2016 · (Permalink)
Then either the diameter or circumference is also irrational so it ends up working out
[deleted] · 1 points · Posted at 06:07:35 on February 14, 2016 · (Permalink)
Which means for every perfect circle, only the diameter or the radius can be rational, but not both.
[deleted] · 1 points · Posted at 06:09:19 on February 14, 2016 · (Permalink)
By definition, though.
qdhcjv · 1 points · Posted at 06:18:28 on February 14, 2016 · (Permalink)
While you're correct, the values expressed in the equation to find pi are irrational (at least, one of them).
[deleted] · 1 points · Posted at 06:26:32 on February 14, 2016 · (Permalink)
Cannot be represented as a ratio of integers
IlanRegal · 1 points · Posted at 07:16:02 on February 14, 2016 · (Permalink)
But it cannot be expressed in a fraction.
Lilcrash · 1 points · Posted at 07:20:49 on February 14, 2016 · (Permalink)
Then either the radius or the circumference is irrational.
pro-gram · 1 points · Posted at 07:31:49 on February 14, 2016 · (Permalink)
ouch, this hurts the brain.
mAnoFbEaR · 1 points · Posted at 07:34:47 on February 14, 2016 · (Permalink)
Also if r is an irrational number, then r=2r/2 which is a ratio. I think it can't be written as a ratio of rational numbers maybe
Forgot-My-Name_again · 1 points · Posted at 07:39:04 on February 14, 2016 · (Permalink)
Cannot be a ratio of integers is more correct. The ratio you are describing has either an irrational numerator or an irrational denominator.
Monkeyman3rd · 1 points · Posted at 07:39:24 on February 14, 2016 · (Permalink)
More specifically it means it cannot be expressed as the ratio of two whole numbers.
Simpae · 1 points · Posted at 07:59:41 on February 14, 2016 · (Permalink)
Is this not because the Formula is using the assumtion that the in the ratio the circle is split into multiple ever smaller triangles with a base that approaching 0?
VacuouslyUntrue · 1 points · Posted at 08:02:14 on February 14, 2016 · (Permalink)
it's not a ratio of integers though.
[deleted] · 1 points · Posted at 08:03:37 on February 14, 2016 · (Permalink)
Not a ratio of one constant integer to another, though.
blackbeltboi · 1 points · Posted at 08:22:54 on February 14, 2016 · (Permalink)
Irrational specifically refers to a number that can not be displayed as a ratio of two integers. Integers are the key here.
Frustratedphdguy · 1 points · Posted at 08:39:10 on February 14, 2016 · (Permalink)
Well you never know the exact value for the circumference of a circle as well. Or if you know it then you won't know the exact value of radius.
skeptic54 · 1 points · Posted at 08:52:11 on February 14, 2016 · (Permalink)
Not a ratio between two integers.
Cydonianknigh · 1 points · Posted at 09:37:24 on February 14, 2016 · (Permalink)
Somebody explain this!
RockSta-holic · 1 points · Posted at 10:02:00 on February 14, 2016 · (Permalink)
But we've used circular mathematics for so long that we define the circumference in terms of pi and the diameter.
Se314en · 1 points · Posted at 10:09:12 on February 14, 2016 · (Permalink)
The point is, in a true circle, either the diameter, or the circumference (or possibly both) must be irrational numbers. So whilst pi is given by circumference/diameter, this 'ratio' cannot be written as one rational number divided by another.
ActuallyRelevant · 1 points · Posted at 10:23:00 on February 14, 2016 · (Permalink)
Pi is not irrational, it is transcendental.
Bruntaz · 1 points · Posted at 10:23:53 on February 14, 2016 · (Permalink)
But either the diameter or circumference (or both) must be irrational so the ratio isn't between 2 integers
g5pw · 1 points · Posted at 10:28:09 on February 14, 2016 · (Permalink)
Ratio between integers. In this case, either the circumference or diameter must be irrational.
zeekar · 1 points · Posted at 10:54:40 on February 14, 2016 · (Permalink)
A rational number is a ratio of integers. So the fact that pi is irrational means that no matter what length unit you pick, the circumference and diameter can never both be whole numbers of that unit.
zwat · 1 points · Posted at 11:24:14 on February 14, 2016 · (Permalink)
More precisely, an irrational number can't be expressed as a ratio of integers. Therefore pi can't be rational, because both the diameter and the circumference can't be integers at the same time.
ktikp · 1 points · Posted at 11:40:53 on February 14, 2016 · (Permalink)
A rational number, more precisely, is a number which can be expressed as the a ratio of two INTEGERS (where of course, the denominator is not 0).
Absolutis · 1 points · Posted at 11:41:00 on February 14, 2016 · (Permalink)
Pack it up boys, this guy solved math.
kugkfokj · 1 points · Posted at 11:50:10 on February 14, 2016 · (Permalink)
Because the definition of rational number is a number that can be expressed as p/q where both p and q are integers. Given any circle you'll never have both the diameter and the circumference to be integers.
joshbadams · 1 points · Posted at 12:28:25 on February 14, 2016 · (Permalink)
Well, imagine you have any irrational number X. The ratio of 3X : 2X = 3X/2X = X. It's a ratio of itself, which is kinda cheating!
Chimpville · 1 points · Posted at 12:41:11 on February 14, 2016 · (Permalink)
I think he means a ratio of whole number.
SimonEddie · 1 points · Posted at 14:36:21 on February 14, 2016 · (Permalink)
Precisely, you can never have the circumference and the diameter of the same circle be whole numbers, specifically because pi is irrational.
HerraTohtori · 1 points · Posted at 16:29:21 on February 14, 2016 · (Permalink)
Pi is not only irrational, but also transcendental. That means it cannot be expressed with any (finite) combination of algebraic operations done on algebraic numbers. Or alternatively, you cannot reduce it to zero using algebraic operations.
For example, something like square root of two is irrational, but it's not transcendent because you can represent it algebraically (√2, or 2½) and it's simple to reduce it to zero ( (√2)2 - 2 = 0 ).
Transcendental numbers - or at least some of the known ones like pi, e, or the golden ratio - can be expressed with infinite series, but not much else.
Ackmar · 1 points · Posted at 22:38:31 on February 14, 2016 · (Permalink)
On my phone, so I can't see other replies. But this means that if the diameter is rational then the circumference is irrational and visa versa. Pi still can't be represented as a ratio of whole numbers.
bobobubs · 1 points · Posted at 22:05:20 on February 19, 2016 · (Permalink)
Isn't pi rational because it is equivalent to 22/7?
DiabloConQueso · 0 points · Posted at 03:24:57 on February 14, 2016 · (Permalink)
That's what makes it so special. And it also cannot be represented by any fraction.
AustiinW · 0 points · Posted at 03:35:08 on February 14, 2016 · (Permalink)
It's not a ratio of 2 whole numbers
ikneverknew · 0 points · Posted at 03:37:29 on February 14, 2016 · (Permalink)
That's because (and why) either the diameter or the circumference of a circle can be a rational quantity, but not both!
maxjohnson77 · 0 points · Posted at 03:55:05 on February 14, 2016 · (Permalink)
But the diameter and circumference cannot both be rational also. So while it is true pi can be expressed as the ratio of circumference and diameter, the ratio consists of irrational numbers, meaning itself is also irrational.
drizzyssbm · 0 points · Posted at 04:09:13 on February 14, 2016 · (Permalink)
*cannot be a ratio of two integers.
CreativelyBland · 0 points · Posted at 04:20:21 on February 14, 2016 · (Permalink)
The diameter and circumference of a circle cannot both be rational numbers. A ratio of an irrational number to a rational number is still irrational in this case.
hitmanpl47 · 0 points · Posted at 04:34:41 on February 14, 2016 · (Permalink)
Not how ratio is defined. There is no fraction for Pi.
[deleted] · 10 points · Posted at 02:35:29 on February 14, 2016 · (Permalink)
Which is also why numbers that are ratios of integers are called the rational numbers. The symbol that represents this set of numbers is Q, which stands for "quotient"; the result you get when you take the ratio of two integers.
[deleted] · 15 points · Posted at 01:54:01 on February 14, 2016 · (Permalink)
The actual definition is "cannot be written as a ratio between two integers".
Stop_Being_Ignant · 15 points · Posted at 01:53:02 on February 14, 2016 · (Permalink)
This would have really helped in highschool
OctagonalHumanist · 18 points · Posted at 01:43:08 on February 14, 2016 · (Permalink)
Oh wow that makes so much sense now
mc_hambone · 3 points · Posted at 02:39:55 on February 14, 2016 · (Permalink)
Whoa.
xXI_KiLLJoY_IXx · 3 points · Posted at 05:51:11 on February 14, 2016 · (Permalink)
*Ratio of integers
mungd · 2 points · Posted at 03:11:15 on February 14, 2016 · (Permalink)
Piqued my interest there... Can you explain your comment with an example? Thank you
Popsumpot · 6 points · Posted at 05:30:35 on February 14, 2016 · (Permalink)
The discovery of irrational numbers was actually one of the most monumental steps forward in human thinking. You could very well argue that it gave birth to philosophy as we know it.
You see, before its discovery, numbers were thought to be rational. Meaning from reason, numbers were thought to be a construct that we came up with to describe the state of the world. That is to mean, we came up with numbers in order to make sense of world.
So then what are fractions? Well again, they were numbers that describes something in the world. For example, 1/3 of an apple, despite being 0.3333 recurring, accurately describes the state of an apple that was cut into a third. The important thing here is that these fractions, no matter how complex, are simple ratios. A massive ratio like 12345/98765, might describe the amount of mass coming off a mountain in a land slide. For the ancients, all ratios were rational - they were things that we made up to describe something with rationality and reason.
So what does this mean? Well, a fraction that was not a ratio couldn't exist. Such things did not exist in the world, and such a number would literally make no sense.
And so, the discovery of the irrational number was a massive paradigm shift. Not only did it change everything we knew about mathematics, but it also changed the way we thought about the universe and the fundamental questions of existence.
The existence of an irrational number (a fraction that is not a ratio, that is to say, you could never get to it by dividing a bigger number by a smaller number) meant that numbers could not have been a human construct. An irrational number does not describe anything in the world, it simply is! If there is nothing in the world that corresponds with the number (in the sense that 1/3 corresponds with an apple that was cut into a third), why then would we think up such a number? It would make no sense, it's existence was irrational, and hence the name.
The impact of this discovery opened up our eyes to the abstracts of the universe. From this, we knew that there were numbers that were removed from human rationality, they were the very fabric of existence. For example, the number pi is the keystone to a circle/sphere/cylinder/cone etc. Without it, we could not make calculations of these shapes. We could approximate it, but without the discovery of it, we could never approach the essence of it. These numbers could not be invented by the human mind, they could only be discovered, because they have always existed as part of the universe.
This opened up a door to a plane of existence that we have never known before - the plane of the abstract. It showed us that there existed things that had no physical manifestation. it is with this key progress in human thinking that Plato would come up with his concept of Forms. It is why there came about cults that worshipped these numbers as if they were God. The entire philosophical field of ontology (the study of being and existence) was birthed, and it allowed the millennia of human thinking of the abstract that followed to get us to where we are today.
All of this was because of the discovery of the irrational number.
mungd · 1 points · Posted at 07:56:05 on February 14, 2016 · (Permalink)
Very interesting, thank you.
LudoRochambo · 2 points · Posted at 03:36:43 on February 14, 2016 · (Permalink)
careful.
sqrt(2) is irrational but sqrt(2)/1 is a ratio. to be precise, it cannot be a ratio of integers.
Gee_Eem · 2 points · Posted at 02:00:47 on February 14, 2016 · (Permalink)
"Ratio" is "reason" in Latin, so irrational numbers are unreasonable numbers.
[deleted] · 7 points · Posted at 02:34:26 on February 14, 2016 · (Permalink)
Reverse causality; "ratio-" in latin more means to account for or judge. Our usage of the world "irrational" as in "can't be argued with" stems from the analogy of argument as a "weighing of sides" to determine a balance. So if someone can't be reasoned or argued with, they are irrational.
Related is the fact that "argue" is sometimes used to denote putting a number somewhere into a ratio.
[deleted] · 1 points · Posted at 04:02:42 on February 14, 2016 · (Permalink)
Neither did I. Thanks for pointing it out.
geoman2k · 1 points · Posted at 05:03:21 on February 14, 2016 · (Permalink)
Yep! Another little known factoid, "imaginary" numbers are named that because they can't be displayed as images or photographs.
dmt267 · 1 points · Posted at 06:40:01 on February 14, 2016 · (Permalink)
Wow same. Probably because of the pronunciation of the word
EllaL · 1 points · Posted at 06:56:40 on February 14, 2016 · (Permalink)
I seriously always just thought it was irrational because it's not rational to have a number like that.
bhowl_ · 1 points · Posted at 07:06:31 on February 14, 2016 · (Permalink)
I've known this for a while and just picked up on the fact that ratio is the root word in irrational. The world makes so much more sense now.
pimpmastahanhduece · 1 points · Posted at 09:03:22 on February 14, 2016 · (Permalink)
Not true. Irrational numbers mean a non integer without a pattern and not a constant.
Left4Cookies · 1 points · Posted at 09:06:00 on February 14, 2016 · (Permalink)
Aaahh!
revesvans · 1 points · Posted at 12:05:00 on February 14, 2016 · (Permalink)
That's a very useful etymological snippet. Why do they not teach that? I always felt like mathematicians were accusing the numbers of being thoughtless and unreliable, a bunch of hippie-numbers that refuse to behave logically.
drac07 · 1 points · Posted at 12:39:02 on February 14, 2016 · (Permalink)
Isn't that neat?
jaredjeya · 1 points · Posted at 12:52:18 on February 14, 2016 · (Permalink)
In fact, "irrational" has the meaning it does in common usage because of how irrational numbers were thought to be illogical - and not the other way round.
doublec3o · 1 points · Posted at 13:07:56 on February 14, 2016 · (Permalink)
Should be "cannot be a ratio of two integers (whole numbers)"
TractorOfTheDoom · 1 points · Posted at 13:40:43 on February 14, 2016 · (Permalink)
They don't teach you that shit in school.
whalemingo · 1 points · Posted at 14:36:09 on February 14, 2016 · (Permalink)
TIL teenagers cannot be a ratio.
qw3rtman · 1 points · Posted at 19:17:14 on February 14, 2016 · (Permalink)
Wouldn't it actually be a ratio of rational numbers?
[deleted] · 1 points · Posted at 02:23:05 on February 21, 2016 · (Permalink)
irRATIOnal
woah
mycall · 0 points · Posted at 01:52:49 on February 14, 2016 · (Permalink)
So if someone is being irrational, they are being negative somehow.
psymunn · 2 points · Posted at 02:41:50 on February 14, 2016 · (Permalink)
Negative numbers can be rational
Psykodeliks · 730 points · Posted at 20:13:39 on February 13, 2016 · (Permalink)
That has to be one of the most interesting articles I've ever read. Thanks for the share.
ltcg87 · 390 points · Posted at 22:56:22 on February 13, 2016 · (Permalink)
If you think thats interesting you should check out the book Zero: The Biography of a Dangerous Idea by Charles Seife.
Thomas__Covenant · 18 points · Posted at 01:30:59 on February 14, 2016 · (Permalink)
This introduced me to the world of math and science (I was 13 at the time, only reading science fiction before then) and it is one of my favorite books. I've purchased it multiple time for myself and others. It was the first book in a series of hundreds of books about math and physics that I've purchased since then.
I cannot recommend this book enough if you have even the slightest interest in math and how the modern world as we know it has been shaped because of it.
thelazerbeast · 6 points · Posted at 06:15:45 on February 14, 2016 · (Permalink)
Hey, uh, what are some of those other books?
Five best maybe? (Accessible ones)
Thomas__Covenant · 7 points · Posted at 01:59:23 on February 15, 2016 · (Permalink)
This is a copy/paste of the list I gave to another. Enjoy!
Math:
The Nothing That Is, by Robert Kaplan - Another book about zero and its history throughout the ages.
Infinity, by Brian Clegg - What's the opposite of zero? This is written much in the same vein as Zero, being a math history book of sorts that's trying to reach a broad audience with a dense subject matter.
The Golden Ratio, by Mario Livio - We've done nothing and everything, but what's in between? This book, again, is a layman's journey through the history of a specific number: Phi. Where we discovered it, how we apply it, and why it's constantly popping up in nature, manufactured or otherwise.
Prime Obsession, by John Derbyshire - This book title explains exactly what happened to me shortly after being introduced to Zero. I have an embarrassing amount of books written on the subject, but this is one of the best to approach the subject in a broad manner. For a more math heavy version, look no further than...
The Music of the Primes, by Marcus du Sautoy - Have some pencil and paper ready, just in case ;)
The Man Who Loved Only Numbers, by Paul Hoffman - Tired of numbers? Let's learn of a man who never would have considered that a possibility. This book revolves around the life and accomplishments of the mathematician Paul Erdos. He was an interesting character, to say the least.
Physics:
The Elegant Universe, by Brian Greene - Jumping to the physics side of things, this serves as an excellent introduction to both relative and quantum theory. While the book is of considerable length, it is, to me, on par with anything Stephen Hawking has written (side recommendation: read anything Hawking has written).
God's Equation, by Amir Aczel - This book is about Einstein and his "greatest blunder", the cosmological constant. It is part math, part astronomy, part history. I also started this section with this book because almost anything written by Amir Aczel is a joy to read. Such as...
Entanglement, by Amir Aczel - If you're unfamiliar with the term, it's a phenomenon that occurs when two particles are "entangled" and thus behave together at the same time. The real fun part about this is that these two particles will enter the same quantum state, regardless of distance (I'm also painting with an extremely, laughably large brush here. Any person reading this who is halfway knowledgeable in the realm of quantum mechanics must surely be furiously typing up a response at tachyon speeds).
Introducing: Time - This is actually a part of a series called "Introducing", which covers a large swath of topics, from physics to philosophy. This one in particular tackles "time" as we know it and what it means to, well, everything. Does time still tick by if a universe is in a completely static state? This, and other paradoxical questions are covered in this book. It's also illustrated, for dummies like me.
A Short History of Nearly Everything, by Bill Bryson - This is a fun romp through the ages of man, from when he flicked his first flint for fire, to when he placed the first foot of extraterrestrial soil. It covers math, science, and all things in between, but never bogging down in any one particular category. He is another author I'd recommend you could pick up anything with his name on it and enjoy.
GiftofLove · 1 points · Posted at 06:45:43 on February 14, 2016 · (Permalink)
Almost every book is available online. Only thing you need is title or author. If you need help let me know
GiftofLove · 3 points · Posted at 06:41:23 on February 14, 2016 · (Permalink)
I'm curious if you have a list of those books that you read following the initiative of reading zero. Do you want to share?
Thomas__Covenant · 2 points · Posted at 01:57:00 on February 15, 2016 · (Permalink)
Sorry for the late response, but here's some of my favorites (tried to do a good split between math and physics):
Math:
The Nothing That Is, by Robert Kaplan - Another book about zero and its history throughout the ages.
Infinity, by Brian Clegg - What's the opposite of zero? This is written much in the same vein as Zero, being a math history book of sorts that's trying to reach a broad audience with a dense subject matter.
The Golden Ratio, by Mario Livio - We've done nothing and everything, but what's in between? This book, again, is a layman's journey through the history of a specific number: Phi. Where we discovered it, how we apply it, and why it's constantly popping up in nature, manufactured or otherwise.
Prime Obsession, by John Derbyshire - This book title explains exactly what happened to me shortly after being introduced to Zero. I have an embarrassing amount of books written on the subject, but this is one of the best to approach the subject in a broad manner. For a more math heavy version, look no further than...
The Music of the Primes, by Marcus du Sautoy - Have some pencil and paper ready, just in case ;)
The Man Who Loved Only Numbers, by Paul Hoffman - Tired of numbers? Let's learn of a man who never would have considered that a possibility. This book revolves around the life and accomplishments of the mathematician Paul Erdos. He was an interesting character, to say the least.
Physics:
The Elegant Universe, by Brian Greene - Jumping to the physics side of things, this serves as an excellent introduction to both relative and quantum theory. While the book is of considerable length, it is, to me, on par with anything Stephen Hawking has written (side recommendation: read anything Hawking has written).
God's Equation, by Amir Aczel - This book is about Einstein and his "greatest blunder", the cosmological constant. It is part math, part astronomy, part history. I also started this section with this book because almost anything written by Amir Aczel is a joy to read. Such as...
Entanglement, by Amir Aczel - If you're unfamiliar with the term, it's a phenomenon that occurs when two particles are "entangled" and thus behave together at the same time. The real fun part about this is that these two particles will enter the same quantum state, regardless of distance (I'm also painting with an extremely, laughably large brush here. Any person reading this who is halfway knowledgeable in the realm of quantum mechanics must surely be furiously typing up a response at tachyon speeds).
Introducing: Time - This is actually a part of a series called "Introducing", which covers a large swath of topics, from physics to philosophy. This one in particular tackles "time" as we know it and what it means to, well, everything. Does time still tick by if a universe is in a completely static state? This, and other paradoxical questions are covered in this book. It's also illustrated, for dummies like me.
A Short History of Nearly Everything, by Bill Bryson - This is a fun romp through the ages of man, from when he flicked his first flint for fire, to when he placed the first foot of extraterrestrial soil. It covers math, science, and all things in between, but never bogging down in any one particular category. He is another author I'd recommend you could pick up anything with his name on it and enjoy.
Ok, well hopefully this is something to get you started. I don't expect you to enjoy all of them (or any of them, really), but if you found Zero even passably interesting, then one of the above is bound to tickle your curiosity in one way or another. Have fun!
GiftofLove · 1 points · Posted at 02:58:41 on February 15, 2016 · (Permalink)*
I have read The Man who Loves only Numbers, LOVED IT, read it many times, Paul Erdos is my hero.
I have read Infinity and Nothing that is.
Some of these books are hard to find digitally for free, but libgen has been serving me well :)
Thank you for you sharing, I look forward to read most of these !
Thomas__Covenant · 1 points · Posted at 04:31:50 on February 15, 2016 · (Permalink)
Yes! I actually have 2 books on Erdos, but this one was more enjoyable.
Yes, I'm not sure how easy it will be to find these, but I definitely think some are worth the entry price of $10-$15. I have an entire wall of books ready to turn into a fire hazard at a moment's notice, haha.
GiftofLove · 1 points · Posted at 05:21:31 on February 15, 2016 · (Permalink)
I found all but one online and now they are resting peacefully with 30,000 others on my iPad. I had thousands of books but slowly trading them in for cash as I build and hoard a bigger digital library :)
Thomas__Covenant · 1 points · Posted at 05:39:19 on February 15, 2016 · (Permalink)
Yeah, I've been slowly converting my library to digital as a just in case. Anything new I've bought in the last 5 years has been digital, but some old things are just hard to find in digital or just flat out do not exist.
GiftofLove · 2 points · Posted at 05:41:20 on February 15, 2016 · (Permalink)
Yeah I get your pain
971365 · 1 points · Posted at 13:43:21 on February 14, 2016 · (Permalink)
+1
Would love to get some recommendations
Philoso4 · 11 points · Posted at 03:28:38 on February 14, 2016 · (Permalink)
I remember taking a philosophy class where the teacher was talking about the mathematical concept of limits, or something like that. He was trying to blow our minds, so I asked the question, "was zero an accepted concept at the time?" Because I happened to have just read that book. He responded that the question was getting in over my head. It was the most annoying cop out I've ever experienced, you can't blow a mind that has already been blown.
flexmuzik · 82 points · Posted at 02:50:13 on February 14, 2016 · (Permalink)
Man it took me like 6 tries before I realized that's not Charles Selfie
MagicOfFriendship · 5 points · Posted at 07:13:45 on February 14, 2016 · (Permalink)
That's not Charles Selfie?
*looks at comment again*
Huh.
atomicretro · 30 points · Posted at 00:40:45 on February 14, 2016 · (Permalink)
that book is incredible. i reread it once every few years just to be able to keep feeling smarter.
pants_full_of_pants · 3 points · Posted at 03:26:25 on February 14, 2016 · (Permalink)*
So you read a lot to get more knawledge, eh? Do you happen to have a new Lamborghini here?
secretly_an_alpaca · 0 points · Posted at 06:06:37 on February 14, 2016 · (Permalink)
They're, uh, real fun to drive around the Hollywood hills.
dabosweeney · 2 points · Posted at 02:54:30 on February 14, 2016 · (Permalink)
That sounds like something that should be confidential, official use only, need to know
LFuzz · 2 points · Posted at 07:03:18 on February 14, 2016 · (Permalink)
Is that the one where the author proves that Winston Churchill is a carrot?
UserNamesCantBeTooLo · 1 points · Posted at 12:12:39 on February 16, 2016 · (Permalink)
Yep.
marsgreekgod · 1 points · Posted at 10:27:45 on February 14, 2016 · (Permalink)
I've been rereading that book its great
calsosta · -3 points · Posted at 02:01:16 on February 14, 2016 · (Permalink)*
Commenting so I can find this later
Edit: Editing my comment so I can find it later.
Okmanl · 14 points · Posted at 02:21:59 on February 14, 2016 · (Permalink)
You won't read it.
RawrCat · 7 points · Posted at 02:38:02 on February 14, 2016 · (Permalink)
You are now a moderator of r/quityourbullshit.
playaspec · 4 points · Posted at 05:08:02 on February 14, 2016 · (Permalink)
Use the 'save' link.
[deleted] · -1 points · Posted at 02:52:27 on February 14, 2016 · (Permalink)
[removed]
mrpunaway · 2 points · Posted at 04:34:03 on February 14, 2016 · (Permalink)
Eh, you don't deserve your downvotes. Most of the time the "Commenting to save this" guy gets the downvotes. Reddit can be fickle sometimes.
flexiverse · -5 points · Posted at 06:21:48 on February 14, 2016 · (Permalink)
By Pareto principle alone Reddit is more than 80% complete and utter fucktards. By in large it's a freebooting site for entertainment and porn. I don't think I've ever met anyone here with more than two brain cells.
an_obscene_username · 4 points · Posted at 06:27:44 on February 14, 2016 · (Permalink)
commenting to save this comment
flexiverse · 1 points · Posted at 06:59:49 on February 14, 2016 · (Permalink)
QED
Blue_Ken · 2 points · Posted at 09:36:09 on February 14, 2016 · (Permalink)
Entertainment and porn aren't the same thing? Reddit isn't even that good for porn. I mostly come here to kill one of those 2 brain cells.
flexiverse · 1 points · Posted at 11:14:34 on February 14, 2016 · (Permalink)
Yep for sure, dunno I've found some rather niche porn I like here. But like you also say, this is just for killing time.
serfis · 2 points · Posted at 13:11:10 on February 14, 2016 · (Permalink)
motodriveby · -3 points · Posted at 00:52:08 on February 14, 2016 · (Permalink)
You need to stay in more.
burnSMACKER · 1718 points · Posted at 19:51:35 on February 13, 2016 · (Permalink)
How irrational
mediumhydroncollider · 136 points · Posted at 21:44:37 on February 13, 2016 · (Permalink)
Very irrational
airstrike · 7 points · Posted at 01:43:19 on February 14, 2016 · (Permalink)
Now that is a fantastic username.
justifications · 6 points · Posted at 08:04:51 on February 14, 2016 · (Permalink)
How can you justify that?
The_Tick_Monster · 1 points · Posted at 08:44:18 on February 14, 2016 · (Permalink)
No just very improbable
regalrecaller · 1 points · Posted at 01:35:53 on February 14, 2016 · (Permalink)
Opposite of rational
[deleted] · 6 points · Posted at 00:32:34 on February 14, 2016 · (Permalink)
I imagine the people who killed him were, naturally, a set of real assholes.
I tried.
ShooterMcSwaggin · 2 points · Posted at 06:26:53 on February 14, 2016 · (Permalink)
Isn't it irrational
Froot-Loops · 1 points · Posted at 02:29:19 on February 14, 2016 · (Permalink)
How bizarre, how bizarre
timbomcchoi · 1 points · Posted at 23:04:24 on February 13, 2016 · (Permalink)
someone was... irate
Dexaan · 0 points · Posted at 22:11:44 on February 13, 2016 · (Permalink)
That is... illogical.
Witetrashman · 0 points · Posted at 22:29:06 on February 13, 2016 · (Permalink)
How ironic.
Hiphopopotamus5782 · 16 points · Posted at 23:49:51 on February 13, 2016 · (Permalink)
That was a neat article, but what did that have to do with the man's murder? It didn't tie the irrationality of the square root of 2 back to the guy who was thrown overboard
ngwoo · 36 points · Posted at 00:20:10 on February 14, 2016 · (Permalink)
People didn't like hearing that something as simple as the diagonal of a square couldn't be represented by a whole number because it challenged their view that the universe was orderly and perfectly crafted.
Hiphopopotamus5782 · 7 points · Posted at 00:26:30 on February 14, 2016 · (Permalink)
I understand that, but what did the first guy have to do with it?
rngisforfailures · 23 points · Posted at 00:41:42 on February 14, 2016 · (Permalink)
The first guy proved mathematically, that irrational numbers exist, and the people that wanted a world of only rational numbers were so upset, they responded by throwing him into the sea and letting him drown.
Dubaku · 19 points · Posted at 02:02:10 on February 14, 2016 · (Permalink)
Bit of an over reaction
CSI_Tech_Dept · 11 points · Posted at 02:20:28 on February 14, 2016 · (Permalink)
Not to mention quite irrational.
n0vag0d · 6 points · Posted at 08:57:09 on February 14, 2016 · (Permalink)
Yeah, they went a bit overboard with that decision.
Hiphopopotamus5782 · 2 points · Posted at 16:28:38 on February 14, 2016 · (Permalink)
Ah okay. There was one throwaway sentence at the very end that said
but that still isn't that great when tying back to the first paragraph
schammy · 1 points · Posted at 17:34:13 on February 14, 2016 · (Permalink)
I agree with you, the article did an awful job tying the intro back in. They might as well have not even had the intro.
KserDnB · 2 points · Posted at 04:17:30 on February 14, 2016 · (Permalink)
They went a bit overboard...
rngisforfailures · 1 points · Posted at 08:56:40 on February 14, 2016 · (Permalink)
I sea what you did there
Willdabeast9000 · 45 points · Posted at 23:44:29 on February 13, 2016 · (Permalink)
This is almost certainly a made up story. The square root of two wasn't even the first known irrational. The Pythagoreans knew that the ratio of lengths between near corners and far corners of a pentagram was irrational before they knew sqrt(2) was irrational. The myth persists because the method is an easy way to introduce young math students to proofs, and because of the "told ya so" nature of the story.
Provokateur · 9 points · Posted at 00:27:47 on February 14, 2016 · (Permalink)
Do you have a source? Not disagreeing, I just find the pythagoreans fascinating (most people forget that they were seriously a cult and secret society, with practices like banning the eating of beans or celebrating music for its mathematical nature) so I'd like to read more about it.
EpikurusFW · 5 points · Posted at 09:00:56 on February 14, 2016 · (Permalink)
There's not a direct source for the tale being untrue but there is no reason to trust it given the evidence cited above. Ancient philosophical biographers didn't treat historical fact with the same reverence that we do today and happily invented all sorts of events in the lives of their subjects in order to emphasise their philosophical theories in a literary manner. Once a good illustrative story gets made up it then gets passed around the other biographers without real concern for whether it is literally true. Another good example is the claim in the biographies that Heraclitus died after burying himself in horseshit because he thought the warmth would drive out his cold. This is an attempt to illustrate his theory that fire is the principle of everything rather than the sort of historical report we can trust. More obviously ahistorical are the reports that Plato was visited by Apollo in the form of a 'bee epiphany' when bees landed on Plato's lips as a baby, indicating his future ability to write 'honeyed words'.
SandorClegane_AMA · 1 points · Posted at 13:13:40 on February 14, 2016 · (Permalink)
Yeah, compare with the Wiki article which is basically saying 'so the story goes but accounts are vague and inconsistent'.
xxyphaxx · 123 points · Posted at 23:06:50 on February 13, 2016 · (Permalink)
With his proof he increased his chances of being murdered by 12/11ths.
CreativelyBland · 17 points · Posted at 04:22:54 on February 14, 2016 · (Permalink)
That fraction is improper, not irrrational.
Timothy_Claypole · 5 points · Posted at 23:29:10 on February 13, 2016 · (Permalink)
By another rational?
[deleted] · 3 points · Posted at 02:07:42 on February 14, 2016 · (Permalink)
After spending the longest time considering whether or not to publish his proof, he realized it was only a rational risk to take, and decided to do so.
[deleted] · -1 points · Posted at 00:54:09 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 11 points · Posted at 01:02:28 on February 14, 2016 · (Permalink)
No it's not.
[deleted] · -4 points · Posted at 01:37:13 on February 14, 2016 · (Permalink)
[deleted]
HowToCantaloupe · 7 points · Posted at 01:38:39 on February 14, 2016 · (Permalink)
It's improper, but far from irrational.
2Rad2BDad · -3 points · Posted at 03:36:26 on February 14, 2016 · (Permalink)
I think his odds were more like 5/7
NoMoreDevilsBlend · 4 points · Posted at 01:33:57 on February 14, 2016 · (Permalink)
Seems like that link got the infamous Reddit hug of death.
OM_NOM_TOILET_PAPER · 2 points · Posted at 01:52:12 on February 14, 2016 · (Permalink)
Try it without HTTPS:
http://nrich.maths.org/2671
NoMoreDevilsBlend · 1 points · Posted at 01:57:41 on February 14, 2016 · (Permalink)*
Cheers! Works. Oh and to add something from the article, multiplying odd numbers with odd numbers will always result in, you guessed it, odd numbers.
masterwit · 1 points · Posted at 03:39:33 on February 14, 2016 · (Permalink)
archive.org wayback machine to the rescue
IJustWantComment · 3 points · Posted at 01:53:26 on February 14, 2016 · (Permalink)
Can I get a SD;CR (site down;couldn't read)?
XcockblockulaX · 2 points · Posted at 02:33:32 on February 14, 2016 · (Permalink)
none of the links are working this web archive version works though: https://web.archive.org/web/20160131215313/http://nrich.maths.org/2671
chairitable · 1 points · Posted at 05:05:43 on February 14, 2016 · (Permalink)
Thanks, my friend!
CatAstrophy11 · 1 points · Posted at 08:20:17 on February 14, 2016 · (Permalink)
Not very easy to read since it has a ton of dead images in it
Propaganda_Box · 5 points · Posted at 00:41:24 on February 14, 2016 · (Permalink)
Can I get a TL;DR?
scumware · 3 points · Posted at 02:27:03 on February 14, 2016 · (Permalink)
The guy that proved the existence of irrational numbers was murdered for his finding.
Propaganda_Box · 1 points · Posted at 02:30:50 on February 14, 2016 · (Permalink)
Thx
weedful_things · 3 points · Posted at 23:06:01 on February 13, 2016 · (Permalink)
I did it. After I learned about i, I realized all math was a lie. I studied a lie for years only to find out it was a lie. I was provoked.
rngisforfailures · 8 points · Posted at 23:15:14 on February 13, 2016 · (Permalink)
Spoiler alert: When you get to quaternions, you meet j and k too.
Fluffiebunnie · 2 points · Posted at 02:27:53 on February 14, 2016 · (Permalink)
Sounds like Ned Flander's name for quarters
[deleted] · 1 points · Posted at 03:07:01 on February 14, 2016 · (Permalink)
Sincerely hope you're joking. "Imaginary" numbers are anything but (It's an awful name) and have some profound and stirringly beautiful properties. I chose one as my response to this thread.
weedful_things · 0 points · Posted at 03:51:19 on February 14, 2016 · (Permalink)*
First they teach me what a square root is, then they teach me about I ! Bullshit!
pm_me_ur_lil_titties · 1 points · Posted at 00:34:51 on February 14, 2016 · (Permalink)
Those kooky pythagoreans!
fun fact: As well as irrational numbers, Pythagoras also had a morbid fear of beans.
https://en.wikipedia.org/wiki/Pythagoreanism#Vegetarianism
blackfox1 · 1 points · Posted at 01:00:34 on February 14, 2016 · (Permalink)
That was awesome, it almost read like a mock horror film, "But sir, there are no numbers between one and two" ominous music.
friend1949 · 1 points · Posted at 01:12:29 on February 14, 2016 · (Permalink)
We use Arabic numbers. Romans used Roman numerals. What did the Greeks use? Was it easy to divide and multiply compared to Arabic?
ThreeHourRiverMan · 1 points · Posted at 01:16:49 on February 14, 2016 · (Permalink)
I like how that article just throws out a proof by contradiction that took me like 4 hours to figure out when I was taking analysis. Good to know it had already been done 2600 years ago, hah.
drew442 · 1 points · Posted at 01:52:06 on February 14, 2016 · (Permalink)
Reddit hug on the Google cache version too? Any other mirrors?
Dubaku · 1 points · Posted at 02:08:49 on February 14, 2016 · (Permalink)
http://nrich.maths.org/2671
ablaaa · 1 points · Posted at 01:56:13 on February 14, 2016 · (Permalink)
[Math Processing Error]
ubsr1024 · 1 points · Posted at 02:18:10 on February 14, 2016 · (Permalink)
Numberphile touched on this story in one of their videos, skip to 4:35 if you don't care about the entire background.
-GheeButtersnaps- · 1 points · Posted at 02:21:50 on February 14, 2016 · (Permalink)
Cool
0fficerNasty · 1 points · Posted at 02:23:11 on February 14, 2016 · (Permalink)
I hope we find the root cause of his negativity.
FelixMontague · 1 points · Posted at 02:35:39 on February 14, 2016 · (Permalink)
What do surd and the $ mean?
rubydrops · 1 points · Posted at 02:55:48 on February 14, 2016 · (Permalink)
The plot thickens. I was told this story in high school. Before I realized it was about a bunch of Greek people I was imagining a noir film or something.
UpvotesFeedMyFamily · 1 points · Posted at 03:00:49 on February 14, 2016 · (Permalink)
Well that's not a very fun fact
Atlas001 · 1 points · Posted at 03:04:23 on February 14, 2016 · (Permalink)
dammit the first paragraphs got me hooked but the webpage is frezzing:(
rydan · 1 points · Posted at 03:16:28 on February 14, 2016 · (Permalink)
Did you tear down the site originally because it couldn't handle the extra math required to encrypt the connection?
MiyamotoKnows · 1 points · Posted at 03:38:29 on February 14, 2016 · (Permalink)
Just read what he discovered. That significantly bothers my logical mind.
A_Lurker_Once_Was_I · 1 points · Posted at 03:51:24 on February 14, 2016 · (Permalink)
I remember learning about that in my discrete mathematics class when we proved that the root of three was irrational. Felt bad for the guy.
Geladbaboon12 · 1 points · Posted at 05:04:04 on February 14, 2016 · (Permalink)
i was gone say pythagorean theorem, but after reading that fuck a trig substitution all partial fraction from now on...
Saudi-Prince · 1 points · Posted at 05:26:12 on February 14, 2016 · (Permalink)
He was killed because he revealed a secret of a secret society. in 500BC this was cutting edge information stuff. Kind of like revealing the plans on how to build a nuclear bomb. It's a great story, but it also helps to put it into context so people can understand why he was killed.
TwoShadez · 1 points · Posted at 05:35:29 on February 14, 2016 · (Permalink)
Good
WeShouldGoThere · 1 points · Posted at 06:05:49 on February 14, 2016 · (Permalink)
You cannot simply square both sides of an equation and leave in equality. I stopped reading at that point as it's a basic algebra error.
HlfCntaur · 1 points · Posted at 06:15:38 on February 14, 2016 · (Permalink)
That's some i•i shit
Wilreadit · 1 points · Posted at 06:53:47 on February 14, 2016 · (Permalink)
Well he deserved it.
CyberBinarin · 1 points · Posted at 08:04:35 on February 14, 2016 · (Permalink)
The article doesn't seem to be working on my android's Google Chrome. It turned from math to philosophy. "How is it possible to prove that there is no ratio making [Math Processing Error]?
The logic is a little fiddly, but not too heavy.
Let's imagine that it is possible to come up with such a ratio to produce [Math Processing Error].
Let's call it [Math Processing Error]."
[deleted] · 1 points · Posted at 08:06:01 on February 14, 2016 · (Permalink)
Was he divided in two?
Otto_Lili_Emmenthal · 1 points · Posted at 08:14:52 on February 14, 2016 · (Permalink)
That's not a cool fact. That's a depressing fact.
Imma gonna crawl into my bed now... :(
maulinrouge · 1 points · Posted at 09:05:22 on February 14, 2016 · (Permalink)
Making a mathematician.
mohittzomar · 1 points · Posted at 09:10:21 on February 14, 2016 · (Permalink)
Wow
Medhivcellar · 1 points · Posted at 09:44:08 on February 14, 2016 · (Permalink)
Here's another tidbit I really like about irrational numbers.
There aren't as many of them as you might think. You can take all the irrational number (including all the rational numbers) and sort them in a specific order and then assign the number one to the first one, 2 to the second and so on. So, in a sense there are just as many irrational numbers as there are whole numbers.
BUT, it isn't so with the set of Real numbers. There are incredibly many more real numbers than there are irrational numbers. Check out cantor's diagonal argument
If you ask me they are misnomers, the irrationals are real and the reals are true imposters.
If my understanding is correct there aren't any questions whose answer is a single specific Real number that is neither rational or irrational. So all those incredibly numerous Real numbers that makes the set of Reals so much bigger than the irrationals? We can't even identify a single one of them.
So you tell me, are the Reals really real?
[deleted] · 1 points · Posted at 10:04:34 on February 14, 2016 · (Permalink)
Learned this on The History of Maths recently. Its worth watching. Good read. Thanks!
dengseng · 1 points · Posted at 10:13:25 on February 14, 2016 · (Permalink)
love this story, makes me appreciate something from school every now and then
WhyYouLetRomneyWin · 1 points · Posted at 10:21:51 on February 14, 2016 · (Permalink)
I don't think this is true. I cannot find any reliable historical evidence that this occurred.
TheGambinosChild · 1 points · Posted at 10:50:58 on February 14, 2016 · (Permalink)
That was really interesting - thanks for posting!
thatsforthatsub · 1 points · Posted at 10:54:04 on February 14, 2016 · (Permalink)
that is very much so not confirmed and might be one of the many myths surrounding pythagoras
HybridVibes · 1 points · Posted at 11:05:49 on February 14, 2016 · (Permalink)
So I went to the story page.. saw a bunch of numbers, letters, squiggle lines all bunched together had an anxiety attack and noped the fuck out of that page...so Ive figured out my fear.. its definitely math.. I mean look at this shit... nope..
\frac {top2}{bottom2} = 2
Next multiply both sides by bottom2 , ending up with
top2 = 2 \times bottom2
Edit: Yes I did go back to the page for this.. it was hard.
[deleted] · 1 points · Posted at 11:40:08 on February 14, 2016 · (Permalink)
Well I didn't understand any of that and regretfully have no motivation to. Not trying to disrespect the post, more being critical of myself.
SiliconOrganism · 1 points · Posted at 12:14:38 on February 14, 2016 · (Permalink)
And the murderer himself, Pythagoras, died because he refused to walk through a field of broad beans
Crank2047 · 1 points · Posted at 13:04:59 on February 14, 2016 · (Permalink)
Are you going to be killed now?
ericarlen · 1 points · Posted at 13:42:17 on February 14, 2016 · (Permalink)
Interesting.
unionjunk · 1 points · Posted at 13:53:35 on February 14, 2016 · (Permalink)
Murdered for his finding? Like blasphemy?
DammitDan · 1 points · Posted at 14:19:14 on February 14, 2016 · (Permalink)
They must have been pretty embarrassed when they found out about pi.
tigerlady1977 · 1 points · Posted at 14:35:11 on February 14, 2016 · (Permalink)
Yes, those Pythagoreans really liked whole numbers...perfect squares, etc.
Constablegarden · 1 points · Posted at 17:17:38 on February 14, 2016 · (Permalink)
I took this to mean that his findings set off an ocd person that had to kill him
[deleted] · 1 points · Posted at 17:38:54 on February 14, 2016 · (Permalink)
This proof doesn't make sense to me. What is top/bottom equal to? 0? 1? either way, it doesn't equal 2
OptomisticOcelot · 1 points · Posted at 05:35:05 on February 15, 2016 · (Permalink)
You should read The Humans by Matt Haig. Great book. Some math.
[deleted] · 0 points · Posted at 00:19:29 on February 14, 2016 · (Permalink)
[deleted]
rngisforfailures · 1 points · Posted at 02:21:24 on February 14, 2016 · (Permalink)
He was ahead of his time like a radical prime.
SOwED · -21 points · Posted at 20:46:19 on February 13, 2016 · (Permalink)*
Not sure how that's a cool fact
Edit: I didn't mean it wasn't interesting, just that being murdered for advancing science isn't cool.
AroundtheTownz · 12 points · Posted at 22:12:26 on February 13, 2016 · (Permalink)
not sure how its not a cool fact
SOwED · 1 points · Posted at 01:36:45 on February 14, 2016 · (Permalink)
Because getting killed for an important advance in mathematics is not cool.
rngisforfailures · 1 points · Posted at 22:46:55 on February 13, 2016 · (Permalink)
The ocean they threw him in was pretty cool...
Euerfeldi · 4918 points · Posted at 19:52:00 on February 13, 2016 · (Permalink)
The Fibonacci sequence is encoded in the number 1/89:
1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034...
175gr · 1364 points · Posted at 22:03:44 on February 13, 2016 · (Permalink)
This comes from the fact that 1/(1-x-x2) is a generating function for the Fibonacci sequence, right?
FUZxxl · 581 points · Posted at 23:01:32 on February 13, 2016 · (Permalink)
Yeah. Set x = 0.1 to get the aforementioned result.
Enlightened_Chimp · 27 points · Posted at 05:37:50 on February 14, 2016 · (Permalink)
Ya, do that
motodextros · 5 points · Posted at 08:04:47 on February 14, 2016 · (Permalink)
username checks out
FlattestGuitar · 1 points · Posted at 13:08:31 on February 14, 2016 · (Permalink)
But then it's not a function...
FUZxxl · 4 points · Posted at 13:15:25 on February 14, 2016 · (Permalink)
The generating function of a sequence is a function such that the coefficients of its power series (Taylor expansion) are the terms of the sequence. For example,
is the power series for the Fibonacci numbers.
If we set x = 0.1, we get
which is the identity /u/Euerfeldi gave in his post.
geweldigzinloos · 519 points · Posted at 00:30:43 on February 14, 2016 · (Permalink)
wut
XkF21WNJ · 502 points · Posted at 00:40:29 on February 14, 2016 · (Permalink)
1/(1-x-x2) = 1 x0 + 1 x1 + 2 x2 + 3 x3 + 5 x4 + 8 x5 + 13 x6 + ...
100/89 = 1/(1-0.1-0.12) = 1 + 0.1 + 0.02 + 0.003 + 0.0005 + ...
[deleted] · 1554 points · Posted at 02:09:29 on February 14, 2016 · (Permalink)
Oh, yeah alright
rick500 · 20 points · Posted at 05:11:59 on February 14, 2016 · (Permalink)
Take it easy baby, make it last all night
Darbaergar · 5 points · Posted at 08:07:39 on February 14, 2016 · (Permalink)
last all night
smithoski · 15 points · Posted at 05:29:00 on February 14, 2016 · (Permalink)
I can see that it's clearly obvious now. Of course.
darkneo86 · 27 points · Posted at 02:35:59 on February 14, 2016 · (Permalink)
Don't feel bad. I'm a programmer and while I might have once known what they are talking about, I don't anymore.
So, yeah, I'll go ahead and say "wut?", again.
dengseng · 5 points · Posted at 10:17:05 on February 14, 2016 · (Permalink)
all the naysayers misunderstood you so badly
what he meant was that it's okay to ask "wut?" even though it seems to be explained in detail already, but given his qualifications of someone who is supposed to be on a deeper understanding of mathematics, he already forgotten about the basics which is fraction series, and so it's okay to ask "wut?" and not feel stupid about it
you people have to not be so mean to others...
[deleted] · -32 points · Posted at 03:37:15 on February 14, 2016 · (Permalink)*
[deleted]
darkneo86 · 28 points · Posted at 04:10:18 on February 14, 2016 · (Permalink)
...wut?
1ans2no1 · 7 points · Posted at 04:32:18 on February 14, 2016 · (Permalink)
Looks like a troll account
casey12141 · -12 points · Posted at 05:42:00 on February 14, 2016 · (Permalink)
This has nothing to do with programming, that's just a series lol
Antonin__Dvorak · 16 points · Posted at 06:45:48 on February 14, 2016 · (Permalink)
Well, in order to be a programmer you (in most cases) need to have a strong foundation in mathematics. OP probably means that he once understood what the above comments were talking about (i.e. when his maths education was still fresh in his mind), but he doesn't anymore.
casey12141 · -10 points · Posted at 06:51:45 on February 14, 2016 · (Permalink)*
It's not the same type of mathematics.
Edit: Some people appear to be confused about this. While Computer Science is by definition a theoretical and mathematical field (primarily relating to discrete math, combinatorics, graph theory, etc), This problem is relating to real analysis, something most Computer Science students would not take in college.
Argue all you want, 99.99999999% of day-job programmers will NEVER need to look at or think about anything in this problem domain. Hence the reason the guy forgot the math in the first place. Learned the absolute basics of sequences/series in college, then forgot because it's not relevant to programming.
[deleted] · 2 points · Posted at 07:13:57 on February 14, 2016 · (Permalink)
[deleted]
Bladelink · 1 points · Posted at 07:37:11 on February 14, 2016 · (Permalink)
Not to mention we spend a shit load of time dealing with this converting between bases. Typically base 10, 2, and hex.
casey12141 · 1 points · Posted at 08:11:25 on February 14, 2016 · (Permalink)
Converting between bases is 1. simple arithmetic, not advanced calculus/real analysis, and 2. not a part of most any programmer's daily work.
casey12141 · -2 points · Posted at 07:18:01 on February 14, 2016 · (Permalink)
Almost all programming is an application of rudimentary logic and discrete math, if that. This is more along the lines of calc 3 or real analysis, which shares no resemblance to anything almost any programmer does.
yarothaw · 2 points · Posted at 07:31:47 on February 14, 2016 · (Permalink)
Hi, computer science major here! Calculus and a couple of higher level maths were core requirements for my degree. I went with differential equations and linear algebra. I took some combinatorics for fun, and while it covered a lot of stuff that would fall under discrete math, it also dealt with generating functions.
So, you think we learn some special kind of math?
casey12141 · -1 points · Posted at 07:42:15 on February 14, 2016 · (Permalink)
Yeah. Calculus , diffeq, and linear algebra are standard but discrete math and combinatorics are pretty unique in application to computer science and engineering students.
Furthermore, the question at hand isn't relating to anything remotely covered under the domain of computer science and programming. If anything I'd say this fits under something like real analysis, which most computer science students would not even consider taking.
loconessmonster · 1 points · Posted at 09:02:52 on February 14, 2016 · (Permalink)
Discrete math and combinatorics is not strictly in application to cs and engineering... Most discrete math courses are a good introduction to proofs for math majors or people who will be taking more proofy courses. Combinatorics is good for lots more applications than just cs and engineering.
casey12141 · 1 points · Posted at 15:28:38 on February 14, 2016 · (Permalink)
Yeah I agree, but at most colleges, look at the majors that require discrete math. It will usually be someting like computer science, computer engineering, cognitive science, etc. Obviously I'm not saying those are the ONLY fields relevent to those topics, but they are the classic ones.
Antonin__Dvorak · -2 points · Posted at 07:30:43 on February 14, 2016 · (Permalink)
I can't speak for every school but at my university the only program more mathematically rigorous than software engineering is pure math itself.
casey12141 · 3 points · Posted at 07:33:03 on February 14, 2016 · (Permalink)*
Well computer science is by definition a more theoretical and mathematically rigorous software engineering.
But as it turns out, Computer Science and academia are entirely seperate from actual progrmaming in industry.
Also, Computer Science students probably wouldn't be taking real analysis. That'd be more in line with electrical engineers or ECE.
Raijinili · 1 points · Posted at 08:16:05 on February 14, 2016 · (Permalink)
Numerical analysis is a thing for programmers. Who's gonna program the physics simulations (e.g. video games, money)?
There are many applications for programming, so there are many people who won't need SOME knowledge that they teach. For example, some programmers will never need databases, while others probably can't imagine not having them as a key part of the curriculum.
In fact, I'd say that real analysis is more useful for actual programmers than academia. My impression is, academics are more into graph theory, combinatorics, and logic, while analysis is more applicable and less abstract.
casey12141 · 1 points · Posted at 08:19:28 on February 14, 2016 · (Permalink)
Yeah you're totally right, it absolutely depends on where you're going into. It also is massively important in the finance industry. Hell, they are hiring a lot of EE's now just for the firm grasp on analysis.
But at that point, we are arguing about specializations, rather than computer science and programming itself. I think you'd agree that the mathematical lingua franca of programmers does not contain or deal with analysis, and that's reflected in the core cirriculum of most CS degrees.
Raijinili · 2 points · Posted at 10:54:38 on February 14, 2016 · (Permalink)
Recall the original comment:
The poster probably learned about series in the process of learning programming, and might have had the impression that it was standard for programming students to take calculus. Calculus is where you first learn about series, not full-blown analysis. My school, for one, required calculus for CS majors.
casey12141 · 1 points · Posted at 15:26:46 on February 14, 2016 · (Permalink)
Yeah. The intro to this material would be covered in calculus. A class almost all STEM and business majors would take.
cptgrudge · 2 points · Posted at 07:10:42 on February 14, 2016 · (Permalink)
Just a series? Granted that's a series representing a polynomial, but computers don't "just know" how transcendental functions like sin/cos/log/etc work. We still need series so that computers can approximate them. Someone had to write those math libraries in the first place!
casey12141 · -3 points · Posted at 07:15:45 on February 14, 2016 · (Permalink)
Yes, but 99.999% aren't writing math libraries, are they?
V1russ · 3 points · Posted at 07:06:24 on February 14, 2016 · (Permalink)
Me too thanks
ck2839 · 4 points · Posted at 06:58:47 on February 14, 2016 · (Permalink)*
The Fibonacci sequence is defined by the sequence a_0 = 1, a_1 = 1 with a_n = a_{n-1} + a_{n-2} for all n∈ℤ, n≥2.
Let G(x) = a_0 + x·a_1 + x2·a_2 + ··· This is called a generating function.
∑∞_{i=2} xi·a_i = x·∑∞_{i=2} xi-1·a_{i-1} + x2·∑∞_{i=2} xi-2·a_{i-2}.
G(x) - x·a_1 - a_0 = x·(G(x)-a_0) + x2·G(x).
G(x) = 1 / (1-x-x2).
abloblololo · 1 points · Posted at 13:46:15 on February 14, 2016 · (Permalink)*
When I write out your last step I get:
G(x) = x / (1-x-x2)
ck2839 · 1 points · Posted at 13:49:52 on February 14, 2016 · (Permalink)
a_0 = a_1 = 1.
G(x) - x - 1 = x·(G(x)-1) + x2·G(x)
G(x) - x - 1 = x·G(x) - x + x2·G(x)
G(x)·(1 - x - x2) = 1
G(x) = 1 / (1 - x - x2).
Maybe you thought that a_0 = 0.
abloblololo · 1 points · Posted at 13:53:17 on February 14, 2016 · (Permalink)*
I set a_0 to 0 for some reason (didn't see your edit)
[deleted] · 4 points · Posted at 14:16:26 on February 14, 2016 · (Permalink)
a_0 is how I look trying to read all this.
Bluffz2 · 0 points · Posted at 13:45:07 on February 14, 2016 · (Permalink)
I don't think you're helping there, mate. And LaTeX doesn't parse in Markdown text fields.
jaredjeya · 1 points · Posted at 13:03:24 on February 14, 2016 · (Permalink)
Binomial expansions! You can write any expression of the form (1 + f(x))n, where n is any real number and f(x) is any function of x, in the form:
1 + nf(x) + (n(n-1)/2!)*f(x)² + (n(n-1)(n-2)/3!)*f(x)3 + ... and so on.
So that's what's being done with the expression above. It only works if -1 < f(x) < 1 though.
In fact you can write most functions as a series of powers of x, so a + bx + cx² + dx3 etc., except some will work for all x, some for -1<x<1 and some for other constraints. It's just that binomial expansions have an easy to remember formula, and the others require differentiation to get the power series.
heydanika · 9 points · Posted at 04:26:26 on February 14, 2016 · (Permalink)*
1/(1-x-x2) = ∑ (x+x2)k =
= Pascal's Triangle. Illuminati confirm!
romulusnr · 2 points · Posted at 09:31:37 on February 14, 2016 · (Permalink)
1/(1-1-1)=-1/2
1/(1-2-4)=-1/5
1/(1-3-9)=-1/11
.....
mybustersword · 1 points · Posted at 04:44:34 on February 14, 2016 · (Permalink)
SLOW DOWN
Odds-Bodkins · 1 points · Posted at 05:00:14 on February 14, 2016 · (Permalink)
is that a Taylor series expansion?
ck2839 · 2 points · Posted at 07:16:26 on February 14, 2016 · (Permalink)*
(I've already posted this elsewhere in the comments)
The Fibonacci sequence is defined by the sequence a_0 = 1, a_1 = 1 with a_n = a_{n-1} + a_{n-2} for all n∈ℤ, n≥2.
Let G(x) = a_0 + x·a_1 + x2·a_2 + ··· This is called a generating function.
∑∞_{i=2} xi·a_i = x·∑∞_{i=2} xi-1·a_{i-1} + x2·∑∞_{i=2} xi-2·a_{i-2}.
G(x) - x·a_1 - a_0 = x·(G(x)-a_0) + x2·G(x).
G(x) = 1 / (1-x-x2). Now substitute x = 0.1.
MOOnorityCow · 1 points · Posted at 05:33:41 on February 14, 2016 · (Permalink)
Now I get it
TrueStarsense · 1 points · Posted at 06:12:44 on February 14, 2016 · (Permalink)
Lol. I'm taking a year off math before college and it unfortunately took me a sec to actually read this.
Bazakac · 1 points · Posted at 07:15:10 on February 14, 2016 · (Permalink)
Fascinating
ApoSupes · 1 points · Posted at 08:41:45 on February 14, 2016 · (Permalink)
Doesn't this give you negative fractions?
Ryugar · 1 points · Posted at 10:47:13 on February 14, 2016 · (Permalink)
Nerd
[deleted] · -2 points · Posted at 02:50:16 on February 14, 2016 · (Permalink)
[deleted]
eternally-curious · 14 points · Posted at 04:41:50 on February 14, 2016 · (Permalink)*
OK, since nobody's actually answered you yet, I'll give it a shot. Although it's hard to explain Calc II like you're 5.
So almost any given expression with a variable can be written as a sum of numbers with patterns. An example is cos(x), which equals equal to sum (((-1)n x2n )/(2n!)) from n = 1 to infinity. So set n = 1, n = 2, n = 3, ... and add up everything. That gets you 1 - x2 /2 + x4 /24 - x6 /720 + ... This equals cos(x) for any value of x.
A more common series representation is 1/(1-x), which is simply sum(xn ) from n = 0 to infinity. Again plug in n = 1, 2, 3, ... and add it all up. The answer is 1 + x + x2 + x3 + x4 + ... Again, this equals 1/(1-x) for any value of x.
Now, the series for 1/(1 - x - x2 ) is a little complicated, but when expanded, it equals 1 x0 + 1 x1 + 2 x2 + 3 x3 + 5 x4 + 8 x5 + 13 x6 + ... You'll notice that the coefficients are numbers in the Fibonacci sequence.
Now, plug in x = 0.1. The original expression becomes 1/(1 - 0.1 - 0.12 ) = 1/(1 - 0.1 - 0.01) = 1/0.89, which, if you multiply top and bottom by 100, equals 100/89.
Finally, plug in 0.1 into the expansion (which is easy because the powers of 0.1 are simply 0.1, 0.01, 0.001, ...). The result is 1 + 0.1 + 0.02 + 0.003 + 0.0005 + ... and this equals 100/89. The top comment describes 1/89, so if you divide each term by 100, you get 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 ...
Hope that was clear. Sorry for any formatting errors (I typed this up on mobile), but the math is all correct.
[deleted] · 5 points · Posted at 05:04:50 on February 14, 2016 · (Permalink)
It's more about differential equations and real analysis tbh.
Define a recurring sequence as a(n+1) = a(n) + a(n-1) for all n greater than or equal to 2. a(0) is 0 and a(1) is 1.
Now, claim that a(n) = xn. Hence, xn+1 - xn - xn-1 = 0 from a(n+1) = a(n) + a(n-1).
xn+1 - xn - xn-1 = xn-1 [x2 - x - 1]. Hence, finding the roots of [x2 - x - 1], namely r(1) and r(2), would produce a recurring pattern such that a(n) = xn and a(n+1) = a(n) + a(n-1).
The roots of x2 - x - 1 are: r(1) = (1+sqrt(5))/2 and r(2) = (1-sqrt(5))/2.
From now on, it's easy to see that c(1)r(1)n+1 + c(2)r(2)n+1 = a(n+1) satisfies a(n+1) = a(n) + a(n-1) for all n greater than 2.
We're left with determining the values of c(1) and c(2).
a(0) = c(1)r(1)0 + c(2)r(2)0 = c(1) + c(2) = 0
a(1) = c(1)r(1) + c(2)r(2) = 1
so:
c(1) = -c(2)
c(1) (r(1) - r(2)) = 1 = c(1) sqrt(5) ; c(1) = 1/sqrt(5)
So a(n) = (1/sqrt(5)) [(1/2)(1+sqrt(5))]n - (1/sqrt(5)) [(1/2)(1-sqrt(5))]n
i.e.: a(3) = 2
And that's why x2 - x - 1 is a generating function for the Fibonacci sequence, namely because its roots along with the proper coefficients can generate any Fibonacci number.
oliverbtiwst · 1 points · Posted at 05:43:03 on February 14, 2016 · (Permalink)
that looks hardly readable by a non post secondary mathematics student.
[deleted] · 1 points · Posted at 06:07:35 on February 14, 2016 · (Permalink)
It's hard to explain such things using a keyboard.
[deleted] · 1 points · Posted at 13:51:04 on February 14, 2016 · (Permalink)
None of these things in this entire thread look readable to me tbh
eternally-curious · 1 points · Posted at 05:47:43 on February 14, 2016 · (Permalink)*
You're absolutely right, but what you just did was essentially derive the series representation of 1/(1 - x - x2 ) (since (1/sqrt(5)) [(1/2)(1+sqrt(5))]n - (1/sqrt(5)) [(1/2)(1-sqrt(5))]n is simply the series form of 1/(1 - x - x2 )). I tried to intentionally avoid that to keep with the spirit of ELI5, because I thought it would get too complex.
I mean, I have a math minor, so I get it, but I doubt others who have less exposure to differential equations will.
[deleted] · 2 points · Posted at 06:11:43 on February 14, 2016 · (Permalink)
I'm doing a major in maths, so I tend to forget how most things that seem very simple to us (like the one I described above) tend to be quite complex for non-math people.
geweldigzinloos · 1 points · Posted at 09:24:25 on February 14, 2016 · (Permalink)
For me the problem has always been 'i dont know what direction to take to solve this math problem' so when someone spouts a giant list of statements and at the end says 'tadaa' i'm just wondering 'why did you do x'. Like for example 'plug in 0.1'. Why 0.1? What's the rationale behind it, how is 0.1 relevant?
Or 'define a generating function like such: <func>'. Why? What thinking went before this?
So it's all just a bunch of random statements which make no sense so me and look like gibberish.. very offputting.
[deleted] · 1 points · Posted at 09:40:18 on February 14, 2016 · (Permalink)
It's not meant to be easily understood by anyone and everyone. That doesn't mean it's all random gibberish tho =/
But I get where you're coming from. I too sometime struggle to understand math concepts sometimes, especially when they aren't explained properly.
ck2839 · 1 points · Posted at 07:10:34 on February 14, 2016 · (Permalink)*
There's a simple proof of all of this. I've already posted it here in the comments.
The Fibonacci sequence is defined by the sequence a_0 = 1, a_1 = 1 with a_n = a_{n-1} + a_{n-2} for all n∈ℤ, n≥2.
Let G(x) = a_0 + x·a_1 + x2·a_2 + ··· This is called a generating function.
∑∞_{i=2} xi·a_i = x·∑∞_{i=2} xi-1·a_{i-1} + x2·∑∞_{i=2} xi-2·a_{i-2}.
G(x) - x·a_1 - a_0 = x·(G(x)-a_0) + x2·G(x).
G(x) = 1 / (1-x-x2). Now substitute x = 0.1.
ck2839 · 1 points · Posted at 07:13:36 on February 14, 2016 · (Permalink)*
Link to a simpler proof.
SCHROEDINGERS_UTERUS · 1 points · Posted at 14:37:34 on February 14, 2016 · (Permalink)*
That's not the usual way of deriving a generating function, though, is it? The derivations I've seen have just been a relatively simple manipulation of sums to get it. The tricky part is getting a formula for the coefficients, but you don't need that to get the generating function.
Edit: The derivations I've seen have gone something like this
http://i.imgur.com/eTV9EQJ.jpg
[deleted] · 1 points · Posted at 15:59:29 on February 14, 2016 · (Permalink)
You and I are basically doing the same thing, hence why we're both ending with x2 -x - 1 as the core of our generating function. It's just that I wanted and actual formula for a(n) rather than the generating function itself. By treating a(n+1) - a(n) - a(n-1) as an homogeneous differential equation (kinda), I set "x" to be equal to the sum of some coefficients times the roots of "x".
That's the usual way to get a precise formula for such recuring patterns, namely a(n) = c(1)r(1)n + c(2)r(2)n . That enables you to evaluate the upper and/or lower limit of a(n), as well as its convergence or lack thereof. Merely deriving the generating function sadly doesn't let us do such things, hence what I did.
Tl;dr : yours is the standard way to get the generating function's characteristic polynomial, mine is the standard way to get a formula for a(n).
KurrKurr · 1 points · Posted at 10:33:09 on February 14, 2016 · (Permalink)
The sum(xn) example.
Did you forget to mention, that this is only true for any value of x with 0<x<1 (or something like that)? Because the series doesn't converge for x>=1, does it?
yomommasofat3 · 6 points · Posted at 03:47:04 on February 14, 2016 · (Permalink)
The comment added some clarity. Might not be a super long ELI5 answer but it elaborates at the very least.
AddictiveSombrero · -1 points · Posted at 03:58:51 on February 14, 2016 · (Permalink)
I'm just saying, it doesn't clarify much to the "wut" guy, since the explanation is only as clear as the original comment.
XkF21WNJ · 3 points · Posted at 02:57:42 on February 14, 2016 · (Permalink)
I didn't want to put more effort into the answer than had been put in the question.
ck2839 · 1 points · Posted at 07:45:05 on February 14, 2016 · (Permalink)*
A full explanation isn't very long actually. See this comment.
AddictiveSombrero · 1 points · Posted at 03:07:58 on February 14, 2016 · (Permalink)
Then why answer at all?
ck2839 · 1 points · Posted at 07:39:14 on February 14, 2016 · (Permalink)*
(I've already posted it elsewhere in the comments)
The Fibonacci sequence is defined by the sequence a_0 = 1, a_1 = 1 with a_n = a_{n-1} + a_{n-2} for all n∈ℤ, n≥2.
Let G(x) = a_0 + x·a_1 + x2·a_2 + ··· This is called a generating function.
∑∞_{i=2} xi·a_i = x·∑∞_{i=2} xi-1·a_{i-1} + x2·∑∞_{i=2} xi-2·a_{i-2}.
G(x) - x·a_1 - a_0 = x·(G(x)-a_0) + x2·G(x).
G(x) = 1 / (1-x-x2). Now substitute x = 0.1.
suju_x_elf · -2 points · Posted at 03:25:53 on February 14, 2016 · (Permalink)
if you can't see how that's a explanation then you should learn more maths
AddictiveSombrero · 2 points · Posted at 03:31:19 on February 14, 2016 · (Permalink)
It's not that I can't, but it's pretty obvious that someone who doesn't understand "1/(1-x-x2) is a generating function for the Fibonacci sequence" couldn't.
oliverbtiwst · 3 points · Posted at 05:39:33 on February 14, 2016 · (Permalink)*
I'll give it a shot:
The number 1 is finite and can be written as an infinite sum of numbers:
1 = 1/2 + 1/4 + 1/8 + 1/16 ... = sum (1/2)n
This can be similarly done for 'finite' expressions such as 1/(1-x):
1/(1-x) = 1 + x + x2 + x3 ... = sum xn
Similar with the fib generating function case:
1/(1-x-x2 ) = 1 + 1x + 2x2 + 3x3 + 5x4 + 8x5 ...
It is miraculous that an expression could return something like the fib sequence, when expanded to it's infinite series version. It has to do with the denominator of the expression, by including both x and x2 in the denom we are able to select the previous two terms to be added to the current term. Similarly to how the natural numbers (1,2,3,4...) only need information about the previous one number, thus in the denom of 1/(1-x) there is only x.
When I first learned this I was amazed as well, but it actually just is that 'coincidental' that it could work out. If you are interested as well, you should do more research from here on.
AddictiveSombrero · 2 points · Posted at 10:43:38 on February 14, 2016 · (Permalink)
Just wondering, at what level of education did you learn this?
da5id2701 · 1 points · Posted at 17:02:11 on February 14, 2016 · (Permalink)
I learned generating functions in combinatorics, which is a 300 level math class at my school. Basically if you study discrete math you'll come across it. Probability generating functions are also useful, so it should come up in probability classes as well.
AddictiveSombrero · 2 points · Posted at 17:30:56 on February 14, 2016 · (Permalink)
I'm English and don't really understand the American education system, can you translate? What's a 300 level math class?
da5id2701 · 1 points · Posted at 17:47:41 on February 14, 2016 · (Permalink)
It roughly means that it's meant to be taken in the 3rd year of college/university. Of course, you can take whatever class you want if you meet the prerequisites, so that's not strict - I took combinatorics in the first semester of my 2nd year without issue. But it's sort of in the third "tier" of math classes, however the faculty at my particular school decided to define that. Other schools might have similar classes at different levels, but you would expect a 200 level combinatorics to be less rigorous, for example.
AddictiveSombrero · 2 points · Posted at 19:04:27 on February 14, 2016 · (Permalink)
Oh, like a 101, 201 class and all that. Thanks for the clarification. That math is still above my level I guess.
oliverbtiwst · 1 points · Posted at 19:46:10 on February 14, 2016 · (Permalink)
Second year Waterloo combinatorics course.
ck2839 · 1 points · Posted at 07:43:07 on February 14, 2016 · (Permalink)
I gave the reason why 1 / (1-x-x2) returns the Fibonacci sequence in this comment.
NC-Lurker · -1 points · Posted at 08:42:25 on February 14, 2016 · (Permalink)
He actually gave the explanation that was the easiest to comprehend, in just 2 lines of basic maths. You only have yourself to blame if you fail to get it.
the-highness · 1 points · Posted at 04:09:59 on February 14, 2016 · (Permalink)
TIL
shomii · 1 points · Posted at 04:47:28 on February 14, 2016 · (Permalink)
One of the roots of 1 - x - x2 is golden ratio.
romulusnr · 1 points · Posted at 09:28:51 on February 14, 2016 · (Permalink)
I... What?
Geambanu · 1 points · Posted at 11:30:45 on February 14, 2016 · (Permalink)
What is a generating function?
New_World_Era · 1575 points · Posted at 20:40:21 on February 13, 2016 · (Permalink)
Wow, I thought I was a big nerd about the golden ratio, but I have never heard about this. Can anyone explain why?
madcaphal · 4674 points · Posted at 23:43:19 on February 13, 2016 · (Permalink)*
I guess because you never read the right book or something.
Edit: Sheeeeeit. Thanks, strangers.
DiamondFalcon · 743 points · Posted at 03:19:12 on February 14, 2016 · (Permalink)
Haha, reminds me of LOST when Jack asks Ben during a nervous flight:
Jack: "How can you read?"
Ben: "My mother taught me."
ItSamanThong · 50 points · Posted at 06:10:48 on February 14, 2016 · (Permalink)
but Bens mom dies giving birth to him?? Oh wait he was being sarcastic wasn't he. Fuck I'm an idiot.
Tezmata · 72 points · Posted at 06:26:34 on February 14, 2016 · (Permalink)
Not even sarcastic, since Jack didn't know that about him. He just straight up lied all the time whenever he felt like it. It was a very nice one-off line with a lot of context behind it.
Nanosauromo · 26 points · Posted at 07:01:52 on February 14, 2016 · (Permalink)
Exactly. Ben did this constantly. At one point he mentions he's a Pisces, but he can't be because he was born in December.
ipslne · 10 points · Posted at 10:51:17 on February 14, 2016 · (Permalink)
If you like shows where you are given everything about the characters and nothing about the plot, check out Evangelion!
[deleted] · 9 points · Posted at 10:54:57 on February 14, 2016 · (Permalink)
Also check this out if you like to be mind fucked and torn into emotional shreds and need a week to decipher what the fuck you just watched. Evangelion is fantastic though, but you will feel very conflicted after everything is said and done.
Slackbeing · 5 points · Posted at 11:32:12 on February 14, 2016 · (Permalink)
"Oh, my best friend is unconscious in a hospital bed, let's fap and come all over her."
ipslne · 1 points · Posted at 11:43:44 on February 14, 2016 · (Permalink)
I take it you didn't watch it then?
That scene has quite a lot of meaning behind it. Part character development, part realism and part immersion. It was a fucked up thing, he knew it was fucked up, and the viewer now feels fucked up. Now everyone's in Shinji's shoes.
There's also a bit of social commentary going on here with regards to the sexualization of characters that is rampant in anime.
[deleted] · 2 points · Posted at 21:58:47 on February 14, 2016 · (Permalink)
I would go as far to say that's the major reason for the scene's existence. Anno hated otaku culture, and was basically pointing at them saying, "HEY, THIS IS YOU, YOU'RE ALL FUCKED UP".
hypervelocityvomit · 1 points · Posted at 10:24:14 on February 15, 2016 · (Permalink)
NGE is really more of a "coming of age" story in anime clothing than a mecha show.
[deleted] · 1 points · Posted at 11:52:47 on February 14, 2016 · (Permalink)
That was the weirdest scene I've ever seen. It actually kind of seemed out of character for Shinji because of how risky doing something like that is. Shinji is a scared kid so just whippin out his dick and jackin off to an unconscious chick when anyone could walk in...bold strategy cotton, especially when a bathroom is right there.
m00fire · 2 points · Posted at 13:29:18 on February 14, 2016 · (Permalink)
Also be sure to watch End of Evangelion (not the dub though as it's fucking horrible) since the actual ending is horse shit and makes no sense at all
[deleted] · 1 points · Posted at 18:57:11 on February 14, 2016 · (Permalink)
Whattt? The ending makes complete sense, what didn't you understand?
Nanosauromo · 23 points · Posted at 07:00:29 on February 14, 2016 · (Permalink)
You know how you can tell when Ben is lying? His mouth is moving.
seeyouspacecowboy- · 6 points · Posted at 05:54:12 on February 14, 2016 · (Permalink)
haha i remember very well this part! I think it was season 5.
NotSpare · 2 points · Posted at 07:57:50 on February 14, 2016 · (Permalink)
Jack: "I have a question."
Ben : "I'm a Scorpio."
Bazoun · 1 points · Posted at 13:34:30 on February 14, 2016 · (Permalink)
Or the numerous similar references in Airplane!
unfulfilledsoul · 1 points · Posted at 05:10:17 on February 15, 2016 · (Permalink)
Liar. His mother died in childbirth! This Ben is pretty shifty.
intensely_human · 42 points · Posted at 03:00:59 on February 14, 2016 · (Permalink)
This is the hardest I've giggled this afternoon.
Castriff · 62 points · Posted at 02:34:17 on February 14, 2016 · (Permalink)
Ah, the old Reddit Matharoo!
artyboi37 · 51 points · Posted at 02:45:12 on February 14, 2016 · (Permalink)
Hold my calculator, I'm going in!
stonejcartman96 · 11 points · Posted at 16:38:53 on February 14, 2016 · (Permalink)
Calculator? You filthy Amateur
MyOtherTagsGood · 9 points · Posted at 20:18:44 on February 21, 2016 · (Permalink)
Here, hold my abacus. I'm a week in and it's weighing me down.
Robo4900 · 4 points · Posted at 19:05:41 on February 26, 2016 · (Permalink)
Psst, amateurs. Hold my slide-rule, I'm going in.
tinderbox89 · 41 points · Posted at 00:23:35 on February 14, 2016 · (Permalink)
Haaaa
Tufflaw · 13 points · Posted at 01:53:51 on February 14, 2016 · (Permalink)
Well done
NotSayingJustSaying · 18 points · Posted at 02:42:16 on February 14, 2016 · (Permalink)
I don't get it....
peanuts421 · 43 points · Posted at 02:54:44 on February 14, 2016 · (Permalink)
This comment assumes he's asking why he didn't know rather than why 1/89th does this
NotSayingJustSaying · 41 points · Posted at 02:58:38 on February 14, 2016 · (Permalink)
Thanks. I'm too dumb for this thread.
MenschenBosheit · 9 points · Posted at 05:38:58 on February 14, 2016 · (Permalink)
This is why I usually stay out of these threads. It's my own little "Schrödinger's smartness" .
BornInTheRSA · 0 points · Posted at 10:24:48 on February 14, 2016 · (Permalink)
That's actually a pretty smart term haha.
SeudonymousKhan · 2 points · Posted at 02:58:01 on February 14, 2016 · (Permalink)
Bravo
JackAceHole · 2 points · Posted at 05:45:54 on February 14, 2016 · (Permalink)
Oh! That must be it.
llehfolluf · 2 points · Posted at 03:58:55 on February 14, 2016 · (Permalink)
Trying to get my son to sleep, you ahole!!!
SadGhoster87 · 1 points · Posted at 07:07:30 on February 14, 2016 · (Permalink)
Wait, I don't get it
[deleted] · 1 points · Posted at 09:01:39 on February 14, 2016 · (Permalink)
Or have a design class
ghunter21 · 1 points · Posted at 04:24:53 on February 14, 2016 · (Permalink)
The ol' Reddit math-a-roo?
myopicview · -6 points · Posted at 02:00:07 on February 14, 2016 · (Permalink)
Ba-dum-tiss!!! I'll be here all week, folks!
jourdan442 · -6 points · Posted at 03:10:16 on February 14, 2016 · (Permalink)
You get an upvote.
[deleted] · 189 points · Posted at 20:54:46 on February 13, 2016 · (Permalink)
http://www.mathpages.com/home/kmath108.htm
versusChou · 11 points · Posted at 02:21:02 on February 14, 2016 · (Permalink)
Ah yes. Trivial.
A_favorite_rug · 1 points · Posted at 12:53:03 on February 14, 2016 · (Permalink)
Could at least made it challanging.
everythingisbase10 · 5 points · Posted at 02:09:16 on February 14, 2016 · (Permalink)
Is there a TeX version of these pages?
ThePantsThief · 4 points · Posted at 06:21:30 on February 14, 2016 · (Permalink)
Right? Reading this stuff in a mono space font is hell
ck2839 · 3 points · Posted at 07:19:35 on February 14, 2016 · (Permalink)*
There's a much simpler proof of all of this. I've already posted it elsewhere in the comments:
The Fibonacci sequence is defined by the sequence a_0 = 1, a_1 = 1 with a_n = a_{n-1} + a_{n-2} for all n∈ℤ, n≥2.
Let G(x) = a_0 + x·a_1 + x2·a_2 + ··· This is called a generating function.
∑∞_{i=2} xi·a_i = x·∑∞_{i=2} xi-1·a_{i-1} + x2·∑∞_{i=2} xi-2·a_{i-2}.
G(x) - x·a_1 - a_0 = x·(G(x)-a_0) + x2·G(x).
G(x) = 1 / (1-x-x2). Now substitute x = 0.1.
[deleted] · 2 points · Posted at 08:23:33 on February 14, 2016 · (Permalink)
Technically, your proof requires proving generating functions are unique. But yes, you're right.
Also, subscripts can be done via star underscore WORDS underscore star.
ck2839 · 1 points · Posted at 08:28:05 on February 14, 2016 · (Permalink)
Thanks, edited the underscores.
Kered13 · 1 points · Posted at 13:43:36 on February 14, 2016 · (Permalink)
Generating functions are fucking magic. Unfortunately they're one of the two subjects I didn't manage to quite grasp out of my freshman discrete math for CS lass (not the actual name of the class).
scoped22 · 3 points · Posted at 01:56:38 on February 14, 2016 · (Permalink)
Oh, now I get it!
WobbleWobbleWobble · 4 points · Posted at 03:46:50 on February 14, 2016 · (Permalink)
Also what I found out is that when you convert the fib sequence into bass 6 then write out just the number in the ones digit, the numbers are recurring and form a pattern.
I'll post numbers and a better explanation when I get home. Here are steps if you get confused :
EX : Base 10 : 8 converts to Base 6 : 10. Then just write down the number 0.
Kubby · 2 points · Posted at 04:49:20 on February 14, 2016 · (Permalink)
That actually is a thing for every single number base.
For base 6, the cycle is 24 digits long, for base 10 it's 60 digits.
https://en.wikipedia.org/wiki/Pisano_period
WobbleWobbleWobble · 1 points · Posted at 05:09:16 on February 14, 2016 · (Permalink)
Wait really? I never realized that, I just found this when I was trying to convert the sequence into musical notes
FalloutShuffle · 2 points · Posted at 05:29:41 on February 14, 2016 · (Permalink)
You should watch this.
ck2839 · 2 points · Posted at 07:17:41 on February 14, 2016 · (Permalink)*
(I've already posted it elsewhere in the comments)
The Fibonacci sequence is defined by the sequence a_0 = 1, a_1 = 1 with a_n = a_{n-1} + a_{n-2} for all n∈ℤ, n≥2.
Let G(x) = a_0 + x·a_1 + x2·a_2 + ··· This is called a generating function.
∑∞_{i=2} xi·a_i = x·∑∞_{i=2} xi-1·a_{i-1} + x2·∑∞_{i=2} xi-2·a_{i-2}.
G(x) - x·a_1 - a_0 = x·(G(x)-a_0) + x2·G(x).
G(x) = 1 / (1-x-x2). Now substitute x = 0.1.
abaddamn · 1 points · Posted at 07:30:50 on February 14, 2016 · (Permalink)
Ever looked at Pascal's triangle?
LudoRochambo · -2 points · Posted at 03:39:45 on February 14, 2016 · (Permalink)
the people who refer to themselves in the way you have are never the ones who are what they want to be.
stop it.
New_World_Era · 2 points · Posted at 03:51:35 on February 14, 2016 · (Permalink)
What? Are you talking about the word "nerd"?
michaelpinkwayne · 1 points · Posted at 04:46:01 on February 14, 2016 · (Permalink)
woah, life chnging advice br0
[deleted] · -5 points · Posted at 02:08:41 on February 14, 2016 · (Permalink)
Isnt the golden ratio boobs to ass
gravitationalBS · -2 points · Posted at 03:34:29 on February 14, 2016 · (Permalink)
No it's not. What does it make of my sexual orientation that I think 1:1.618033899749 is way better than any boob:ass?
MadTux · 72 points · Posted at 21:08:14 on February 13, 2016 · (Permalink)
Now I'm confused. Surely that sum is an irrational number?
AcellOfllSpades · 259 points · Posted at 21:33:59 on February 13, 2016 · (Permalink)
.5 + .25 + .125 + ... = 1
MadTux · 100 points · Posted at 22:03:57 on February 13, 2016 · (Permalink)
Oh yeah.
mcdoolz · 3 points · Posted at 23:34:32 on February 13, 2016 · (Permalink)
Mmm bow bow
juxtaposition21 · 3 points · Posted at 00:26:55 on February 14, 2016 · (Permalink)
Dae bow bow
theonejuancarlos · 3 points · Posted at 00:31:51 on February 14, 2016 · (Permalink)
Chika chika
CoolLikeAFoolinaPool · 1 points · Posted at 15:01:14 on February 14, 2016 · (Permalink)
Duff man can't breathe ohhhhhhh NOOO!
tesseract4 · 0 points · Posted at 04:30:59 on February 14, 2016 · (Permalink)
Mmmm Bow Bow
condor700 · 151 points · Posted at 22:38:54 on February 13, 2016 · (Permalink)
And don't call him Shirley
AcellOfllSpades · 7 points · Posted at 22:44:24 on February 13, 2016 · (Permalink)
Dammit, wish I could've thought to make that reference.
LetMeLickYourCervix · 2 points · Posted at 01:19:06 on February 14, 2016 · (Permalink)
I don't get it, it's been a while since my last math class.
AcellOfllSpades · 4 points · Posted at 01:28:54 on February 14, 2016 · (Permalink)
Reference to the movie Airplane!. Funniest movie I've ever seen.
[deleted] · 1 points · Posted at 02:35:59 on February 14, 2016 · (Permalink)
Or "Flying High!" In some places.
The shit has hit the fan.
NoGodNoGodPleaseNoNo · 1 points · Posted at 02:45:15 on February 14, 2016 · (Permalink)
Is it still meta when it's been a couple of days?
surelyucantbserious · 1 points · Posted at 21:49:18 on February 14, 2016 · (Permalink)
No.
KyleStanley3 · 3 points · Posted at 02:19:12 on February 14, 2016 · (Permalink)
I always thought it approached 1 but never quite equaled it
AcellOfllSpades · 6 points · Posted at 02:25:57 on February 14, 2016 · (Permalink)
No finite number of terms will equal 1. But that's not a finite number of terms. It's exactly 1 if you have infinite terms. The left side is just a number - numbers don't move. They can't approach anything.
If you were talking about 1 + 1/2 + 1/4 + 1/8 + ... + 1/2n, then you could say that as n goes to infinity, that series approaches 1. But in the case I gave above, nothing changes, so nothing can be approaching anything.
Asterix1806 · 1 points · Posted at 08:33:10 on February 14, 2016 · (Permalink)
What's the difference between a series and the limit of a sum anyway?
AcellOfllSpades · 2 points · Posted at 16:47:19 on February 14, 2016 · (Permalink)
Nothing. An infinite series is defined as the limit of its partial sums as the number of terms goes to infinity.
[deleted] · -4 points · Posted at 03:03:47 on February 14, 2016 · (Permalink)
[deleted]
AcellOfllSpades · 4 points · Posted at 03:19:01 on February 14, 2016 · (Permalink)
If n is finite, yes.
If n is infinite, no. Infinite sums are defined as the limit of their partial sums. By definition, Σ₁∞ (1/2n) = 1.
Odds-Bodkins · 1 points · Posted at 05:03:05 on February 14, 2016 · (Permalink)
Sorry but you're wrong for the reason that, e.g., 0.999999... = 1.
Limits at infinity are counter-intuitive, but also the reason that things like calculus work.
SpaceMonkey_Mafia · 1 points · Posted at 05:50:12 on February 14, 2016 · (Permalink)*
As long as your model of maths doesn't allow for infintessimals
AcellOfllSpades · 1 points · Posted at 07:08:03 on February 14, 2016 · (Permalink)
Limits don't have anything to do with infinitesimals. .9999... is equal to 1 even in the hyperreals.
SpaceMonkey_Mafia · 1 points · Posted at 07:34:47 on February 14, 2016 · (Permalink)*
I don't see why that's the case. A number that approaches an infinitely small number is could fall under either a hyperreal number or a limit. Though I haven't done any formal math training any time recently.
AcellOfllSpades · 1 points · Posted at 07:39:46 on February 14, 2016 · (Permalink)
No, they really don't. I don't have time to provide a better source right now, but on the Wikipedia page for hyperreals there are three mentions of the word "limit". One is not about hyperreals but the general idea of infinitesimals being used in limits, one is about hyperreals being abandoned in favor of limits, and one is talking about the set-theoretic construction of the hyperreals.
Limits are specifically defined using ε,δ ∈ ℝ. .999... is not 1 minus an infinitesimal even in the hyperreals.
Tamerlane-1 · 1 points · Posted at 01:39:24 on February 14, 2016 · (Permalink)
1/17+1/289+1/4913...=.0625
CaesarTheFirst1 · 39 points · Posted at 21:34:10 on February 13, 2016 · (Permalink)
Note that it's not 0.0112358132134..., the 0.0000008 and 0.00000013 both have a digit in the 7th digit (8 and 1).
catsnstuffz · 3 points · Posted at 02:20:02 on February 14, 2016 · (Permalink)
Can get murdered for saying shit like that
LoveLoveLoveOctopus · 5 points · Posted at 21:38:27 on February 13, 2016 · (Permalink)
The Fibonacci sequence is infinite so you infinitely approach 1/89
Bobius · 0 points · Posted at 08:04:37 on February 14, 2016 · (Permalink)
This is an awful description.
ilovelsdsowhat · 2 points · Posted at 04:08:03 on February 14, 2016 · (Permalink)
An infinite series can converge to a finite, rational number. Converging means that, as the number of terms in the series approaches infinity, the sum approaches a certain number. Sometimes that number is a finite number and sometimes it's rational, too! :)
MadTux · 2 points · Posted at 07:14:19 on February 14, 2016 · (Permalink)
Yes, it just doesn't look that way at first ..
Something like 0.5 + 0.25 + 0.125 etc is a lot easier to see, somehow.
Atmosck · 1 points · Posted at 05:18:09 on February 14, 2016 · (Permalink)
What makes you think that?
heap42 · 1 points · Posted at 23:26:58 on February 13, 2016 · (Permalink)
purely the fact that the number we are talking about is 1/89 says its a rational number, since a rational number is defined by each number that can be represented unsing one natural number(nominator) and one integer(numerator) which 1/89 is.
ezryder27 · 0 points · Posted at 01:54:00 on February 14, 2016 · (Permalink)
It can't be irrational if it was generated from a fraction. Irrational numbers cannot be written as fractions.
megustcizer · 6 points · Posted at 00:38:39 on February 14, 2016 · (Permalink)
Black... and... white are... all I see....
[deleted] · 6 points · Posted at 00:44:48 on February 14, 2016 · (Permalink)
In my infancy...red and yellow then came to be...
megustcizer · 1 points · Posted at 00:55:55 on February 14, 2016 · (Permalink)
Reaching out to me... lets me see...
TheHoveringSojourn · 2 points · Posted at 02:07:47 on February 14, 2016 · (Permalink)
DOO DOO DO DO DOO DOO DO DO
[deleted] · 2 points · Posted at 02:58:06 on February 14, 2016 · (Permalink)
As below so above and beyond I imagine...
BaconWang · 2 points · Posted at 03:38:24 on February 14, 2016 · (Permalink)
Drawn outside the lines of reason...
Paz436 · 4 points · Posted at 03:59:26 on February 14, 2016 · (Permalink)*
Kangaroo done hang the jury with the... wait.
[deleted] · 3 points · Posted at 05:08:11 on February 14, 2016 · (Permalink)
Push the envelope, watch it bend
GreasyJungle · 2 points · Posted at 05:12:46 on February 14, 2016 · (Permalink)
Overthinking...overanalyzing...separates the body from the mind
[deleted] · 2 points · Posted at 10:39:23 on February 14, 2016 · (Permalink)
Withering my intuition, missing opportunities
ClassicSwarley · 3 points · Posted at 08:16:02 on February 14, 2016 · (Permalink)
Is there an Abruzzi sequence by any chance?
[deleted] · 2 points · Posted at 23:09:37 on February 13, 2016 · (Permalink)
This is the craziest one here. What the fuck
[deleted] · 4 points · Posted at 01:39:08 on February 14, 2016 · (Permalink)
[deleted]
Kudospop · 1 points · Posted at 02:37:22 on February 14, 2016 · (Permalink)
That not what the original comment says, but try 1/998999 and you'll get the idea.
oliverbtiwst · 1 points · Posted at 06:44:28 on February 14, 2016 · (Permalink)
You can't add them together, they have to be unflattened.
intensely_human · 1 points · Posted at 03:03:33 on February 14, 2016 · (Permalink)
Just to split hairs here, the sequence is not encoded in the number because there is no way to get that sequence from the number. You can get 1/89 from the Fibonacci sequence by turning the sequence into that series by writing out the zeroes, but I can't see a way to get the sequence from the number 1/89.
Klashus · 1 points · Posted at 03:16:39 on February 14, 2016 · (Permalink)
Fibonacci patters that occur in nature are some amazing things.
A_Lurker_Once_Was_I · 1 points · Posted at 03:42:09 on February 14, 2016 · (Permalink)
Holy shit. Had I known this, I would have printed this out instead of the actual sequence up to some number for my professor hahaha
Schizoid_Llama · 1 points · Posted at 04:59:10 on February 14, 2016 · (Permalink)
Something something Tool
Kz_Rob · 1 points · Posted at 05:41:04 on February 14, 2016 · (Permalink)
Yes I was going to say this as well, but I was going to add a little. Isn't the fibbinaci sequence the one that accounts for a lot of things in nature? Like the way a shell swirls or a galaxy from afar? Awesome.
awsmdustin94 · 1 points · Posted at 05:45:55 on February 14, 2016 · (Permalink)
Look up the song "Lateralus" by Tool. Its about that sequence. Its really good.
0-1-1-2-3-5-8-13-21 · 1 points · Posted at 06:11:22 on February 14, 2016 · (Permalink)
I know not who I am!
skepticalrick · 1 points · Posted at 06:26:22 on February 14, 2016 · (Permalink)
Could I get an ELI5?
ck2839 · 1 points · Posted at 07:23:18 on February 14, 2016 · (Permalink)
Link. Then substitute x=0.1.
dadbrain · 1 points · Posted at 07:05:45 on February 14, 2016 · (Permalink)
89 = 1 + 1 +2 + 3 + 5 + 8 + 13 + 21 + 34 + 55, and is one of the natural fibonacci numbers.
89 decimal is 1000100010.0010001001... in base golden ratio according to wolframalpha, but I think that's been rounded off from 1000100010.00100010001...
Random832 · 1 points · Posted at 08:29:40 on February 14, 2016 · (Permalink)
Also 1/9899, 1/998999, if you want a bit more space for the pattern to be recognizable.
TheDisapprovingBrit · 1 points · Posted at 09:31:59 on February 14, 2016 · (Permalink)
9/11 conspiracy confirmed.
t-- · 1 points · Posted at 10:26:49 on February 14, 2016 · (Permalink)
i think my calculator is retarded. it says 1/89 = 0.0112359550561798
PM_ME_YOUR_FEELINGS9 · 1 points · Posted at 11:57:43 on February 14, 2016 · (Permalink)
I'm a retard. Can you explain what makes the Fibonacci sequence so special?
datindianguy · 1 points · Posted at 12:18:39 on February 14, 2016 · (Permalink)
Always been obsessed with the Fibonacci sequence. Thank you so much!
Unionlaw · 1 points · Posted at 12:42:48 on February 14, 2016 · (Permalink)
The sequence was first explored by chinese mathmen thousands of years earlier. The geographic divide between east and west necessarily required the west to discover for itself math principals well known and in common use in the east.
RecharginMyLaza · 1 points · Posted at 12:43:49 on February 14, 2016 · (Permalink)
When it said "mathematical fact" I was thinking of things like being able to do the multiplication table of 9 on your hands.
TurdFerguson495 · 1 points · Posted at 12:44:03 on February 14, 2016 · (Permalink)
Keep spiraling out
MrTesticlops · 1 points · Posted at 13:48:57 on February 14, 2016 · (Permalink)
In other matters, the golden ration is the golden rule, my dogs body follows it.
DammitDan · 1 points · Posted at 14:21:20 on February 14, 2016 · (Permalink)
Black
And
White are
All I see
In my infancy
Red and yellow then came to be
Reaching out to me
Lets me see
Anar_Isilye · 1 points · Posted at 21:45:47 on February 14, 2016 · (Permalink)
1+1/(1+1/(1+1/(1+1/(1+1/(1+1/(1+1/(1+1/(.....
http://talklikeaphysicist.com/wp-content/uploads/2008/08/golden-ratio-tattoo.jpg
Thearctickitten · 1 points · Posted at 22:43:54 on February 14, 2016 · (Permalink)
I don't get it I thought the Fibonacci sequence was add the previous two terms and get the third?
bbcreddit · 1 points · Posted at 23:00:25 on February 14, 2016 · (Permalink)*
No it is not: 1/89=0.01123595505617977528089887640449438202247191011235955056179775280898876404494382022471910112359550562... Edit: Yes it is, sorry... (After seeing http://www.mathpages.com/home/kmath108.htm)
hypervelocityvomit · 1 points · Posted at 09:42:31 on February 15, 2016 · (Permalink)
Also, 1/9 = .1 1 1 1 1 1... (boring, but please keep reading)
1/81 = 1/92 = .0 1 2 3 4 5 6 7...
Now why is that so?
Well, 1/81 = (1/9)2 = 0.111111...2
(If you go on, it gets messier, because of carries.)
Also, 1/729 = 0.001371...
This one gets messy quickly because the digits are larger, but wait! We can get around that by using more 9's.
1/99 = .01 01 01 01...
1/992 = .00 01 02 03 04 05 06 07 08...
1/993 = .00 00 01 03 06 10 15 21 28...
Proof: same as above. Really, try it.
[deleted] · 1 points · Posted at 10:53:50 on February 15, 2016 · (Permalink)
God fucking damn it. Just when you think you found out something new in maths turns out someone else discovered it in '95.
sacern · 1 points · Posted at 01:45:10 on March 25, 2016 · (Permalink)
The Fibonacci sequence is used in the song "Lateralus" by Tool.
https://www.fibonicci.com/fibonacci/tool-lateralus/
[deleted] · 0 points · Posted at 00:21:57 on February 14, 2016 · (Permalink)
Would this be useful for encryption?
1100101000 · 4 points · Posted at 01:32:18 on February 14, 2016 · (Permalink)
How would the Fibonacci sequence relate to encryption?
Ryaubee · 0 points · Posted at 01:57:05 on February 14, 2016 · (Permalink)
keep it in your pants, Lars von Trier.
SleepWouldBeNice · 0 points · Posted at 03:06:01 on February 14, 2016 · (Permalink)
I count out the Fibonacci sequence in my mind when I'm trying to hold my orgasm.
itdoesntmatteranyway · 0 points · Posted at 03:06:50 on February 14, 2016 · (Permalink)
When I was a little kid my mother told me not to stare into the sun. So once when I was six I did.
notashleyjudd · 0 points · Posted at 03:16:23 on February 14, 2016 · (Permalink)
And the Fibonacci sequence can be used to easily convert miles to kilometers or vice versa.
18BPL · 2751 points · Posted at 23:15:15 on February 13, 2016 · (Permalink)*
Gabriel's Horn, a cone formed by revolving the curve y=1/x where x is greater than or equal to 1. It has an infinite surface area, but a finite volume. In other words, it can be filled with paint, but it can't be painted
Edit: Okay, maybe it can be painted, I don't fucking know, I'm just a lowly HS Calc student. I'm sorry my quick and dirty analogy has offended some of you.
MrMoby · 548 points · Posted at 04:27:37 on February 14, 2016 · (Permalink)
To help with grokking that fact, consider the area under the normal distribution - it's equal to 1 (a finite number). However, the length of the boundary of that area is infinite.
0ne_Winged_Angel · 433 points · Posted at 06:41:54 on February 14, 2016 · (Permalink)
grok (verb): understand (something) intuitively or by empathy.
Huh, TIL!
Gaff3r · 149 points · Posted at 07:29:51 on February 14, 2016 · (Permalink)
“But the Martian language is so much more complex than is English [that] I’m not certain that it will ever be possible for us to think in Martian…. [T]ake this one word: ‘grok.’ Its literal meaning, one which I suspect goes back to the origin of the Martian race as thinking, speaking creatures… is quite easy. ‘Grok’ means ‘to drink’….
[But it could also mean] a hundred other English words, words which represent what we think of as different concepts, even pairs of antithetical concepts. And ‘grok’ means all of these, depending on how you use it. It means ‘fear,’ it means ‘love,’ it means ‘hate’–proper hate, [as] you cannot possibly hate anything unless you grok it completely, understand it so thoroughly that you merge with it and it merges with you–then and only then can you hate it. By hating yourself….
The Martians seem to know instinctively what we learned painfully from modern physics, that the observer interacts with the observed simply through the process of observation. ‘Grok’ means to understand so thoroughly that the observer becomes a part of the process being observed–to merge, to blend, to intermarry, to lose personal identity in group experience. It means almost everything we mean by religion, philosophy, and science–and it means as little to us as color means to a blind man.” – Robert A. Heinlein, from "Stranger in a Strange Land."
Arancaytar · 14 points · Posted at 09:32:45 on February 14, 2016 · (Permalink)
That's the origin? Wow, TIL.
Knotdothead · 4 points · Posted at 14:58:37 on February 14, 2016 · (Permalink)
I highly recommend adding this book to your reading list.
Actually, I recommend adding everything by Hienlien to your list.
hypervelocityvomit · 2 points · Posted at 08:14:38 on February 15, 2016 · (Permalink)
(╯°□°）╯︵ ┻━┻
Knotdothead · 1 points · Posted at 12:40:02 on February 15, 2016 · (Permalink)
What on earth?
Never seen this one.
t00oldforthisshit · 1 points · Posted at 12:42:55 on February 15, 2016 · (Permalink)
It's pretty much the same thing as the concept of samadhi from yogic philosophy... Heinlein was a brilliant and original thinker, but he did make that concept up entirely out of the blue.
[deleted] · 5 points · Posted at 08:19:33 on February 14, 2016 · (Permalink)
Give a man water, and he is quenched for a day. Teach a man to stop breathing underwater, and he groks.
wraneus · 4 points · Posted at 14:13:36 on February 14, 2016 · (Permalink)
lets be water brothers!
[deleted] · 4 points · Posted at 13:57:08 on February 14, 2016 · (Permalink)
Sounds like grok is very similar to squanch...
SkyezOpen · 6 points · Posted at 14:09:27 on February 14, 2016 · (Permalink)
Go grok yourself.
Yeah, feels right.
Shashama · 2 points · Posted at 04:28:17 on February 15, 2016 · (Permalink)
This whole time I thought it was a word Futurama made up...
PM_ME_UR_BOOBS_MLADY · 1 points · Posted at 19:45:46 on February 14, 2016 · (Permalink)
I always like to say the grok something is to know it like an artist knows a brush
dont_wear_a_C · 6 points · Posted at 07:32:25 on February 14, 2016 · (Permalink)
Too many TILs in this thread for me to handle.
vote_me_down · 3 points · Posted at 13:04:54 on February 14, 2016 · (Permalink)
That's no longer true. It's now simply synonymous with "understand", because so many pompous people have used it to sound intelligent without bothering to learn its meaning.
badmuther · 4 points · Posted at 09:17:25 on February 14, 2016 · (Permalink)
Like "embiggens," grok is a cromulent word.
karma3000 · 2 points · Posted at 11:23:54 on February 14, 2016 · (Permalink)
A perfectly cromulent word. I'm glad your vocabulary has been embiggened. And thus the circle of meme has now been completed.
Fatesurge · 3 points · Posted at 12:04:42 on February 14, 2016 · (Permalink)
PSA: Nobody uses this except for a tiny subpopulation of ubergeeks.
Djburnunit · 1 points · Posted at 13:18:34 on February 14, 2016 · (Permalink)
Shouldn't PSA's be accurate? The word became common slang in the 1960s amongst hippies and sci fi buffs, neither of which were exactly micro cultures. And they still use it today.
Fatesurge · 2 points · Posted at 13:50:56 on February 14, 2016 · (Permalink)
My statement applies to the modern day that we live in, although, I have a feeling that it would have applied just as well in the 60's.
Djburnunit · 6 points · Posted at 14:26:20 on February 14, 2016 · (Permalink)
"A feeling"? Why not just research it?
Stranger In A Strange Land was hugely popular and — unlike most sci-fi published before it — was a mainstream success and vastly influential. Likewise "grok" became a mainstream (or "counter-culture lite") word amongst the younger generation, and is still used in mainstream books and films.
But go with your feelings if you choose; the irony won't be lost on me.
Fatesurge · 1 points · Posted at 00:24:00 on February 15, 2016 · (Permalink)
I have done research, namely having conversations with people. Nobody that I have ever met in real life uses the term. I have seen a few people online use it, but it is not at all common. I conclude that it is rarely in use and that it sounds like you are offended by your or your friends being classified as ubergeeks. Wear the badge with pride my friend.
Djburnunit · 1 points · Posted at 02:27:35 on February 17, 2016 · (Permalink)
Oh, no offense at all. Some of my best friends are geeks.
Knotdothead · 2 points · Posted at 15:10:57 on February 14, 2016 · (Permalink)
It was more of a fad word for most people back then. Of course, it was started by geeks and hippies being hipsters.
When the words fifteen minutes was up, it was the geeks and hippies who kept it alive.
Djburnunit · 1 points · Posted at 18:02:22 on February 14, 2016 · (Permalink)
Funny, I belong to a Bowie group, two members in the last half hour were using "grok." Neither are geeks or hippies, though they are Gen X musicians.
Like I say, believe what you want. I'm no hippie or geek, I can tell you that. And I haven't touched Heinlein since high school — where SIASL was required reading for AP English.
duhvorced · 1 points · Posted at 12:40:56 on February 14, 2016 · (Permalink)
'Grok' was coined by Robert Heinlein in his novel, Stranger in a Strange Land (1961)
[deleted] · 1 points · Posted at 15:57:03 on February 14, 2016 · (Permalink)
From "Stranger in a Strange Land". Great book.
TMinAK · 1 points · Posted at 17:14:26 on February 14, 2016 · (Permalink)
It's a Heinlein word.
Habtra · 1 points · Posted at 19:13:01 on February 14, 2016 · (Permalink)
Is it from "A history of nearly everithing"? I read it in French and the verb was gnoquer, but it reminded me of it immediately and has the same definition.
EnkoNeko · -2 points · Posted at 09:59:46 on February 14, 2016 · (Permalink)
Oh wow, English
good fucking job
t00oldforthisshit · 4 points · Posted at 12:38:45 on February 14, 2016 · (Permalink)
No, Martian.
EnkoNeko · 1 points · Posted at 08:15:56 on February 15, 2016 · (Permalink)
Where from?
(and don't say Mars)
t00oldforthisshit · 1 points · Posted at 12:44:05 on February 15, 2016 · (Permalink)
See all of the above
EnkoNeko · 1 points · Posted at 13:43:27 on February 15, 2016 · (Permalink)
Oh ok. Thanks.
ChaplnGrillSgt · 5 points · Posted at 06:52:03 on February 14, 2016 · (Permalink)
The light bulb went off. Thanks.
trznx · 1 points · Posted at 12:03:38 on February 14, 2016 · (Permalink)
Ohhh, grokking. Have an upvote.
grok_spock · 1 points · Posted at 14:03:59 on February 14, 2016 · (Permalink)
I find this logical
nobunaga_1568 · 1 points · Posted at 14:34:08 on February 14, 2016 · (Permalink)
Would any continuous distribution that goes to infinity in at least one direction also have finite area and infinite boundary?
nappingrabbit · 1 points · Posted at 07:20:17 on February 14, 2016 · (Permalink)
Up vote for the Martian word!!!!
imgonnabutteryobread · 312 points · Posted at 03:54:02 on February 14, 2016 · (Permalink)
It's pretty mind-boggling, but infinite surface area enclosing finite volume makes sense. A better way to visualize would be to consider an infinitely large, elastic sheet being plucked up off its mounting surface. This would now enclose a finite volume, although the sheet would be too large to make/paint/whatever.
GrammatonYHWH · 1001 points · Posted at 06:24:17 on February 14, 2016 · (Permalink)
I like the cake analogy.
Take a cake and cut it in half. Cut the right half in half. Keep cutting the right-most part in half.
In theory, you can keep cutting the rightmost half an infinite amount of time.
After an infinite amount of time, stack all the pieces on top of one another.
You have a finite amount of cake which requires an infinite amount of frosting to cover.
sugarfairy7 · 187 points · Posted at 06:35:24 on February 14, 2016 · (Permalink)
Very nice analogy, I will use this in my lecture, thank you :)
Tranquillititties · 21 points · Posted at 08:29:40 on February 14, 2016 · (Permalink)
Ou should watch Vsauce supertasks video on YouTube, that's where I heard this the first time. He also gives some more examples.
sugarfairy7 · 2 points · Posted at 02:57:40 on February 15, 2016 · (Permalink)
Thank you for the recommendation.
CodeJack · 3 points · Posted at 13:39:42 on February 14, 2016 · (Permalink)
Handy link: https://www.youtube.com/watch?v=ffUnNaQTfZE
YT_Reddit_Bot · 3 points · Posted at 13:39:56 on February 14, 2016 · (Permalink)
GratefulGrape · 14 points · Posted at 09:02:09 on February 14, 2016 · (Permalink)
Isn't this the same concept as the joke:
An infinite number of mathematicians walk into a bar. The first one orders a beer, the second one wants to show he's more temperate than the first, but still willing to unwind, so he orders a half a beer. The game of one upsmanship is afoot. The third says I'll take half of that and orders a quarter of a beer. The next orders an eighth.the mathematicians go on and on, halving the previous one's order.
After a while, the bartender gets fed up and hands them 2 beers, shakes his head and says, "You mathematicians just don't know your limits."
sugarfairy7 · 4 points · Posted at 02:56:39 on February 15, 2016 · (Permalink)
Omg, do you have more of these jokes? I need to tell these and see students facepalm their desks :D Please deliver!
GratefulGrape · 1 points · Posted at 14:44:45 on February 15, 2016 · (Permalink)
Are you trolling me?
sugarfairy7 · 2 points · Posted at 18:27:00 on February 15, 2016 · (Permalink)
No, sorry. I seriously love them. Do you know the shortest math joke? Let epsilon < 0.
Also I found more on my own :D
https://www.reddit.com/r/math/comments/aga6u/hey_reddit_got_any_good_math_jokes/
[deleted] · 9 points · Posted at 09:35:10 on February 14, 2016 · (Permalink)
Not quite. The punchline of your joke is just based on the fact that 1+1/2+1/4+...1/2n converges to 2. Gabriels horn is a bite more complicated.
[deleted] · 11 points · Posted at 16:00:56 on February 14, 2016 · (Permalink)
The joke would demonstrate Gabriel's Horn if the bartender said, "I have enough beer, but there aren't enough mugs."
Because the amount of beer converges to 2, but the amount of mugs goes to infinite.
VoilaVoilaWashington · 5 points · Posted at 18:03:29 on February 14, 2016 · (Permalink)
That's actually a really clever way of making it make sense.
[deleted] · 5 points · Posted at 08:44:19 on February 14, 2016 · (Permalink)
Here's a great VSauce video about supertasks and Gabriel's Horn. The video starts with Michael explaining /u/imgonnabutteryobread's analogy.
n-ion · 1 points · Posted at 14:30:12 on February 14, 2016 · (Permalink)
I will use this in life in general
[deleted] · -14 points · Posted at 08:17:31 on February 14, 2016 · (Permalink)
You will confuse the students like me who know that you can't divide a cake beyond atoms and still frost them. Ergo you can't frost it at all when the frosting no longer sticks due to lack of friction, and therefore a finite amount of cake is absolute and an infinite amount of frosting covering that cake is only possible by frosting the frosting and just sprinkling in the cake as you go. You are finitely caking the infinite frosting at that point, and after an infinite amount of time the ratio of cake to frosting is so small that you essentially just have an infinite amount of frosting, which you should then sell to fat people and 3.) Profit
Tocoapuffs · 3 points · Posted at 09:17:41 on February 14, 2016 · (Permalink)
Fine
Once your volume is defined as a fraction, your surface area is bigger.
Or just split the atom, you know, Idc.
[deleted] · 3 points · Posted at 16:01:46 on February 14, 2016 · (Permalink)
You have an irrational sense of humor
[deleted] · 1 points · Posted at 16:34:37 on February 14, 2016 · (Permalink)
Gabriel's Horn doesn't work as a concept once you take it into the real world of discrete molecules.
[deleted] · 0 points · Posted at 16:41:14 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 3 points · Posted at 16:46:08 on February 14, 2016 · (Permalink)
Oh sorry it was so funny I forgot to laugh
sugarfairy7 · 1 points · Posted at 02:54:28 on February 15, 2016 · (Permalink)
Maybe I'm just stupid but I found this really funny :D it makes sense at first, then becomes chaotic and ends in nonsense. Reminds me of a dad joke somehow. Well, I hope you feel better to know that you made at least one person laugh :)
[deleted] · 41 points · Posted at 07:18:14 on February 14, 2016 · (Permalink)*
[deleted]
CosmicZen · 1 points · Posted at 22:24:49 on February 14, 2016 · (Permalink)
Lmfao
sh41 · 12 points · Posted at 08:49:29 on February 14, 2016 · (Permalink)
How can you do anything after an infinite amount of time?
pomlife · 2 points · Posted at 17:22:45 on February 14, 2016 · (Permalink)
It's called a hypothetical.
hypervelocityvomit · 1 points · Posted at 08:20:36 on February 15, 2016 · (Permalink)
http://en.wikipedia.org/wiki/Speed_stacking
quepasascar · 1 points · Posted at 04:27:20 on February 19, 2016 · (Permalink)
Carefully.
akimbocorndogs · 13 points · Posted at 06:58:20 on February 14, 2016 · (Permalink)
Vsauce did a video on this recently, it's pretty mind blowing:
https://youtube.com/watch?v=ffUnNaQTfZE
Gougaloupe · 4 points · Posted at 06:49:04 on February 14, 2016 · (Permalink)
Now I feel more smarter and more hungry.
A_favorite_rug · 3 points · Posted at 12:45:08 on February 14, 2016 · (Permalink)
Hungry for knowledge?
Evagelos · 7 points · Posted at 06:48:36 on February 14, 2016 · (Permalink)
Isn't this similar to Zeno's Paradox?
killallzombies · 7 points · Posted at 07:24:51 on February 14, 2016 · (Permalink)
This is precisely what I was thinking.
In Zeno's Paradox you take the hypothetical distance between you and another person standing in front of you, and you close half of that distance (by stepping half the distance between you and that person). After walking half the distance between you and said person, take half of your current distance, and walk towards the person again. Proceed to keep walking half the distance of the previous space, and you will find that you will never reach the other person. This new analogy with the cake just adds another mind-blowingly cool dimension to an already awesome paradox. Thanks /u/GrammatonYHWH for sharing
brickmaster32000 · 8 points · Posted at 07:50:00 on February 14, 2016 · (Permalink)
The important part to realize is that the paradox is illustrating a flaw in your logic. In this case the fault is the assumption that all infinite sum are infinite when this is not the case.
killallzombies · 1 points · Posted at 10:28:55 on February 14, 2016 · (Permalink)
You're absolutely right, and it wasn't until I read his cake analogy that I realized it. That's the mind-blowing "dimension" I hadn't considered until the end of my post. It's almost like a paradox inside another paradox!
Tyler11223344 · 1 points · Posted at 08:17:04 on February 14, 2016 · (Permalink)
Except the flat sides of the cake will remain a constant size (the radius of the cake times the height), and all infinite sums of a constant (that's not 0) will infinite
brickmaster32000 · 2 points · Posted at 09:57:44 on February 14, 2016 · (Permalink)
Exactly which is why the cake will have infinite surface area. I was referring to Zeno's Paradox not the cake though.
Tyler11223344 · 1 points · Posted at 10:38:08 on February 14, 2016 · (Permalink)
Ohhhhh, my bad, thought you were referring to the cake
belladas · 3 points · Posted at 06:40:47 on February 14, 2016 · (Permalink)
Best analogy 2016
stdebo · 1 points · Posted at 06:48:45 on February 14, 2016 · (Permalink)
Works well with a loaf of bread and butter as well.
ExplosiveBEAR · 1 points · Posted at 07:00:53 on February 14, 2016 · (Permalink)
This helped me understand it the best. Thank you
SadGhoster87 · 1 points · Posted at 07:09:55 on February 14, 2016 · (Permalink)
Just dump a bucket over the top of it. Covered with frosting.
Electrodynamatrix · 1 points · Posted at 07:49:23 on February 14, 2016 · (Permalink)
That's the analogy that made me finally get it! Well done
Gonnaragretthis · 1 points · Posted at 07:55:55 on February 14, 2016 · (Permalink)
This made it click for me! Thanks!
skryb · 1 points · Posted at 08:09:43 on February 14, 2016 · (Permalink)
mathematicians prefer pie
steveryans2 · 1 points · Posted at 08:21:17 on February 14, 2016 · (Permalink)
Now I just want cake...
ArkiusAzure · 1 points · Posted at 08:23:41 on February 14, 2016 · (Permalink)
Vsauce here, what is cake?
F54280 · 1 points · Posted at 09:23:01 on February 14, 2016 · (Permalink)
Help, I am stuck at this part!
ThugLife_ · 1 points · Posted at 09:30:56 on February 14, 2016 · (Permalink)
And to get an infinite amount of frosting you could just make the frosting into a solid, then cut that an infinite amount of times. Then bam! Infinite frosting. Right?
Irregulator101 · 1 points · Posted at 09:45:48 on February 14, 2016 · (Permalink)
This still doesn't make sense to me. "After an infinite amount of time" is impossible...?
ivylicious · 1 points · Posted at 10:01:25 on February 14, 2016 · (Permalink)
"After infinite"
SquareBottle · 1 points · Posted at 10:23:33 on February 14, 2016 · (Permalink)
In philosophy, there's a debate in which one side argues that math is best understood as a construct while the other argues that it is best understood as a discovery. I think you just convinced me that both are wrong. Math isn't invented, nor is it observed. It's not passive in either way! It's a proactive thing that's here only to mess with us. :P
Mistbeutel · 1 points · Posted at 11:09:15 on February 14, 2016 · (Permalink)
Citation needed. The physical universe has physical properties that prevent this. Eventually you will be splitting atoms, then smaller and smaller particles, but how do you cut a probability function of the tiniest piece of cake in half?
Nuclear_Ace · 1 points · Posted at 11:09:28 on February 14, 2016 · (Permalink)
Thanks, this is the first one I actually understood.
TheSlyPig04 · 1 points · Posted at 11:15:32 on February 14, 2016 · (Permalink)
This is why I hate infinity and by extension math. "After an infinite amount of time"??? Is that not a meaningless statement? After???
aapowers · 1 points · Posted at 11:51:54 on February 14, 2016 · (Permalink)
Wouldn't you eventually get down to the atomic level if you kept halving?
Or is this just a thought experiment to express a mathematical concepts?
GrammatonYHWH · 2 points · Posted at 13:17:25 on February 14, 2016 · (Permalink)
Yup, just a thought experiment. Most math paradoxes break down under common sense scrutiny
willezz · 1 points · Posted at 11:55:06 on February 14, 2016 · (Permalink)
I still don't get it :(
MechanicalPotato · 1 points · Posted at 12:21:54 on February 14, 2016 · (Permalink)
This is basicaly Xenos paradox, isn't it? The one with achilles and the tortoise.
aaa27070 · 1 points · Posted at 12:42:47 on February 14, 2016 · (Permalink)
gg supertasks
Crank2047 · 1 points · Posted at 13:06:14 on February 14, 2016 · (Permalink)
Beautiful
JakkuScavenger · 1 points · Posted at 13:17:26 on February 14, 2016 · (Permalink)
You need an infinitely thin knife to do that though!
[deleted] · 1 points · Posted at 13:46:20 on February 14, 2016 · (Permalink)
Wait, why do you have a "finite" amount of cake, if the half can be cut infinitely?
Attempt12 · 1 points · Posted at 14:16:53 on February 14, 2016 · (Permalink)
Should've frosted it before you started cutting then ?
buenotaco55 · 1 points · Posted at 14:17:59 on February 14, 2016 · (Permalink)
I don't think this is true.
You only need finitely many frostings because the original cake (which needs the same frosting as the cut up cake!) needs only finitely many frostings.
InsuredByBeretta · 1 points · Posted at 14:24:01 on February 14, 2016 · (Permalink)
In that same line of thinking, why could you not just do the same to the frosting. In theory, keep dividing a finite amount of frosting up by half - an infinite amount of times?
triffid_boy · 1 points · Posted at 14:27:07 on February 14, 2016 · (Permalink)
Then some smart arse comes along and says that you can only cut the cake slivers to approximately atom width. So there are a finite number of slices.
Jopomo · 1 points · Posted at 14:46:54 on February 14, 2016 · (Permalink)
Ultimately though it's all theoretical. You can't cut a cake that way in reality, a cake has probably never been cut perfectly in half. There is no infinite elastic sheet, there is no curve of y=1/x because the material to make up that curve is never going to be perfect.
Just like the notion of a perfect circle or square, it's an interesting and occasionally useful concept in mathematics, it's theoretically a shape, but it isn't real. If it seems difficult to get your mind around, just know that it's probably because it can't actually exist. That's the way of thinking I prefer.
poncho531 · 1 points · Posted at 14:49:25 on February 14, 2016 · (Permalink)
And as always
Thanks for watching
awhaling · 1 points · Posted at 15:22:40 on February 14, 2016 · (Permalink)
This is the only one that has made sense to me
thevoiceless · 1 points · Posted at 19:54:27 on February 14, 2016 · (Permalink)
How does this explain anything? You jumped straight from the example to what it's supposed to show without giving any explanation in-between...If you're cutting a cake into slices, each slice still has a finite surface area, right?
GrammatonYHWH · 1 points · Posted at 05:45:11 on February 15, 2016 · (Permalink)
The theory is that you can make an infinite number of slices which each have a finite amount of area. Infinity multiplied by anything is infinity.
thevoiceless · 1 points · Posted at 06:02:17 on February 15, 2016 · (Permalink)
Aaaand now I feel stupid
Thanks :)
blippyz · 1 points · Posted at 19:59:49 on February 16, 2016 · (Permalink)
I understood it before reading your cake analogy but now it just made it more confusing. So you've taken something finite (amount of frosting needed) and somehow transformed it into something infinite. You've also taken 100% (amount of frosting covering the cake) and transformed it into less than 100% (same amount of frosting no longer covers all the infinite slices) without taking any of it away. I feel like this is just word play now and doesn't actually show anything.
VacuouslyUntrue · 1 points · Posted at 08:05:09 on February 14, 2016 · (Permalink)
This kind of maths works because mathematical objects are infinitely divisible. Since real objects are made from finitely many smaller indivisiable objects, atoms, chemicals whatever, you can't actually perform these operations on them. That's not even mentioning that it would take an infinite amount of time to do so, even if you could.
I don't really like these real world analogies. People can understand cutting up a chodelike cylinder, and covering it in some kind of theoretical paint.
SKYHIGH800 · 1 points · Posted at 06:59:18 on February 14, 2016 · (Permalink)
But you can't keep cutting a cake infinitely many times...
Doom-Slayer · 3 points · Posted at 07:15:37 on February 14, 2016 · (Permalink)
"In theory"
The idea is you can keep making the surface area bigger and bigger and bigger as long as you want by slicing more cake, but the starting amount of cake remains the same.
snowfaller · 1 points · Posted at 11:43:08 on February 14, 2016 · (Permalink)
This doesn't have to be too large to paint, it's more that it's too small at the one end to create on even an atomic scale let alone paint. I'm not so certain the surface area can be infinite, you'd hit a theoretical microscopic limit. If you keep dividing by x you never get to zero. Is that really infinite?
hypervelocityvomit · 1 points · Posted at 08:32:32 on February 15, 2016 · (Permalink)
Gabriel's horn (GH) has infinite area. Let's construct a smaller horn which is still infinite:
The first length unit of GH has more surface area than a simple tube of length 1, diameter 1/2; Proof: its minimum diameter is 1/2, so its surface area must be greater.
The 2nd length unit of GH has more surface area than a simple tube of length 1, diameter 1/3; proof is the same with 1/3. Etc, etc.
Adding these, you get a surface of 1/2 + 1/3 + 1/4 + 1/5 +..., a sum of infinitely many fractions, and you know that GH has more surface area than pi times that sum. That reduces our question to the following:
"Does the sum 1/2 + 1/3 + 1/4 + 1/5 +... grow towards infinity?"
It does. Let's make this sum smaller and prove that it's still infinite:
(We're putting larger numbers in the denominators, the smallest power of two that's >= the old denominator. The individual fractions didn't increase, so the >= relation holds.)
But the latter sum is:
There are infinitely many powers of two, so that sum grows without limit.
If you tried the same trick with the volume of GH, you would end up with some sum like 1/2 + 1/4 + 1/8 + ... which would be finite.
snowfaller · 1 points · Posted at 12:37:34 on February 15, 2016 · (Permalink)
Ah thanks I understand it now. I was thinking of reductions in size, which leads to misunderstanding but you can see a problem there. How are you gonna paint the very tip of the horn? Pretty hard considering you can't see where it ends. You could grab some spray paint and say it lies within an area but that's about it.
hypervelocityvomit · 1 points · Posted at 14:05:22 on February 15, 2016 · (Permalink)
The "tip" is infinitely far away, so when it comes to practical issues, you can't even get to the tip.
The underlying mathematical problem is even worse because of the finite area. (Although a clever mathematician could say "give me a transparent horn and I'll paint its inside by filling it and then I'll let the paint dry", there would still be one issue: the layer of paint would be extremely thin at most places.)
snowfaller · 2 points · Posted at 16:41:51 on February 15, 2016 · (Permalink)
There is the practical issue of the tip getting past atom thin very quickly. There's a whole other theoretical issue that none of the atoms are where we think they are and they're moving at all times. We could get pretty close by bringing it to near absolute zero and using carbon atoms. We can't 3D print carbon atoms anyway it's a tricky scenario. Then what do you do when you get past that? We don't even understand how the quantum world works, let alone how to control or make it work with physics in our current understanding.
If we knew the entirety of what there was to know about physics, who knows. Maybe it would still be a mind bending problem pushing the limits of our minds and philosophy.
singham · 1 points · Posted at 14:08:29 on February 14, 2016 · (Permalink)
It is not as obvious as you make out to be. The integrals are where the magic happens. If you slightly increase the exponents, the volume too becomes infinite.
shabinka · -2 points · Posted at 06:02:30 on February 14, 2016 · (Permalink)
I'm not sure why its mind boggling, as you get towards large x the value is practically 0, but it still exists so you have surface area but no contribution to volume. Its kind of like looking at a step function.
PrimalPower · 5 points · Posted at 06:22:29 on February 14, 2016 · (Permalink)
It's mind boggling because it's one of those things that is true to mathematics but probably breaks some form of physical reality.
shabinka · 1 points · Posted at 06:50:37 on February 14, 2016 · (Permalink)
But why. Something seems like a flag line. Acts like a flat line, and you're surprised. Its like having a step function that goes to zero at say 5, goes on to infinity. This has a finite volume but has infinite surface area.
[deleted] · 1 points · Posted at 06:40:33 on February 14, 2016 · (Permalink)
[deleted]
PrimalPower · 1 points · Posted at 06:44:24 on February 14, 2016 · (Permalink)
Just the concept of surface area changes to something different at some point.
shabinka · 1 points · Posted at 06:52:10 on February 14, 2016 · (Permalink)
This makes sense as you bring thing out to infinity. You have a number that looks like zero, but you keep stretching things out.
UlyssesSKrunk · 2 points · Posted at 06:32:43 on February 14, 2016 · (Permalink)
What you're ignoring is that as X gets bigger the area also approaches 0.
shabinka · 1 points · Posted at 06:43:21 on February 14, 2016 · (Permalink)
That is literally the words that I wrote..............
FolkSong · -1 points · Posted at 07:01:44 on February 14, 2016 · (Permalink)
It's mind boggling because if you imagine a container filled with paint, the idea that you couldn't paint the surface makes no sense.
But the answer is that the container becomes so shallow as you move away from the center that the depth is less than the thickness of a coat of paint, and eventually less than the thickness of an atom.
shabinka · -2 points · Posted at 07:49:20 on February 14, 2016 · (Permalink)
Before you downvote me like an idiot. Look at surf area. Surface area depends on length.
FolkSong · 0 points · Posted at 15:58:44 on February 14, 2016 · (Permalink)
I didn't downvote you jackass
[deleted] · -1 points · Posted at 07:08:27 on February 14, 2016 · (Permalink)
It's not that mind boggling. There are infinite numbers between 1 and 2. None of those numbers are 3.
Bobius · 3 points · Posted at 07:58:21 on February 14, 2016 · (Permalink)
You clearly don't understand what he means by infinite here.
Pick a number - as big as you like. It's more than that.
And no matter what number you pick, the surface area will always be bigger.
SadGhoster87 · 0 points · Posted at 07:09:22 on February 14, 2016 · (Permalink)
No, it would enclose an infinite volume.
Bobius · 2 points · Posted at 07:59:08 on February 14, 2016 · (Permalink)
The integral of pi times 1/x2 is finite. So no, it isn't.
donquixote1991 · 31 points · Posted at 04:24:15 on February 14, 2016 · (Permalink)
I just had a flashback to Calc II in community college. Thanks!
rock217 · 20 points · Posted at 05:56:57 on February 14, 2016 · (Permalink)
So, what, we're just screwing around then?
[deleted] · 14 points · Posted at 06:20:48 on February 14, 2016 · (Permalink)
Lots of math looks this way from the outside. Take imaginary numbers as a simple example.
Say you have an apple. With the apple, you can cut it into pieces (rational numbers), or owe two apples to me (so you have -1 apples total, giving us negative numbers), or have no apples (sad day). But, can you have i apples? (i being the square root of negative one) Of course not! i is imaginary! So why mess with i? It doesn't apply to my apples! To your apples, complex numbers are nothing more than a mathematical concept that just doesn't apply, but they are huge in electrical engineering.
So, yes. Gabriel's Horn (and other discoveries in math) might make many people say, "why does this matter?", but maybe it is like the complex numbers to electrical numbers: just a concept looking for its apples. (:
[deleted] · 13 points · Posted at 06:59:41 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 2 points · Posted at 08:00:09 on February 14, 2016 · (Permalink)*
How can two circles not intersect but intersect at the same time at imaginary points? Where are those imaginary points? Before you answer you should know I study engineering ( and I've taken the electrical systems class already ) so I know what complex numbers are and all that but I can't understand this and it is also driving me nuts. Where are the imaginary points of intersection of two circles that don't intersect???? My mental picture right now is two circles seen from the sides ( so you only see two lines ), not intersecting ( the lines don't touch each other) and also a point above or under the circles which you can a point at which they intersect. Is that what complex numbers mean? If yes then this doesn't make any fucking sense. If yes, then I would suggest not calling them point at which the circles intersect because they don't intersect. I would just call it a solution to a problem.
Turtle_78 · 2 points · Posted at 12:57:22 on February 14, 2016 · (Permalink)
I think the previous comment is imagining two circles flat on a 2 dimensional plane rather than circles rotated at some angle to that plane. The description of intersection would seem to correspond to the solution of some quadratic equation, yes.
No, they do not physically intersect. Maybe they intersect in the complex plane?
I suppose another solution would be that the circles intersect at all points, but that probably brings the question of whether or not they can be distinguished as separate objects, to which I would expect the answer would be that mathematically they cannot.
I might have some of this stuff wrong, so anyone is free to correct me if I do.
Synophmn · 1 points · Posted at 14:58:26 on February 14, 2016 · (Permalink)
Maybe not. As far as my understanding of the size of the universe goes, I'd say it's a place with an infinite surface area that contains only a finite volume.
joshthewaster · 7 points · Posted at 03:12:57 on February 14, 2016 · (Permalink)
Came looking for this. Didn't actually know it was named either so thanks.
alko100 · 5 points · Posted at 04:03:13 on February 14, 2016 · (Permalink)
At what point does the the interior close to not let in any more paint?
If you zoom in, shouldn't there still be a continuous tunnel to the end?
hijomaffections · 15 points · Posted at 04:24:43 on February 14, 2016 · (Permalink)
The tunnel closes too quickly.
It's like the series 1 + 1/2 + 1/4 ... which gives you 2 but for which there are infinite terms.
If that is in units of beers (like the joke), you would need infinite cups to pour out those volumes but only 2 beers worth to fill out the order
iamerror87 · 1 points · Posted at 06:27:34 on February 14, 2016 · (Permalink)
Maybe I'm totally missing the theroy here but I suck at math.
But doesn't 1+1/2+1/4 equal 1 and 3/4?
420dankmemes1337 · 2 points · Posted at 06:30:40 on February 14, 2016 · (Permalink)
He meant it continues on
+1/8+1/16 and so on
iamerror87 · 1 points · Posted at 06:38:19 on February 14, 2016 · (Permalink)
Oh my bad. I'm really bad at math lol.
[deleted] · 2 points · Posted at 07:45:14 on February 14, 2016 · (Permalink)
You don't seem bad at math, you seem "bad" at not knowing what ... means but you wouldn't consider yourself bad at English for not knowing what anfractuous means right? :)
iamerror87 · 1 points · Posted at 21:22:00 on February 14, 2016 · (Permalink)
I'll admit I was under the influence last night so I may have missed the "...". I just read where he stated the equation and then said " you end up with 2" and it didn't compute in my drunken head.
I am pretty bad with math though but I'm slowly getting better at it. I'm 28 so long past school days, but I could never grasp it in school.
[deleted] · 0 points · Posted at 06:04:48 on February 14, 2016 · (Permalink)*
That sounds stupid: You can just take two cups ( and even one ) to pour out the total volume. You can take any series of infinite numbers and say "you need infinite cups to pour out the infinite volumes". It's a redundancy. Why are you surprised that you need infinite cups to pour out infinite volumes?
I'm not a native English speaker so maybe I'm not getting an implied meaning in the pour out /fill the order analogy but I think I got it.
datarancher · 3 points · Posted at 06:42:46 on February 14, 2016 · (Permalink)
He's referring to a joke. A group of n mathematicians walk into a bar. "What'll you have?", asks the bartender. The first mathematician says "A beer please." The second one approaches the bar, but orders a half pint instead. Before he can fetch their orders, the third requests a quarter pint and a fourth demands an eighth. The annoyed bartender grumbles, pours out two pints, and says "that should serve all of you."
[deleted] · 1 points · Posted at 07:53:40 on February 14, 2016 · (Permalink)
Thanks! I'm gonna put it a different way: If the cone can be filled with paint, it can be painted because the paint filling the cone paints the walls therefore painting the cone.
One could divide the cone into infinite pieces and try to paint them all, but saying those infinite pieces can't be painted is not true ( explanation above ).
ScrewAttackThis · 0 points · Posted at 06:21:05 on February 14, 2016 · (Permalink)
If I remember correctly, it takes pi amount of something to fill, or something like that. Maybe it's not pi but another irrational number. It's a finite number but cannot be represented exactly in the real world (well Gabriel's horn can't exist in the real world).
Gabriel's horn fucked with my head until I realized that.
kgottfri · 4 points · Posted at 03:32:49 on February 14, 2016 · (Permalink)
This is essentially my understanding of how the space of the universe is defined
Camellia_sinensis · 10 points · Posted at 05:47:18 on February 14, 2016 · (Permalink)
Bro, that's a vuvuzela.
probablymade_thatup · 5 points · Posted at 23:24:48 on February 14, 2016 · (Permalink)
Which is mathematically different. A vuvuzela has finite surface area, but infinite volume
Camellia_sinensis · 3 points · Posted at 23:28:49 on February 14, 2016 · (Permalink)
Ohhhhhh, this one is good.
thentherewerefour · 2 points · Posted at 23:41:22 on February 14, 2016 · (Permalink)
oh! too clever by half.
great pun.
ythl · 5 points · Posted at 04:51:26 on February 14, 2016 · (Permalink)
Well, half of it would be painted (the inside half)
fuckallkindsofducks · 5 points · Posted at 05:27:13 on February 14, 2016 · (Permalink)
Now... Assume that the horn is very very very thin. So thin that the inner surface area is almost the same as the outer. Now the amount of paint required to paint the outside then is no more than twice the amount of paint required to fill (and paint) the inside.
This seems to make sense but there's something probably wrong... Anyone who knows?
almightySapling · 3 points · Posted at 06:08:18 on February 14, 2016 · (Permalink)
Or, worded slightly differently, if Gabriel's horn is made of paper, and I fill it with paint, would the paint not bleed through and thus coat the exterior?
This is why I don't do applied math. Reality is always getting in the way and fucking shit up.
[deleted] · 1 points · Posted at 16:25:36 on February 14, 2016 · (Permalink)
eventually the tube of paper is so tight that paint can't get through
n1c0_ds · 1 points · Posted at 06:12:22 on February 14, 2016 · (Permalink)
Welcome to engineering
[deleted] · 2 points · Posted at 14:54:21 on February 14, 2016 · (Permalink)
What would happen if I were to fully submerge it in a bucket of paint?
18BPL · 2 points · Posted at 19:29:44 on February 14, 2016 · (Permalink)
You would need an infinitely deep bucket of paint
[deleted] · 3 points · Posted at 19:31:57 on February 14, 2016 · (Permalink)
2deep4me
MuttyMo · 2 points · Posted at 17:58:32 on February 14, 2016 · (Permalink)*
How dare you make a clever analogy that helps explain a wildly abstract concept but is also subject to distinction when you take the analogy way too fucking literally? How dare you?
For real good analogy. I'm a 40 year old lawyer who needs an online conversion tool to calculate percentages, and this made sense to me!
CookieTheSlayer · 3 points · Posted at 05:24:54 on February 14, 2016 · (Permalink)
Oh wow I proved that in my high school math class yesterday. The question never told me the name of the solid though :/
Edit: not yesterday, I meant on Friday
psycho-logical · 2 points · Posted at 04:39:05 on February 14, 2016 · (Permalink)
As a Gabriel, guess I know what I'm naming my penis!
NedryOS · 12 points · Posted at 05:38:36 on February 14, 2016 · (Permalink)
Interesting surface area, disappointing volume.
[deleted] · 1 points · Posted at 05:18:55 on February 14, 2016 · (Permalink)
[deleted]
ptgkbgte · 1 points · Posted at 05:52:22 on February 14, 2016 · (Permalink)
I named mine Optimus Prime.
EWSTW · 1 points · Posted at 06:13:49 on February 14, 2016 · (Permalink)
Black hole kinda thing maybe?
Rickwh · 1 points · Posted at 06:23:46 on February 14, 2016 · (Permalink)
What about the reverse (inside) side of the cone, if the area inside is finite, then must the inside layer of such a theoretical cone, be finite?
trigger-gnamatree · 1 points · Posted at 06:24:26 on February 14, 2016 · (Permalink)
If and only if
squirreltalk · 1 points · Posted at 06:27:03 on February 14, 2016 · (Permalink)
I got to wondering if fractals might have the same pattern -- finite area contained within infinite perimeter -- and it turns out that they can!
https://en.wikipedia.org/wiki/Koch_snowflake
SpiritF · 1 points · Posted at 06:34:42 on February 14, 2016 · (Permalink)
doot doot
SamSlate · 1 points · Posted at 07:00:24 on February 14, 2016 · (Permalink)
Why don't you just dip a full one in another horn?
RabiesTingles · 1 points · Posted at 07:01:36 on February 14, 2016 · (Permalink)
I wish I could upvote a Wikipedia article. That thing was concise, informative, fun to read, and not overly technical.
[deleted] · 1 points · Posted at 07:50:16 on February 14, 2016 · (Permalink)
I'm sorry but if it can be filled with paint, it can be painted because the paint filling the cone paints the walls therefore painting the cone.
chato94 · 1 points · Posted at 07:53:34 on February 14, 2016 · (Permalink)
Michael Stevens from vsauce recently made a video that explains this more intuitively (can't link on mobile right now). Basically, another way to understand this is to imagine a cube, and then slice that cube vertically into equal parts, and then stack those parts on top of one another on their smallest face.
By cutting those initial slices as thin as you want, you can have as many squares as you want (which means that your delicate stack of faces can get as tall as you want). The surface area tends toward infinity as slices get infinitesimally thin, but when you get each block glue it back together (you're gonna need quite a lot of glue), you get the original cube with a finite volume.
sluuuurp · 1 points · Posted at 08:06:27 on February 14, 2016 · (Permalink)
Well since we're obviously allowing idealized infinite objects and paints in this thought experiment, it could be painted because a finite volume of paint could cover an infinite area.
sephrinx · 1 points · Posted at 08:13:08 on February 14, 2016 · (Permalink)
What if you dropped it into a big bucket of paint equal to its volume +1?
CBtheDB · 1 points · Posted at 08:24:04 on February 14, 2016 · (Permalink)
What if you picked it up and dropped it in a pool of paint? What would happen then?
kingfrito_5005 · 1 points · Posted at 08:25:30 on February 14, 2016 · (Permalink)
Ah the first day of Calc I, that was a fun class honestly.
tburn1 · 1 points · Posted at 08:28:32 on February 14, 2016 · (Permalink)
This approach made it understandable for me:
"A perhaps more convincing approach is to treat the horn as a stack of disks with diminishing radii. As their shape is identical, one is tempted to calculate just the sum of radii, which produces the harmonic series that goes to infinity. A more careful consideration shows that one should calculate the sum of their squares. Every disk has a radius r=1/x and an area π·r2 or π/x2. The series 1/x diverges but 1/x2 converges. In general, for any real ε>0, 1/x1+ε converges."
everfalling · 1 points · Posted at 08:37:10 on February 14, 2016 · (Permalink)
just throw the damn thing in a bucket of paint.
TwelveTrains · 1 points · Posted at 08:37:22 on February 14, 2016 · (Permalink)
Gross, a mobile link...
[deleted] · 1 points · Posted at 09:17:55 on February 14, 2016 · (Permalink)
That was my goto
adequateatbestt · 1 points · Posted at 09:20:53 on February 14, 2016 · (Permalink)
I hate you for this.
butthankyou
[deleted] · 1 points · Posted at 09:45:49 on February 14, 2016 · (Permalink)
i hate it when mathematicians do this.
physical constraints mean that in fact it can also be painted. paint is not some concept that is infinitely thin, and a horn like that will at one point be too thin to allow paint in between, meaning that at that point it WILL be painted.
in other words, the only reason the surface area is "infinite", is due to sloppy boundary conditions picked by someone who would probably paint themselves into a corner in real life.
HaagenBudzs · 1 points · Posted at 09:54:05 on February 14, 2016 · (Permalink)
Hey, I just saw this in calculus 2. You are actually wrong. This is called a false paradox because it seems that an infinite surface area can't be painted by a finite amount of paint, but it can. However this is purely theoretical. You can paint an infinite surface with every finite amount of paint as long as the layer of paint will be small enough. But yeah I guess you can also argue that the layer would actually almost equal zero in thickness, but this would only keep you from saying the surface is painted in practice, not theoretically. I'm sorry for my mathematical English, it's hard you know...
[deleted] · 1 points · Posted at 10:11:48 on February 14, 2016 · (Permalink)
Isn't that a contradiction, filling with paint/painting are similar functions. To fill with paint is to paint it?
dengseng · 1 points · Posted at 10:26:28 on February 14, 2016 · (Permalink)
I had an assignment question to explain this topic just recently, I was mind boggled because the more I tried to explain, the more paradoxical it seemed, in the end my teacher didn't mark it at all because shit looks like a thesis paper on paint without limit of how small its size can be
Slacker5001 · 1 points · Posted at 10:58:27 on February 14, 2016 · (Permalink)
Maybe I'm incorrect but I assisted a calc class last semester, more or less did the job of a TA without the grading or the grad student status. And this was a challenge problem on a project they had. But the professor at the time explained it to me like "Imagine you used thinner and thinner coats of paint." In essence, since volume is in units cubed and surface area in units squared, there is no proper way to compare them like that. You could technically paint it with a finite volume of paint if you spread it to infinitely thin coats. At least that was my understanding at the time. I wouldn't even begin to know how to show this rigorously.
Plasma_000 · 1 points · Posted at 11:05:49 on February 14, 2016 · (Permalink)
A similar property can also be formed with recursive fractals
GreySummer · 1 points · Posted at 11:15:37 on February 14, 2016 · (Permalink)
Neatly put.
[deleted] · 1 points · Posted at 11:30:14 on February 14, 2016 · (Permalink)
Isn't that surface/volume thing also true for 3d fractals?
NAN001 · 1 points · Posted at 11:42:30 on February 14, 2016 · (Permalink)
Problem solved.
CyborgSlunk · 1 points · Posted at 11:56:40 on February 14, 2016 · (Permalink)
Vsauce has a whole video about this stuff.
_nil_ · 1 points · Posted at 13:05:00 on February 14, 2016 · (Permalink)
I will never look at Dr Who the same again.
[deleted] · 1 points · Posted at 13:18:32 on February 14, 2016 · (Permalink)
Which is odd... since filling it with paint should do half of the work already.
eaglessoar · 1 points · Posted at 13:33:44 on February 14, 2016 · (Permalink)
Maybe you can help me with this because I've always questioned that notion. So obviously this is all hypothetical. Take a Gabriel's horn of max radius two, fill it with paint, put a Gabriel's horn of max radius 1 inside the other horn which is filled with paint, wouldn't the smaller horn be coated on its exterior?
kbtrpm · 1 points · Posted at 13:54:46 on February 14, 2016 · (Permalink)
This is not as contradictory as it seems. The volume is finite, but you cannot fill it. Suppose the horn is pointing up and you are pouring in the paint in the center. As the horn fills up, it will take longer and longer for the paint to flow towards the edges. You will have quickly emptied your can with the right amount of paint, but it would take infinitely long for the paint to even out. In fact, the horn is so shallow at the top, that filling the last bit amounts to painting it.
LudoRochambo · 1 points · Posted at 14:26:10 on February 14, 2016 · (Permalink)
for anyone that will look, area is a squared measure and volume is cubic. so you find the edge case of when the volume, being cubed gets smaller fast enough compared to area. since n3 > n2 when numbers are bigger than 1, its opposite when numbers are smaller than 1. so the smaller the numbers, the volume gets EVEN smaller. thus you can get the sum of volume bits to converge while the sum of area bits to not converge. the horn is just one of the examples of functions at this edge case.
exactly with that reasoning you can deduce that since perimeter is linear (power 1) and area is squared (power 2) you can get infinite perimeter and finite area at some edge case. one example is the Koch Curve.
SwankyCletus · 1 points · Posted at 18:14:32 on February 14, 2016 · (Permalink)
Damnit cane here to say this. It boggles the mind
thehighschoolgeek · 1 points · Posted at 18:20:15 on February 14, 2016 · (Permalink)
https://www.youtube.com/watch?v=ffUnNaQTfZE You've got to see this!
thentherewerefour · 1 points · Posted at 23:39:14 on February 14, 2016 · (Permalink)
It took me a while, but after some reading I realized you can explain this as being very like a cone with an infinitely long tip at the narrow end.
You could approximate it visually as a cone with a line joined to the tip if that helps, then just smooth it out in your imagination and keep in mind that the "line" is actually an ever thinning cone reaching off asymptotically towards the horizon (the x-axis).
The final thing to realize is that the volume inside the cone converges to a finite quantity because as you progress downwards into it, its getting smaller so much faster than it is getting farther away from the part of the cone that has the bulk of the real holding capacity.
lowdownporto · 1 points · Posted at 05:49:27 on February 15, 2016 · (Permalink)
this is also one of my favorite mathematical paradoxes. You could fill it with paint, which would cover the full surface area on the inside, but painting the surface area would take an infinite amount of paint.
Broan13 · 1 points · Posted at 05:33:31 on February 14, 2016 · (Permalink)
I remember randomly noticing something like this when teaching Calc 3 at our high school.
"Oh look! It is an infinite shape with a specific middle location...that's odd."
[deleted] · -1 points · Posted at 05:55:23 on February 14, 2016 · (Permalink)
It can be painted: there's a value of x at which the circumference is so small that you can't even see it therefore you stop painting there. But you could use machines... There's a value of x at which the circumference is smaller than the smallest form of paint used and you would have to stop there. Yes, I am an engineering student :)
ClemDev · 0 points · Posted at 06:08:21 on February 14, 2016 · (Permalink)
Well duh, It's an imaginary shape. You could just say, all shapes that are impossible to create, are impossible to paint.
Exaskryz · 720 points · Posted at 02:22:03 on February 14, 2016 · (Permalink)
Learned this most recently from Matt Parker:
3435 is the only number (besides 1) where if you split each digit up, raise each digit to that digit's power, and sum all of those products, you get the same number back.
33 + 44 + 33 + 55 = 3435.
TrikkyMakk · 44 points · Posted at 05:14:46 on February 14, 2016 · (Permalink)
No more after that into infinity?
Exaskryz · 48 points · Posted at 05:28:05 on February 14, 2016 · (Permalink)*
Nope.
I don't know what the proof is, but a topic I would explore is the rate at which a number grows compared to its maximum value by adding digits. 99 is n digits long. You could only add up to 99 by adding another digit 9 onto the candidate number. So if the candidate number is already so much larger than a string of n 9's, the value of the candidate number grows faster than the sum of the products of each digit raised to itself.
With some numbers, it's impossible for 999,999,999,999 to sum up to itself because 12 * 99 = 4,649,045,868 -- oh so much smaller. Adding another 9 digit onto that number (adding a value of 9 trillion) to that parent number isn't going to make the child number even come close to the parent number.
99 is 387,420,489, so some upper bound is probably only 10 digits long. At that point, you'd get a maximum sum from 9,999,999,999 which is 3,874,204,890.
(There is a quirk with a nine digit number where if you allow for 00=0, the property works. But 00=1, so that number loses the property.)
Edit: Here's the video I learned of it in: https://www.youtube.com/watch?v=wt5cRQY8F30. Matt shows the nine-digit number.
Edit 2: Here's a video featuring Matt that shows the argument for 00=1. https://youtu.be/BRRolKTlF6Q?t=401 As well as other problems with zero.
silverdevilboy · 11 points · Posted at 12:04:11 on February 14, 2016 · (Permalink)
The video itself explains why 00 is NOT 1. It's not a defined number, it might be a removable singularity but that depends on the function.
halfajack · 2 points · Posted at 20:01:15 on February 14, 2016 · (Permalink)
If it is defined (and it is often useful for it to be) it is generally defined to be 1.
silverdevilboy · 2 points · Posted at 20:48:42 on February 14, 2016 · (Permalink)
No, it is defined based on the function it is an undefined point of. For any function which has an undefined value, it is assigned a value in a useful way if the value is equal to the limit of the function when approaching that point. Xx does not have a defined limit on the complex numbers when approaching that point, because it depends on direction. It does on the reals. 0x does, and x0 does, and they are different.
If you assign it a value, it depends entirely on what the function is defined as near 0.
halfajack · 3 points · Posted at 21:25:19 on February 14, 2016 · (Permalink)
You only seem to be considering it from an analytic approach, though. How many functions are there from the empty set to the empty set? There are 00 = 1. How many ways can you choose 0 things when you have 0 things to choose from? 1 = 00 . In analysis, 00 should be left undefined, but in other areas defining 00 = 1 makes perfect sense.
silverdevilboy · 1 points · Posted at 23:44:00 on February 14, 2016 · (Permalink)
Because even in those contexts, the reason you're choosing it is part of analysis.
The number of functions from a set of size n to itself is nn, restricted to n real, so as n goes to 0, its limit is 1.
Choosing 0 from 0 is either choosing n from n, or choosing 0 from n, which is n0 or nn again restricted to reals.
In the majority of cases where 00 is going to be 0, the equivalents in set theory are trivial and uninteresting, being trivially empty over the entire domain, but it is not remotely true in any field to claim that it is sensible to just assume 00 is 1. There are ALWAYS situations where it is just wrong.
narbris · 21 points · Posted at 05:57:33 on February 14, 2016 · (Permalink)
Yep, short answer 2,999,999,999 is the last number where the powers are larger than the number itself, so you can stop looking after that. Side note: this is only special in base 10. Any other base might have their own special numbers like this.
sonicandfffan · 11 points · Posted at 10:20:32 on February 14, 2016 · (Permalink)
Almost true. There's a third number where this works - 438579088 is also a canouchi number
Alo_14 · 25 points · Posted at 10:53:48 on February 14, 2016 · (Permalink)
That only works if you take 00 = 0, which is incorrect
sonicandfffan · 16 points · Posted at 11:06:00 on February 14, 2016 · (Permalink)
Apparently it's common convention in this area of maths to take 00 =0. Not a convention im a huge fan of so I don't disagree with you.
https://oeis.org/A046253
[deleted] · 3 points · Posted at 17:16:40 on February 14, 2016 · (Permalink)
00 =0 in some math? Why?
sonicandfffan · 3 points · Posted at 18:49:25 on February 14, 2016 · (Permalink)
Because lim x->0 of xy = 0
Of course lim y-> 0 gives 1 so xy is indeterminate at (0,0). In certain cases like set theory it is convenient to define it as 1 (think - how many permutations of the empty set are there? There's still one permutation even if the set itself is empty). It's far more common for these cases to be given as examples, hence why people tend to think 00 = 1 (rather than that it's indeterminate). In the case were talking about (PDDI numbers), I assume it's more convenient to take 00 to be defined as 0, although I'm certainly no expert in PDDI numbers (I imagine it's a very niche topic), so I can't say for certain what the experts in this field think about 00.
zazu2006 · 2 points · Posted at 13:29:23 on February 14, 2016 · (Permalink)
This makes me feel like it isn't real math.
googolplexbyte · 6 points · Posted at 14:55:48 on February 14, 2016 · (Permalink)
No math is real math. It all just a language with a set of rules.
[deleted] · 1 points · Posted at 17:22:47 on February 14, 2016 · (Permalink)
Debatable
Alo_14 · 1 points · Posted at 11:19:06 on February 14, 2016 · (Permalink)
Ah hadn't seen anyone do it before, fair enough
kingcowman · 7 points · Posted at 15:28:14 on February 14, 2016 · (Permalink)
And Trey Stone?
Wootery · 3 points · Posted at 12:54:49 on February 14, 2016 · (Permalink)
Is there a similar scarcity of such numbers using a base other than 10?
CoolLikeAFoolinaPool · 3 points · Posted at 15:08:34 on February 14, 2016 · (Permalink)
Kindof similar to narcissistic numbers like 8208. If you raise each number to the power of 4 (number of digits in the number) and add them up you get 8208.
opceryu · 2 points · Posted at 14:38:36 on February 14, 2016 · (Permalink)
I used to do windsurfing and in any sailing sport you need to have a sail number in order to other people (other racers, referees, spectators etc.) to indentify you in the sea since it is hard the see the person's face from such a distance. İnterestingly enough it was my sail number 3435 and also the numbers of most important cities to me.
Spiralofourdiv · 2 points · Posted at 17:15:52 on February 16, 2016 · (Permalink)
A base 10 perfect digit-to-digit invariant!
It's not difficult to proof that there are finitely many of these kinds of numbers in any given base. There are only four PDDIs in the base 10 decimal system, two of them are trivial: 0 and 1.
I actually have 3435 as my phone PIN.
Exaskryz · 1 points · Posted at 17:43:24 on February 16, 2016 · (Permalink)
Awesome wiki link.
I didn't see in that link, if there were, if there are infinitely many Canouchi numbers (besides 0 and 1) due to an infinite number of bases. Any idea if there might be?
Spiralofourdiv · 1 points · Posted at 18:00:00 on February 16, 2016 · (Permalink)*
I think we can prove that ourselves:
The theorem I know states that for any given base there is a finite number of PDDIs. There may be very many in some bases, but usually it's just a handful. Let's collect each PDDI for each base and make it a set, so there is a set for the four base 10 PDDIs, a set for the base 2 PDDIs, for base 3 PDDIs, etc.
As you said, there is a base for every natural number, so there are countably infinite bases. We now have a countably infinite collection of non-empty, finite sets. The union of a countably infinite number of sets all with order >1 must have a countably infinite order.
We can prove this with some more rigor by considering the set of all these sets, let's call it S. So S = {s1, s2, s3, ... , sn} where sn is the set of PDDIs of base n. Create a bijection from each element in S to an element in the natural numbers. This is clearly a bijection because a set of PDDIs exists for every natural number (i.e. every base). Therefore, S is countably infinite (it can be put in a one to one correspondence with the natural numbers). Lastly, each element s in S is a set with finite and positive order because it's the collection of all the PDDIs for a base. In counting the number of individual PDDIs, we make a new set, let's call it P and it is necessarily true that |P| >= |S| because every s in S contains an element p in P and by definition every p in P is also in some s in S. That last part is really just getting rid of the extra parenthesis/brackets that exist in S when you compare it to P (i.e. S and P are almost the same set, but the elements of S are are sets, the elements of P are numbers; realistically S just has some brackets that organize the PDDIs to correspond with their base, the last bit shows that omitting those brackets cannot make the set smaller).
Ergo, there are at least a countably infinite number of PDDIs if we consider any and all possible bases.
Exaskryz · 2 points · Posted at 18:20:34 on February 16, 2016 · (Permalink)
Edit: My post was created prior to seeing your post about bijections. I have not taken high enough maths to understand that part. Maybe after my law exam I'll try to wrestle with understanding it.
I'm getting lost in this. I can understand the countably infinite following a countably infinite argument. But I don't know where we can say that's applicable here.
I got lost in this because bases 2, 5, and 8 on the Wiki only have one PDDI. This is what I'm questioning - is 2, 5, and 8 the norm, or the exception, or just part of a pattern where every third base only has one PDDI. What I'm interested in is the count of bases with PDDIs besides (0 and) 1.
I guess another perspective to this question is how many numbers are there (infinitely many, or finitely) that can be represented in at least one base as a PDDI? The Wiki lists in base 10 that both 28 and 29 are PDDIs (in base 9 and base 4, respectively). But there seem to be inconsistent gaps between them.
I would also consider the possibility that a number can be a PDDI in multiple bases, and perhaps there are a finite quantity of PDDIs that appear in multiple bases to have the property. Unlikely based on the first nine bases, but I wouldn't rule them out.
This is all coming from being out of a maths class for many years, so I could be overthinking it or going in a totally wrong direction.
Spiralofourdiv · 2 points · Posted at 18:37:38 on February 16, 2016 · (Permalink)*
Ah. Well... if we discount the trivial case, the question becomes much more complex, and we'd have to query a number theorist. Same goes for asking if there are patterns to how many PDDIs a given base has. But if we are counting trivial PDDIS...
I think you are overthinking and I am over explaining.
Basically, there is a base for every number, and there will be a PDDI (or many) for every base, and since natural numbers are countably infinite, there cannot be fewer PDDI's than there are numbers. But each of these PDDI's is distinct in it's own base. 1 is a trivial PDDI for every base, so for example an infinite set of PDDIs could be {1, 1, 1, 1, 1, ...}, where each 1 is the trivial PDDI for a different base.
If we are not counting trivial PDDIs, or we are turning them into base 10 numbers to rid ourselves of overlap before we count, then... hmm. Well, if I had a proof that there is a finite number of bases with only trivial PDDI's, then we could confidently say there are infinitely many non-trivial PDDIs, but I don't know if such proof exists concerning the number of bases with trivial (or non-trivial) PDDIs...
I would hazard a guess that yes, there are an infinite number of bases with non-trivial PDDIs and thus an infinite number of non-trivial PDDIs, and that it can be proven, but I don't have the time (nor perhaps the knowledge) to prove that, and hazarding a guess is not math :-(
Exaskryz · 2 points · Posted at 22:15:23 on February 16, 2016 · (Permalink)
Still appreciate the discussion we had. Thanks for your time!
juanton_soup · 1 points · Posted at 18:00:32 on February 14, 2016 · (Permalink)
This sounds like some random stat of Lebron James just trying to make him sound better.
db0255 · 2 points · Posted at 04:59:15 on February 15, 2016 · (Permalink)
LeBron is the greatest of all time because he has the most assists in the third quarter in games where their team was losing by a prime number for a majority of the game and in which they eventually won on a Tuesday night before a full moon.
So he has that going for him.
martixy · 1 points · Posted at 13:54:37 on February 14, 2016 · (Permalink)
I bet there's other numbers, just not in base10.
Notsoace · 3923 points · Posted at 20:49:04 on February 13, 2016 · (Permalink)
It's impossible to comb all the hairs on a tennis ball in the same direction without creating a cowlick.
weebiloobil · 3023 points · Posted at 20:56:15 on February 13, 2016 · (Permalink)
Amusingly this is called the Hairy Ball Theorem
universal_particles · 4212 points · Posted at 22:16:47 on February 13, 2016 · (Permalink)
This is the best redirect on wikipedia I have ever seen
SlimSlamtheFlimFlam · 1036 points · Posted at 23:46:36 on February 13, 2016 · (Permalink)
We tried to name a civic center after him (was the most popular in a vote) but they decided not to.
The family's changed how they pronounce their last name to "bails," probably out of embarrassment l 😂
Ihavetoleavesoon · 718 points · Posted at 00:17:14 on February 14, 2016 · (Permalink)
The real question is, why did they name their son Harry?
zwich · 562 points · Posted at 01:03:53 on February 14, 2016 · (Permalink)
Yeah! Why not Richard?
BordomBeThyName · 873 points · Posted at 01:37:47 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Richard_Assmann
Literally dickbutt.
i_hardly_knowername · 78 points · Posted at 02:15:53 on February 14, 2016 · (Permalink)
I'm Cosmo Kramer, the Assman!
P-Rickles · 5 points · Posted at 03:53:00 on February 14, 2016 · (Permalink)
Dr. Cosmo Kramer. Proctology.
[deleted] · 5 points · Posted at 12:54:50 on February 14, 2016 · (Permalink)
So....YOURE the assman?
Wink.
----_____---- · 3 points · Posted at 13:53:54 on February 14, 2016 · (Permalink)
Million to one chance, doc...million to one.
Sagarmatra · 15 points · Posted at 02:46:35 on February 14, 2016 · (Permalink)
In Holland, Dick de Kok, rarely but possibly also spelled as Cock, is a name that is seen in the wild every now and then. I never do not giggle.
Taleya · 6 points · Posted at 11:05:01 on February 14, 2016 · (Permalink)
One guy I encountered had the name Luong Kok Chiu
...yes, it was pronounced how you're thinking
kaevondong · 12 points · Posted at 06:37:12 on February 14, 2016 · (Permalink)
Dick Assman
BordomBeThyName · 4 points · Posted at 06:59:47 on February 14, 2016 · (Permalink)*
That one is a lot better. You should be getting all this karma instead of me.
fetusy · 12 points · Posted at 03:45:21 on February 14, 2016 · (Permalink)
Did work for a Richard N. Debutts a few years back. Giggled everytime I saw Dick N. Debutts on paper.
humicroav · 5 points · Posted at 04:14:24 on February 14, 2016 · (Permalink)
That's dickbuttmann
freefrogs · 6 points · Posted at 05:01:49 on February 14, 2016 · (Permalink)
There's also former International Olympic Committee chairman, Dick Pound. Why he couldn't have gone by Richard I have no idea....
Related_TIL · 3 points · Posted at 04:09:11 on February 14, 2016 · (Permalink)
Dickbutt man
ThePantsThief · 2 points · Posted at 06:24:14 on February 14, 2016 · (Permalink)
He's an ass man
dustyramsbottom · 2 points · Posted at 06:36:41 on February 14, 2016 · (Permalink)
My brother's name is Richard... Dick Ramsbottom
PureVegetableOil · 2 points · Posted at 09:02:57 on February 14, 2016 · (Permalink)
Mathematics is amazing.
Just_Kos · 1 points · Posted at 04:07:56 on February 14, 2016 · (Permalink)
He may have been an Assman, but was he an ass man? Or perhaps he was just an ass, man.
Splinter1010 · 1 points · Posted at 08:22:19 on February 14, 2016 · (Permalink)
Dick Buttman actually.
votelikeimhot · 1 points · Posted at 08:37:16 on February 14, 2016 · (Permalink)
He forever altered the way we perceive passing wind?
Guyote_ · 1 points · Posted at 09:04:28 on February 14, 2016 · (Permalink)
I'm the ASSMAN!
Pizzashack · 1 points · Posted at 10:04:52 on February 14, 2016 · (Permalink)
Dick butt man to you.
LordEng1ish · 1 points · Posted at 11:45:35 on February 14, 2016 · (Permalink)
There was some football player named Dick Butkus or something
Blayblee · 1 points · Posted at 12:30:59 on February 14, 2016 · (Permalink)
Mm, not really. It's more like Dick Buttdude.
skelebone · 1 points · Posted at 12:58:13 on February 14, 2016 · (Permalink)
Don't forget the "I got pumped by the Assman" Dick Assman
mariocart · 1 points · Posted at 13:26:13 on February 14, 2016 · (Permalink)
Yer a wizard, dickbutt
NotUrMomsMom · 1 points · Posted at 14:07:04 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Dick_Pound
SkyezOpen · 1 points · Posted at 14:14:13 on February 14, 2016 · (Permalink)
Ironically preferred boobs.
probabilityEngine · 10 points · Posted at 01:37:12 on February 14, 2016 · (Permalink)
With a middle name that starts with N, too.
Reggie_Popadopoulous · 6 points · Posted at 01:59:02 on February 14, 2016 · (Permalink)
That was the most 12 year old laugh I've had all day
"Dick baals lol"
nightwing2024 · 2 points · Posted at 01:36:22 on February 14, 2016 · (Permalink)
Or Cocken
[deleted] · 2 points · Posted at 01:44:27 on February 14, 2016 · (Permalink)
Richard N.
oooleviton · 2 points · Posted at 03:08:25 on February 14, 2016 · (Permalink)
I once met a girl named Crystal Dick. She was 12 years old, so not a married name.
Mirshikar · 1 points · Posted at 01:30:22 on February 14, 2016 · (Permalink)
Shut up, Richard.
jwilcz94 · 1 points · Posted at 02:36:57 on February 14, 2016 · (Permalink)
Middle name 'N'
[deleted] · 1 points · Posted at 02:56:57 on February 14, 2016 · (Permalink)
Or Sandy?
Or Peter?
john_the_quain · 1 points · Posted at 03:27:27 on February 14, 2016 · (Permalink)
Richard Nicholas Baals.
Aminstro · 1 points · Posted at 05:29:24 on February 14, 2016 · (Permalink)
Dick Johnson.
Dick Dick.
wysoaid · 1 points · Posted at 12:41:18 on February 14, 2016 · (Permalink)
Or Dicken
wysoaid · 1 points · Posted at 12:41:59 on February 14, 2016 · (Permalink)
Or Dixon
stoter1 · 1 points · Posted at 13:08:37 on February 14, 2016 · (Permalink)
Why not Zoidberg?
asclepius42 · 1 points · Posted at 21:44:36 on February 14, 2016 · (Permalink)
Richard Nicholas Baals
ChiefDinoRider · 74 points · Posted at 01:09:43 on February 14, 2016 · (Permalink)
I'm guessing his Dad suggested it, and his Mum didn't catch it until it was too late.
Glitch29 · 5 points · Posted at 04:59:16 on February 14, 2016 · (Permalink)
Back then, mom probably had less of a say in it. :-/
Young_Neil_Postman · 2 points · Posted at 07:43:56 on February 14, 2016 · (Permalink)
Just like what happened to Major Major Major Major!
[deleted] · 1 points · Posted at 14:18:29 on February 14, 2016 · (Permalink)
Like that kid Lanesra
hborrgg · 7 points · Posted at 01:26:31 on February 14, 2016 · (Permalink)
According to his wikipedia page it used to be pronounced in a way that didn't sound like "hairy".
paradoxically_cool · 6 points · Posted at 01:04:51 on February 14, 2016 · (Permalink)
probably pronounced like that little English wizard
MeredithofArabia · 5 points · Posted at 01:19:55 on February 14, 2016 · (Permalink)
Draco?
1SweetChuck · 1 points · Posted at 04:14:01 on February 14, 2016 · (Permalink)
There is a family I know with the last name Knauf, where the K is pronounced. They named one of their sons Jack.
Mooosebumps · 1 points · Posted at 05:21:50 on February 14, 2016 · (Permalink)
I have a coworker named Jack Dicks
drone42 · 7 points · Posted at 00:52:48 on February 14, 2016 · (Permalink)
A local radio morning show near where I live used a sound clip from a news report about that every chance they get. It's kind of annoying now.
Leath_Hedger · 3 points · Posted at 01:26:37 on February 14, 2016 · (Permalink)
Hey we all played Diablo 2, we know how it's pronounced.
Satans__Secretary · -3 points · Posted at 04:37:03 on February 14, 2016 · (Permalink)
Fuck that game.
DeefLoL · 3 points · Posted at 01:48:39 on February 14, 2016 · (Permalink)
I remember this. I even voted. At least we have a street named after him haha
kommiesketchie · 2 points · Posted at 04:04:25 on February 14, 2016 · (Permalink)
Relevant
GotHamm · 2 points · Posted at 04:55:28 on February 14, 2016 · (Permalink)
In 5th grade I had a teacher with the last name Ball and I wondered if her brothers name was Harry. We also had a Ms.Butts (she went by Ms.B) and Ms.Cockman
ObeyMyBrain · 1 points · Posted at 08:18:47 on February 14, 2016 · (Permalink)
Heh, I went to Greenfield Jr. High in El Cajon, CA in the late 80's. Our PE coaches were Harry Balls and John Hiscock plus Mrs. Tucker. Apparently after Hiscock retired they hired a guy named Longerbone but that was after my time.
Lady_Luna23 · 2 points · Posted at 05:28:42 on February 14, 2016 · (Permalink)
I voted for this.
I didn't voted in the re-election of Obama. But I voted for the Harry Baals Civic Center.
[deleted] · 1 points · Posted at 03:27:49 on February 14, 2016 · (Permalink)
[deleted]
Satans__Secretary · 1 points · Posted at 04:37:30 on February 14, 2016 · (Permalink)
Baal just means "lord", it "Lord over all that flies".
Flick1981 · 1 points · Posted at 05:10:07 on February 14, 2016 · (Permalink)
My question is why the hell did that city council decide to turn that down? Think of all the tourist dolllars that town missed out on.
Ditto_B · 1 points · Posted at 05:27:54 on February 14, 2016 · (Permalink)
So, you guys decided to scratch Harry Baals off the list?
ch-12 · 1 points · Posted at 06:07:14 on February 14, 2016 · (Permalink)
Baal is the final boss in Diablo 2 expansion.. I always pronounced as "bail".. Would have loved to see the Harry Baals center tho
TacticalTruth · 1 points · Posted at 07:03:07 on February 14, 2016 · (Permalink)
I don't know their history, but 'bails' is what I would have assumed at first.
I'm thinking at some point being named 'Balls" was better than being named after the devil. How times have changed.
romulusnr · 1 points · Posted at 09:32:55 on February 14, 2016 · (Permalink)
"I'ma gonna put theya bails inna sling!"
dementeddr · 1 points · Posted at 19:20:46 on February 26, 2016 · (Permalink)
Yeah, now the get to be named after an ancient pagan god.
BaconSoul · 0 points · Posted at 12:44:39 on February 14, 2016 · (Permalink)
I remember this. Good times. Who am I kidding it's Fort Wayne save me please
[deleted] · 85 points · Posted at 00:59:36 on February 14, 2016 · (Permalink)
My favourite that has since been removed was
itz4mna · 2 points · Posted at 15:52:56 on February 14, 2016 · (Permalink)
C (programming language)
shitting all over your memory redirects to this page
befuchs · 6 points · Posted at 01:17:44 on February 14, 2016 · (Permalink)
We love Harry here in the Fort
calebsfreakingsick · 5 points · Posted at 01:55:37 on February 14, 2016 · (Permalink)
Ayyy shout out to my fellow Fort Wayne residents!
XSymmetryX · 3 points · Posted at 00:31:10 on February 14, 2016 · (Permalink)
Legendary 😂
PetrRabbit · 3 points · Posted at 01:41:19 on February 14, 2016 · (Permalink)
"A hairy doughnut, on the other hand, is quite easily combable."
Ticantundra · 3 points · Posted at 06:12:21 on February 14, 2016 · (Permalink)
we have a road named after him; Harry Baals Dr.
PickThymes · 3 points · Posted at 09:17:53 on February 14, 2016 · (Permalink)
His wife's name was "Minnie Baals". Gold
first_aids_kit · 2 points · Posted at 01:57:45 on February 14, 2016 · (Permalink)
https://www.youtube.com/watch?v=BScrP-lW60E
News report for the uninitiated
Frogblaster77 · 2 points · Posted at 02:39:10 on February 14, 2016 · (Permalink)
If I had gold...
TheSlitheringSerpent · 2 points · Posted at 02:55:25 on February 14, 2016 · (Permalink)
I assume this was recently added to the page by one of the more charismatic members of Reddit, but when checking out Harry Baal's Wikipedia page you can find this beauty:
[deleted] · 2 points · Posted at 02:56:07 on February 14, 2016 · (Permalink)
From the wiki (seriously):
[deleted] · 2 points · Posted at 03:31:18 on February 14, 2016 · (Permalink)
His wife's name was Minnie Baals teehee
hello_dali · 2 points · Posted at 05:41:19 on February 14, 2016 · (Permalink)
Welcome to front-page Fort Wayne! We won't be here again for awhile.
KnivesAndShallots · 1 points · Posted at 03:25:49 on February 14, 2016 · (Permalink)
Also, this is the one and only time I'd ever click on a link to hairy ball one pole animated.gif.
family_with_benefits · 1 points · Posted at 03:53:58 on February 14, 2016 · (Permalink)
I love that this is what my city is known for
rynowiz · 1 points · Posted at 10:37:39 on February 14, 2016 · (Permalink)
Yeah! My hometown mentioned in a thread about math. Makes me happy. Glad hairy balls (or Harry Baals) could make this happen.
droans · 1 points · Posted at 16:54:35 on February 14, 2016 · (Permalink)
To make it better, he was also considered to be one of the best mayors Fort Wayne ever had.
brickmack · 0 points · Posted at 03:54:38 on February 14, 2016 · (Permalink)
Fort Wayne person (Fort Wayner? Fort Waynenite? Dafuq are we called?) here. Theres a road named after him. I always laugh driving by it
StinkyBrittches · 6 points · Posted at 23:46:09 on February 13, 2016 · (Permalink)
Hairy balls require cow licks, check.
relevantusername- · 4 points · Posted at 01:19:41 on February 14, 2016 · (Permalink)
That's honestly a sentence I didn't expect to read today.
MyonicS · 6 points · Posted at 11:26:53 on February 14, 2016 · (Permalink)
In germany we call it the Theorem of the hedgehog, every evenly combed hedgehog has a naked spot.
Fun Fact: A professor of physics proved with this Theorem at a science slam that the city "Bielefeld" does not exist, which is a german urban legend.
GeorgeJung94 · 2 points · Posted at 00:28:53 on February 14, 2016 · (Permalink)
Risky click.
FartingBob · 2 points · Posted at 00:48:20 on February 14, 2016 · (Permalink)
I wasnt expecting to be so utterly lost when reading about something called "hairy ball theorem".
marcopennekamp · 2 points · Posted at 10:07:19 on February 14, 2016 · (Permalink)
/r/nocontext
renoracer · 1 points · Posted at 23:16:18 on February 13, 2016 · (Permalink)
How many people are licking tennis balls for this to be a thing?
Stars-in-the-night · 1 points · Posted at 01:09:25 on February 14, 2016 · (Permalink)
Thank you, now I'm spending my Saturday night reading about hairy balls.
colonelchurro · 1 points · Posted at 03:20:16 on February 14, 2016 · (Permalink)
I understand myself more completely now. Thank you.
[deleted] · 1 points · Posted at 03:34:05 on February 14, 2016 · (Permalink)
Yeah, I'm not gonna click that.
Alderis · 1 points · Posted at 05:14:30 on February 14, 2016 · (Permalink)
Risky click of the day.
crank_bank · 1 points · Posted at 12:56:58 on February 14, 2016 · (Permalink)
paulrulez742 · 1 points · Posted at 14:10:40 on February 14, 2016 · (Permalink)
I haven't had the math classes yet to pretend to comprehend what that means.
posherspantspants · 1 points · Posted at 15:53:37 on February 14, 2016 · (Permalink)
risky click of the day
monkeyman80 · 1 points · Posted at 22:01:20 on February 14, 2016 · (Permalink)
Professor teaching it to us: " it doesn't matter how hairy my balls are.."
ecnednepedni · 1 points · Posted at 03:31:58 on February 18, 2016 · (Permalink)
The YouTube channel "MinutePhysics" made a video on this that is pretty entertaining. Here is the link: https://www.youtube.com/watch?v=B4UGZEjG02s.
tylertime98 · 1 points · Posted at 02:50:54 on March 8, 2016 · (Permalink)
Hehehehehe
0876 · 1264 points · Posted at 22:59:52 on February 13, 2016 · (Permalink)
The interesting implication is that, due to this fact, there will always be at least one cyclone happening on earth at any time.
zarraha · 266 points · Posted at 23:34:22 on February 13, 2016 · (Permalink)
I don't think it applies, because wind speed is of variable strength. You could, theoretically, have all wind on the planet cease for just an instant. Also, you could have winds spinning in a circle at 1 mph, which barely counts as a "cyclone"
NosemaCeranae · 673 points · Posted at 23:55:58 on February 13, 2016 · (Permalink)
From the article.
IntoTheEverblack · 854 points · Posted at 00:26:22 on February 14, 2016 · (Permalink)
I like how the article called him uninteresting before he even commented.
akaioi · 65 points · Posted at 01:14:01 on February 14, 2016 · (Permalink)
I call this a ... priposte
PeterQuincyTaggart · 9 points · Posted at 03:04:33 on February 14, 2016 · (Permalink)
That was A+
prancingElephant · 7 points · Posted at 08:46:26 on February 14, 2016 · (Permalink)
That's preposterous.
akaioi · 1 points · Posted at 18:44:15 on February 14, 2016 · (Permalink)
Will you pretend to prefer my predilections?
[deleted] · 24 points · Posted at 04:27:37 on February 14, 2016 · (Permalink)
"people proposing this scenario are generally uninteresting"
Thetomas · 3 points · Posted at 10:24:05 on February 14, 2016 · (Permalink)
wikiburn!
[deleted] · 11 points · Posted at 02:18:53 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Rekt
wertymanjenson · 1 points · Posted at 09:43:22 on February 14, 2016 · (Permalink)
Well, he didn't even read it.
A_Wizzerd · 1 points · Posted at 13:25:54 on February 14, 2016 · (Permalink)
Ha! I threw that shit before I came in the room!
zarraha · -7 points · Posted at 00:08:13 on February 14, 2016 · (Permalink)
It's unrealistic that everywhere would be zero. But the theorem assumes that it is zero nowhere, that is, there is some wind on every single spot on the planet at all times, which is also unrealistic.
mrmahoganyjimbles · 6 points · Posted at 00:50:06 on February 14, 2016 · (Permalink)
Well, how would we define wind? It's moving air particles. Air would only not be moving at absolute zero, and It's even more unrealistic to assume anywhere would reach absolute zero except for labs, which 1) use carbon, which isn't really an air particle, and 2) tests absolute zero in closed systems that would not affect the wind.
NewbornMuse · 6 points · Posted at 00:51:24 on February 14, 2016 · (Permalink)
I wouldn't consider individual air particles wind. Wind is bulk movement (convection, not diffusion).
zarraha · 1 points · Posted at 01:48:17 on February 14, 2016 · (Permalink)
Well, if we're zooming into the microscopic level then I suppose 10 air molecules circling each other counts under this definition of "cyclone" so the statement is almost trivially true.
ScLi432 · 101 points · Posted at 23:51:04 on February 13, 2016 · (Permalink)
Cyclone meaning some swirling air, not a hurricane
Gryphon0468 · -1 points · Posted at 03:24:30 on February 14, 2016 · (Permalink)
Cyclone is the same thing as a hurricane, just on the western side of the Pacific Ocean.
scharfes_S · 10 points · Posted at 03:36:39 on February 14, 2016 · (Permalink)
That's Typhoon.
Fozzaroo · 9 points · Posted at 04:54:44 on February 14, 2016 · (Permalink)
I think there is a bit of a confusion here. In Oceania (Australia, NZ and the Pacific Islands) Hurricane/Typhoon type of storms are called Tropical Cyclones. Cyclones without the word tropical appended to it means just that, a coil of air mass at any speed rotating around a central point as the original poster above has stated. (Though in the Australian media a lot of people just drop the word tropical due to everyone usually being aware of what they're talking about)
Gryphon0468 · 1 points · Posted at 08:31:10 on February 14, 2016 · (Permalink)
No that's Asia. In Australia they're called Cyclones. Same thing as an American Hurricane.
ScLi432 · 5 points · Posted at 06:30:29 on February 14, 2016 · (Permalink)
I understand that. What I meant was you're interpreting the meaning of the word "cyclone" to mean in a large tropical storm, while in this context the word is being used to describe swirling air.
goerila · 9 points · Posted at 01:42:46 on February 14, 2016 · (Permalink)*
The theorem is working with continuous vector fields. A vector field can have variable "Strength" aka magnitude of the vectors and still be continuous. Clearly the zero wind case is unrealistic because there is always wind somewhere.
For your wind in a circle, wind is continuous, so if you mean a circle as in a circle from our perspective on the ground, then you would have problems with continuity of the velocity of air. Now if you mean a great circle (a circle around the globe) the problem is that as you approach a pole you are going to be having a higher and higher angular velocity in order to keep that 1 mph limit. This will give you a cyclone at the north and south poles.
Edit: Furthermore, you may wonder if the 3 dimensions fuck this up. They don't you could take the average velocity at every height on the globe (a continuous operation) then project that 3 dimensional vector down to two dimensions (another continuous operation). And now you have a perfectly good continuous vector field on the sphere.
raverbashing · 2 points · Posted at 09:30:25 on February 14, 2016 · (Permalink)
They probably mean that there's a point where air speed curl is different than zero (this curl I mean https://en.wikipedia.org/wiki/Curl_(mathematics) )
zarraha · 1 points · Posted at 14:50:56 on February 14, 2016 · (Permalink)
Yeah, that's probably it. Every cyclone has nonzero curl, but I would not consider every point with nonzero curl to be a cyclone.
PM_ME_ANYTHING_UWANT · 2 points · Posted at 01:24:09 on February 14, 2016 · (Permalink)
No you couldn't, wind is caused by convection or the heating of air by the sun, it's about energy and so for as long as the sun exists there will be wind.
LuxDeorum · 1 points · Posted at 01:29:21 on February 14, 2016 · (Permalink)
It doesn't apply. The theorem supplies the existence of singular points. So you could have the wind moving south to north everywhere in the world all the time and just canceling out at the poles (two zero points)
xigdit · 13 points · Posted at 06:56:06 on February 14, 2016 · (Permalink)
This is true but it kind of means the opposite of what you would think it means. It doesn't mean, there's always going to be a storm, it means, there's always going to be an "eye," a place of complete calm. (And the article further elaborates that this only pertains to a given 2-D layer of atmosphere, so in reality there's no assurance that we'd have a canonical cyclone anywhere that goes from sea level up to the clouds)
TwoFiveOnes · 6 points · Posted at 03:42:25 on February 14, 2016 · (Permalink)
Also not sure if it applies because the Earth isn't a mathematical sphere.
TheOldTubaroo · 6 points · Posted at 10:15:13 on February 14, 2016 · (Permalink)
It is a topological sphere, and I believe that is enough here.
TwoFiveOnes · 0 points · Posted at 10:58:31 on February 14, 2016 · (Permalink)*
Really? I thought the theorem was that
SnS2 is nontrivializableparallelizable. This refers to vector fields or the tangent bundle so necessarily to the Cinfty (or Ck) structure of the sphere, right? Or can you define a tangent bundle on topological manifolds so that the theorem is also true?Edit: S2 is non parallelizable, TS2 is non trivializable
TheOldTubaroo · 2 points · Posted at 12:02:34 on February 14, 2016 · (Permalink)
Quoting from the article, "it follows that for any compact regular 2-manifold with non-zero Euler characteristic, any continuous tangent vector field has at least one zero", so it's the topological properties of the sphere that are important, as far as I can see.
TwoFiveOnes · 1 points · Posted at 13:44:27 on February 14, 2016 · (Permalink)
Well yes, but then what does the theorem mean about (only) topological spheres? It's like saying "a paracompact smooth manifold admits partitions of unity"; what does this mean about paracompact topological spaces? In cases like the Gauss-Bonet theorem it turns out that some differentiable definitions (integration) can actually be restated for topological manifolds. But is that the case? Is the hairy ball theorem about positive Euler characteristic topological manifolds? Or just about smooth manifolds whose underlying topological manifold has positive Euler characteristic? These are genuine questions, I honestly don't know. But I ask them because the Earth can be quite pointy!
[deleted] · 7 points · Posted at 23:32:35 on February 13, 2016 · (Permalink)
TIL cyclones are hair
leftofzen · 3 points · Posted at 09:10:20 on February 14, 2016 · (Permalink)
This is extremely misleading because the magnitude of the 'cyclone' according to the hairy ball theorem can be of any magnitude; this would most often be of extremely small magnitude; not nearly enough to be considered an actual cyclone.
randarrow · 5 points · Posted at 05:18:46 on February 14, 2016 · (Permalink)
Does this explain the great spots on Jupiter and neptune, along with the hex vortex on Saturn?
moom · 1 points · Posted at 00:42:18 on February 15, 2016 · (Permalink)*
No. As with many things scientific and mathematical, it didn't really survive the attempted translation into human language. It's not really saying anything about storms, nor about large storms, nor about long-lasting storms. It's just saying something like "At any given moment, there is some spot on the face of the earth that, at that moment, has no wind."
ProdigalSheep · 1 points · Posted at 04:44:13 on February 14, 2016 · (Permalink)
Whoa
greyskyeyes · 1 points · Posted at 12:35:47 on February 14, 2016 · (Permalink)
Somehow this means that the same science that causes my bad hair days is also relevant to the weather (which is also relevant to my bad hair days).
singham · 1 points · Posted at 14:14:15 on February 14, 2016 · (Permalink)
It's not a cyclone if it is small.
[deleted] · 1 points · Posted at 01:23:12 on February 14, 2016 · (Permalink)
Even more: there will always be at least two.
tellisk · 1 points · Posted at 03:35:05 on February 14, 2016 · (Permalink)
Not necessarily. This explains how 1 would be possible.
[deleted] · 1 points · Posted at 14:41:49 on February 14, 2016 · (Permalink)
Ah, of course, they can be infinitely close (a.k.a. the same point). Thanks for pointing that out.
tellisk · 1 points · Posted at 15:49:51 on February 14, 2016 · (Permalink)
No problem. I kind of fell down the rabbit hole of looking for information about when this started being called the "hairy ball theorem" (like, was it named that at a time when kids and redditors wouldn't think it's hilarious?). And read almost the entire Talk page looking for that info just before seeing your comment. I think the third image on the Wikipedia page also illustrates what it looks like (and there's an animated version if you click it).
[deleted] · 0 points · Posted at 00:05:15 on February 14, 2016 · (Permalink)
[deleted]
lelarentaka · 3 points · Posted at 03:39:58 on February 14, 2016 · (Permalink)
I'm not sure if you meant the mathematical topology or the dirty topology, but the earth is a sphere where that theorem is concerned. Unless there's a core bore I'm not aware of? Donut earth?
whacko_jacko · 1 points · Posted at 05:00:56 on February 14, 2016 · (Permalink)
If you count caves or tunnels, then I suppose the genus would be pretty large.
Camjw1123 · 1 points · Posted at 11:37:35 on February 14, 2016 · (Permalink)
No, its actually not since the theorem really needs the object to be homeomorphic to a sphere. Since genus is a topological invariant this is equivalent to the earth having genus zero, but it doesn't! If you think about a tunnel through a mountain (which there are loads of) this gives the earth a strictly positive genus! There are also some funky rock formations which give the earth bigger holes, so unfortunately the theorem doesn't actually apply :(
lelarentaka · 1 points · Posted at 14:51:41 on February 14, 2016 · (Permalink)
haha fair enough!
klparrot · 0 points · Posted at 09:29:05 on February 14, 2016 · (Permalink)
Except that the atmosphere is not of constant pressure, so wind blowing into an area doesn't necessitate wind blowing out of that area. Not immediately, anyway.
Shadecraze · 14 points · Posted at 01:31:30 on February 14, 2016 · (Permalink)
TIL: Cowlick is 1 hair strand standing up.
in my language "you look like cow licked your hair" is used for NO hair standing up, and all of them looking slick. weird
Zeus-Is-A-Prick · 9 points · Posted at 08:21:50 on February 14, 2016 · (Permalink)
A cow won't lick your hair flat, it would lick in an upward motion causing your hair to stick up.
ElBiscuit · 2 points · Posted at 09:07:11 on February 14, 2016 · (Permalink)
But how would a cow lick a tennis ball?
Zeus-Is-A-Prick · 7 points · Posted at 09:17:04 on February 14, 2016 · (Permalink)
With its tongue.
the_russian_narwhal_ · 2 points · Posted at 01:51:17 on February 14, 2016 · (Permalink)
Weird, here in texas atleast a cow lick is where you have some hair sticking up
F-0X · 284 points · Posted at 21:50:08 on February 13, 2016 · (Permalink)
No it's not. A tennis ball is not totally covered in hair. You need a hair at every point for this to be true; if there's even one single hairless spot, a flat-combing will be possible.
This is precisely because a sphere with one point removed is homeomorphic to a disc.
0876 · 853 points · Posted at 23:00:17 on February 13, 2016 · (Permalink)
I think you're splitting hairs.
Bananawamajama · 4 points · Posted at 01:28:53 on February 14, 2016 · (Permalink)
Well apparently OP didn't, someone had to
guy_with_an_account · 2 points · Posted at 12:27:09 on February 14, 2016 · (Permalink)
No, he's homeomorphing spheres.
flyZerach · 1 points · Posted at 05:32:03 on February 14, 2016 · (Permalink)
Yeah dude, I think he should cut it out.
Bamword15 · 0 points · Posted at 04:14:14 on February 14, 2016 · (Permalink)
He's just getting brushed back.
[deleted] · 43 points · Posted at 00:34:15 on February 14, 2016 · (Permalink)
Consider a spherical cow...
NewbornMuse · 29 points · Posted at 00:52:51 on February 14, 2016 · (Permalink)
A cow's surface is homeomorphic to a sphere*, so we get the same result.
*If you only consider skin, and consider orifices as closed. With all orifices considered, it's closer to a torus.
thedeejus · 100 points · Posted at 01:18:17 on February 14, 2016 · (Permalink)
a cow is already a taurus
NewbornMuse · 7 points · Posted at 01:26:40 on February 14, 2016 · (Permalink)
eyooooo
magpac · 1 points · Posted at 07:48:24 on February 14, 2016 · (Permalink)
And a multi-holed one at that.
Now I need to know, what is the genus of a human being? (no homo).
RobertAPetersen · 2 points · Posted at 04:58:17 on February 14, 2016 · (Permalink)
In a vacuum, I'm assuming?
Maoman1 · 5 points · Posted at 06:10:54 on February 14, 2016 · (Permalink)
Which sprays milk uniformly in every direction simultaneously.
[deleted] · 1 points · Posted at 17:34:41 on February 14, 2016 · (Permalink)
A [mathematical] field of milk.
poizan42 · 16 points · Posted at 22:47:02 on February 13, 2016 · (Permalink)
The hairs on a tennis ball are not infinitesimally thin either.
aixenprovence · 6 points · Posted at 22:51:04 on February 13, 2016 · (Permalink)
Not with that attitude they're not.
[deleted] · 9 points · Posted at 01:27:18 on February 14, 2016 · (Permalink)
You're a homeomorphic.
Maoman1 · 1 points · Posted at 06:11:20 on February 14, 2016 · (Permalink)
I'm homeomorphobic.
[deleted] · 2 points · Posted at 00:34:51 on February 14, 2016 · (Permalink)
Wouldn't you need two points?
tellisk · 3 points · Posted at 03:37:29 on February 14, 2016 · (Permalink)
Nope! This shows how it's possible with only one.
WaitForItTheMongols · 2 points · Posted at 02:05:17 on February 14, 2016 · (Permalink)
Is it homeomorphic to a disc because that point turns into the edge of the disc, and the point opposite to the one that was removed becomes the center?
F-0X · 1 points · Posted at 10:13:57 on February 14, 2016 · (Permalink)
Essentially, yes.
UndeadBread · 1 points · Posted at 02:56:05 on February 14, 2016 · (Permalink)
Yeah, you tell that mother fucker!
alanaa92 · 1 points · Posted at 05:05:12 on February 14, 2016 · (Permalink)
I don't think the sphere would appreciate being called homeomorphic.
Valyrian_Tinfoil · 1 points · Posted at 06:23:08 on February 14, 2016 · (Permalink)
That doesn't make practical sense, though, because "a point" is a completely relativistic term; it can be as small as you want it to be. Nothing ever covers all points in a 3 dimensional reality, such as we experience. So for the purposes of that theorem, it's totally kosher.
F-0X · 1 points · Posted at 10:22:50 on February 14, 2016 · (Permalink)
A point is not relativistic at all in a topological sense. The theorem he's referring to states there is no non-vanishing section of the tangent bundle on a sphere. The tangent bundle is defined at all points, thus a section is defined at all points, so to talk about sections requires us to talk about all points.
I even gave an example of where ignoring just one point yields a case in which the claim is obviously false, too.
romulusnr · 1 points · Posted at 09:34:41 on February 14, 2016 · (Permalink)
Depends on what qualifies as a cyclone. Even if you put the epicenter on a line, there would still be a cyclonic pattern around that point in the hairs.
sargeantbob · 1 points · Posted at 21:04:36 on February 14, 2016 · (Permalink)
The topologist with the save
FlamingNipplesOfFire · -3 points · Posted at 23:04:53 on February 13, 2016 · (Permalink)
K, yeah I'm sure he as well as every other person could get the point. Worse than insurance agents arguing about admonition of fault vs guilt.
TomasTTEngin · 4 points · Posted at 00:05:23 on February 14, 2016 · (Permalink)
I'd like to imagine some mathematically inclined ATP tour pro sitting in the locker room with a comb and a tube of fresh-smelling wilson brand balls doing calculations and totally forgetting to go outside and play their match.
SuchCoolBrandon · 3 points · Posted at 01:25:28 on February 14, 2016 · (Permalink)
This explains why I have so much trouble combing balls.
johnnymo1 · 1 points · Posted at 23:50:20 on February 13, 2016 · (Permalink)
Note that you have to be trying to comb it flat, i.e. tangent to the sphere, otherwise the normal vector at each point is an example of a smooth non-vanishing vector field.
[deleted] · 1 points · Posted at 00:57:06 on February 14, 2016 · (Permalink)
Wouldnt there be two cowlicks?
[deleted] · 1 points · Posted at 01:58:13 on February 14, 2016 · (Permalink)
No, imagine starting at an arbitrary point (let's call it the south pole). Now come every hair individual directly away from the south pole. Eventually, the issue of the cowlick arises at the north pole, but only there.
robbiedenali · 1 points · Posted at 00:58:41 on February 14, 2016 · (Permalink)
Can this explain why the universe cannot be homogenous? I.e. As soon after the big bang as there was space (i.e. a volume in which everything exists) at least one place was remarkable? As the universe expanded and cooled perhaps the at least 1 remarkable place became more diverse and more numerous. (Contrary to popular belief I'm stone cold sober right now)
[deleted] · 1 points · Posted at 02:08:08 on February 14, 2016 · (Permalink)
This sounds like folk wisdom, like you can't make an omelette without cracking some eggs.
"You know what Pa always says, you can't comb all the hairs on a hairy ball the same direction without a cowlick."
Supersnazz · 1 points · Posted at 02:30:23 on February 14, 2016 · (Permalink)
I understand the maths behind this, but it fails to take into account that the hairs themselves can swirl but still be flat, and not create a cowlick.
zacree · 1 points · Posted at 02:36:37 on February 14, 2016 · (Permalink)
aw
aw man wait
wait
hilarymeggin · 1 points · Posted at 02:40:09 on February 14, 2016 · (Permalink)
The cowlicks would be at the poles, right?
Aleblanco1987 · 1 points · Posted at 02:48:16 on February 14, 2016 · (Permalink)
A corollary of that theorem is that's always a place in earth with 0 wind.
super__sonic · 1 points · Posted at 03:20:37 on February 14, 2016 · (Permalink)
what if you comb them all radiating out from the center!!!11
Coequalizer · 1 points · Posted at 03:22:12 on February 14, 2016 · (Permalink)
As a corollary, since you can comb all the hairs on a cat flat, a cat cannot be continuously deformed into a ball. By the classification theorem for closed surfaces, it follows that the cat must have (at least one) hole. This is the "cat's asshole theorem."
SchemeMcGee · 1 points · Posted at 04:04:38 on February 14, 2016 · (Permalink)
How come Trump can do it???
moxiejeff · 1 points · Posted at 04:32:22 on February 14, 2016 · (Permalink)
364/36523 * 22 / 2 approximates 1/2
Checks out
dankmanlet · 1 points · Posted at 04:39:05 on February 14, 2016 · (Permalink)
Yep. And because of this, there is always at least one point on earth with completely still air (if you think of the direction of the hairs as wind).
Son_of_the_devil · 1 points · Posted at 04:43:24 on February 14, 2016 · (Permalink)
This also works for any 2n-sphere embedded in R2n+1 (e.g a 5 dimensional sphere)
sueca · 1 points · Posted at 04:57:55 on February 14, 2016 · (Permalink)
I had to look on wikipedia what a cowlick was (non-native English speaker) and then it became weirdly obvious when it was something as simple as "looks like whatever hair looks like after being licked by a cow"
Kiefyking · 1 points · Posted at 05:02:33 on February 14, 2016 · (Permalink)
This would be on any sphere though wouldn't it, not just tennis balls lol
JV19 · 1 points · Posted at 06:04:25 on February 14, 2016 · (Permalink)
This one actually makes a lot of sense, though.
[deleted] · 1 points · Posted at 06:08:06 on February 14, 2016 · (Permalink)
Some claim that a real world implication is that you cannot comb a dog since its isomorphic to a ball. But I claim that a dog is a torus.
Gonewiththeears · 1 points · Posted at 06:20:30 on February 14, 2016 · (Permalink)
You can't comb the hair on a coconut.
Ceejae · 1 points · Posted at 06:24:01 on February 14, 2016 · (Permalink)
Or without unproductive use of your time.
sensors · 1 points · Posted at 08:10:33 on February 14, 2016 · (Permalink)
*With the inexplicable exception of Donald Trump's hair
VacuouslyUntrue · 1 points · Posted at 08:14:21 on February 14, 2016 · (Permalink)
There is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. You can comb the tennis ball because it has those ridges which are vanishing portions of the 'hairs as vector fields' interpretation.
Lose_GPA_Gain_MMR · 1 points · Posted at 09:01:01 on February 14, 2016 · (Permalink)
I inadvertently found this out when as a kid I realized all the short haired kids have cool cyclone shapes somewhere on their heads.
judgej2 · 1 points · Posted at 09:02:32 on February 14, 2016 · (Permalink)
Does that have any relation to the great red dot/storm on Jupiter?
Ravenchant · 1 points · Posted at 09:13:15 on February 14, 2016 · (Permalink)
To add to this: it's impossible with a 3-dimensional ball, but possible in 2 and 4 dimensions.
WoooKnows · 1 points · Posted at 09:18:47 on February 14, 2016 · (Permalink)
give it to donald trump, he would do it.
neoballoon · 1 points · Posted at 09:54:05 on February 14, 2016 · (Permalink)
This doesn't seem surprising or counterintuitive to me. I'd be more surprised if it were possible
kellysmith · 1 points · Posted at 11:25:30 on February 14, 2016 · (Permalink)
Or a Trump wig.
sunpeace · 1 points · Posted at 12:59:37 on February 14, 2016 · (Permalink)
Define cowlick please. Is it each hair having more and more horizontal angle as you comb?
realist_konark · 1 points · Posted at 13:17:06 on February 14, 2016 · (Permalink)
But what is the proof to it?
henrikose · 1 points · Posted at 16:36:51 on February 14, 2016 · (Permalink)
This is one of the things I do not really think I need math to tell me.
sargeantbob · 1 points · Posted at 21:03:49 on February 14, 2016 · (Permalink)
What about the radial direction?
shitforhead · 1 points · Posted at 00:13:09 on February 15, 2016 · (Permalink)
What if you comb them all straight up?
OneTerriblePancake · 1 points · Posted at 03:44:50 on February 15, 2016 · (Permalink)
What if you had a special circular comb, that was the exact circumference of the ball?
I'm not trying to be a smartass, I really want to know
[deleted] · 4166 points · Posted at 19:10:45 on February 13, 2016 · (Permalink)
There is an entire book explaining how 1+1=2 works and makes sense
[deleted] · 4339 points · Posted at 20:57:36 on February 13, 2016 · (Permalink)*
[deleted]
simple_mech · 1709 points · Posted at 00:11:52 on February 14, 2016 · (Permalink)
For picking up chicks at the bar, I presume.
[deleted] · 2397 points · Posted at 00:15:48 on February 14, 2016 · (Permalink)*
[deleted]
simple_mech · 3422 points · Posted at 00:28:43 on February 14, 2016 · (Permalink)
I'm assuming your username is the common response.
sandm000 · 731 points · Posted at 01:21:42 on February 14, 2016 · (Permalink)
Please respond only in the options presented in the question.
Alarid · 119 points · Posted at 03:36:13 on February 14, 2016 · (Permalink)
"This tastes funny" is also a relevant response.
sxadvcthrwy · 5 points · Posted at 07:53:08 on February 14, 2016 · (Permalink)
Taser is always an option.
skelebone · 4 points · Posted at 12:54:21 on February 14, 2016 · (Permalink)
Let's keep this about Rampart.
sandm000 · 1 points · Posted at 12:55:33 on February 14, 2016 · (Permalink)
That is an acceptable answer
allahu_snackb4r · 7 points · Posted at 03:17:21 on February 14, 2016 · (Permalink)
WILLYOUSTFU
GunPoison · 1 points · Posted at 09:06:56 on February 14, 2016 · (Permalink)
Show working.
[deleted] · 1 points · Posted at 09:56:35 on February 14, 2016 · (Permalink)
If you insist on that, you might also have fun with the question "yes or no: did you stop beating your wife?"
dfsgdhgresdfgdff · 1 points · Posted at 10:33:03 on February 14, 2016 · (Permalink)
"No."
Triquetra4715 · 1 points · Posted at 19:43:24 on February 14, 2016 · (Permalink)
I find nothing gets panties wet like being tricked.
ireadthatcomment · 6 points · Posted at 01:38:48 on February 14, 2016 · (Permalink)
Rekt. Well played.
reinhart_menken · 2 points · Posted at 11:10:54 on February 14, 2016 · (Permalink)
You have such wit for a simple mech.
singham · 1 points · Posted at 14:15:31 on February 14, 2016 · (Permalink)
RELEVANT. V RELEVANT.
Thrownaway_4_2_day · 1 points · Posted at 17:05:10 on February 14, 2016 · (Permalink)
To pieces.
[deleted] · 0 points · Posted at 05:28:54 on February 14, 2016 · (Permalink)
It would be the common 2nd response. The first being, "No."
[deleted] · 148 points · Posted at 01:29:32 on February 14, 2016 · (Permalink)
[deleted]
arandombritishguy · 12 points · Posted at 04:13:24 on February 14, 2016 · (Permalink)
Trying to work this one through hurts by brain. The "always" you've thrown in there makes it so much more complicated as it means the whole sentence could be a fallacy also, not just the answer of no haha.
dengseng · 0 points · Posted at 10:37:26 on February 14, 2016 · (Permalink)
Schrodinger's response
Lun06 · 324 points · Posted at 00:30:42 on February 14, 2016 · (Permalink)
throws drink in your face
Leprechorn · 154 points · Posted at 01:10:35 on February 14, 2016 · (Permalink)
Joke's on them... I would never date someone who willingly destroys their own property
TimS194 · 118 points · Posted at 03:21:57 on February 14, 2016 · (Permalink)
throws your drink in your face
[deleted] · 14 points · Posted at 04:58:49 on February 14, 2016 · (Permalink)*
Ill have my lawyer to contact your lawyer
puskathethird · 2 points · Posted at 10:45:58 on February 14, 2016 · (Permalink)
Joke's on them... That is how my people drink
sonyka · 1 points · Posted at 09:57:37 on February 14, 2016 · (Permalink)
That is one of the classiest things I've ever heard.
I gotta remember that.
Inteli_Gent · 6 points · Posted at 05:22:34 on February 14, 2016 · (Permalink)
They didn't destroy it, they just redistributed it.
gnieboer · 1 points · Posted at 12:49:10 on February 14, 2016 · (Permalink)
Hmm, I don't see a lot of campfire romance or candlelit dinners in your future.
thevdude · 1 points · Posted at 16:27:56 on February 14, 2016 · (Permalink)
That's why I don't beat my girlfriend. Who do something like that to their own property?
[deleted] · 1 points · Posted at 23:51:20 on February 14, 2016 · (Permalink)
Ok Dwight
akronix10 · 11 points · Posted at 04:05:55 on February 14, 2016 · (Permalink)
Now I'm as wet as you are
gliph · 7 points · Posted at 01:41:22 on February 14, 2016 · (Permalink)
dripping
That wasn't an option!
Xerkule · 258 points · Posted at 01:17:21 on February 14, 2016 · (Permalink)
They can just say "no" to the first question and "fuck no" to the second question.
TheNightWind · 15 points · Posted at 03:38:43 on February 14, 2016 · (Permalink)
But he only asked one question.
Xerkule · 4 points · Posted at 07:41:23 on February 14, 2016 · (Permalink)
That one question refers to a second question that will be asked next.
[deleted] · 0 points · Posted at 13:50:51 on February 14, 2016 · (Permalink)
I'm glad im not the only one who realized this!
Kaell311 · 4 points · Posted at 06:25:52 on February 14, 2016 · (Permalink)
Or just "go away". And not answer the other.
wysoaid · 1 points · Posted at 12:38:08 on February 14, 2016 · (Permalink)
Yeah, because why should they have the option to say "no."
Valyrian_Tinfoil · -4 points · Posted at 06:27:14 on February 14, 2016 · (Permalink)
Not if they want to make logical sense
hyperbolical · 5 points · Posted at 14:15:29 on February 14, 2016 · (Permalink)
If you answer no to the question, it doesn't mean your answer to the implied question has to be "Yes". It can be literally anything but "No", and the answers will not have been the same.
Fuck no, nah, negative, go away, not in a million years, etc...
Valyrian_Tinfoil · 1 points · Posted at 03:49:55 on February 15, 2016 · (Permalink)
He's asking if the answers will be the same, not what her answers are.
hyperbolical · 3 points · Posted at 03:57:25 on February 15, 2016 · (Permalink)
Ok? So when she says "No", that just means her answers won't be the same.
That doesn't mean she would say "Yes".
chiablo · 50 points · Posted at 01:34:55 on February 14, 2016 · (Permalink)
The answer is always "what?"
And before you can explain it again, they've lost any and all respect or interest in you.
spenrose22 · 11 points · Posted at 05:13:26 on February 14, 2016 · (Permalink)
and thats when you walk away laughing cause you don't care and aren't a desperate neck beard
TrumpfLaser · 12 points · Posted at 01:28:29 on February 14, 2016 · (Permalink)
Logic based reply: If you asked me to go home with you my answer would be the same for both questions.
SadGhoster87 · 1 points · Posted at 07:11:21 on February 14, 2016 · (Permalink)
But what's the second question?
idreamofkitty · 9 points · Posted at 02:08:39 on February 14, 2016 · (Permalink)
Call me slow, but both 'yes' and 'no' means she is going home with you, right?
gecko_08 · 12 points · Posted at 03:10:26 on February 14, 2016 · (Permalink)
Correct
SadGhoster87 · -2 points · Posted at 07:11:27 on February 14, 2016 · (Permalink)
Woosh
RatherCynical · 2 points · Posted at 02:17:00 on February 14, 2016 · (Permalink)
It would be most effective with binary yes/no answers, a smart girl should quickly realise that "maybe" or "perhaps" ambiguities can break the logical sequence.
Pasty_White_Boy · 2 points · Posted at 03:38:33 on February 14, 2016 · (Permalink)
Any number multiplied by itself is positive, which is why this riddle works
GingerWithFreckles · 1 points · Posted at 01:24:41 on February 14, 2016 · (Permalink)
No+yes=no (right?)
TrumpfLaser · 1 points · Posted at 02:00:40 on February 14, 2016 · (Permalink)
Yes - No = Yes
GingerWithFreckles · 5 points · Posted at 02:23:18 on February 14, 2016 · (Permalink)
I believe the answer would be rape then :P
TrumpfLaser · 1 points · Posted at 02:27:52 on February 14, 2016 · (Permalink)
A positive minus a negative results in a positive outcome. ;D
TrumpfLaser · 1 points · Posted at 02:31:17 on February 14, 2016 · (Permalink)
Well shit, that logic math didn't add up the way I was thinking it would.
XtremeGuy5 · 1 points · Posted at 01:38:10 on February 14, 2016 · (Permalink)
Lol I've never heard this before
Martel- · 1 points · Posted at 01:41:17 on February 14, 2016 · (Permalink)
maybe
punsforgold · 1 points · Posted at 02:36:00 on February 14, 2016 · (Permalink)
I think you need to workshop that one a bit buddy.
Yeahdudex · 1 points · Posted at 03:58:23 on February 14, 2016 · (Permalink)
that will get aprox. zero people laid.
Meto1183 · 1 points · Posted at 04:25:27 on February 14, 2016 · (Permalink)
"No" "Will you go home with me?" "fuck off"
AllPurposeNerd · 1 points · Posted at 04:46:42 on February 14, 2016 · (Permalink)
"...I'm not sure."
[deleted] · 1 points · Posted at 04:53:33 on February 14, 2016 · (Permalink)
"I cannot honestly answer your question since you've constructed it in a manner that requires me to answer one of the two questions dishonestly. Also, I find you unattractive."
amlybon · 1 points · Posted at 04:56:28 on February 14, 2016 · (Permalink)
No. Then when you ask me to go home with you I tell you to fuck off.
Glitch29 · 1 points · Posted at 05:00:51 on February 14, 2016 · (Permalink)
If I never hear that one again, it will be too soon.
kenj0418 · 1 points · Posted at 05:13:50 on February 14, 2016 · (Permalink)
She answer "Yes" and then leaves before you have a chance to actually ask her to go home with you.
goodguys9 · 1 points · Posted at 05:14:32 on February 14, 2016 · (Permalink)
That's a terrible logic based question. /s
But seriously you're committing the fallacy of begging the question (this means you are giving a premise in the form of a question, without allowing them to disagree with the premise), so it wouldn't work on all those sexy logic majors you're targeting with logic based pick up lines.
sqqueen · 1 points · Posted at 05:34:09 on February 14, 2016 · (Permalink)
"What?"
Chillreave · 1 points · Posted at 05:35:31 on February 14, 2016 · (Permalink)
What do you do when someone says 'Perhaps'?
ADSRelease · 1 points · Posted at 05:41:36 on February 14, 2016 · (Permalink)
Took me a second to figure out. That's so bad it's beautiful.
Unoewho · 1 points · Posted at 06:21:32 on February 14, 2016 · (Permalink)
"No" and "probably not". Never said the second question had to be yes or no.
BigglesNZ · 1 points · Posted at 07:23:15 on February 14, 2016 · (Permalink)
"Huh, what? Get lost, weirdo" - chicks, probably
rubberseatbelt · 1 points · Posted at 08:29:20 on February 14, 2016 · (Permalink)
"If I asked you to go home with me would" is the first question. However, I don't see a second question. There is an inference of a second question, but it doesn't exist. Right?
Not_The_Expected · 1 points · Posted at 09:12:24 on February 14, 2016 · (Permalink)
No. Negative. Nada. Nope. Never. Not yes. Maybe
[deleted] · 1 points · Posted at 10:02:18 on February 14, 2016 · (Permalink)
"No."
"So, do you want to go home with me? You can't say no..."
"Not a chance."
You can solve this problem by initially asking: "Yes or no: If I asked you 'Yes or no: do you want to go home with me?', would your answer to that question be the same as your answer to this question?"
thatsforthatsub · 1 points · Posted at 10:56:12 on February 14, 2016 · (Permalink)
I don't wanna go home with you, and you have no power to dictate my possible answers.
[deleted] · 1 points · Posted at 11:18:50 on February 14, 2016 · (Permalink)
"Umm, you're weird leave me alone."
[deleted] · 1 points · Posted at 12:32:42 on February 14, 2016 · (Permalink)
You did not specify that they had to answer Yes or no to the second question. So they could simply say no and then answer go away to the second question.
thorium220 · 1 points · Posted at 12:37:24 on February 14, 2016 · (Permalink)
It will not be the same answer because I will word it differently.
squigs · 1 points · Posted at 12:40:03 on February 14, 2016 · (Permalink)
Unfortunately, this bar is in a land where they will answer ja or da, you don't know which means yes, and half the population always lies.
Graydeeus · 1 points · Posted at 13:43:05 on February 14, 2016 · (Permalink)
Trapping girls in logical paradoxes, because maths students can be creepy stalkers too.
madkeepz · 1 points · Posted at 13:52:04 on February 14, 2016 · (Permalink)
Here's another one: "do your parents know we're fucking tonight?"
mgosiris · 1 points · Posted at 13:57:29 on February 14, 2016 · (Permalink)
ERR
[deleted] · 1 points · Posted at 14:21:41 on February 14, 2016 · (Permalink)
Probably not
DeliciousVegetables · 1 points · Posted at 15:02:38 on February 14, 2016 · (Permalink)
My answer would be different from your answer to this question, wouldn't it?
Vextin · 1 points · Posted at 15:42:21 on February 14, 2016 · (Permalink)
Perfect timing, time to go get me a valentine.
Arkell_V_Pressdram · 1 points · Posted at 17:05:55 on February 14, 2016 · (Permalink)
"Your conditions on the answers do not sufficiently encompass all the possible answers to the question you asked. You might as well ask 'Purple or Flint, Michigan: If I asked you to go home with me, would your answer to that question be the same as your answer to this question?'. Therefore I reject the conditions you impose. If you find this unacceptable that is your problem. In any case I will positively assert to you that I will not go home with you. Also, you're ugly and stupid."
[deleted] · 1 points · Posted at 17:48:50 on February 14, 2016 · (Permalink)
She then throws you off by telling you to "eat a dick".
isit2003 · 1 points · Posted at 18:14:54 on February 14, 2016 · (Permalink)
"No."
"Will you go home with me?"
"Fuck no."
logos__ · 1 points · Posted at 19:21:21 on February 14, 2016 · (Permalink)
"Or".
Derice · 1 points · Posted at 19:53:11 on February 14, 2016 · (Permalink)
Maybe
MooseEngr · 1 points · Posted at 20:46:56 on February 14, 2016 · (Permalink)
What a strabge game. The only way to win is to not play.
hypervelocityvomit · 1 points · Posted at 09:48:39 on February 15, 2016 · (Permalink)
stab
wjwwjw · 1 points · Posted at 15:10:13 on July 19, 2016 · (Permalink)
The issue is that you act as if "yes or no" is one single question on its own. Followed by the stuff regarding to coming home. So actually if this would be a pick up line it would not make any sense.
justtoreplythisshit · 0 points · Posted at 00:59:39 on February 14, 2016 · (Permalink)
That's where you got your username from?
Pure_Reason · 0 points · Posted at 02:17:56 on February 14, 2016 · (Permalink)
WILLY OUST FU
DatDrummerGuy · -4 points · Posted at 00:49:00 on February 14, 2016 · (Permalink)
I said that too many times and they were too stupid to understand this shit.
Skyros · 2 points · Posted at 06:55:00 on February 14, 2016 · (Permalink)
'I just read through 300 pages proving how 1+1=2. I think the two of us could probably prove it in the next 10 minutes.'
iWISHiHAD · 2 points · Posted at 03:10:09 on February 14, 2016 · (Permalink)
"Hey, do you like apples?"
slaps paper with a phone number on the glass
_Cool_CoolCoolCool_ · 1 points · Posted at 14:23:27 on February 14, 2016 · (Permalink)
No, in that case, it would be 1+1= 3
Treczoks · 1 points · Posted at 14:48:20 on February 14, 2016 · (Permalink)
No, you take the proof for 1+1=2 and stack it on top of the proofs for 1+2=3 and 2+2=4, and you'll be able to reach the cookie jar.
henrikose · 1 points · Posted at 16:32:20 on February 14, 2016 · (Permalink)
It sure is relevant, if you succeed picking up one.
pavel_lishin · 1 points · Posted at 19:52:23 on February 16, 2016 · (Permalink)
1+1 chicks at the same time.
Bonebreaker420 · 1 points · Posted at 18:42:53 on February 21, 2016 · (Permalink)
Bb g g gg gg IBM
IMO Moo Vk
[deleted] · 1 points · Posted at 18:56:26 on May 7, 2016 · (Permalink)
1+1=71
CodeplayerX · 1 points · Posted at 04:57:06 on February 14, 2016 · (Permalink)
Well sometimes after picking chicks up at a bar 1+1=3, at least until the postpartum depression kicks in and she knocks it back down to two.
IcanCwhatUsay · 0 points · Posted at 03:54:44 on February 14, 2016 · (Permalink)
"I got her numbe'a, how do you like 'dem apples?"
WeeOtter · 7 points · Posted at 01:04:16 on February 14, 2016 · (Permalink)
Tell that to Terrence Howard
compasrc · 7 points · Posted at 05:56:04 on February 14, 2016 · (Permalink)
This seems really superfluous because they start the whole proof by using the derivative of 1 to prove it. Can we not all just accept that if you have 1 thing and 1 more thing, there are now 2 things? I just don't understand how they complicate such a simple concept so much.
[deleted] · 4 points · Posted at 06:45:39 on February 14, 2016 · (Permalink)
I think the point is proving something mathematically without using math... Like if I say 1 + 1 = 2 in my system, what's to stop someone from saying how do I know your system is even right?
And you stop that person by proving 1 + 1 = 2 without adding 1 and 1
Reddits_Worst_Night · 3 points · Posted at 00:48:20 on February 14, 2016 · (Permalink)
At that point, they don't actually show it, they just say that "From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2" which is on page 379 of volume 1. They don't actually finish the proof until page 86 of Volume 2, which is where you find the footnot
appropriate-username · 1 points · Posted at 13:44:16 on February 14, 2016 · (Permalink)
e.
P8zvli · 2 points · Posted at 01:27:30 on February 14, 2016 · (Permalink)
Real number analysis in a nutshell
sweetgreggo · 2 points · Posted at 14:25:58 on February 14, 2016 · (Permalink)
Sounds like something Douglas Adams would have written.
r1p4c3 · 1 points · Posted at 08:50:48 on February 14, 2016 · (Permalink)
What book?
IshKebab · 1 points · Posted at 11:10:19 on February 14, 2016 · (Permalink)
I'm pretty sure that's an axiom. You can't "prove" it.
Kered13 · 1 points · Posted at 13:49:15 on February 14, 2016 · (Permalink)
You can start there, but why when you can start with much simpler axioms? Modern mathematics usually starts with ZFC set theory, and constructs the natural numbers from sets. Then you can define addition over natural numbers and show that 1+1=2.
[deleted] · 1 points · Posted at 12:35:54 on February 14, 2016 · (Permalink)
Safe to assume you are talking about PM?
XenoD · 1 points · Posted at 16:57:19 on February 14, 2016 · (Permalink)
Except it isn't a theorem but rather the definition of the number two.
WILLYOUSTFU · 2 points · Posted at 17:24:32 on February 14, 2016 · (Permalink)
All math starts as axioms, which are statements we accept as being true. You can say 1+1=2 by definition, but you can start with different axioms too. A common way of getting to 1+1=2 is to start with Peano's axioms, which include:
0 is a natural number
succ(a) is the successor function, and yields the next natural number
Then we define addition
a + 0 = 0 the additive identity is 0
a + succ(b) = succ(a+b)
So with the definition 1= succ(0), and 2 = succ(succ(0))....
x = 1 + 1
x = succ(0) + succ(0)
x = succ(succ(0)+0)
x = succ(succ(0))
Substitute the first line for x, and our definition of 2, and we get 1+1=2.
Russle and Whitehead took so many pages to prove 1+1=2 because they wanted to construct modern mathematics from even simpler axioms than Peanos.
XenoD · 2 points · Posted at 17:27:13 on February 14, 2016 · (Permalink)
I think you hit the nail on the head.
BiggerJ · 0 points · Posted at 07:11:02 on February 14, 2016 · (Permalink)
Like when a child, in the fashion of Mindy from the Mindy and Buttons cartoons in Animaniacs, asked, "Hello, Mister Man/Lady! Why? Why? Why? Why? Okay love you buh bye."
Kilo_G_looked_up · 254 points · Posted at 20:54:13 on February 13, 2016 · (Permalink)
whats the name of the book?
xmachina · 592 points · Posted at 21:23:39 on February 13, 2016 · (Permalink)
Principia Mathematica by Whitehead and Russell.
TheHollowJester · 525 points · Posted at 23:04:36 on February 13, 2016 · (Permalink)*
It's not the whole book though.
EDIT: Just to clarify, it was not to nitpick. It's fucking Principia, one of the most important books written in history. It's not just about how '1+1=2'.
[deleted] · 322 points · Posted at 23:54:01 on February 13, 2016 · (Permalink)*
[removed]
MaceWumpus · 146 points · Posted at 01:33:34 on February 14, 2016 · (Permalink)
And Descartes', which all of the others are named after (Newton's directly, the others indirectly).
jayarepe · 29 points · Posted at 04:26:38 on February 14, 2016 · (Permalink)
Please, please, please: do NOT put Descartes in front of DeHorse...
jayarepe · 16 points · Posted at 04:36:42 on February 14, 2016 · (Permalink)
I created a reddit account just to post that joke. I've been waiting to deploy that silly joke since age 14, so thanks Internet!
JXEYES · -3 points · Posted at 06:15:50 on February 14, 2016 · (Permalink)
Epic
AreUFuckingRetarded · -4 points · Posted at 06:35:33 on February 14, 2016 · (Permalink)
This joke has been done on reddit before, and more cleverly I might add. You are not original.
[deleted] · 9 points · Posted at 06:52:29 on February 14, 2016 · (Permalink)*
[deleted]
TreeOct0pus · 7 points · Posted at 08:25:27 on February 14, 2016 · (Permalink)
Nothing good comes of a username like that, I imagine.
Sadsharks · 7 points · Posted at 00:11:22 on February 14, 2016 · (Permalink)
And Moore's.
Paradoxlogos · 8 points · Posted at 03:13:55 on February 14, 2016 · (Permalink)
And Malaclypse The Younger's Principia Discordia.
roxum1 · 3 points · Posted at 03:59:17 on February 14, 2016 · (Permalink)
Hail Eris!
lambdaknight · 2 points · Posted at 03:40:37 on February 14, 2016 · (Permalink)
Both are incredibly important.
sirry · 2 points · Posted at 05:37:27 on February 14, 2016 · (Permalink)
Goedel would probably disagree...
Since he proved that the whole project was misguided
kreie · 1 points · Posted at 07:33:02 on February 14, 2016 · (Permalink)
And Eris's
blitzzerg · 1 points · Posted at 11:02:06 on February 14, 2016 · (Permalink)
you will have to prove that 1+1=2 to make that assumption.
CyclonusRIP · 7 points · Posted at 04:32:37 on February 14, 2016 · (Permalink)
Probably, but the idea that 1+1=2 seems super simple but when you really start to think about it proving 1+1=2 already depends on quite a lot. You have the notion of equality with =, the notion of an operation with +, and these funny symbols that surround them. 1+1=2 seems pretty simple when you think about it in terms of I have one apple and I get another apple so now I have 2 apples, but that is kind of putting the cart before the horse in a mathematical sense. Math might help describe the physical world, but it doesn't depend on it. Math should be true regardless, and once you start thinking in those terms 1+1=2 is actually a really complicated idea.
af0929 · 3 points · Posted at 05:54:31 on February 14, 2016 · (Permalink)
ELI5 why this 3 volume set sells for over $1K?
TheHollowJester · 6 points · Posted at 10:48:59 on February 14, 2016 · (Permalink)
Because it's old and people collect these things. The one you liked to was published in 1962.
db0255 · 2 points · Posted at 11:32:07 on February 14, 2016 · (Permalink)
Because it's a masterpiece and THE seminal book in modern mathematics
Obyeag · 2 points · Posted at 04:27:34 on February 14, 2016 · (Permalink)
Not really that important, it was a failure after all.
[deleted] · 6 points · Posted at 00:58:31 on February 14, 2016 · (Permalink)
Not to be confused with the identically named book by Newton (co-incidentally, this was mentioned briefly in a book I was reading a few hours ago)
db0255 · 3 points · Posted at 11:14:06 on February 14, 2016 · (Permalink)
The one Godel pooped all over?
Vamprat · 5 points · Posted at 22:48:27 on February 13, 2016 · (Permalink)
I mean, this roughly translates to what /u/NanotechNinja said
tgeorge17 · 2 points · Posted at 03:13:21 on February 14, 2016 · (Permalink)
https://archive.org/details/PrincipiaMathematicaVolumeI
For those that want a nice easy weekend read..
brickmack · 2 points · Posted at 03:56:52 on February 14, 2016 · (Permalink)
Damn Whitehead and Russell never could complete anything
[deleted] · 1 points · Posted at 05:41:29 on February 14, 2016 · (Permalink)
I love Russell. As a philosophy student he is one of my greatest inspirations.
Leporad · 1 points · Posted at 06:33:33 on February 14, 2016 · (Permalink)
This is the proof. What am I looking at?
https://en.wikipedia.org/wiki/Principia_Mathematica#/media/File:Principia_Mathematica_54-43.png
NanotechNinja · 1513 points · Posted at 22:01:55 on February 13, 2016 · (Permalink)
Why Did We Fucking Bother, Fuck This Shit, by Whitehead and Russell.
[deleted] · 426 points · Posted at 01:18:32 on February 14, 2016 · (Permalink)*
[deleted]
ijkk · 13 points · Posted at 02:24:53 on February 14, 2016 · (Permalink)
yeah that's where I learned about it
NanotechNinja · 6 points · Posted at 06:44:18 on February 14, 2016 · (Permalink)
I actually really liked that book. Very cool cover art (which is clearly the best way to judge a book) :P
DraconisRex · 3 points · Posted at 10:30:53 on February 14, 2016 · (Permalink)
Heh... fuckin' Doug.
MyOldUsernameSucked · -13 points · Posted at 04:07:15 on February 14, 2016 · (Permalink)*
Please, Hofstadter's a hack at best.
EDIT: Wow, you guys take this Hofstadter quip way too seriously.
Reddits_Worst_Night · 10 points · Posted at 00:50:46 on February 14, 2016 · (Permalink)
The subtitle is: The entire project was futile anyway.
[deleted] · 6 points · Posted at 02:29:19 on February 14, 2016 · (Permalink)
Nonsense, the book was very influential and had very little to do with proving 1+1=2 in particular. Popular accounts like that Hofstadter book focus on Gödel and set theory etc. but ignore Russell's and Principia's influence on the most important philosopher since Kant, namely Wittgenstein.
Reddits_Worst_Night · 10 points · Posted at 02:51:35 on February 14, 2016 · (Permalink)
I would contest the claim that Wittgenstein was the most important philosopher since Kant. I'd put Heidegger up there myself, or perhaps, though I hate to admit it, Peter Singer. Wittgenstein is almost a swear word in my philosophy faculty, if there is anybody who likes him, they're too ashamed to admit it.
As for the influence on others, it still doesn't change the fact that Whitehead and Russel had a stated goal, which has been shown to be impossible. I'm probably one of about 5 people in this thread who has actually read PM, rather than stuff like the Hofstadter.
EighthScofflaw · 2 points · Posted at 07:59:50 on February 14, 2016 · (Permalink)
Is your department heavily continental or something?
Reddits_Worst_Night · 1 points · Posted at 11:53:06 on February 14, 2016 · (Permalink)
More like heavily analytical.
db0255 · 1 points · Posted at 11:33:27 on February 14, 2016 · (Permalink)
Let's be real here. GEB wasn't a walk in the park either.
serfis · 1 points · Posted at 13:29:30 on February 14, 2016 · (Permalink)
Where would Frege fit in, importance wise? Logic classes were my favorite philosophy classes, and it seemed to me that he was very important in that particular area.
[deleted] · 2 points · Posted at 15:56:27 on February 14, 2016 · (Permalink)
[deleted]
serfis · 1 points · Posted at 16:45:38 on February 14, 2016 · (Permalink)
Got it. Very cool, thanks for insight.
NewbornMuse · -3 points · Posted at 00:49:31 on February 14, 2016 · (Permalink)
Must have been retitled for foreign markets.
Eplone · 4 points · Posted at 10:09:58 on February 14, 2016 · (Permalink)
There's a graphic novel called Logicomix, if you're interested in the story behind it.
Nardog14 · 1 points · Posted at 07:49:38 on February 14, 2016 · (Permalink)
I wanted to be.... that book
FinalFate · 1 points · Posted at 02:43:38 on February 14, 2016 · (Permalink)
Terryology
convoy465 · 0 points · Posted at 08:15:11 on February 14, 2016 · (Permalink)
The name of the book you ask? Albert Einstein.
[deleted] · 23 points · Posted at 00:47:19 on February 14, 2016 · (Permalink)
They should get the author to write about how 1x1 doesn't equal 2, which Terrance Howard thinks is the case.
articfire77 · 14 points · Posted at 03:30:33 on February 14, 2016 · (Permalink)
He also apparently thinks that everyone else thinks the square root of two is two. Maybe that's the root of his anger.
[deleted] · 6 points · Posted at 01:50:37 on February 14, 2016 · (Permalink)
[deleted]
Eskelsar · 3 points · Posted at 04:57:10 on February 14, 2016 · (Permalink)
Wait what is that serious
[deleted] · 1 points · Posted at 21:50:23 on February 14, 2016 · (Permalink)
Unfortunately yes, here is the original article I believe. He calls his 'mathematical breakthrough' Terriology.
http://www.rollingstone.com/tv/news/terrence-howards-dangerous-mind-20150914
Bozzz1 · 3 points · Posted at 04:57:21 on February 14, 2016 · (Permalink)
Someone should show him this diagram and ask him to do the same thing with a row of 1 apple by a column of 1 apple and see what he gets.
[deleted] · 2 points · Posted at 04:53:33 on February 14, 2016 · (Permalink)
Jeeeeeeesus
koproller · 336 points · Posted at 19:56:27 on February 13, 2016 · (Permalink)*
That's absolutely not the cool part.
The cool part is that this proof, got proven wrong/incomplete (in this case incomplete) (Kurt Godel)
zilpe · 659 points · Posted at 20:12:21 on February 13, 2016 · (Permalink)
It's not that the proof is wrong, it's that what they were attempting to do was shown to be impossible. They weren't trying to prove 1+1=2, they were trying to provide a rigorous frame work from which you could derive ALL of mathematics. Obviously 1+1=2 should be derivable in this framework which is why the "proof" is so long, most of it is simply setting up the framework.
What Godel showed isn't that their proof is wrong, but rather no matter how they create this framework there will be mathematically true statements about arithmetic which are unprovable.
koproller · 30 points · Posted at 20:17:01 on February 13, 2016 · (Permalink)
You are right, I was lazy. I added a lazy edit.
almightySapling · 92 points · Posted at 22:29:52 on February 13, 2016 · (Permalink)
But you're still wrong. Russel and Whitehead's proof that 1+1=2 is neither incomplete nor wrong.
What Gödel showed was that their more general attempt was futile: no matter how comprehensive your axiom system, there will always be some statements that can't be proven or disproven.
bg93 · 6 points · Posted at 00:35:00 on February 14, 2016 · (Permalink)
Could you explain a little more how it is that no axiom system can prove all true systems in arithmetic?
BigBucksGentleman · 29 points · Posted at 00:40:00 on February 14, 2016 · (Permalink)
It is more or less that no (sufficiently strong) consistent system (being able to prove no contradictions) is complete (being able to prove all true statements).
What Gödel did was to construct a mathematical statement that states, "I am not provable." If the system can prove it, then there is a contradiction. If the system can't prove it, then it is incomplete (because it is true).
[deleted] · 1 points · Posted at 20:30:56 on February 14, 2016 · (Permalink)
How do we know that Mathematica statement to be true? If it were false then the system won't have to prove it.
jywn4679 · 1 points · Posted at 23:47:58 on February 14, 2016 · (Permalink)
If it's false then it cannot be proven, making it true.
almightySapling · 15 points · Posted at 10:01:42 on February 14, 2016 · (Permalink)*
At the behest of others, I have decided to do a brief (well, that's the plan, we will see) write-up of the key points of Godel's proof.
First, we start with formal logic.
You don't just start with axioms. You need a language. A language consists of the functions, relations, and constants1 that, in conjunction with logical symbols and variables, your statements will be made from.
The language of Peano Arithmetic has 1 unary function: S. S stands for successor, and its standard interpretation is "+1". PA has no relations, and 1 constant, 0. The standard interpretation of 0 is 0, shockingly.
With this are a small number of axioms that basically explain how S should behave, as well as Induction. Also, we can define the functions + and * and the relation < using PA. It's a very concise system that does arithmetic.
So, you have a language, so you can make formulae. There is a nice, concrete definition for something called a "well-formed formula" but the basic idea is that the formula "makes sense". Like it's not just a random combination of symbols. Formulae may contain any number of variables, and we refer to formulae with no free variables as "sentences". That means that a formula may have variables, but each must be associated with a quantifier (for example, in "for all x, x =2*y" the variable y is free, but x is bound).
A proof, then, is a finite sequence of formulae such that each formula is either an axiom, or follows from 1 or more previous formulae in the sequence using a rule of inference. So if you have "P" and "P implies Q" then you can put "Q".
Now, very cleverly, Godel found a way to take any symbol, formula, or even an entire proof and encode it to a unique natural number (that is, two symbols, formula, or proofs have the same Godel Number if and only if they are the same). So for a formula P, we denote the Godel Number of P as #P. The exact encoding doesn't matter too much, but basically you just "number" the symbols of the language (this goes to infinity, because there is no limit on the number of variable symbols you can use) and then encode the formula using primes. If P is the formula "x=0" and #x is 17, #= is 1 and #0 is 2, then #P is 217 * 31 * 52.
The bulk of his work is in the next part. Godel showed that there is a formula that takes a single variable x, and is true when there is a proof of the statement whose Godel Number is x. This is amazing. I would argue this is the meat of the proof, because it must have been a nightmare. Let's call this formula Prov(x).
Some consequences of the above. If PA can prove P, then PA can prove Prov(#P), since if PA can prove P, there's a proof of P, so Prov(#P) is true in all models, so Prov(#P) is provable. And we notice now that, in particular, "not Prov(#P)" is a formula with one free variable.
Then we have The Diagonal Lemma. The Diagonal Lemma says that in certain axiom systems of arithmetic, for any formula F in the language, that has one free variable, there is some sentence P such that the axioms prove "P if and only if F(#P)". And what do you know? PA happens to be just strong enough to be one of those axiom systems!
So, that means if I take a formula with one free variable, oh, say "not Prov(#P)" then we see that there is some formula P such that PA proves "P if and only if not Prov(#P)" (*). What does this mean?
Well, we pretty much know PA is consistent. So what can we say about P? If P is provable then we concluded above that PA proves Prov(#P). But (*) tells us PA proves not Prov(#P). That would mean PA is inconsistent. So we conclude P is not provable. And if P is not provable, then PA proves not Prov(#P). In this case, (*) tells us P.
So PA is an axiom system, and it cannot prove the true statement P.
So that gives us that at least PA can't prove all true statements in arithmetic. What if we take some other axiom system that's strong enough to do arithmetic? Well, we aren't considering inconsistent axiom systems, because of course they are complete, and the axiom system is strong enough to do arithmetic, so it satisfies all the parts of this proof that PA was necessary for, so this proof applies, and we see any axiom system fails to prove all true statements.
-1 : technically, these are function symbols, relation symbols, and constant symbols. They have no meaning in the language alone.
If you have any questions about specifics here, I would be glad to help if I can.
almightySapling · 9 points · Posted at 01:17:31 on February 14, 2016 · (Permalink)
"How" is just "because it has been proven." I wish there was a more fulfilling answer, but there isn't. Maybe looking at it in a different light will explain it better.
There are some very important details that tend to be glossed over when people reiterate Gödel's theorems. Perhaps most importantly, it's not just any type of axiom system that fails to be sufficient. It's recursively enumerable axiom systems, which means one can find a Turing machine that uniquely defines the set of axioms in some way.
Otherwise, we could simply take the set "all true statements" to be our axiom system, and then it would be complete.
So in this sense, Gödel's theorem kind of says "there does not exist a Turing machine capable of deciding all true statements".
kogasapls · 3 points · Posted at 06:23:27 on February 14, 2016 · (Permalink)
There is absolutely a more fulfilling answer. You could instead explain Godel's proof instead of just citing it.
almightySapling · 7 points · Posted at 07:28:49 on February 14, 2016 · (Permalink)
His proof is very complicated. There are just too many points that would amount to "and then Godel proved X" that I may as well just say "Godel proved the whole theorem".
I mean, if you really want, I could break it down, but I just don't think it offers a ton more insight.
kogasapls · 4 points · Posted at 07:30:44 on February 14, 2016 · (Permalink)
I'm not the one who needs the explanation. But there are ways to explain his incompleteness to laymen without getting extremely technical. You miss some of the finer details but the proof is still intact.
Phapples · 1 points · Posted at 12:05:03 on February 14, 2016 · (Permalink)
I always liked Turing's version of it, the only issue being that people often take it to mean "Oh well computers will never be as smart as people anyway, we already knew that".
kaibee · 3 points · Posted at 07:51:43 on February 14, 2016 · (Permalink)
So... it's basically the halting problem?
almightySapling · 7 points · Posted at 10:25:41 on February 14, 2016 · (Permalink)
You may be joking, but you are actually sort of correct!
The proofs of each have a lot of similarities, and there is a weaker form of Incompleteness that is a direct consequence of the undecidability of the halting problem.
kaibee · 1 points · Posted at 18:31:23 on February 14, 2016 · (Permalink)
Huh, maybe I've learned something from all of these CS classes :v
LE4d · 1 points · Posted at 07:40:38 on February 14, 2016 · (Permalink)
http://qntm.org/g
JamEngulfer221 · 1 points · Posted at 08:38:49 on February 14, 2016 · (Permalink)
Prove it
heap42 · 1 points · Posted at 23:29:31 on February 13, 2016 · (Permalink)
at least in Peano Arithmetic.
Shaxys · 5 points · Posted at 00:50:15 on February 14, 2016 · (Permalink)
If this refers to how some statements can't be proven or disproven; no. No matter what axiomatic system you have there's always two possibilities: 1) there's some statements that can't be proven/disproven or 2) the system is inconsistent and unreliable (not interesting).
heap42 · 5 points · Posted at 00:57:34 on February 14, 2016 · (Permalink)
I am fairly sure that Predicate logic(First order logic is complete) Same holds for Pressburger Arithmatic... sure you dont have everything but still... Also, Gödels Completeness itself is has some restrictions... something about beeing a set of axioms strong enought to do arithmetic etc...
nilcit · 3 points · Posted at 04:01:39 on February 14, 2016 · (Permalink)
yeah, first order logic can be show to be both consistent and complete
[deleted] · 264 points · Posted at 20:16:52 on February 13, 2016 · (Permalink)*
It's not that the proof for 1+1=2 was proven wrong exactly, rather Gödel showed there are some true statements of number theory (or any system capable of representing itself) that you cannot prove are true. He showed that Principia Mathematica was necessarily incomplete.
Edit: I like how the parent comment to this was quietly edited to include my incompleteness remark and now I'm getting downvotes.
ImS0hungry · 2 points · Posted at 03:22:50 on February 14, 2016 · (Permalink)
That would be the Gödel's incompleteness theorem. I just finished watching a show about it on Netflix. Really fascinating stuff.
Really makes me think that Riemann's hypothesis is true, but that we can't prove it!
[deleted] · 3 points · Posted at 03:42:19 on February 14, 2016 · (Permalink)
Didn't know about the Netflix doc, I'll check it out, thanks. All my info comes from the book Gödel, Escher, Bach.
[deleted] · 1 points · Posted at 07:48:45 on February 14, 2016 · (Permalink)
[deleted]
ImS0hungry · 2 points · Posted at 22:46:41 on February 14, 2016 · (Permalink)
It was a 4-part series called the Story of Maths. Not sure which episode exactly though.
MediumHorse · 1 points · Posted at 06:28:47 on February 15, 2016 · (Permalink)
Thanks!
youssarian · 3 points · Posted at 00:10:54 on February 14, 2016 · (Permalink)
To be fair, Godel's incompleteness theorem was probably a joykill for just about everyone.
[deleted] · 1 points · Posted at 02:16:50 on February 14, 2016 · (Permalink)
No, we get erections in the logic class just mentioning it. Last year's prof said it was "almost poetic".
heap42 · 1 points · Posted at 23:31:40 on February 13, 2016 · (Permalink)
No. The proof is correct. Also, proof cannot be complete(i think) completeness is the property of an algorithm/calculus. also 1+1=2 this is a true and proven statement. However the original paper, tried to prove that everything can be proven in peano arithmetic, AKA Completeness, but Gödel proved that this is not the case.
[deleted] · 6 points · Posted at 19:21:17 on February 13, 2016 · (Permalink)
Link?
antijudo · 8 points · Posted at 20:56:49 on February 13, 2016 · (Permalink)
The proof is given on page 379 of principia mathematica: volume I. Actually it is still to be finalized, that is done somewhere in volume II, but I can't find the right page right now.
GangreneMeltedPeins · -2 points · Posted at 03:24:09 on February 14, 2016 · (Permalink)
I dont know why you bothered. Its not like that guys gunna read it.
OZONE_TempuS · 25 points · Posted at 19:23:43 on February 13, 2016 · (Permalink)
The proof is 362 pages, I doubt you want to read it.
[deleted] · 29 points · Posted at 19:24:18 on February 13, 2016 · (Permalink)
I would like to see
OZONE_TempuS · 16 points · Posted at 19:25:29 on February 13, 2016 · (Permalink)
I can't find Whitehead and Rusell's proof but here's one.
heap42 · 2 points · Posted at 23:33:11 on February 13, 2016 · (Permalink)
Thats Natural Deduction....
youssarian · 2 points · Posted at 00:12:42 on February 14, 2016 · (Permalink)
Do you know a resource I could use to learn more about this stuff? I've had an interest in philosophy for a while, but particularly in stuff like this, where you take basic statements and just use the four basic laws of logic to deduce stuff.
[deleted] · 3 points · Posted at 02:25:16 on February 14, 2016 · (Permalink)
http://plato.stanford.edu/entries/logic-classical/
You can start here, but I'm afraid you'll eventually need big fat books.
[deleted] · 1 points · Posted at 02:18:04 on February 14, 2016 · (Permalink)
Oh yeah but that's MND, vastly different.
thatJainaGirl · 2 points · Posted at 23:14:48 on February 13, 2016 · (Permalink)
"The simplest thought, like the concept of the number 1, is a complex logical underpinning..."
[deleted] · 2 points · Posted at 00:09:45 on February 14, 2016 · (Permalink)
There's also one about zero (by coincidence titled Zero) which describes the concept of zero. Apparently the mathematical concept wasn't derived in the west until ~1200 c.e. I never read the book but I remember hearing that the author somehow proved that Winston Churchill was a carrot (or something).
ColeSloth · 2 points · Posted at 01:07:58 on February 14, 2016 · (Permalink)
What exactly is this whole 1+1=2 not being true thing? I'm good with basic math and geometry but never branched out into even knowing any n and n+ or ! Stuff.
How is adding one of something and another of the same something hard to prove that it equals two of that thing?
jywn4679 · 1 points · Posted at 23:53:17 on February 14, 2016 · (Permalink)
It's very easy to prove, depending on what sort of proof you want or what foundations you are working from. What they were really doing was trying to create a firm foundation for all of mathematics, and to check it was working they showed 1+1=2, because if they couldn't prove that then their foundation wasn't very good.
woflcopter · 2 points · Posted at 01:40:50 on February 14, 2016 · (Permalink)
Do you know what it's called?
Troub313 · 1 points · Posted at 00:01:56 on February 14, 2016 · (Permalink)
I was going to come here to say 1 + 1 = 2 is the coolest math fact.
MrShutCo · 1 points · Posted at 00:37:15 on February 14, 2016 · (Permalink)
Didn't they have three books, and like 300 pages into the second one they finally proved 1+1=2?
Reddits_Worst_Night · 1 points · Posted at 00:46:22 on February 14, 2016 · (Permalink)
Principia Mathematica does a bit more than that. It proves it, then proves around 1000 things.
von_Hytecket · 1 points · Posted at 01:38:09 on February 14, 2016 · (Permalink)
...And then Gödel and Wittgenstein pooped on the parade.
TheRealZoidberg · 1 points · Posted at 01:40:38 on February 14, 2016 · (Permalink)
What's it called? :) Edit: Someone else already asked and it got answered, so ignore this, but thanks anyway!
americangame · 1 points · Posted at 01:50:50 on February 14, 2016 · (Permalink)
But 1+1 can equal 3 for very large values of 1.
shiguoxian · 1 points · Posted at 02:56:09 on February 14, 2016 · (Permalink)
Are you referring to OP's mom?
americangame · 1 points · Posted at 03:32:00 on February 14, 2016 · (Permalink)
What's 1.4 +1.4 = 2.8. Now round everything to have no decimal point and you'll see that 1+1=3
cinemarshall · 1 points · Posted at 01:55:58 on February 14, 2016 · (Permalink)
What about for large values of 1
complex_reduction · 1 points · Posted at 02:11:58 on February 14, 2016 · (Permalink)
Serious question, I've heard this trivia before and I've always wondered, why do you need hundreds of pages to "officially prove" 1 + 1 = 2?
I mean, get an apple, put it next to another apple, you now have two apples. That's your proof.
[deleted] · 1 points · Posted at 02:15:13 on February 14, 2016 · (Permalink)
It's just a part of a much bigger work.
Jedimastert · 1 points · Posted at 02:16:14 on February 14, 2016 · (Permalink)
What's the book?
Kaeloso · 1 points · Posted at 02:36:17 on February 14, 2016 · (Permalink)
but without dimming the x as the integer 1+1 = 11
SimAyo · 1 points · Posted at 02:51:59 on February 14, 2016 · (Permalink)
What is the name of the book ?
appropriate-username · 2 points · Posted at 13:53:21 on February 14, 2016 · (Permalink)
Principia mathematica--written to prove everything in math but then the authors gave up and after that somebody proved that it's impossible to do that.
Bashar_Al_Dat_Assad · 1 points · Posted at 04:05:22 on February 14, 2016 · (Permalink)
No there isn't. If you're thinking of Principia Mathematica it attempts to prove all of math (later shown impossible by Gödel). It's not necessary to prove all of math to prove 1+1=2 since it's trivially derived from whatever axioms your formalism of mathematics espouses, so what Principia Mathematica attempted to do is not reducible to proving 1+1=2.
Padre_of_Ruckus · 1 points · Posted at 04:48:45 on February 14, 2016 · (Permalink)
1+1=3, sorry ;)
blacksheeprising · 1 points · Posted at 05:01:32 on February 14, 2016 · (Permalink)
I prefer the one about 2+2=5.
putzu_mutzu · 1 points · Posted at 05:24:51 on February 14, 2016 · (Permalink)
doesn't the existence of infinte numbers prove that 1+1 does NOT equal 2?
yugung · 1 points · Posted at 05:41:32 on February 14, 2016 · (Permalink)
There's one for 2+2=5 too!
Sunwoken · 1 points · Posted at 05:53:54 on February 14, 2016 · (Permalink)
In my Real Analysis class, the professor spent 20 minutes explaining why 1=/=0 was an important axiom for the theorem we were learning.
bookworm2692 · 1 points · Posted at 06:00:25 on February 14, 2016 · (Permalink)
In my first maths lesson this year, my teacher dictated what to do to create this.
Let a = b
a = b
ab = b2
ab - a2 = b2 - a2
a(b - a) = (b + a)(b - a)
a = b + a
Let a = 1
1 = 1 + 1
1 = 2
appropriate-username · 1 points · Posted at 13:56:57 on February 14, 2016 · (Permalink)
FTFY, took me way too long to see it though.
bookworm2692 · 1 points · Posted at 04:51:54 on February 15, 2016 · (Permalink)
Yeah I know it's dividing by zero. I guess that's why they say weird things happen when you divide by zero right?
appropriate-username · 1 points · Posted at 05:16:59 on February 15, 2016 · (Permalink)
I was just always told you get infinity.
bookworm2692 · 2 points · Posted at 05:23:36 on February 15, 2016 · (Permalink)
Yeah. My teachers always said "never divide by zero it gets weird" but in a book I got for Christmas once it explained you get infinity
09jtherrien · 1 points · Posted at 06:05:26 on February 14, 2016 · (Permalink)
When my professor told me that the proof that proved this was like 300 pages long, I didn't believe him.
reddit__scrub · 1 points · Posted at 06:21:33 on February 14, 2016 · (Permalink)
I mean, a book could be just one page. With mostly whitespace.
But holy shit 300 pages for that would make me gouge my eyes out.
InfanticideAquifer · 1 points · Posted at 06:24:23 on February 14, 2016 · (Permalink)
The point of the book isn't to prove that 1+1=2. That's a small application of the machinery that they develop in the book.
Leporad · 1 points · Posted at 06:33:20 on February 14, 2016 · (Permalink)
No. That's a lie.
The proof in the book is less than half a page.
Number1AbeLincolnFan · 1 points · Posted at 06:36:35 on February 14, 2016 · (Permalink)*
Can someone explain how a proof like this is even possible without being self referential?
As a layman, it seems to me that all of mathematics is based on extrapolation of a handful of fundamental givens and that we assign labels to these things. For example, that integers are incremented by adding 1 to each. The labels we give these groups of things are just shorthand.. like the symbol "6" really just means 1+1+1+1+1+1.
I don't know.. it's just weird to me because it seems like it would boil down to a pointless semantic argument about the definition of words. The entire concept of 2 is that it is 1+1. Apparently, I am wrong, but it seems to me like Alfred Nobel having to prove the dynamite he invented was, in fact, dynamite.
Randomnerd29 · 1 points · Posted at 06:51:33 on February 14, 2016 · (Permalink)
tell that to the banark tarski paradox. 1+1 can equal 1. FML math you had one job!
appropriate-username · 1 points · Posted at 14:17:21 on February 14, 2016 · (Permalink)
Where in the video does the guy say that?
Randomnerd29 · 2 points · Posted at 20:43:52 on February 14, 2016 · (Permalink)
at 18 minutes 55 seconds. it doesn't actually mean 1+1 equals one. it means that it is mathematically possible for one object to double itself without adding anything else. its pretty cool. you should watch the whole video. it also does a good job explaining how huge infinity is. for example, if you subtract any finite number it would still equal infinity. Infinity-1=Infinity
rshorning · 1 points · Posted at 07:10:19 on February 14, 2016 · (Permalink)
Except that with Boolean Algebra, 1+1 = 1
No, I'm not making that up either. This is not the fallacious proof where 0 = 1, but rather that the domain of answers is limited to 0 and 1 (or true and false..... but you can use numeric conventions as they are also used in computing). The "+" symbol in this case is a synonym for the "or" operator in Boolean algebra. The other cases similar to addition work out just fine though:
therefore
appropriate-username · 1 points · Posted at 14:18:26 on February 14, 2016 · (Permalink)
Don't see why the last line is a conclusion of the above few lines, I always thought all those four were assumptions in BA.
Forgot-My-Name_again · 1 points · Posted at 07:40:43 on February 14, 2016 · (Permalink)
and it is a REALLY important book in the history of Mathematics (if you are thinking about the same one I am).
Will_admit_if_wrong · 1 points · Posted at 07:42:49 on February 14, 2016 · (Permalink)
That's nothing it took Euclid until his 7th book, and there are 13!
I've been studying the first six all year.
[deleted] · 1 points · Posted at 08:11:30 on February 14, 2016 · (Permalink)
Someone give Terrence Howard a copy of this book.
pukahontas · 1 points · Posted at 08:15:37 on February 14, 2016 · (Permalink)
This didn't take a book, but, isn't a=a the identity theorem? What a crazy theory.
rubberseatbelt · 1 points · Posted at 08:31:18 on February 14, 2016 · (Permalink)
1/3 + 1/3 +1/3 = 1
.333 + .333 + .333 = .999 1 != .999 Therefore, 2 != .999 + .999 but 2 = 2/3 + 2/3 + 2/3
appropriate-username · 2 points · Posted at 14:20:02 on February 14, 2016 · (Permalink)
You lost your trailing dots there.
FTFY ^
_Duffman · 1 points · Posted at 09:15:50 on February 14, 2016 · (Permalink)
I have studied this. And I almost failed that course.
Ori_553 · 1 points · Posted at 09:35:00 on February 14, 2016 · (Permalink)
What is that book?
appropriate-username · 1 points · Posted at 14:20:34 on February 14, 2016 · (Permalink)
Principia mathematica, but it's been proven to be impossible to finish.
PonkyBreaksYourPC · 1 points · Posted at 10:06:55 on February 14, 2016 · (Permalink)
PonkyBreaksYourPC · 1 points · Posted at 10:06:56 on February 14, 2016 · (Permalink)
UsablePizza · 1 points · Posted at 10:43:27 on February 14, 2016 · (Permalink)
But when engineering 1+1 = 3 for sufficiently large values of 1.
HW90 · 1 points · Posted at 10:58:25 on February 14, 2016 · (Permalink)
Until you do boolean algebra where 1+1=1
[deleted] · 1 points · Posted at 11:47:13 on February 14, 2016 · (Permalink)
I remember having to do some maths papers in engineering intermediate. When the lecturer devoted a whole lecture to proving 1+1=2 I decided I was glad I was going to be in engineering school the following year, and away from the mathematicians.
cisnotation · 1 points · Posted at 12:14:59 on February 14, 2016 · (Permalink)
Ugh I always hated proofs like these... it's so simple yet so hard to prove.
Raikhyt · 1 points · Posted at 13:21:25 on February 14, 2016 · (Permalink)
Hey, they couldn't even get it published at first because the publisher they went to couldn't find anyone who could read it.
random314 · 1 points · Posted at 14:48:44 on February 14, 2016 · (Permalink)
Oh god... Theorems and Axioms. I vaguely remember being forced to take those math theory courses as req for comp science...
king_olaf_the_hairy · 6912 points · Posted at 19:27:28 on February 13, 2016 · (Permalink)
The decimal fractions of seven are the same six recurring digits, in the same order, but starting from a different one each time.
1/7 = 0.142857142857...
2/7 = 0.285714285714...
3/7 = 0.428571428571...
4/7 = 0.571428571428...
5/7 = 0.714285714285...
6/7 = 0.857142857142...
Euerfeldi · 4438 points · Posted at 19:48:10 on February 13, 2016 · (Permalink)
Things like these still make me think that some parts of math are black magic
Chel_of_the_sea · 317 points · Posted at 03:58:17 on February 14, 2016 · (Permalink)
It's a consequence of the fact that 10 is a primitive root mod 7.
vagile · 98 points · Posted at 04:29:53 on February 14, 2016 · (Permalink)
can you explain this?
Chel_of_the_sea · 398 points · Posted at 04:42:23 on February 14, 2016 · (Permalink)
To an extent, sure.
Consider some prime number (let's say 5) and consider a number that isn't a multiple of it (say, 9). What we're interested in is the remainder when 9 is divided by 5 (4, in this case), and the pattern that develops if we look at the powers of 9.
The powers of 9 go 1, 9, 81, 729... and the remainders go 1, 4, 1, 4... These two values repeat forever, and we say that 9 has order 2 modulo 5. It turns out that, when you write a fraction in a specific base system (decimal, binary, etc), the length of the repeating "decimal" (or repeating digits in whatever base) depends on the order of the base you're working in modulo the denominator of the fraction.
This is why fractions with 9 on the bottom produce easy, single-digit repetition, because 10 has order 1 modulo 9. Same with 3: 10 has order 1 modulo 3. It's worse with numbers like 11, because 10 has order 2 modulo 11 (so you can get decimals like .090909090909...). But the worst of them all, for small numbers, is 7.
The order of a number mod 7 (or mod any number) cannot possibly be bigger than the number itself minus 1 (in the case of mod 7, the order is at most 6). A number that reaches this maximum is called a primitive root, and unfortunately for math students everywhere, 10 is a primitive root mod 7 - that is, 10 has order 6 mod 7. As a result, fractions over 7, when written in decimal, have repeating segments 6 digits long.
Interestingly, if we choose a "nicer" base, this problem vanishes. In base 8, for example, fractions with 7 on the bottom have only a one-digit repeating part, just like fractions over 9 in decimal.
Endur · 13 points · Posted at 11:10:51 on February 14, 2016 · (Permalink)
What do you do for a living? I'm curious
Chel_of_the_sea · 11 points · Posted at 18:50:59 on February 14, 2016 · (Permalink)
At the moment I tutor kids in the SAT. I'm trying to get a job at a community college atm.
JakkuScavenger · 1 points · Posted at 14:32:20 on February 14, 2016 · (Permalink)
They're probably a math professor.
__PM_ME__ · 7 points · Posted at 16:28:53 on February 14, 2016 · (Permalink)
Or a janitor
Chel_of_the_sea · 3 points · Posted at 18:58:57 on February 14, 2016 · (Permalink)
I'd certainly love to be. Not that I've had any luck actually getting a job.
carlhead · 4 points · Posted at 11:17:16 on February 14, 2016 · (Permalink)
Hah, and here in your original comment I thought you were just making up words!
I_am_lonely_pm_me · 4 points · Posted at 13:10:26 on February 14, 2016 · (Permalink)
Things like this make me want to study math
Math can be cool. It can also be very boring
But ultimately, there are a million and one people who are much much much better than me at math so there's probably no point
574N13Y · 5 points · Posted at 13:54:58 on February 14, 2016 · (Permalink)
this is not true
I_am_lonely_pm_me · 1 points · Posted at 16:41:25 on February 14, 2016 · (Permalink)
Saying which part isn't true probably helps
FlamingSwaggot · 3 points · Posted at 18:00:47 on February 14, 2016 · (Permalink)
574N13Y · 1 points · Posted at 10:21:14 on February 15, 2016 · (Permalink)
effort
[deleted] · 3 points · Posted at 14:52:39 on February 14, 2016 · (Permalink)
There is no shame in being good enough to make a living in something but not revolutionize the field. In fact, thats what the majority of people are at in terms of skill level.
adelie42 · 2 points · Posted at 18:00:15 on February 14, 2016 · (Permalink)
Too lazy to find the source, but I've heard that with respect to intellect if you can grasp algebra all higher math simply requires time and dedication to learn.
Lack of interest is completely understandable, but you are in no way incapable of learning it reading the right books and practice.
Chel_of_the_sea · 1 points · Posted at 19:01:26 on February 14, 2016 · (Permalink)
There are plenty of people who're better than math than me, too. I have a Master's in it, but I don't really intend to study it too much further than that. There are folks who spend PhD and an entire career studying the behavior of things like primitive roots (in fact, there's a very celebrated theorem about them that has more known proofs than almost any other).
I_am_lonely_pm_me · 1 points · Posted at 07:59:38 on February 15, 2016 · (Permalink)
Fair enough.
What can you do with a math degree aside from teaching?
Chel_of_the_sea · 1 points · Posted at 08:11:57 on February 15, 2016 · (Permalink)
Depends on the kind of math. Combinatorists often do comp sci, analysis experts often develop engineering approximations and theorems, topologists and algebraists tend to be into physics.
I_am_lonely_pm_me · 1 points · Posted at 08:30:24 on February 15, 2016 · (Permalink)
Thanks
Asterix1806 · 2 points · Posted at 08:52:40 on February 14, 2016 · (Permalink)
What's the smallest primitive root mod10 bigger than 7?
[deleted] · 6 points · Posted at 11:09:52 on February 14, 2016 · (Permalink)
[deleted]
Chel_of_the_sea · 3 points · Posted at 19:03:11 on February 14, 2016 · (Permalink)
3 and 7 are the only remainders of primitive roots mod 10. If you're thinking of 3 and 7 as symbols for equivalence classes then they're the only ones (but in that case, "bigger" makes no sense because the equivalence classes aren't ordered), but not if you're thinking of them as symbols for the natural numbers one usually writes 3 and 7. In fact, any number of the form 10n+3 or 10n+7 is a primitive root mod 10.
Chel_of_the_sea · 2 points · Posted at 18:53:58 on February 14, 2016 · (Permalink)
Do you mean the smallest primitive root mod 7 bigger than 10? Uh, well, there are 2 basic prim roots mod 7 (there's a function for this that's pretty easy to evaluate in your head for small numbers): 3 and 5. So 10 (which is 1*7 + 3) would be followed by 12 (which is 1*7 + 5).
[deleted] · 2 points · Posted at 10:58:31 on February 14, 2016 · (Permalink)*
[deleted]
TheFlyingDrildo · 4 points · Posted at 13:20:03 on February 14, 2016 · (Permalink)
Yes 8 in base 10 equals 10 in base 8
red_eleven · 5 points · Posted at 14:27:00 on February 14, 2016 · (Permalink)
Hey just like multiplying percents, amirite?
Burnaby · 1 points · Posted at 16:30:51 on February 14, 2016 · (Permalink)
3 in base 8 is not 8 in base 3, it's 22
Chel_of_the_sea · 1 points · Posted at 18:51:34 on February 14, 2016 · (Permalink)
Right. Your digits in base 8 are "ones", "eights", "sixty-fours", "two-hundred-fifty-sixes", and so on.
autoposting_system · 2 points · Posted at 12:47:34 on February 14, 2016 · (Permalink)
Jesus christ math is amazing
Cortye · 2 points · Posted at 14:21:59 on February 14, 2016 · (Permalink)
You sir are awesome. I'm a physics teacher with a huge love for maths. Premission to use this explanation for my future classes?
Chel_of_the_sea · 3 points · Posted at 18:48:08 on February 14, 2016 · (Permalink)*
'course. Feel free to recommend me for a job, too, if you happen to live in Washington or Oregon >.>
Also, madam :P
Cortye · 2 points · Posted at 22:13:12 on February 14, 2016 · (Permalink)
How about the Netherlands? And I am really sorry madam!
Chel_of_the_sea · 1 points · Posted at 02:46:08 on February 15, 2016 · (Permalink)
Sure, I'd be down to work for the Danes :P
misterblade · 1 points · Posted at 15:55:35 on February 14, 2016 · (Permalink)
Yes, sure go ahead - permission granted.
UsablePizza · 2 points · Posted at 10:36:52 on February 14, 2016 · (Permalink)
I like the part about "nicer" base. Really, if we were base 8 everything would be nicer. We could half 1000 until reaching 1; computers wouldn't need binary kilo / mega (1024 vs 1000) and so on.
We could even count to 24 (30) easily on our hands.
Lighterlow · 8 points · Posted at 11:02:44 on February 14, 2016 · (Permalink)
well in binary we can count to 1023 on our hands
UsablePizza · 2 points · Posted at 11:25:17 on February 14, 2016 · (Permalink)
And I can literally think of millions of reasons why binary is better. (I only need 64 :P)
aaeme · 6 points · Posted at 11:21:55 on February 14, 2016 · (Permalink)
The base of the number only has any meaning when writing it or naming it. As counting on our hands doesn't involve writing, I can only assume you want to rename the numbers something like this: one, two, three, four, five, six, seven, octy, octy-one, octy-two, octy-three, ..., octy-seven, biocty, biocty-one, biocty-two, ..., triocty, ..., etc.
I think that's a great idea but I doubt most people would.
googolplexbyte · 3 points · Posted at 14:17:36 on February 14, 2016 · (Permalink)
Each finger represents an order of 2 and you can encode 1024 numbers on your hands based on which fingers you have up or down.
i.e. if you have your hands out palms away from from you;
00000 00100 which is 4 would be represented by putting your middle finger up on you right hand.00001 10000 which is 48 would be represented by putting both your thumbs up.I don't think it's viable because some numbers are ridicolously hard to hold, such as any even number because holding my ring finger up without my pinky finger is painful.
I much prefer the base six version where you use the left hand to count how many times you've reached six and restart the count on your right hand again, this allows simple counting to 35 (who even needs to count to 1023) with no hand strain and little more complexity than normal hand counting.
JakkuScavenger · 1 points · Posted at 14:35:12 on February 14, 2016 · (Permalink)
It should be one, two, three, four, five, six, seven, ten, eleven..., seventeen, twenty, twenty-one,..., twenty-seven, thirty,..., seventy-seven, one hundred, etc.
JakkuScavenger · 2 points · Posted at 14:32:58 on February 14, 2016 · (Permalink)
/r/base60masterrace
googolplexbyte · 1 points · Posted at 14:03:18 on February 14, 2016 · (Permalink)
Is there a nicest base?
I'd imagine base 6 is nicest for this as all primes (par 2 & 3) are 6n ± 1.
Chel_of_the_sea · 2 points · Posted at 18:49:03 on February 14, 2016 · (Permalink)*
A "nice" base for this purpose would be a minimum of lambda(n)/n, where lambda is the Carmichael function. 6 is one such minimum, since lambda(6) = 2 and 2/6 = 1/3, which is lower than any smaller number. You can do better, though: if you choose base 30, for example, you get lambda(30) = 4 and 4/30 = 2/15 is much less than 1/3.
DonQuixoteReference · 1 points · Posted at 15:26:19 on February 14, 2016 · (Permalink)
The things you learn about people you thought you knew...
Chel_of_the_sea · 1 points · Posted at 19:11:58 on February 14, 2016 · (Permalink)
I don't exactly make a secret of being mathematically inclined, lol. I have a graduate degree in it.
DonQuixoteReference · 1 points · Posted at 19:22:16 on February 14, 2016 · (Permalink)
Yeah, it's just nice to see what people you know are really into.
Chel_of_the_sea · 1 points · Posted at 19:24:32 on February 14, 2016 · (Permalink)
It might be easier to list the things I'm not really into!
DonQuixoteReference · 1 points · Posted at 19:28:31 on February 14, 2016 · (Permalink)
I might be interested in that list...
ikahjalmr · 1 points · Posted at 19:55:29 on February 23, 2016 · (Permalink)
Is it always nicer when you divide the 10 in a base system by base-1?
Chel_of_the_sea · 1 points · Posted at 19:58:50 on February 23, 2016 · (Permalink)
Can't do base 1, nor am I sure what you're asking.
ikahjalmr · 1 points · Posted at 23:06:12 on February 23, 2016 · (Permalink)
Besides base 1, does n/n-1 always divide nicely in base n?
Chel_of_the_sea · 1 points · Posted at 04:53:55 on February 24, 2016 · (Permalink)
Yes. n always has period 1 mod n-1, because n has remainder 1 when divided by n-1. The powers of 1, which are 1, 1, 1, 1, 1..., all have remainder 1.
ikahjalmr · 1 points · Posted at 05:24:03 on February 24, 2016 · (Permalink)
Ah wow very interesting stuff
SquatMaster3000 · 4 points · Posted at 04:40:56 on February 14, 2016 · (Permalink)
A black magic spell.
Fmorris · 2 points · Posted at 11:32:28 on February 14, 2016 · (Permalink)
Then how do we get the digits that we get?
The multiplicative group modulo 7 (of which 10 is a generator) is: {3, 6, 2, 5, 1, 4, 0}
But the decimal digits we get are: {1, 4, 2, 8, 5, 7}
What is the link between the two?
zilti · 1 points · Posted at 12:14:17 on February 14, 2016 · (Permalink)
Those are my favourite math facts. Sometimes you suddenly notice something, and find out it's because of something else you thought is completely unrelated.
Nosrac88 · 1 points · Posted at 16:57:27 on February 14, 2016 · (Permalink)
In layman terms that means what exactly?
I_HAVE_FRIENDS_AMA · 1 points · Posted at 18:42:51 on February 14, 2016 · (Permalink)
I like this sentence.
My_Perfect_Boy · 2670 points · Posted at 01:49:16 on February 14, 2016 · (Permalink)
No it just means there is order to the universe
[deleted] · 1675 points · Posted at 02:15:43 on February 14, 2016 · (Permalink)
No, it just means that a certain number divided by a certain number equals a number. We just make the patterns significant.
[deleted] · 417 points · Posted at 02:33:04 on February 14, 2016 · (Permalink)
Actual it's more a description of a certain part of reality. If it was just a number that only had significance because we gave significance that then it probably wouldn't also be a naturally occurring phenomenon but it is.
[deleted] · 784 points · Posted at 03:17:45 on February 14, 2016 · (Permalink)*
[deleted]
TikiTDO · 528 points · Posted at 04:22:56 on February 14, 2016 · (Permalink)*
Except this also happens in say, base 12... In that case the decimal component is a repeating variation on ...186a35...
In fact this patter repeats itself in some way for any integral base, though not for an fractional/irrational base due to how decimals are represented in those cases.
Just because numbers are an abstraction, does not mean that the concepts that are being abstracted do not exhibit interesting patterns. I could argue that in fact these abstractions, and the patterns encoded there in are more "real" than anything in the physical world.
Edit: Since this comment got some popularity, I'd figure I'd paste my math rant from below.
A lot of time certain patterns do depend on other conditions. For instance, 1/7 in base 7 is simply 0.1, while 1/7 in base e is a non-repeating decimal. In fact the very idea of a "number" is deceptively much more complex than most people believe.
In general, math is better understood as a sort of language than some sort of immutable idea. It allows people to strictly define information in such a way that anyone else that understand that language can figure out exactly what is encoded. The beauty of math is that it allows people to define (nearly) any type of information, and to ensure that it can be understood in the exact same way by anyone else that understand the principles used to encode that information (mathematical axioms).
This is in contrast to a natural language, which may allow the exact same statement to be interpreted in different ways based on any number of contextual factors (say the mood of the reader).
Unfortunately, most schools do not present math that way until way into upper level university math courses, and by that point most people will never see the material, and will never realize how dreadfully they were cheated by our utterly horrible education system. The worst part is, once you learn to see math that way all of those strange rules and patterns that you had to memorize for school level classes become extraordinarily obvious. So much so that you could probably condense all 12 years of school math education down into a semester or two.
We do this all under the guise of it being "easier to understand," which is really just code for "we don't want to put in the work to figure out how to teach it correctly so even kids can get it, so we just teach it like we've always done."
[deleted] · 165 points · Posted at 05:10:08 on February 14, 2016 · (Permalink)
This comment chain is like a math nerd rap battle. Each comment I read I hear BOOM! or OOOOOOOH!
Broan13 · 108 points · Posted at 05:31:39 on February 14, 2016 · (Permalink)
It is a common fight between two major camps that typically are variations on "Platonism" (the idea that math exists in some abstract way and we only discover it) and "Nominalism" (the idea that we make definitions and put names on things, and therefore construct mathematics).
I am not treating the field of the philosophy of math with anything more than the broadest of brushes though. A good text I have read is on Aristotilean Realism which offers a 3rd idea that is a bit of a combination, but more of a real world version of platonism.
TheRealCalypso · 50 points · Posted at 06:50:15 on February 14, 2016 · (Permalink)
OOHHHHHHHHHHHH!
onFilm · 1 points · Posted at 17:38:12 on February 14, 2016 · (Permalink)
Lol you nerd
1rdc · 13 points · Posted at 07:07:50 on February 14, 2016 · (Permalink)
tbh this is the coolest math fact to me :D
saltinstien · 1 points · Posted at 08:28:13 on February 14, 2016 · (Permalink)
Me too! This is a dilemma I've never even imagined before, but now can't stop thinking about.
earthlingHuman · 5 points · Posted at 07:27:01 on February 14, 2016 · (Permalink)
I was gonna comment with the 'why not both' meme, then I read the second paragraph. Pleasantly surprised
BrosenkranzKeef · 3 points · Posted at 09:39:07 on February 14, 2016 · (Permalink)
It's clearly a combination of both. Natural patterns exist with or without humanity, we simply happen to have discovered the patterns. We made sense of those natural patterns by assigning logical definitions to describe them. Obviously "mathematics" doesn't exist without us because it's a word we came up with and assigned a definition to, just like every other thing we've ever described. But nature doesn't care what we call it because it's already there doing its thing.
XtremeGoose · 3 points · Posted at 12:47:02 on February 14, 2016 · (Permalink)
It really isn't that clear. Very clever people have spent their lives debating both extremes. Whilst obviously the names for things is a human construct, the idea that the "real numbers" actually exist or are some useful abstract tool we invented is very much up for debate.
WilliamPoole · 3 points · Posted at 14:08:55 on February 14, 2016 · (Permalink)
Since you'll never find, say, a 7 in the wild, it will always be up for debate..
BrosenkranzKeef · 2 points · Posted at 19:26:08 on February 14, 2016 · (Permalink)
Besides the numeral statues here on campus, "numbers" don't exist. We've never caught a glimpse of wayward digits floating through space, that's an idiotic idea. But the fact is that if there are several ducks standing by a pond, there is a certain number of them no matter what you call it. Objects in the universe are numerous and patterns exist. Numbers are things that we came up with to describe those objects and patterns.
I'm of the opinion that in some cases scientists and philosophers think way too hard about stuff that really is common sense.
XtremeGoose · 2 points · Posted at 06:13:48 on February 15, 2016 · (Permalink)
Of course when you talk about number of ducks it seems obvious, but then start talking about how electrons only have spins of ±h/4π, and how the wave function describes quantum systems so unreasonably well (a wave function that has absolutely no physical interpretation until you take its modulus squared). You only need to look at the Higg's mechanism to see how a purely mathematical solution manages to predict the existence of whole new particles.
agentmuu · 2 points · Posted at 09:25:23 on February 14, 2016 · (Permalink)
This reminds me of the descriptivist vs prescriptivist argument of linguistics
TikiTDO · 1 points · Posted at 20:02:20 on February 14, 2016 · (Permalink)
I never really understood that argument. It's an impossible distinction, at least within the context of our Universe. What would it mean for math to "exist" in some way? For us it means that the idea is somehow realized within the Universe we inhabit. If the idea does not exist in that way, then for all intents and purposes it does not exist for us.
Whether the idea "exists" in some abstract way or not is meaningless to people, since we would at least need to define what it means for an idea to "abstractly exist." What more, as you mentioned there are other perspectives. What if we define what it means to "abstractly exist" and find that only some of math is "discovered" from this abstract existence, while other math is a purely original construct. There are a near infinite number of way to mix these ideas.
In fact, you can draw benefit from viewing math as a superposition of both concepts, and applying just the right mix to whatever problem you have at hand. That I feel is the only proper answer.
Broan13 · 1 points · Posted at 20:10:08 on February 14, 2016 · (Permalink)
I don't have any answers for you, nor can I contribute much as I am not a philosopher, much less a philosopher of math.
To some extent I think the relationships exist in nature already, and that we discover them. To another extent I think we provide specific definition and define structures and discover the relationships inherent in that structure.
[deleted] · 1 points · Posted at 16:49:58 on February 19, 2016 · (Permalink)
I agree with your conclusion. The thing for me about all this is, and maybe it's because I'm not half as smart or educated on this topic as everyone else here, I can't see how someone might think that an idea doesn't actually exist. Of course it exists. It exists like any other phenomenon. It's synapses in a brain. Just because it's abstract and not tangible like a rock doesn't take it out of reality somehow. We accept other small electrical signals to exist, why if the context is in a human brain does it come in to question? Because it requires another human brain and language to decode it? That happens with other types of electrical signals we use every day. The content of an idea doesn't have to be logically true or false for that idea to just exist.
shylocxs · 0 points · Posted at 12:32:27 on February 14, 2016 · (Permalink)
Boom y'all!
cmagnificent · 4 points · Posted at 05:49:45 on February 14, 2016 · (Permalink)
I'm glad to be part of the entertainment. Really, XCOM 2 is just taking fucking forever to finish downloading on Steam. That's why this is happening.
[deleted] · 1 points · Posted at 12:04:53 on February 14, 2016 · (Permalink)
Im doing math...moms spaghetti
Spaghetti_Robotti · 0 points · Posted at 12:07:15 on February 14, 2016 · (Permalink)
What do blondes and spaghetti have in common? They both wiggle when you eat them.
[deleted] · 13 points · Posted at 04:29:51 on February 14, 2016 · (Permalink)*
[deleted]
TikiTDO · 43 points · Posted at 04:34:59 on February 14, 2016 · (Permalink)*
In base 12 the pattern is 186a35. Or say, in base 19 the pattern is 2:13:10:16:5:8
In fact there are three rules about how this number is represented.
If the base is divisible by 7 then any number that is itself not a multiple of 7 divided by 7 is a non-repeating decimal point.
If the base + 1 or base - 1 is divisible by 7, then any number that is itself not a multiple of 7 divided by 7 will be a short sequence of repeated numbers, multiplied by the actual number. So for instance 1/7 in base 15 is 0.2222... while in base 22 it's 0.3333...
For all other integer bases, any number that is itself not a multiple of 7 divided by 7 will be the exact same sequence of repeating numbers.
It's not exactly an unexpected pattern, in fact it shows up across all sorts numbers in all sorts of bases. The number 7 just illustrates that property quite well in base 10. The number 5 exhibits the exact same property in base 7 for example.
It is simply an artifact of how the division operation works. So in this case it's not really a property of any specific number, but a property of the operation of division itself. It's still a cool fact about math that most people might never think about, but it has nothing to do with the number 7. You don't need to understand all that much math to see how it arises. Just do the division by hand and it will quickly become obvious.
cmagnificent · -18 points · Posted at 04:43:17 on February 14, 2016 · (Permalink)
Alright, what is the value of the following in base 12 -
1/7
2/7
3/7
4/7
5/7
6/7
TikiTDO · 26 points · Posted at 04:47:15 on February 14, 2016 · (Permalink)
You can type things into wolfram alpha yourself.
If you really can't be bothered:
1/7: 0.186a35186a3518..._12
2/7: 0.35186a35186a35..._12
3/7: 0.5186a35186a351..._12
4/7: 0.6a35186a35186a..._12
5/7: 0.86a35186a35186..._12
6/7: 0.a35186a35186a3..._12
[deleted] · 3 points · Posted at 05:29:14 on February 14, 2016 · (Permalink)
[deleted]
TikiTDO · 16 points · Posted at 06:01:50 on February 14, 2016 · (Permalink)*
That's actually not always true. A lot of time certain patterns do depend on other conditions. For instance, 1/7 in base 7 is simply 0.1, while 1/7 in base e is a non-repeating decimal. In fact the very idea of a "number" is deceptively much more complex than most people believe.
In general, math is better understood as a sort of language than some sort of immutable idea. It allows people to strictly define information in such a way that anyone else that understand that language can figure out exactly what is encoded. The beauty of math is that it allows people to define (nearly) any type of information, and to ensure that it can be understood in the exact same way by anyone else that understand the principles used to encode that information (mathematical axioms).
This is in contrast to a natural language, which may allow the exact same statement to be interpreted in different ways based on any number of contextual factors (say the mood of the reader).
Unfortunately, most schools do not present math that way until way into upper level university math courses, and by that point most people will never see the material, and will never realize how dreadfully they were cheated by our utterly horrible education system. The worst part is, once you learn to see math that way all of those strange rules and patterns that you had to memorize for school level classes become extraordinarily obvious. So much so that you could probably condense all 12 years of school math education down into a semester or two.
We do this all under the guise of it being "easier to understand," which is really just code for "we don't want to put in the work to figure out how to teach it correctly so even kids can get it, so we just teach it like we've always done."
Anyway, that's a bit of a sore point. Sorry for the rant.
singul4r1ty · 1 points · Posted at 09:09:20 on February 14, 2016 · (Permalink)
Wolfram Alpha will tell you all of these if you type in "1/7 in Base 12" etc. The pattern clearly repeats and starts at different positions.
cmagnificent · -6 points · Posted at 09:14:27 on February 14, 2016 · (Permalink)
Alright, then let's do it in a base 7 system. In base 7, 1/7 would be .1, 2/7 would be .2 and so on and so forth.
The pattern depends on the base system chosen and is not inherent to mathematics as a whole.
singul4r1ty · 1 points · Posted at 09:35:06 on February 14, 2016 · (Permalink)
In any base fractions of that base will be as you described. It does depend on the Base system, but 7 is interesting because it has the cycling repeating decimal in any Base that's not a multiple of 7 or +/-1
spaceman_spiffy · 5 points · Posted at 12:33:32 on February 14, 2016 · (Permalink)
I came here expecting to discover new words I could write in my calculator like BOOBS, but now I'm struggling to reconcile my perceptions of mathematical abstractions and the universe.
JohnRando · 3 points · Posted at 08:21:15 on February 14, 2016 · (Permalink)
I want some of your math drugs
[deleted] · 1 points · Posted at 10:05:32 on February 14, 2016 · (Permalink)
Everyone in this thread is so smart, and here I am just trying to figure out a way to counter Secret Pally.
_oceanix · 1 points · Posted at 14:09:00 on February 14, 2016 · (Permalink)
Ya'll are smart
freejosephk · 2 points · Posted at 06:50:33 on February 14, 2016 · (Permalink)
Sure, but this doesn't mean "there is order in the universe." There are patterns in a rigidly constructed logical language, but the universe is not made of numbers. It's made of energy and mass, and time and space, and probability wave functions.
thirdegree · 2 points · Posted at 11:18:51 on February 14, 2016 · (Permalink)
The universe isn't made by numbers, but it is described by them.
shylocxs · 3 points · Posted at 12:36:30 on February 14, 2016 · (Permalink)
Described by them independently or innately self-describing?
thirdegree · 1 points · Posted at 12:38:38 on February 14, 2016 · (Permalink)
Not sure what you mean.
shylocxs · 1 points · Posted at 12:59:40 on February 14, 2016 · (Permalink)
Does math have an existence separate from the universe? Separate even from all universes?
TikiTDO · 2 points · Posted at 19:46:00 on February 14, 2016 · (Permalink)
Math is a set of ideas, which are themselves ordered structures. It doesn't really make sense to ask whether ideas exist separate from a Universe or not, unless you can exhaustively/mathematically define what it means for an idea to be "separate" from a realized, physical object or in this case a set of objects.
The idea that there is order in the Universe arises out of the fact that the Universe can be described by such ordered ideas, both in part and likely in whole. What more, not just described, but described often in a concise and simple form as opposed to a myriad of exceptions and special rules that would have to account for countless random phenomenon. In other words the logical relation is "there is order in the Universe" because "the Universe can be clearly described by math."
freejosephk · 1 points · Posted at 20:19:41 on February 14, 2016 · (Permalink)
Yes, but even then mathematics and the universe exist independent of each other. Do they not?
thirdegree · 1 points · Posted at 20:45:40 on February 14, 2016 · (Permalink)
I don't know.
wertymanjenson · 2 points · Posted at 09:37:29 on February 14, 2016 · (Permalink)
I love how bitchy you guys just got with each other.
[deleted] · 43 points · Posted at 04:15:38 on February 14, 2016 · (Permalink)
Couldn't you use that logic to claim that basically any natural phenomenon isn't actually a natural phenomenon? Just because that phenomenon would look different when seen with different tools doesn't mean it's not there.
[deleted] · 58 points · Posted at 04:23:39 on February 14, 2016 · (Permalink)*
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SlickMaw · 21 points · Posted at 04:48:52 on February 14, 2016 · (Permalink)
Isn't this a contested viewpoint between mathematicians and scientists?
[deleted] · 39 points · Posted at 04:55:46 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 9 points · Posted at 05:12:34 on February 14, 2016 · (Permalink)
Reality is that which still exists when you stop believing in it.
If you give two people the same set of mathematical rules they can derive the same proofs and verify them. Two computers running the same computer program will return the same results. If I work out a computer program by hand, I'll get the same result as a computer.
All of those things seem to indicate that math has a reality outside of any particular physical manifestation of it. None of those things need to have any relationship with the real world at all.
[deleted] · 13 points · Posted at 05:22:56 on February 14, 2016 · (Permalink)*
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platoprime · 6 points · Posted at 05:39:19 on February 14, 2016 · (Permalink)
I agree that numbers are abstractions but patterns like Pi do occur in nature. It's the ratio of the circumference of a circle to it's diameter. While numbers themselves are abstractions they are used to describe reality. No matter the units or base number system you use your Pi will be equivalent to my Pi just expressed differently.
And an electron certainly "knows" precisely how much it's charge is because it "knows" how to behave as if it had that precise amount of charge. While the numerical representation of that is an abstraction it is equivalent to any other abstraction that represents the electron's charge.
cmagnificent · 4 points · Posted at 05:42:09 on February 14, 2016 · (Permalink)
As I've expressed elsewhere already, the question then becomes, are all abstractions real? You've admitted that Pi is an abstraction based on other observations/properties, "circle", "circumference", "diameter", and "ratio".
There is no debate on whether or not abstractions can pertain to real objects, the question is, does that make the abstractions themselves "real"?
abagofit · 7 points · Posted at 06:02:54 on February 14, 2016 · (Permalink)
doesn't that all boil down to a semantic debate over the word real?
cmagnificent · 2 points · Posted at 06:10:35 on February 14, 2016 · (Permalink)
Shh, don't tell anyone, I'm having fun.
Also, "natural". Is "natural" anything that happens in the universe, in which case abstractions, and the patterns that emerge out of abstractions are certainly "natural", or does "natural" only refer to non-human constructs?
_username_goes_here_ · 2 points · Posted at 08:40:43 on February 14, 2016 · (Permalink)
I once had a metaphysics class, taught by a philosopher of language, who saved the last bit of reading for a piece about how all metaphysical arguments were actually problems of language. Was a neat way to cap the course.
platoprime · 4 points · Posted at 06:07:29 on February 14, 2016 · (Permalink)
It depends on what you mean by "real". Abstractions are absolutely real at least to some degree. If we take "real" to mean something I can hold in my hand or touch then your consciousness doesn't qualify as "real" but I think you might disagree and say that you do in fact have a consciousness and I believe you. I'd say that means that specific definition of "real" is only useful for discussing if something is a physical object. In that case of course numbers aren't "real" but it seems dishonest to imply that mathematicians think numbers are "real" physical objects you can hold. To demand to see a "two" and then say that because I can't show you one that you can touch that proves that numbers aren't "real" is juvenile and no more correct than saying your consciousness doesn't exist because you can't "show" it to me.
If we take google's definition
Okay so if it occurs in fact then it's real. Well I'd say integers occur in fact; there is no base number system in which one plus one does not equal two. The way you express "one" and "two" is expressed differently in binary but the math comes out exactly the same no matter which base system you use. So integers exist.
Let's address the original topic; 1/7 does not equal 0.142857142857. You can't express 1/7 exactly as a decimal just like you can't express 1/3 exactly as a decimal. As you correctly pointed out the interesting behavior of 1/7 disappears in other base systems however other such interesting behaviors from inexact decimal expressions of fractions emerge in other base systems. This means that all base number systems have the "real" property of being unable to express all of it's fractions as exact decimals. Except base one I guess.
TL;DR
Ultimately we are talking about emergent properties of systems and we are asking ourselves if those properties are "real". Your consciousness is just an emergent property of matter so I think the answer to "do abstractions exist?" is the same as asking "do I exist?" Since that is the only thing I can be truly certain of I'd answer with a resounding yes; yes, abstractions do exist.
cmagnificent · 1 points · Posted at 06:20:45 on February 14, 2016 · (Permalink)
I can certainly work with the google definition provided, for now at least.
So let's look at the second part:
Then let's take the definition of axiom (the foundation of mathematics) from WolframMathworld
Axioms, and thus the foundations of mathematics itself is stated as a pre-supposition, from which all other patterns and emergent properties derive.
Given that, it would seem that mathematics is not "real" in google's definition of the term.
I will agree, there is a hell of a grey area when asking about the reality of abstractions. I mean, I have abstractions, I experience them, as do countless other people, but they are obviously not of the same "stuff" as physical objects or forces.
platoprime · 1 points · Posted at 08:59:57 on February 14, 2016 · (Permalink)
You're pretending that mathematics is based on baseless assumptions that we could all discover to be incorrect next week but that isn't the case. It is axiomatic that there is no integer between one and two; not because it is an assumption but that is literally how we are defining one and two. The axioms of math don't dictate the truths of math but are instead derived from math using proofs not guesses.
Any axioms that are used that are assumptions are essentially meaningless ones meaning that if you make different assumptions then you are using a different system of math but one that will produce equivalent answers to the math we use now.
You're conflating the types of axioms to make it sound like mathematical axioms are made up truths like they sometimes are used in philosophical discussion to narrow the scope of the argument.
7+5=5+7 is not an assumption.
takua108 · 4 points · Posted at 05:52:03 on February 14, 2016 · (Permalink)*
When do perfect circles occur in nature?
EDIT: According to the first result on Google, never. I'll admit to being not entirely sober right now but the fact that a perfect circle itself is an abstraction created by humans, and all that that implies, is blowing my mind right now.
platoprime · 3 points · Posted at 06:11:45 on February 14, 2016 · (Permalink)*
I'm pretty sure the event horizon of a black hole is a perfect sphere which is made of an infinite number of perfect circles.
Edit: I'll add that photons orbit black holes at their event horizon and would also produce perfect circles in a slowly rotating black hole with no in-falling matter.
takua108 · 3 points · Posted at 06:14:42 on February 14, 2016 · (Permalink)
Well yeah, that's all that you can perceive with your human eyes. It's probably also surrounded by an infinite number of fourth-dimensional metaspheres, and so on to infinity
platoprime · 5 points · Posted at 06:17:20 on February 14, 2016 · (Permalink)
Don't care; still a naturally occurring circle. It's (the circle) a two dimensional object not a fourth dimensional object
takua108 · 3 points · Posted at 06:28:36 on February 14, 2016 · (Permalink)
I was actually half-joking, but before your edit, I was thinking about gravity. I know nothing about physics beyond a handful of successful Mun landings (emphasis on "landings") in Kerbal Space Program, but: is it possible to build an artificial object and put it into orbit around a celestial body at as close of an approximation to a perfect circle as possible? Would there be any way to "prove" it was "perfect"? At that point, you'd be using mathematics to create an artificial thing, in order to prove that the artificial concept of a perfect circle was, indeed, a naturally-occurring thing, given the right circumstances... then my head hurt and I stopped, and now I'm reading about black holes. Fun stuff!
BattleAnus · 2 points · Posted at 07:51:35 on February 14, 2016 · (Permalink)
The fact that the object being orbited is not a perfect sphere would mean the gravitational forces would not be perfectly spherical either. The only thing I could think that would exhibit a perfectly spherical field of gravity would be a single particle, but that's way outside my layman's knowledge of particle physics.
platoprime · 1 points · Posted at 10:11:15 on February 14, 2016 · (Permalink)
If it wasn't a perfect sphere that would shift its' center of gravity. In that case the gravity would be equal at any equidistant point from the center of gravity which would just be shifted a teeny tiny amount from the center.
BattleAnus · 2 points · Posted at 17:56:26 on February 14, 2016 · (Permalink)
I don't think that's true though. Yes the center of mass would move, but the gravity wouldn't be the same from every point equidistant from the center of gravity. We can look at this example of the gravity of a massive cube-shaped object and see that any deviation from a perfect sphere would create a distortion in the gravitational field.
platoprime · 1 points · Posted at 04:58:52 on February 15, 2016 · (Permalink)
Looks like you're correct.
platoprime · 1 points · Posted at 10:10:21 on February 14, 2016 · (Permalink)
Theoretically I don't see why not; it'd just be getting the precision perfect which is probably impossible but hey.
If the highest and lowest point in your orbit were identical then you'd be orbiting in a perfect circle.
shylocxs · 1 points · Posted at 12:39:39 on February 14, 2016 · (Permalink)
The electron doesn't know anything, it merely is. And circles don't exist in the natural world in s perfect form.
[deleted] · 2 points · Posted at 05:51:16 on February 14, 2016 · (Permalink)
Yes, Pi would still exist, even unnamed.
cmagnificent · 2 points · Posted at 06:01:30 on February 14, 2016 · (Permalink)
How?
[deleted] · 2 points · Posted at 06:03:30 on February 14, 2016 · (Permalink)
Because the geometric object, a circle, exists completely independently of humans, and Pi is merely the term we use to explain the relationship between the circumference of a circle and it's radius. That is true regardless of human existence and names, and would be true in any universe with the same geometry.
cmagnificent · 1 points · Posted at 06:12:18 on February 14, 2016 · (Permalink)
Yes, I am not arguing that real properties don't exist. What I am arguing is that the systems we use to describe those properties, such as mathematics are nothing more than abstractions, and not existent things in and of themselves.
[deleted] · -4 points · Posted at 06:27:53 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 2 points · Posted at 06:32:36 on February 14, 2016 · (Permalink)
No, the word red does not exist if there's no one around to say or use the word red. Does the color red exist? Yes, almost certainly.
[deleted] · -3 points · Posted at 06:48:15 on February 14, 2016 · (Permalink)
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cmagnificent · 2 points · Posted at 06:55:45 on February 14, 2016 · (Permalink)
Except numerous people were arguing with me and others even directly cited where and how this is actually a pretty contentious debate among scientists and mathematicians.
Don't get me wrong, I'm glad you agree with me, though I am now greatly concerned about your reading comprehension level.
[deleted] · -1 points · Posted at 07:08:15 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 3 points · Posted at 07:12:05 on February 14, 2016 · (Permalink)
And what was the context in which I kept repeating the obvious? Could it be that others kept disregarding the obvious, thus necessitating a restatement of it?
shylocxs · 1 points · Posted at 12:42:20 on February 14, 2016 · (Permalink)
But would pi exist unobservably?
[deleted] · 1 points · Posted at 12:58:17 on February 14, 2016 · (Permalink)
Sure, it's simply what we name a ratio that exists with or without us.
[deleted] · 1 points · Posted at 06:00:10 on February 14, 2016 · (Permalink)
As long as circles still exist the concept of pi would still exist. It wouldn't equal 3.14 but the nature of a circle wouldn't cease to exist just because a person never thought to come up with the use of radians to describe a circle.
cmagnificent · 1 points · Posted at 06:09:19 on February 14, 2016 · (Permalink)
Yes, but the use of "radians" to describe it, is an abstraction of the circle. The description of the circle is not the same thing as the circle itself. The mathematical description of an object, is not the same as the really existing object.
fingurdar · 1 points · Posted at 06:20:28 on February 14, 2016 · (Permalink)*
If a tree falls in a forest but nobody is around to hear it, does it still make a sound?
Yes, it does. The physical phenomenon that we have dubbed a "sound wave" would still occur throughout a portion of spacetime, regardless of whether or not a sentient being is there to perceive or classify it.
It's only problematic if we are overly-focused on semantics. Abstractions in and of themselves are not "real" except in the mind of the abstractor, but that which is being abstracted upon exists independently of the "abstraction".
Continuing down the line of thinking summarized above, "yes" and "no" are abstractions of duality and non-duality (i.e., something either exists in spacetime independently of other things throughout spacetime, or it does not). So, before meaningful communication existed, the abstraction of "yes" and "no" did not (technically) exist, but that which "yes" and "no" abstract upon (duality and non-duality) still existed.
That is my take on the topic, anyway--I don't claim to have all the answers, as this is one of the most fundamental questions in all of philosophy, but to me personally this line of thinking makes the most sense.
cmagnificent · 2 points · Posted at 06:24:03 on February 14, 2016 · (Permalink)
And to me, personally, it seems that the tacit concession is that while mathematics can certainly correspond to and describe a physical object in supreme detail, that does not make the description of that object as real as the object itself, thus mathematics aren't "real" in the sense we think of as every day physical objects being "real".
fingurdar · 1 points · Posted at 06:31:17 on February 14, 2016 · (Permalink)
Well said--although I think some people may define "mathematics" as being (or, perhaps, as including) the subject of the abstraction, rather than only the abstraction itself.
cmagnificent · 2 points · Posted at 06:35:10 on February 14, 2016 · (Permalink)
Very true. There's no rule that says you can't abstract based on an abstraction. If anything, I would call mathematics an extremely high-level abstraction, which also partially explains it broad usefulness. Its near-total detachment from any specific corresponding physical phenomena means its generality can be applied to countless phenomena regardless of their apparent difference.
saremei · 1 points · Posted at 12:35:45 on February 14, 2016 · (Permalink)
Oh but the mathematics are real. If we came across a sentient alien race, you would likely discover that while they use different numeric systems and different units of measure, their mathematical equations would most certainly be identical for things we have completely right. Units are arbitrary, equations are not.
mythozoologist · 1 points · Posted at 07:38:27 on February 14, 2016 · (Permalink)
No such thing as a perfect circle to derive pi from anyways.
cmagnificent · 1 points · Posted at 07:49:05 on February 14, 2016 · (Permalink)
Well, that's where the power of abstraction comes in. From a massive set of imperfect circles, we can abstract what a perfect circle would be and from that perfect circle we can then abstract the value of pi.
Marthman · -1 points · Posted at 06:13:50 on February 14, 2016 · (Permalink)*
Have you read the "platonism in metaphysics" SEP page?
No miracles argument?
indispensability argument?
Singular term argument?
Ontic Structural Realism, which is kin to (if not, just) mathematical realism, is quickly becoming the accepted position in theoretical physics. Have you read the SEP on that?
And you do realize that sets and other non number entities/structures count as mathematical objects, right?
The way you've just laid down your position so... assuredly, without noting that it's your opinion (and technically not even the majority one, according to philpapers) for the less educated to lap up with zero context doesn't sit well with me. I was going to be a little bit more critical with you, but I see from your history that you post in /r/philosophy and know who Heidegger is (not that that's any standard metric- but most non-philosophy-oriented people have no idea who that is), so I'll leave it at: I wish you had been a little more objective, less opinionated, and perhaps more willing to explain both sides for people to make their own decision.
And if you don't understand the other side, or can't post both sides of the argument because of that lacking, then you're completely unjustified in posting you opinion as if it were fact so that the stemlord hivemind just accepts it without batting an eyelash.
Knowledge is power. You seem to have it. Don't abuse it.
As for myself and my opinion... well, Plato was wrong about abstracta. Aristotle is where it's at.
cmagnificent · 2 points · Posted at 06:27:23 on February 14, 2016 · (Permalink)*
There are plenty of others who are rather articulately arguing for the other side of the issue. That's how a debate works. I'm not here to educate others on the various positions wrapped up in the discussion of whether or not contemporary forms of platonism are correct, I am solely here to argue my position on the issue.
Marthman · 1 points · Posted at 06:43:03 on February 14, 2016 · (Permalink)
Except you didn't indicate it was merely your position, and wrote about the issue as if what you were saying was fact.
Do you believe anything that isn't empirically demonstrable?
cmagnificent · 0 points · Posted at 06:46:49 on February 14, 2016 · (Permalink)
Do you mean "believe" as take as fact, or "believe" as in may use a theory or a concept that isn't empirically demonstratable in my daily life?
No to the first, and even then I bite the problem of induction, hard. Half-yes to the second, because even then I only use things that experientially help me, but I know that my experience doesn't constitute an infallible data set.
Marthman · 1 points · Posted at 06:54:36 on February 14, 2016 · (Permalink)
Okay, here's what I mean:
is there any proposition you hold as true that isn't empirically demonstrable?
Or are you just a nihilist in numerous senses (ethical, mereological, etc.)?
How do you empirically prove that what your senses tell you is true?
Do you believe the scientific method (in its various iterations) is a reliable source of knowledge? Do you believe you have a mind? That others aren't p-zombies?
Do you think infallibility is necessary to believe something?
cmagnificent · 1 points · Posted at 06:57:17 on February 14, 2016 · (Permalink)
I do not believe in non-contextual and non-relational truths, no.
Marthman · 1 points · Posted at 07:03:07 on February 14, 2016 · (Permalink)
I have no idea what you mean by that. Would you care to explain?
Did you want to answer the other questions?
Are you saying you don't believe it's true that dinosaurs existed as anything more than fossils?
What theory of truth do you subscribe to?
cmagnificent · 0 points · Posted at 07:09:47 on February 14, 2016 · (Permalink)
I'm saying that what is evaluated as truth, both in broader social context and on an individual subjective is mediated by context and relationships. To frame it in the Phil 101 way, I don't believe in any capital "T" Truths, but countless, little "t" truths.
To go with your dinosaur example, given the context of knowledge of the process of how bone fossilizes, and given the context of the existence of dinosaurs (both of which are predicated on an innumerable number of given contexts) at this juncture, I would argue that dinosaurs once did in fact exist. Absent the necessary context for that evaluation, and the contexts that underlie those contexts, I cannot make any meaningful statement on the matter.
So arguments begin and end with what given contexts are agreed upon.
Marthman · 1 points · Posted at 07:13:23 on February 14, 2016 · (Permalink)
So you believe that there is a difference between these two types of truth? What empirical methods did you utilize to come to this belief?
cmagnificent · 0 points · Posted at 07:16:39 on February 14, 2016 · (Permalink)
History of science mostly, of which I will freely admit that I learned primarily from second-hand sources. Theories and concepts in the sciences are predicated on the theories and knowledge that came before, as well as through empirical tests, and those empirical tests expose relationships between entities in the world, whose truth would not exist absent those relationships.
Marthman · 1 points · Posted at 07:36:53 on February 14, 2016 · (Permalink)
Perhaps I am misunderstanding, but how would history of science be able to empirically evince anything vis a vis abstract categorization per se?
It seems like you can't empirically evince it because you're abstractly categorizing types of truth.
The propositional attitude you hold in regard to the proposition, (a) "there are different types of truth," is one of assent. You believe (a) is true. But I don't see what empirical process you engaged in to arrive at this propositional attitude.
cmagnificent · 0 points · Posted at 07:43:45 on February 14, 2016 · (Permalink)
The entirety of my life experience? Reading about how old truths were overturned as new knowledge came to light? The fact that different observers can have different experiences of a given phenomena?
You're trying really hard to go Socratic on my argument and not doing that good of a job of it. So let me help.
If, what I say is true, and there are no capital "T" truths, only little "t" truths that are relative to given context, what is the purpose or use of making a distinction between these two kinds of truth, seeing as given the proper context any little "t" truth, will appear to be a capital "T" truth?
And for that question, I have no answer and I am still struggling with it.
Marthman · 0 points · Posted at 08:00:48 on February 14, 2016 · (Permalink)
But empiricism relies on sense experience, which, in principle, precludes abstract reasoning about the concept of truth.
(a) is not a posteriori knowledge, which is what empiricism yields.
I was actually curious about whatever it is you seem to know that I don't about empirical knowledge. I took a charitable, dialectical tack rather than an accusatory argumentative one.
What do you believe that "good" means?
Towards what end?
In any case, it seems like you don't believe all bachelors are unmarried men, and that triangles have three sides. Why not?
Lastly, do you not believe that you're not a brain in a vat?
cmagnificent · 0 points · Posted at 08:06:15 on February 14, 2016 · (Permalink)
Yes, I have derived my perception and definition of truth based off of my life experiences, that is the order that it went in.
Throwing out philosophical terms and arguments from the history of philosophy is not dialectics.
For the objective of showing a fault or flaw in my argument, you were doing a poor job of attain that objective. In that given context, that is what "good meant"
Given the context of the definition of the word "bachelor" in English, yes all bachelor's are unmarried men, because that's the context of the definition of bachelor. Same thing for triangles.
I am intensely skeptical of being a brain in a vat, but I cannot discount it as a possibility.
Marthman · 1 points · Posted at 08:27:33 on February 14, 2016 · (Permalink)
Except you can't perceive truth with empirical methods, no?
your life experiences might inform your judgements about what truth ought to be considered but I don't see how they constitute the basis for a priori knowledge about the concept of truth itself.
https://en.m.wikipedia.org/wiki/Dialectic
How would you be able to judge that, considering the fact that you hold your arguments as correct?
No, that's what "not that good of a job" meant, which basically means you mostly repeated yourself.
Okay so then you do hold a priori beliefs?
So you don't believe that triangles have three sides because your intellect is able to understand the concept sans experience?
Okay, but can't you believe that P despite possibilities of not-P?
shylocxs · 1 points · Posted at 12:51:55 on February 14, 2016 · (Permalink)
I agree with your position for one simple but also highly complex reason: how is mathematics privileged enough that it gets to be real while other abstract concepts are not so privileged.
shylocxs · 0 points · Posted at 12:48:58 on February 14, 2016 · (Permalink)
Isn't it ironic to provide a diatribe against a comment and then, like a seven mile rapper, to just slam some Aristotle down on the stage?
Or was that your intention all along?
Marthman · 2 points · Posted at 17:42:55 on February 14, 2016 · (Permalink)*
So no, it's not ironic when the entire point of my post was to indicate that he should have surveyed the other side of the argument if he wasn't going to indicate that what he was saying was just his opinion (which, by the way, was terribly reasoned, as I expected from someone who just acts as if nominalism is fact).
I indicated that this was unacceptable because what he was saying is not a fact at all, despite his implying it.
And if you don't believe me, reread his posts. He claims to not believe anything that isn't empirically demonstrable, then in the same breath, espouses nominalism. No empirical endeavor evinces nominalism.
This is misleading to people who don't know anything about the topic, and thus, intellectually irresponsible. Then I proceeded to demonstrate that his reasoning processes are incoherent, and his beliefs untenable- which I knew would be the case when he cocksuredly indicated that platonism was false despite having no way of demonstrating this due to his epistemological commitments.
So again, when I "slam Aristotle down on the stage," as you so put it, I do so under the banner of opinion, thus setting the example for how to appropriately proceed with this conversation.
takua108 · 1 points · Posted at 05:48:38 on February 14, 2016 · (Permalink)
Definitely true.
Not necessarily true!
Not necessarily true!
EDIT: Thinking more about this, I might not be correct, but either way now my brain hurts.
saremei · 1 points · Posted at 13:02:24 on February 14, 2016 · (Permalink)
If the computers are running the same program and returning different values, then one of them has a hardware fault.
They should return the exact same values. And working it out by hand should return the same value as well as the underlying math never changes.
takua108 · 1 points · Posted at 14:30:17 on February 14, 2016 · (Permalink)
And how do you emulate multicore processing and race conditions and undefined behavior "by hand"?
[deleted] · 1 points · Posted at 02:45:44 on February 15, 2016 · (Permalink)
One operation at a time.
gruesomeflowers · 1 points · Posted at 07:16:15 on February 14, 2016 · (Permalink)
Question: Isn't that like saying two people who know how to spell a word the same way will spell the word the same why when asked how to spell it correctly? The two people are using the same rules, so why would they not arrive at the same answer? The same goes for the computer. It was programmed by "us" with a set of rules. But if you change or update the program, then the methods and results become the new reality. Which seems to be what people are, as organic computers. And in all fairness, I'm not sure if i'm agreeing with you, disagreeing, or just attempting to add to the conversation.
shylocxs · 1 points · Posted at 12:37:54 on February 14, 2016 · (Permalink)
If reality used to be a friend of mine.
drew4232 · 2 points · Posted at 05:25:54 on February 14, 2016 · (Permalink)
Whether or not you call the distance between objects by a specific unit, their distance is still existent. The concept of mathematics exists merely as a way to rationalize real "values" that simply don't have naturally assigned units. Just because an electron doesn't know that it has a charge of 1.60217662 × 10-19 coulombs doesn't mean that the properties that those abstractions describe are non-real. Whether or not you decide to assign the name or concept of the coulomb to this electron, it is still has real properties that such a unit describes. Irregardless of the existence of the base of our systems of measurement, their are values that are real, and are quantitative, and while our specific measurements of those things are non-real and abstract, they serve as a comprehensible means to understand very real things. For example, the Fibonacci sequence is a real, set ratio. It exists naturally in the universe, and can be observed throughout everything in existence. No matter what unit system you are using, no matter how abstract to us, if it is a comprehensible reflection of reality, the ratio between units will still be the same. Due to the fact that any system capable of measuring such phenomenon will require parallels to aspects of reality to be useful in understanding aspects of the universe, like the definite charge of electrons, any unit of measure will result in the same understanding of these real things. The units and math merely describe real things that will be observed and understood through any abstract rationalization of the phenomenon observed, if the rationalization is to be, well, rational. We may choose abstract ways to communicate these ideas, the concepts involved are still real. I don't know if we could change each others minds, but I do believe that we are describing real things with our mathematics, and that as such, math is an inevitable component in any rational universe.
cmagnificent · 5 points · Posted at 05:34:52 on February 14, 2016 · (Permalink)
Yes, real things are real. I am not arguing that. The debate is whether or not mathematical values are real, or are merely descriptions of those real objects.
Is the mathematical description of the charge of an electron as real as the physical property that is the charge on an electron os is it merely a description of that property?
platoprime · 3 points · Posted at 05:41:01 on February 14, 2016 · (Permalink)
I agree; numbers describe real things but they aren't real things themselves.
dublohseven · 1 points · Posted at 06:28:37 on February 14, 2016 · (Permalink)
Yeah, duh, who was saying otherwise?
deasnutz · 1 points · Posted at 07:17:42 on February 14, 2016 · (Permalink)
The numbers.
drew4232 · 2 points · Posted at 05:58:47 on February 14, 2016 · (Permalink)*
I don't think that's where the debate goes, because of course those numbers are made up. They are not inherent in the universe. The names and units are of course made up. I think the debate is more on whether or not the mathematics exist as an inherent part of the universe or not, and while I am not arguing whether real things are real or not, I can see how I gave that impression. I more mean to say that because any rationalization of phenomenon in this universe would have inevitable parallels, to the point that any unit created would share ratios that describe natural phenomenon, that math exists in the universe. IE: No matter what unit you use to describe the Fibonacci sequence, the ratio between spacing of the units will be identical, and that as such, math exists naturally and we are merely describing it.
No one thinks that 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0; or the relations between those numbers, existed before we created them, and the debate is whether or not they are parallels to things that existed before the descriptors, or if they have no bearing in reality.
cmagnificent · 1 points · Posted at 06:06:44 on February 14, 2016 · (Permalink)
So you're describing mathematical applications to real world phenomena. What about mathematical abstractions that have no real life, physical analogues. Pure math, as it were? Is that "real" in the same way an electron will always have the same charge, or is it "real" only by way of the agreed upon axioms of mathematics, which are human abstractions?
[deleted] · 1 points · Posted at 05:57:16 on February 14, 2016 · (Permalink)
Now that I've read further into this I think we're making the same argument from different angles. What I was trying to say is that the math, in this case the fractions of 7 in a base ten system, isn't in itself a "naturally occurring phenomenon", but it is describing something that can be described in any number of ways. Mathematical constants, things like pi, don't only occur in base 10. They translate into something real and tangible.
cmagnificent · 1 points · Posted at 06:04:48 on February 14, 2016 · (Permalink)
I disagree on "real and tangible", but that similar or identical patterns will emerge, regardless of the base system used, is not something I am contesting.
[deleted] · 1 points · Posted at 06:14:56 on February 14, 2016 · (Permalink)
A circle having a diameter and circumference is just as real as an electron having a charge, is it not?
cmagnificent · 1 points · Posted at 06:28:57 on February 14, 2016 · (Permalink)
Is the description of that circumference, and the description of that diameter the same thing as the circumference of the diameter themselves, or are they nothing more than descriptions made by humans of the properties of that object?
AgAero · 1 points · Posted at 08:47:09 on February 14, 2016 · (Permalink)
...aaaand you've lost me.
drew4232 · 2 points · Posted at 09:45:04 on February 14, 2016 · (Permalink)
Yeah, yeah, sorry about that
[deleted] · 1 points · Posted at 07:02:42 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 1 points · Posted at 07:10:52 on February 14, 2016 · (Permalink)
I'm not quite following your connection to mathematics being necessary for the existence of the central nervous system.
Crazyalbo · 1 points · Posted at 11:11:53 on February 14, 2016 · (Permalink)
Well shit man, you got your stuff all sorted out. Math just doesn't exist in the real world because we created it. I'll be honest that seems a little screwy. I feel like I lean towards math being intrinsically a part of the universe but I guess you would refute that by saying what you just did. But the guy ain't wrong either about the base 12 also having a reoccurring phenomena. Same result in a different situation.
But I guess that's why it's a philosophical point of moot. Weird that this is actually a debated topic. Figured everybody was like, "yes there is a order to the world and its our job to discover it."
dannybrickwell · 1 points · Posted at 12:45:35 on February 14, 2016 · (Permalink)
But the fact that there is this completely incidental order to an abstract description tells us something about the thing we're describing. Its representation in the language we use might be arbitrary, but there is something about it that's different from the other things.
Twitstein · 1 points · Posted at 17:35:06 on February 14, 2016 · (Permalink)*
Yes, but why all the 'it must be this, so it can't be this', when enumeration is just the lens we apply to math to work with, in this case, material behaviour within the universe?
cmagnificent · 2 points · Posted at 17:45:30 on February 14, 2016 · (Permalink)
Because that's the topic of the discussion. The fundamental question is whether or not math is real in the same way physical objects are real, or is mathematics a system of description.
I have been arguing that "math is just the lense we apply to work with." This entire time.
Twitstein · 1 points · Posted at 19:36:53 on February 14, 2016 · (Permalink)
Yes, and I've corrected/reworded my answer to more accurately reflect that discussion. The universe does the math, we do the enumeration.
[deleted] · 1 points · Posted at 05:10:34 on February 14, 2016 · (Permalink)
[deleted]
runnerx01 · 8 points · Posted at 05:25:14 on February 14, 2016 · (Permalink)
Nope...
Consider, 1/10 is 0.1 in base 10. Convert that to base 2 (binary) and you have 0.0001100110011.....
Where the 0011 keeps repeating forever. In this example we have taken a rational number and turned it into a number requiring infinite precision in base 2. But this is a repeating decimal, and thus not irrational.
A true irrational number will have no repeating pattern in any number base. If we convert pi (3.14159265...) to binary
11.00100100 00111111 01101010 10001000 10000101... (Which I was too lazy to do myself, so I got that here Binary Pi ) It does not repeat.
More information in the number one answer here.
math.stackexchange
[deleted] · 1 points · Posted at 05:53:06 on February 14, 2016 · (Permalink)
To put it more simply, irrational numbers will be irrational in any rational base, and if you use an irrational base that number and it's multiples will be the only whole numbers.
(We could create a base pi system. It just turns out it's completely useless)
cmagnificent · 2 points · Posted at 05:15:17 on February 14, 2016 · (Permalink)
I would doubt it, considering changing the base system doesn't change the value the number has. Like if I hold out all my fingers on one hand, in base ten, we would represent that as "5", while in base five we would represent that as "10", but I'm still holding the same number of fingers up.
So, in anything other than base pi, pi would still be an irrational number.
(Please for the love of God no one start advocating for use of base pi.)
chiefhowler · 1 points · Posted at 05:11:45 on February 14, 2016 · (Permalink)
Seems obvious to me that it's Mathematical Anti-Realism. Abstraction is kind of a human forte
cmagnificent · 5 points · Posted at 05:23:54 on February 14, 2016 · (Permalink)
That's my take too, and I'm honestly kind of stunned I have to be defending it so vigorously. It seemed so patently obvious to me, but I apparently severely underestimated just how contentious a debate it actually is.
LordAcorn · 5 points · Posted at 05:35:05 on February 14, 2016 · (Permalink)
i think you overestimated peoples understanding of thought
chiefhowler · 2 points · Posted at 05:32:45 on February 14, 2016 · (Permalink)
I see science as a continually evolving model used to make useful predictions.
cmagnificent · 4 points · Posted at 05:39:29 on February 14, 2016 · (Permalink)
"Theories thus become instruments, not answers to enigmas, in which we can rest. We don't lie back upon them, we move forward, and, on occasion, make nature over again by their aid." - William James
brendel000 · 2 points · Posted at 05:53:19 on February 14, 2016 · (Permalink)
I think it's because a lot of people see maths as a kind of physic : "something that explain world" instead of a tool used by physic to describe nature, because they often learned math directly with a physic application. That's basically what you were (very well) explaining in this thread.
inclination · 1 points · Posted at 05:32:23 on February 14, 2016 · (Permalink)
Like most fundamental concepts, it just depends on where you draw the line.
[deleted] · 2 points · Posted at 05:54:21 on February 14, 2016 · (Permalink)
Just because it's abstract doesn't mean it isn't real. The property exists regardless of how we choose to define it.
chiefhowler · 1 points · Posted at 06:03:17 on February 14, 2016 · (Permalink)
Yep, and I'm saying that definition we use is what we call science. And I contest that science, in and of itself, isn't the property.
I'm honestly too high to explain myself, so yea we can agree to disagree.
youlookdumbinabowtie · 0 points · Posted at 05:25:53 on February 14, 2016 · (Permalink)
I know fuck-all about math and Mathematical-antirealiwhatsit, but if we can use math to shoot a satellite into space and travel BILLIONS of miles with the unfathomable accuracy needed to reach Pluto at juuuuust the right time and place and with the proper speed for it to successfully enter the planetoid's orbit, and we can achieve countless other similar feats rather predictably using contemporary mathematical objects and descriptions to guide us, well then what difference does it make if those descriptions are "intrinsic to the universe" or not?
cmagnificent · 3 points · Posted at 05:37:20 on February 14, 2016 · (Permalink)
To me it's like asking if a photograph, or a series of photographs of a cow is the same thing as a cow. While the photographs, the "description" of the cow, might tell us a hell of a lot about the cow, they are still merely descriptions, however elegant and precise they may be.
yonghokim · 1 points · Posted at 05:37:53 on February 14, 2016 · (Permalink)
philosophically. people want to know. as for you, you sound like an empiricist.
youlookdumbinabowtie · 1 points · Posted at 05:58:19 on February 14, 2016 · (Permalink)
He said we cannot verify these things as intrinsic to the universe so he assumes they are not intrinsic, though obviously that cannot be verified either. So you assume that the methodology that delivers tangible results over and over and over again is not intrinsic while tacitly admitting that there is no evidence you'd find acceptable to change your stance. Empirically, people want results. As for you, you sound like a denialist.
Phantom707 · 3 points · Posted at 04:55:04 on February 14, 2016 · (Permalink)
It's also a major point in certain fields of philosophy, where it has been highly developed.
awoelt · 1 points · Posted at 04:27:58 on February 14, 2016 · (Permalink)
Silence fiends! Your unintelligible witch spells can't work on me!
[deleted] · 1 points · Posted at 05:01:47 on February 14, 2016 · (Permalink)*
[deleted]
cmagnificent · 3 points · Posted at 05:06:37 on February 14, 2016 · (Permalink)
"I mean, ostensibly, yes. Honestly, we hacked most of it together with Perl."
(I know lisp is a functional language, still funny.)
welsh_dragon_roar · 1 points · Posted at 05:27:51 on February 14, 2016 · (Permalink)
There = 2.
Checkmate, atheists!
cmagnificent · 1 points · Posted at 05:32:56 on February 14, 2016 · (Permalink)
Well fuck. I guess I need to reevaluate some things then. Get me a priest, a rabbi and an imam, I've got some shit to sort out.
redditninemillion · 1 points · Posted at 05:53:01 on February 14, 2016 · (Permalink)
Aren't prime numbers a naturally occurring set of values?
cmagnificent · 1 points · Posted at 06:03:34 on February 14, 2016 · (Permalink)
For things like that, I really prefer the term, emergent. Prime numbers will always emerge given the agreed upon axioms of arithmetic. However, those axioms are human conceptualizations and not inherent properties of the universe.
redditninemillion · 1 points · Posted at 06:13:58 on February 14, 2016 · (Permalink)
Why aren't human conceptualizations inherent properties of the universe?
cmagnificent · 1 points · Posted at 06:30:35 on February 14, 2016 · (Permalink)
Because then we run into nasty philosophical problems such as, as I brought up earlier, the existence of unicorns. I can certainly conceptualize a unicorn and I can even describe a unicorn. If I ever got to utterly indescribable levels of boredom, I may even mathematically describe a unicorn. Does that make unicorns an inherent property of the universe?
redditninemillion · 1 points · Posted at 06:42:47 on February 14, 2016 · (Permalink)
Yes. Their conceptualization and description are inherent properties of the universe. That's why they exist as describable concepts
cmagnificent · 1 points · Posted at 06:43:47 on February 14, 2016 · (Permalink)
Then again, by that logic unicorns are inherent properties of the universe. They exist as describable concepts, they can be conceptualized and described, that doesn't make them real.
redditninemillion · 1 points · Posted at 06:51:20 on February 14, 2016 · (Permalink)
The concept and description of unicorns are inherent properties of the universe because they exist. Actual unicorns are not inherent properties of the universe because they don't exist. Different things
EattheRudeandUgly · 1 points · Posted at 07:03:45 on February 14, 2016 · (Permalink)
What would a naturally occurring two look like? just Curious
cmagnificent · 1 points · Posted at 07:14:05 on February 14, 2016 · (Permalink)
It doesn't exist, hence my use of it. Two is just an expression of a relationship, that there are two of something.
Twitstein · 1 points · Posted at 17:30:17 on February 14, 2016 · (Permalink)
which can be perfectly described using the values of math - an abstraction which, for example, the electron embodies. When math describes the embodiment of nature, its abstraction is redundant.
cmagnificent · 2 points · Posted at 17:43:43 on February 14, 2016 · (Permalink)
Which I have at no point argued against. Merely that the math only describes it and is not some magical property of the universe itself.
takua108 · 1 points · Posted at 05:38:18 on February 14, 2016 · (Permalink)
I'm already seeing where this thread is going and I'm very excited to read the rest of it. This is amazing.
([5])
AgAero · 1 points · Posted at 08:53:37 on February 14, 2016 · (Permalink)
This concept exists in physics. Tensor quantities have this property of invariance with respect to coordinate system. e.g. a velocity vector is the same geometric thing no matter if you try to describe it in cartesian, cylindrical, or (fuck it!) even hyperbolic coordinates.
Actually, this idea of invariance is one of the grand unifying notions of physics. Conservation of momentum can be derived from invariance of the properties of a system with respect to changes in position. Conservation of energy can be derived from invariance with respect to time.
coleman57 · 3 points · Posted at 06:53:26 on February 14, 2016 · (Permalink)
This pattern is simply the resonance of 7 against 10: the pattern created by dividing by 7 in base 10. Dividing by 5 in base 9 yields a different pattern. But since king olaf was remarking on the fact that there was such an extensive pattern at all, rather than the details of the pattern itself, the fact remains cool in any context.
retrospectr3 · 3 points · Posted at 07:29:16 on February 14, 2016 · (Permalink)
While I agree with everything you said, I arrive at a different conclusion about numbers and nature.
Numbers are an arbitrary construct the same way language is. There is nothing inherent that says grass is "green" and not "blue" other than the way our language developed. But that doesn't take away from its utility. The fact remains that photon particles bouncing off grass making it green are similar to the ones reflected off of grasshoppers making them green. Just like the Pythagorean theorem would remain true for a number system of any base and the golden ratio would still be found in nature.
[deleted] · 11 points · Posted at 03:21:22 on February 14, 2016 · (Permalink)
Thats not really true. There are more than just base 10 number systems. Just because we have described most things in a base 10 system doesn't really impact that its a naturally occurring phenomenon. Sumerian's used a base 60 number system.
Orca_Orcinus · 2 points · Posted at 09:05:15 on February 14, 2016 · (Permalink)
They actually used base 12, ten fingers and toes plus a null or cypher digit. A finger was used as an indicator as to which group of ten you were dealing with, say the thumb meant 1-10 (the first decimal), then you count nomally as we do today, then end by "not" counting the thumb, to indicate that decimal is complete. You do this 10 times, once for each finger and you have 120. From there you get sexagesimal.
cmagnificent · 9 points · Posted at 03:46:04 on February 14, 2016 · (Permalink)*
I went to concert
lilhughster · 4 points · Posted at 03:51:55 on February 14, 2016 · (Permalink)
I think you mean "it may be uncommon in other bases". This is definitely a natural occurring phenomenon. We may have made the representation, but the pattern is not man made.
Legion3 · 2 points · Posted at 04:13:53 on February 14, 2016 · (Permalink)
It's just pure random chance. In all the possible occurrences, there have to be patterns eventually. Doesn't mean it's important or that it's made at all. It just is.
Twitstein · 1 points · Posted at 18:05:55 on February 14, 2016 · (Permalink)
Not random chance at all. The patterns are identifiable because the universe operates under it's own laws. While the universe goes through varied and often catastrophic change, all the evidence is, is that those laws don't change. Laws, such as the conservation of energy, suggest our universe has always been here in one form or another, going though its changes, according to the laws which govern it.
Legion3 · 1 points · Posted at 00:07:11 on February 15, 2016 · (Permalink)
This isn't about laws. This is numbers. I understand what you mean with the conservation of energy/mass etc and other scientific laws. But this is no such law.
This is just a cool mathematical image that we see because we have specified what the division means (what 1/7 actually means, to explain it better, the way we defined divide is what allows us to view the pattern), and as others have said better than I have, that it only occurs in base 10 numerical systems, not base n.
Imagine having a full grid of numbers, with 1-10 on the X&Y with 1-10 going diagonal down the middle. This will produce this pattern (replicated on the axis around the diagonal integers) and the pattern, is legitimately, viewable. This, however does not mean this is a scientific law, nor anything worth while. It may lead us to discover new laws, ideas etc. But as of yet, it's merely a cool sequence that means diddly squat.
Twitstein · 2 points · Posted at 02:46:18 on February 15, 2016 · (Permalink)
To refer to the original post then, the universe is the coolest mathematical fact I know of. Of the enumeration we've done, which proves this universe, the laws are the most significant.
cmagnificent · -1 points · Posted at 03:55:51 on February 14, 2016 · (Permalink)
The systems that the pattern depend on and emerge from are entirely human constructs and therefore, yes, are manmade quod erat demonstrandum.
Mathematical Realism - Not Even Once.
[deleted] · 0 points · Posted at 04:12:04 on February 14, 2016 · (Permalink)
Actually patterns could emerge that don't rely on a base 10 system.
cmagnificent · 5 points · Posted at 04:23:50 on February 14, 2016 · (Permalink)
I never argued otherwise.
salocin097 · 3 points · Posted at 03:52:38 on February 14, 2016 · (Permalink)
However, similar patterns occur in other systems. For example: .99999.... =1 is the same as .888888....=1 in a base 9 system.
CLG_Portobello · 1 points · Posted at 04:04:28 on February 14, 2016 · (Permalink)
Numbers are a construction, a good one tho
Trippze · 2 points · Posted at 06:35:05 on February 14, 2016 · (Permalink)
you would still see a pattern with base 12, as long as 12 has a 0 after the first number, like 10
[deleted] · 2 points · Posted at 07:48:45 on February 14, 2016 · (Permalink)
It's like math fan fiction.
thedudeliveson · 2 points · Posted at 08:01:08 on February 14, 2016 · (Permalink)
I'm afraid a lot of people are overlooking the simple fact that I cannot hold two in my hand.
cmagnificent · 1 points · Posted at 08:02:31 on February 14, 2016 · (Permalink)
Right? You'd think that would be the end of the argument.
[deleted] · 1 points · Posted at 04:33:19 on February 14, 2016 · (Permalink)
fibonacci numbers in nature https://www.youtube.com/watch?v=ahXIMUkSXX0 there are patterns in nature that follow a certain mathematical order regardless of numbering system.
cmagnificent · 2 points · Posted at 04:37:44 on February 14, 2016 · (Permalink)
I never at any point argued there weren't. Those objects are real, certainly. The mathematics we use to describe and define them are man made abstractions based off of physical objects.
Suckonmyfatvagina · 1 points · Posted at 04:45:08 on February 14, 2016 · (Permalink)
Joy mother fucking kill.
Messisfoot · 1 points · Posted at 04:56:24 on February 14, 2016 · (Permalink)
Best answer.
Has everyone been watching the philosophy channel posted in the TIL? Such rich stuff.
3kixintehead · 1 points · Posted at 05:31:08 on February 14, 2016 · (Permalink)
And not just whether you use a base 10 system or not, but also the way underlying mathematical axioms are chosen.
Biggest_dong · 1 points · Posted at 05:34:25 on February 14, 2016 · (Permalink)
It's still a construct of this mathematical world and thus part of the order. It's conceivable so it exists.
cmagnificent · 2 points · Posted at 05:38:30 on February 14, 2016 · (Permalink)
Are all abstractions real then? A unicorn is an abstraction of "horse" + "horn", is it as real as horses and horns?
brownestrabbit · 2 points · Posted at 05:56:25 on February 14, 2016 · (Permalink)
Even the words used to describe those things are all abstractions, despite pointing at 'real' or 'imagined' animals. You're totally accurate in your argument.
Biggest_dong · 1 points · Posted at 10:36:40 on February 14, 2016 · (Permalink)
Yes, a unicorn is a horned horse. Duh
Twitstein · 1 points · Posted at 18:16:33 on February 14, 2016 · (Permalink)
As far as us being beings who perceive and conceptualize things, yes, the unicorn is real. It just doesn't exist.
Valyrian_Tinfoil · 1 points · Posted at 06:05:36 on February 14, 2016 · (Permalink)
But isn't a base 10 number system a naturally occurring phenomena? I mean, it didn't arise from outside of reality.
cmagnificent · 1 points · Posted at 06:14:06 on February 14, 2016 · (Permalink)
That pulls us back to the question of the reality or naturalness of all abstractions then. Obviously, math still works regardless of the base system we use for it, but base 10 math certainly didn't exist before human cognition. So, are all abstract cognitions as "real" or "natural" as base ten. See my unicorn example.
teefour · 1 points · Posted at 06:11:26 on February 14, 2016 · (Permalink)
I'm too
drunktired to do the math now, but wouldn't a similar pattern emerge in base 12?cmagnificent · 1 points · Posted at 06:27:36 on February 14, 2016 · (Permalink)
Yes, it does. Someone already went through that, and regardless of the base system, a repeating pattern does emerge.
needhaje · 1 points · Posted at 06:18:35 on February 14, 2016 · (Permalink)
These are the types of arguments that I prefer to see on Reddit.
[deleted] · 1 points · Posted at 06:39:01 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 1 points · Posted at 06:44:27 on February 14, 2016 · (Permalink)
It's okay in about an hour you'll find some nice cheerful porn and will be able to forget it ever happened.
auctor_ignotus · 1 points · Posted at 06:54:19 on February 14, 2016 · (Permalink)
Sound reasoning but a slippery slope. Are you speaking from somewhere outside of nature? Is base 10 arbitrary or conventional and why? Does it speak to human nature and would that be less fascinating?
cmagnificent · 1 points · Posted at 07:00:18 on February 14, 2016 · (Permalink)
In order. -
No.
Considering computers may relay the information to humans in base 10, but perform the calculations themselves in binary, yes base 10 is an arbitrary system, as any base system yields the same results.
In my opinion, human nature is a tricky term, and it would not be less fascinating.
jackskis · 1 points · Posted at 07:12:12 on February 14, 2016 · (Permalink)
This represents a very profound pattern in nature that transcends the base 10 system. They would repeat in other bases as well...
cmagnificent · 1 points · Posted at 07:13:16 on February 14, 2016 · (Permalink)
It's a pattern in mathematics and numerical systems. Whether or not mathematics and numerical systems count as "part of the natural world" is kind of the entirety of the debate.
[deleted] · 1 points · Posted at 07:19:36 on February 14, 2016 · (Permalink)*
You're stating that there is no order or mathematical nature to the Universe because numbers are arbitrary? Mathematics are present in the natural world, and it's elucidations have nothing to do with numerical systems. The framework of the Universe is defined by quantitative functions/relationships, not by numbers themselves. Functions don't give a shit whether you define the world in base 10 or base 256, they still maintain their consistency. The fabric of space time has been defined to a high precision by mathematics to present an accurate image of the reality of gravitational distortion of space. The relative shape of the framework doesn't change based on the number system used.
If, however, you are just saying that numbers themselves, and not mathematical relationships, are arbitrary...then yeah, no poop. Numbers are referential, that doesn't change the fact that concrete relationships exist when we look at the world in a quantitative fashion, regardless of what type of discreet system is used. Marginalizing mathematics because to put forth a philosophical fap argument about how numbers "aren't real" is a waste of time. It doesn't change the fact that mathematics is the structural language of physical reality. It doesn't change the fact that things like the precision of GPS or the functioning of integrated circuits would not be possible without these mathematical relationships.
To make this a little bit clearer, the part of mathematics that are consistently present are the operators. Multiplication, equalities, exponents, division, addition, subtraction. The number systems can change, but the relationships as defined by the operators will remain regardless.
cmagnificent · 1 points · Posted at 07:33:12 on February 14, 2016 · (Permalink)
My entire argument is that the distortions of space were already there. They were not "defined" by mathematics, mathematics makes a very good description of the already existent physical property. The universe didn't write itself in math. Math merely provides a very powerful abstractive tool to help us understand and describe these physical phenomena.
In other words, the universe has no structural language of its own. We as thinking sentient beings use the structural language of mathematics to describe what we observe.
To go along with recent discoveries, there were still gravitational waves before the mathematical models for them were created. There were gravitational waves before there were entities capable of conceptualizing mathematics at all. The universe does not care about our models and systems, it merely is.
[deleted] · 1 points · Posted at 16:30:21 on February 14, 2016 · (Permalink)*
You're making an unprovable argument here. It seems 'obvious', but without entities being around to see the existence of something, there's no way to know it exists at all. Something has to be observed to exist.
There is absolutely no proof for this. For all we know we could be in a highly advanced species' simulation which has been programmed completely using mathematical systems. The fact that mathematics perfectly describes a multitude of phenomena with high precision indicates that it's very possible that the Universe is built upon mathematics. It's also possible that these properties are arbitrary and emergent.
It's not a matter of a caring Universe, and I'm not sure what that notion has to do with this discussion. It's a matter of mathematical definitions of reality being far more true than talking about it in a system of words. When we sit here and use words to argue that mathematics are an abstraction of reality, we are further abstracting our own perception of reality via the English language. At least with mathematics, once you know the framework, you have an intuitive understanding of reality that makes the abstractions drop away. Opposingly, arguments like this are engaging a word game that detracts from the real world. So, why is this important enough for you to argue this earnestly? What useful knowledge about the Universe does someone get through arguing the semantics of mathematics philosophy? It's all wretch and no vomit, it never gets anywhere. It's a circle of words that just drives a person to further abstract away from reality, moreso than if you were learning mathematics, yet you are passionately trying to use this symbolic language to undermine the significance of mathematics. What I'm curious about is why...what's the motivation here? What's the end game for this philosophical circuit?
cmagnificent · 1 points · Posted at 17:39:43 on February 14, 2016 · (Permalink)*
That's called an argument from ignorance and it's a logical fallacy. At that point I can claim that literally anything could be an inherent property of the universe and because you can't conclusively prove that it isn't, I am therefore right? No that's not how it works. Considering the Universe was here before we developed mathematics, I see no logical reason to assume that the universe is written in math.
If you read through the rest of my arguments, you will see that I at no point argue that mathematics isn't useful. In fact, at more than one point, I argue that its high level of abstraction gives it its generality that allows it to describe so many phenomena so well. I'm not "undermining the significance" of mathematics. The other side of this debate is arguing for a significance we have no evidence for, and I'm the unreasonable one for arguing we shouldn't believe something without evidence to support it?
No one is arguing that math isn't pretty neat. It is. The entire argument is whether or not math is an inherent property of the universe or a man-made series of abstractions developed to help describe that universe. Neither answer says that math isn't important or not useful, it's just asking the basic question of what math actually is.
rasto_x · 1 points · Posted at 07:26:47 on February 14, 2016 · (Permalink)
3 comments in and my brain hurts
cmagnificent · 1 points · Posted at 07:35:06 on February 14, 2016 · (Permalink)
Even though it's not a muscle, your brain does kind of behave like one. You know you're actually getting a good workout when you're feeling the burn, and you know you're pushing the boundaries of what your knowledge at present is capable of when your brain starts to hurt.
[deleted] · 1 points · Posted at 07:34:39 on February 14, 2016 · (Permalink)*
If I'm getting your jist correctly, are you suggesting things like the pattern described by the function of say, relativity, is one that is only observed due to our number system?
Observed mathematical patterns in the Universe are made practical with numbers, but the relationships themselves are not impacted by the number system used. Patterns in the Universe have operational relationships, that is, defined by multiplication, addition, equality, exponents, integrals, and derivatives. The relationships do not change when the number system used to quantify them changes.
If you're just talking about the arbitrariness of numbers, sure...but what a pointless argument.
cmagnificent · 1 points · Posted at 07:39:09 on February 14, 2016 · (Permalink)
That's not what I'm saying, at all. You have horrifically misconstrued my point, and I have argued rather consistently that real phenomena are, in fact, real.
What I am arguing is that descriptions of phenomena are not the same thing as phenomena themselves. As I said earlier, a picture of a cow is not the same thing as a cow. Following from that, the mathematical description of a gravitational wave is not the same thing as a gravitational wave.
In this sense mathematics is not "real" in the same way we think of everyday objects of our experience being "real".
If I need to open a physics textbook, you need to brush up on your reading comprehension.
Fuzzywraith · 1 points · Posted at 08:43:40 on February 14, 2016 · (Permalink)
This guy fucks
PM_ME_DANK_MANGOS · 1 points · Posted at 08:55:54 on February 14, 2016 · (Permalink)
wouldn't numbers/ratios like Pi, Euler's number, and the Fibonacci sequence be noticeable regardless? and why do they show up in nature if they are arbitrary?
McCHitman · 1 points · Posted at 13:31:43 on February 14, 2016 · (Permalink)
It's all fake and made up if you think about it. Someone wanted an outcome and one point in time and made something up to give them that outcome. It became gospel and the rest is history
Attempt12 · 1 points · Posted at 14:07:59 on February 14, 2016 · (Permalink)
What?
randomguy186 · 1 points · Posted at 14:39:56 on February 14, 2016 · (Permalink)
I am not certain, but I think a comparable pattern would occur in a different base if the number squared was one less than half the base squared.
So in base 10, you have 10 x 10 = 100, and half of that is 50.
With 7, you have 7x7=49, which is one less than 50. 7 x 7 = 49, which is one less than half of 10
awhaling · 1 points · Posted at 15:00:35 on February 14, 2016 · (Permalink)
These phenomenons happen in other number bases too.
cmagnificent · 1 points · Posted at 17:40:36 on February 14, 2016 · (Permalink)
Except as has been pointed out elsewhere, base 7 +- 1. So the emergence of this particular pattern is dependent on the choice of base system, which is an arbitrary decision.
awhaling · 1 points · Posted at 17:47:33 on February 14, 2016 · (Permalink)
I fail to see why that matters, if patterns still emerge.
cmagnificent · 1 points · Posted at 17:50:49 on February 14, 2016 · (Permalink)
Because, that means any pattern that does emerge, is a result of the initial framing which is arbitrary and is not some inherent property of mathematics, much less reality.
awhaling · 1 points · Posted at 18:02:57 on February 14, 2016 · (Permalink)
But different patterns appear in every number base. They are inherent properties of mathematics. Just because one pattern shows up in one number base, doesn't make it any less significant.
I get what you are saying, but I fail to see how it makes any difference significance wise
cmagnificent · 1 points · Posted at 18:07:21 on February 14, 2016 · (Permalink)
The initial statement I responded to claimed the emergence of those patterns as a "naturally occurring phenomena" which is what my argument was against. Since the emergence of any given pattern is dependent on the arbitrary framing used, it is not a naturally occurring phenomena.
awhaling · 1 points · Posted at 18:18:54 on February 14, 2016 · (Permalink)
In that case, I agree with you. It is not natural. But the patterns are inherent in mathematics.
RainaDPP · -1 points · Posted at 03:40:55 on February 14, 2016 · (Permalink)
Here's a weird question to think about. Why is our natural number system base 10, when there's technically 11 states to our fingers? No fingers up is a valid state.
(The answer is probably that 0 wasn't really a thing until the Babylonians or whoever invented it. I'm sure nothing was a concept, but zero wasn't a number that could be counted.)
WTF_SilverChair · 3 points · Posted at 03:49:36 on February 14, 2016 · (Permalink)
Because you can't do math on the fingers using all 11 states.
cmagnificent · 2 points · Posted at 04:00:36 on February 14, 2016 · (Permalink)
Well, until the development of algebra, there wasn't really a pressing need for zero as a concept distinct from nothing.
ALargeRock · 2 points · Posted at 03:49:28 on February 14, 2016 · (Permalink)
Arabic invented it. I believe they were Muslims. I know Al-gebra is an Islamic word.
[deleted] · 3 points · Posted at 03:58:32 on February 14, 2016 · (Permalink)
It was the indians actually. The arabs adopted, promoted it.
ALargeRock · 1 points · Posted at 04:19:09 on February 14, 2016 · (Permalink)
Ah ok. Thank you!
RainaDPP · 2 points · Posted at 04:29:50 on February 14, 2016 · (Permalink)
Here is where I'm pulling my information from. It looks like it was originally conceptualized by Sumerians, then the Babylonians got it from them. The Mayans came up with the concept independently about 700 years later.
The first place that zero as a number was used seems to be in India, which made its way over to Baghdad and got adopted into the Arabic number system.
Porrick · 1 points · Posted at 04:50:13 on February 14, 2016 · (Permalink)
10, not being prime, is a more useful number than 11. Of course, 12 would be more useful still (having even more factors), and there's something nice about powers of 2 like 16.
Here are some other base systems people use - none of them quite as popular as 10, of course.
PC__LOAD__LETTER · 25 points · Posted at 03:00:00 on February 14, 2016 · (Permalink)
I'd argue that numbers aren't really a naturally occurring phenomena. If there are five apples on the ground, there isn't actually a "5" in existence; those are all completely distinct and unique objects that are just existing. It's the human mind that groups and enumerate them because it's useful for us.
Numbers and math are no more real than ideas, and math has order because of its logical basis.
tyrannonorris · 42 points · Posted at 03:33:26 on February 14, 2016 · (Permalink)*
Number systems aren't naturally occurring but math IS!
If there are 5 apples on the ground then regardless of number system, there are still 5 apples on the ground. If you divide the circumference of a circle by its diameter you will always get the same result, even if your number system doesn't call it 3.14, that will always be pi mathematically.
Quick edit: the deviding by 7 thing is a product of our number system though haha.
PC__LOAD__LETTER · 9 points · Posted at 04:01:43 on February 14, 2016 · (Permalink)
Is that true though? Doesn't it take a mind to distinguish those objects and then enumerate them?
Similarly for the circle - those measurements are true by the definition that we have ascribed to it. There are no perfect circles in nature.
Splazoid · 7 points · Posted at 04:10:34 on February 14, 2016 · (Permalink)
It does take a mind to label the quantity, but if all of humanity disappeared, there would still be five apples beneath this tree. Numbers are an abstract which exist wholly apart from human acknowledgement. Much like gravity would remain if all humanity disappeared. The thing is that even if all physical matter burned up, there would still exist the possibility of real number sets.
PC__LOAD__LETTER · 5 points · Posted at 04:23:14 on February 14, 2016 · (Permalink)
Well gravity is completely separate as it isn't abstract. But in what way do abstract things exist apart from a mind? If all minds capable of understanding abstract concepts like numbers suddenly disappeared from the universe, in what exact capacity would those concepts exist?
Twitstein · 1 points · Posted at 20:05:23 on February 14, 2016 · (Permalink)
Varying forms of chaos, I suspect. e.g. We only achieve a limited range of perception from our senses, relative to the energy spectrum that exists. My one use of lysergic acid showed me how mundane the daily level of our sense operation is in that regard. And, in that regard, the universe is itself a math abstract.
Splazoid · 1 points · Posted at 04:41:45 on February 14, 2016 · (Permalink)
They would continue to exist by their very nature. If all minds capable of understanding the abstract concept of numbers ceased to exist, the five apples under the tree remain. They do not cease to exist nor does their quantity change. The concept of their being five of something is still just as logical and coherent in a hypothetical world without conscious beings.
PC__LOAD__LETTER · 2 points · Posted at 07:02:17 on February 14, 2016 · (Permalink)
The problem is that properties like "logical" and "coherent" don't make any sense without minds.
harcole · 1 points · Posted at 08:20:42 on February 14, 2016 · (Permalink)
Nominalists sounds retarded. Smart enough to make concepts but it's retarded concepts
brownestrabbit · 2 points · Posted at 05:58:16 on February 14, 2016 · (Permalink)
No. There would just be a quantity of apples with no abstraction to describe them.
Splazoid · 2 points · Posted at 06:38:42 on February 14, 2016 · (Permalink)
There would be no description, but the quantity of apples has not changeded. Numbers are not created by the mind, they are discovered. Prior to humans describing the concept of five, five apples could indeed exist.
PC__LOAD__LETTER · 0 points · Posted at 07:07:38 on February 14, 2016 · (Permalink)
It seems like 5 apples could exist without a human to see them and call them five - but the problem with this scenario is that you are using logic to reach back to a point in time that completely lacks that logical framework. Saying that there were "five apples" before humans existed to witness them is to describe a completely fictional scenario in our common terms. Those apples weren't "five," those apples weren't even discrete nam-able (and countable) objects; it's humans who press math onto nature, not the other way around.
Splazoid · 2 points · Posted at 07:16:22 on February 14, 2016 · (Permalink)
I wholehearted disagree with you on the basis of platonism.
PC__LOAD__LETTER · 1 points · Posted at 07:31:47 on February 14, 2016 · (Permalink)
And I would disagree with you on the basis of empiricism.
harcole · 1 points · Posted at 08:22:17 on February 14, 2016 · (Permalink)
No worry, logic is no natural, he won't use it
Twitstein · 1 points · Posted at 19:09:40 on February 14, 2016 · (Permalink)
Interesting. There are no apples unless the universe observes there to be those things, in time. "..quantum Zeno effect, in which a quantum state would decay if left alone, but does not decay because of its continuous observation." In this case, the term observation refers to the inclusion of regions of energy pertaining to matter operating under universal law. What causes the universe to cease 'observing' or 'including' things? Time. Where time ceases to exist, things aren't observed by the universe. So, there's no point in time where apples exist separately from a form of abstraction.
brownestrabbit · 1 points · Posted at 19:52:23 on February 14, 2016 · (Permalink)
I think you are thinking too much about it.
Apples are real regardless of observers.
And.
The abstraction of numbers is created to describe said apples. In fact, the word 'apples' and the letters and the sounds are also all fabricated abstractions as well.
Twitstein · 1 points · Posted at 20:18:52 on February 14, 2016 · (Permalink)
Forget enumeration for a minute. The universe is itself a mathematical abstraction (operates under mathematical laws. We know this because we've discovered them). So, as I've posted elsewhere here, the universe does the math, and we do the enumeration to understand the math. Look at what the universe fabricates with its math.
brownestrabbit · 1 points · Posted at 21:12:24 on February 14, 2016 · (Permalink)
No. We use mathematical abstractions to attempt to understand the world around us.
The crux of this whole discussion and argument is that what you are claiming, i.e. "the universe does math" is false.
You are pointing to the universe and saying that it exists "because math". That is literally no different than pointing to the universe and all creation and saying it exists "because God".
The fact that math is useful does not prove it is real or exists in and of itself.
Twitstein · 1 points · Posted at 23:00:14 on February 14, 2016 · (Permalink)
If it offends you that the universe does the math, take it up with the universe. I'm just reporting what science has already discovered. If you want to extrapolate unhappily, that's your business.
brownestrabbit · 1 points · Posted at 23:41:30 on February 14, 2016 · (Permalink)
The problem here is not my feeling about it.
Science and the philosophy of science have not rested upon a certain conclusion in this matter.
So I respectfully disagree with your assertions or claims of authority.
[deleted] · 1 points · Posted at 04:27:08 on February 14, 2016 · (Permalink)
[deleted]
PC__LOAD__LETTER · 1 points · Posted at 04:34:13 on February 14, 2016 · (Permalink)
Interesting point about the discrete objects and plants doing math, I hadn't considered it in that way before.
Splazoid · 1 points · Posted at 04:38:53 on February 14, 2016 · (Permalink)
You're agreeing with me..
[deleted] · 1 points · Posted at 04:47:50 on February 14, 2016 · (Permalink)
[deleted]
Splazoid · 1 points · Posted at 04:52:32 on February 14, 2016 · (Permalink)
Well I was saying that the concept of a number is abstract. There is no object "two". There can be two of something, but the integer itself is abstract. This remains true if there are only physical agents at play without consciousness.
[deleted] · 1 points · Posted at 05:03:14 on February 14, 2016 · (Permalink)
[deleted]
Splazoid · 1 points · Posted at 05:06:35 on February 14, 2016 · (Permalink)
You're just being pedantic. It's not that the concept is abstract, it's an abstract concept. The concept of rain water, or gummy bears, or jump ropes are all concepts of tangible things. These are not conceptually abstract in the way a number is.
Durty_ · 1 points · Posted at 09:30:04 on February 14, 2016 · (Permalink)
doesnt a black hole appear as a perfect circle?
Twitstein · 1 points · Posted at 18:37:52 on February 14, 2016 · (Permalink)
1/ Any line that connects end to end is a perfect circle. It may not be a perfect geometry, but it is a perfect circle.
2/Anyway, I say nature has perfect geometric circles. One comes to mind, the ripple/wave from a drop of water falling into still water.
PC__LOAD__LETTER · 2 points · Posted at 18:58:53 on February 14, 2016 · (Permalink)
"Lines" do not exist though - and beyond that, an ellipse is a "line that connects end to end" as is definitely not a perfect circle.
Regarding the water ripples, they are actually not perfect circles: http://physics.stackexchange.com/questions/1289/waves-in-water-always-circular
Twitstein · 1 points · Posted at 19:24:07 on February 14, 2016 · (Permalink)
Lines exist in relativity, and we live in a relative universe. They may not be a property of circles and elipses, but how we describe their circumference. Thanks for the link, and for pointing out the lack in my ripples argument.
EltaninAntenna · 1 points · Posted at 09:51:08 on February 14, 2016 · (Permalink)
Well, if you divide a real circumference by a real diameter, you're going to get different values more or less close to pi. Only a mathematical abstraction will get you pi. In fact, you cannot get a precise value of pi by measurement, only by calculation.
Twitstein · 1 points · Posted at 18:31:39 on February 14, 2016 · (Permalink)
Very good!!!
[deleted] · 2 points · Posted at 03:13:41 on February 14, 2016 · (Permalink)
Numbers represent the amount of apples present in a given situation. While they are symbolic representations, they still concern very real things.
remigiop · 2 points · Posted at 03:31:35 on February 14, 2016 · (Permalink)
Except when they don't i
shostakov · 1 points · Posted at 05:33:37 on February 14, 2016 · (Permalink)
The irony is that ideas are real. They are one and the same with the state of some physical system. This conversation, for example, is real; to argue otherwise is to argue against the physical reality of the electrons and whatnot that it comprises.
PC__LOAD__LETTER · 1 points · Posted at 05:38:47 on February 14, 2016 · (Permalink)
Ideas are real when they are being thought by a mind, yes. But can they exist without a mind? That's what's being discussed.
Whothrow · 1 points · Posted at 06:00:21 on February 14, 2016 · (Permalink)
Pluto, the planetlet, is an idea; you have never seen it with your naked eye, nor can you see it without a pretty hefty piece of hardware.
Pluto exists independently of your mind, has for a long time, willl continue long after.
Its existence was postulated in the 1800's and was confirmed in 1930. Using ideas. Ideas that turn out to be universally applicablle. Literally in this case.
A mind is irrelevent. The planetlets will continue to spin.
PC__LOAD__LETTER · 1 points · Posted at 06:59:03 on February 14, 2016 · (Permalink)
Ok, but Pluto is a hunk of physical material floating in space. In what capacity do ideas themselves exist outside of a mind?
Whothrow · 1 points · Posted at 07:15:22 on February 14, 2016 · (Permalink)
Can you prove Pluto doesn't exist?
PC__LOAD__LETTER · 1 points · Posted at 07:33:07 on February 14, 2016 · (Permalink)
The answer to your leading question (leading to where, I'm not sure, you'll have to do a little more leading) is obviously no.
Whothrow · 1 points · Posted at 07:41:45 on February 14, 2016 · (Permalink)
So, by virtue of the fact that you agree that Pluto exists and, you cannot verify the existence of Pluto with any means available to you, and because of the prior Pluto is only an idea, it must be the case that things exist without your mind, ergo things exist without your mind.
Things not existing without your mind was your premise. A thing that exists without your mind has been shown.
PC__LOAD__LETTER · 1 points · Posted at 09:11:34 on February 14, 2016 · (Permalink)
You're misunderstanding my premise entirely. I'm saying that invented concepts like math, not discovered objects like a planet, cannot exist without your mind.
Let me put it this way - Math is like language. Language is useful for humans because it lets us express and reason about our environment. But language would not exist if beings were not there to use it.
Whothrow · 1 points · Posted at 13:59:56 on February 14, 2016 · (Permalink)
I disagree. Maths are discovered, not invented.
shylocxs · 1 points · Posted at 12:55:36 on February 14, 2016 · (Permalink)
Isn't math just serious logic? So, is logic real?
Twitstein · 1 points · Posted at 18:29:23 on February 14, 2016 · (Permalink)*
We distinguish a difference between mental energy and physical matter. Both are real. Both can or do exist, to an extent, independently of eachother. So, the product from identifying, categorizing and enumeration become real, because we conceive them.
[deleted] · -17 points · Posted at 03:02:20 on February 14, 2016 · (Permalink)
[deleted]
PC__LOAD__LETTER · 5 points · Posted at 03:04:39 on February 14, 2016 · (Permalink)
I don't understand what you're trying to convey.
[deleted] · -9 points · Posted at 03:06:52 on February 14, 2016 · (Permalink)
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[deleted] · 4 points · Posted at 03:15:33 on February 14, 2016 · (Permalink)
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Kaliedo · 3 points · Posted at 03:17:21 on February 14, 2016 · (Permalink)
Why are you insulting him for this? He's right, and makes an important point we often forget; math is not the language of the universe, it's not something intrinsic to the world. It's a system of logical rules and statements that, combined, happen to allow us to explain some of the phenomena that happen around us. Math is something wholly man-made. The fact that it works does not change that.
[deleted] · -2 points · Posted at 03:21:48 on February 14, 2016 · (Permalink)
[deleted]
PC__LOAD__LETTER · 1 points · Posted at 04:35:59 on February 14, 2016 · (Permalink)
Says the guy ending his posts with "kek" and "fam"
PC__LOAD__LETTER · 3 points · Posted at 03:16:17 on February 14, 2016 · (Permalink)
I was stating a fact that gave credence to the argument that numbers and math are not real "things." Whether or not that's true, it's a view that the person I replied to did not have, and so in my mind was worth addressing.
But it seems like you're getting off on not being able to see the forest for the trees, so I'll let you get back to that, "fam."
poundruss · -2 points · Posted at 03:22:37 on February 14, 2016 · (Permalink)
man you try hard. it's just reddit chill
[deleted] · -8 points · Posted at 03:11:49 on February 14, 2016 · (Permalink)
[deleted]
PC__LOAD__LETTER · 5 points · Posted at 03:22:27 on February 14, 2016 · (Permalink)
Ah go fuck yourself.
neotropic9 · 2 points · Posted at 08:06:09 on February 14, 2016 · (Permalink)
It depends what you mean by "reality". We're talking about mathematical abstractions here which are entirely divorced from the physical universe.
heliotach712 · 1 points · Posted at 04:18:13 on February 14, 2016 · (Permalink)
the hell do you mean a "naturally occurring phenomenon"? What's "natural" about it? And how is it a phenomenon? That's like saying that the rules of chess are a "naturally occurring phenomenon".
trey82 · 1 points · Posted at 08:54:47 on February 14, 2016 · (Permalink)
You can drown in the ocean.
You cannot drown in a drop of water
playaspec · 1 points · Posted at 05:16:07 on February 14, 2016 · (Permalink)
No, it's just math that forms a pattern. Only out minds give it any significance.
That claim is so cringe worthy, but I have to ask anyway. What "naturally occurring phenomenon"??
No its NOT. It's just a sequence of numbers. It has NO significance to reality.
[deleted] · 2 points · Posted at 05:23:51 on February 14, 2016 · (Permalink)
We're talking about two completely different things, but I appreciate your concern.
[deleted] · 1 points · Posted at 03:04:22 on February 14, 2016 · (Permalink)
Actually I have no idea why I'm posting but I felt like everybody needed to hear my opinion
[deleted] · 8 points · Posted at 02:32:22 on February 14, 2016 · (Permalink)
So, patterns are meaningless.
cmagnificent · 7 points · Posted at 03:19:56 on February 14, 2016 · (Permalink)
Patterns are intrinsically meaningless, yes. They do have constructed meanings, or contextual meanings, but it is fair to say that patterns have no meaning in and of themselves.
[deleted] · 1 points · Posted at 04:14:34 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 2 points · Posted at 04:24:37 on February 14, 2016 · (Permalink)
No, nihilism as a philosophy also rejects constructed and emergent meaning as well, not merely intrinsic meaning.
[deleted] · 1 points · Posted at 04:35:07 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 3 points · Posted at 04:46:50 on February 14, 2016 · (Permalink)
Which is not the same as nihilism, and still not what I'm arguing.
Meaning has to be meaningful for something, there's isn't a magical "meaning" hardwired into the universe and if there were, there would be no disagreements about what constitutes something as meaningful.
[deleted] · 1 points · Posted at 04:55:31 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 2 points · Posted at 04:58:57 on February 14, 2016 · (Permalink)
In that scenario you described, you're missing a couple of steps. The first is that you immediately recognize it as human writing, which is already an assumption of meaning. If a cow were to walk by the same wall, it wouldn't distinguish the writing on the wall as anything meaningful. It only has meaning for you, because of the context of you being human, and being able to recognize writing. The squiggles on the wall have no intrinsic meaning beyond that context.
[deleted] · 1 points · Posted at 05:05:03 on February 14, 2016 · (Permalink)
[deleted]
cmagnificent · 2 points · Posted at 05:11:07 on February 14, 2016 · (Permalink)
Okay what's the use of saying meaning is an intrinsic property of the universe, while simultaneously negating the intrinsic value of any specific meaning?
[deleted] · 1 points · Posted at 04:31:25 on February 14, 2016 · (Permalink)
How do you figure a pattern is the definition of intrinsic meaning? The essence of all meaning is patterns?
MalekJive · 7 points · Posted at 02:48:18 on February 14, 2016 · (Permalink)
Or, everything has a pattern, and some are easier to notice than others.
Cum_Trumpster69 · -1 points · Posted at 03:09:23 on February 14, 2016 · (Permalink)
heavy
[deleted] · -4 points · Posted at 04:00:36 on February 14, 2016 · (Permalink)
Thats retarded. Sounds deep, but its stupid and untrue.
Stop spewing shit that you blew outta your ass and which has no grounding in reality.
20EYES · 2 points · Posted at 04:06:50 on February 14, 2016 · (Permalink)
Prove this statement to be false please.
I'm waiting...
[deleted] · 2 points · Posted at 04:32:01 on February 14, 2016 · (Permalink)
You could be less of an asshole and simply say that what he said was a platitude. You know, if you didn't want to sound like an ignorant ass.
Porrick · 1 points · Posted at 04:51:05 on February 14, 2016 · (Permalink)
Meaning, like beauty, is in the eye of the beholder.
[deleted] · 2 points · Posted at 03:55:03 on February 14, 2016 · (Permalink)
Got it, everything is meaningless
dot-pixis · 6 points · Posted at 04:08:19 on February 14, 2016 · (Permalink)
The only meaning is the meaning we assign to things.
That's a bit better than 'everything is meaningless,' don't you think?
[deleted] · 1 points · Posted at 04:43:15 on February 14, 2016 · (Permalink)
Nahh
[deleted] · 1 points · Posted at 04:07:09 on February 14, 2016 · (Permalink)
no but like fractions man
lordfarquadscat · 1 points · Posted at 04:09:54 on February 14, 2016 · (Permalink)
We have developed a way to express the order in the universe.
NasalSnack · 1 points · Posted at 04:12:49 on February 14, 2016 · (Permalink)
So there is order to "our" universe.
[deleted] · 1 points · Posted at 04:46:59 on February 14, 2016 · (Permalink)
Order in other words..
CodeOmega0 · 1 points · Posted at 06:03:21 on February 14, 2016 · (Permalink)
Exactly. Humans are the ones who designed base 10 mathematics. The fact that we arbitrarily decided that we would use these 10 symbols, and then start over with multiple next to each other just so happened to work out into a pattern with a specific prime number.
Humans are great at finding patterns. Figuring out why they exist takes a while, and that's if there even is an answer.
chalkdoc21 · 1 points · Posted at 06:30:42 on February 14, 2016 · (Permalink)
To correct you its not the division of a certain number it's the division of any number in regards the the recurring decimal patterns.
[deleted] · 5 points · Posted at 03:52:40 on February 14, 2016 · (Permalink)
Pfft only in the base-10 counting system. Show me another cool fraction of 7 in another base.
Grokent · 1 points · Posted at 05:37:58 on February 14, 2016 · (Permalink)
In base 12 it's 186a35 someone above said. I'm on my phone however so I'm too lazy to check. Pop 2/7 in base 12 into wolfram alpha and see what you get.
SuperSocrates · 1 points · Posted at 05:15:45 on February 14, 2016 · (Permalink)
Dunno if you are serious but elsewhere in this thread someone did exactly that.
[deleted] · 4 points · Posted at 04:00:17 on February 14, 2016 · (Permalink)
Reddit blasphemy. Prepare your inbox.
My_Perfect_Boy · 1 points · Posted at 20:03:50 on February 15, 2016 · (Permalink)
dude...wow you were right
The_Irvinator · 2 points · Posted at 03:36:45 on February 14, 2016 · (Permalink)
"Illusions Mr.Anderson!..."
Sinidir · 2 points · Posted at 04:30:42 on February 14, 2016 · (Permalink)
Woah woah slow down there Darth Vader.
lrony · 12 points · Posted at 02:54:12 on February 14, 2016 · (Permalink)
You do realize this is a human construct? It's a consequence of having a base 10 numeral sys--- ah, fuck it. Not worth it.
PC__LOAD__LETTER · 14 points · Posted at 03:02:15 on February 14, 2016 · (Permalink)
Hey you know this logical mathematical framework that we constructed? If you look closely and break it down, there's some neat patterns that almost seem as if they result directly from that logic.
Whothrow · 1 points · Posted at 06:11:15 on February 14, 2016 · (Permalink)
A triangle is still a triangle regardless of the framework. It has an essential triangleness that exists without you.
PC__LOAD__LETTER · 3 points · Posted at 06:31:23 on February 14, 2016 · (Permalink)
Where and how? If I make up an imaginary object and tell no one about it, does that object retain its essential objectness after I die? Did it exist before me? The concept of a circle, for example, is useful for humans but does not exist (perfectly) in nature.
Whothrow · -1 points · Posted at 07:14:36 on February 14, 2016 · (Permalink)
The circle argument, which you cannot prove btw, is why I used A triangle. The concept of a (perfect) triangle does exist in nature. Water, for instance, is neither imaginary, nor will cease to exist, with or without you. It will, often enough, be in a platonic ideal state, arranged in sufficently trangular position, to retain its triangleness, regardless of wether or nor you were able to see it.
Maskirovka · 1 points · Posted at 12:54:48 on February 14, 2016 · (Permalink)
I'm not the person you originally replied to, but I think Plato would have changed his mind if he had known anything about quantum mechanics. This "triangular" water you speak of is a human construct as well. (I assume you're referring to the "bent" shape we say that water molecules have). This shape doesn't really exist...only the relative positions of the electrons wave functions around the hydrogen remain "bent" relative to the oxygen or an arbitrarily selected plane.
So, while all water molecules share the same properties, individual water molecules have emergent properties.
I mean, does an atom that decays radioactively have some platonic form before it decays but not after? I don't know Plato that well, but would he have said that it's part of uraniumness to eventually become lead? I highly doubt it.
midwestwatcher · 4 points · Posted at 04:29:22 on February 14, 2016 · (Permalink)
No, math has nothing to do with the universe. It just the philosophy of number, and humans have made a philosophy with certain patterns (and still some gaps).
[deleted] · 0 points · Posted at 05:25:54 on February 14, 2016 · (Permalink)
Yes! Thank you!
Futurist110 · 1 points · Posted at 04:21:12 on February 14, 2016 · (Permalink)
If so, then couldn't theists claim that this is proof for God's existence? ;)
[deleted] · -1 points · Posted at 08:06:35 on February 14, 2016 · (Permalink)
[deleted]
Maskirovka · 2 points · Posted at 13:31:33 on February 14, 2016 · (Permalink)
Order yes, purpose no. Order can come from chaos and randomness as long as there are solid and unchanging rules for what can happen and what can't happen. You can argue about whether or not your God created those rules in the first place, but you can't argue that order comes from chaos. It happens all around us all the time and it isn't disputed by anyone except those who haven't bothered to learn about it.
http://youtu.be/HvXbQb57lsE
[deleted] · 0 points · Posted at 17:16:57 on February 15, 2016 · (Permalink)
[deleted]
Maskirovka · 1 points · Posted at 22:06:42 on February 15, 2016 · (Permalink)
I know a house had a builder because I have NEVER seen houses spring up out of the ground on their own. I have also built houses personally, so I know what is required to build one. I've also built a radio before and I understand the principles and mathematics behind electromagnetism. There's absolutely nothing magical about building radios. Humans do these kinds of things and we can repeat them and show other humans how to do them. There is no mystery in your examples...yet you're ascribing a sense of mysticism to them...why?
You're talking about making inferences. Yes, we do that all the time. It's one way we get clues about the past...and making inferences about evidence we find is the only way to make inferences about the past before humans began recording history in writing.
Thing is, there's a huge difference between making inferences about the past based on physical evidence and reasoning and doing what you're doing, which is reasoning from a predetermined conclusion (that the universe has purpose and design). How do you make the leap from physical evidence to "God did it"?
[deleted] · 1 points · Posted at 03:28:28 on February 16, 2016 · (Permalink)
[deleted]
Maskirovka · 1 points · Posted at 04:39:01 on February 16, 2016 · (Permalink)
No, it didn't happen by chance. Evolution is not random. This is a common misconception that people have about evolution. Organisms evolve based on their interaction with their environment. The human brain is simply a more highly adapted and more complex version of every other brain and nerve bundle we see in nearly every multicellular organism on earth. Humans survive and reproduce more successfully because of our intelligence...it's beneficial to us in our environment so it exists.
If you believe god created the universe with the big bang (as your link suggests) and then let it go, that's not a claim I can really say anything about. However, if you believe god creates miracles and intervenes in the daily lives of humans, then that sort of thing is disputable.
You have no evidence that those writings were inspired by God. You just have writings written by humans. Beyond that you have no proof because what you're saying is by definition supernatural.
Again, I don't know why this is reason to believe anything religious. We can't see atoms or electrons either, but we understand them through our use of mathematics, scientific tools, reasoning, experiment, etc. We can't see wind, but we can understand that it is caused by changes in air pressure and that we can feel the force applied by the elements and molecules that make up our atmosphere.
There are MANY unscientific claims in the bible including the claim of a virgin birth, changing of water to wine, walking on water, resurrection...all of these are unscientific claims.
Anyway we don't need to discuss all that. Let's just say for the sake of the discussion I grant you that there aren't any unscientific claims in the bible I'm not sure why that makes the bible worthy of particular special consideration. There are many books which lack unscientific claims...
I don't know what you're talking about here. I mean, I know you're telling me what you believe, but I don't understand how you started down this path of thought from what we were talking about.
Urban_Savage · 1 points · Posted at 04:42:25 on February 14, 2016 · (Permalink)
Doesn't it just mean there is order to the concept of mathematics?
businesstravis · 1 points · Posted at 04:43:18 on February 14, 2016 · (Permalink)
Checkmate, atheists
LexUnits · 1 points · Posted at 04:50:16 on February 14, 2016 · (Permalink)
And that makes you feel better!?
Sentient__Cloud · 1 points · Posted at 04:55:36 on February 14, 2016 · (Permalink)
But why is there order? Isn't the universe crazy and chaotic?
Kiefyking · 1 points · Posted at 05:00:53 on February 14, 2016 · (Permalink)
Tell that to chaos
Weekend833 · 1 points · Posted at 05:08:35 on February 14, 2016 · (Permalink)
Yeah, and it isn't necessarily a decimal system.
playaspec · 1 points · Posted at 05:10:50 on February 14, 2016 · (Permalink)
Found the numerologist. It doesn't 'mean' anything. It just is.
kaevondong · 1 points · Posted at 06:32:42 on February 14, 2016 · (Permalink)
God that's even scarier
c3534l · 1 points · Posted at 06:34:22 on February 14, 2016 · (Permalink)
The universe is governed by black magic.
bunker_man · 1 points · Posted at 06:35:39 on February 14, 2016 · (Permalink)
Even more primal. This universe could have been a different universe instead. These mathematical truths could never have been anything else. They would exist in the empty void.
Toodlez · 1 points · Posted at 06:49:14 on February 14, 2016 · (Permalink)
OH GOD FREE WILL IS AN ILLUSION
BigglesNZ · 1 points · Posted at 07:19:50 on February 14, 2016 · (Permalink)
Some say math is the purest science.
Arcadian2 · 1 points · Posted at 08:17:13 on February 14, 2016 · (Permalink)*
for something that had a chaotic beginning it sure does has order.
kingfrito_5005 · 1 points · Posted at 08:26:41 on February 14, 2016 · (Permalink)
Nope, magic.
AnAppleSnail · 1 points · Posted at 10:05:45 on February 14, 2016 · (Permalink)
Just order to numbers. Base 10 and modulus 7 are related in funny ways.
GuitarBeats · 1 points · Posted at 10:20:42 on February 14, 2016 · (Permalink)
Which is equally as scary. Why is the universe bound by laws and order
Nomicakes · 1 points · Posted at 10:37:56 on February 14, 2016 · (Permalink)
And as we all know, order begins somewhere between 1 and Graham's Number.
[deleted] · 1 points · Posted at 10:42:44 on February 14, 2016 · (Permalink)
The abstract concept of mathematics is the mind-blowing part. Once you accept its self-evidence, its curiosities are trivial, and speak no more about 'order to the universe' than the fact that 1 + 1 = 2.
NecroJack · 1 points · Posted at 11:40:27 on February 14, 2016 · (Permalink)
Black magic.
brohanshaw · 1 points · Posted at 14:12:28 on February 14, 2016 · (Permalink)
No it just means we've organized our perception of the universe into a foreseeable predictable pattern
[deleted] · 1 points · Posted at 14:26:25 on February 14, 2016 · (Permalink)
No it doesn't. Math is a tool of the human brain; an invention. We find models that are descriptive to the natural world, but that natural world is noisy and therefore our models have imperfections. We can only quantify the deviations from our model using statistics.
CPA-Poke · 1 points · Posted at 14:45:29 on February 14, 2016 · (Permalink)
See: Fibonacci
SSpacemanSSpiff · 1 points · Posted at 14:47:59 on February 14, 2016 · (Permalink)
God designed that shit well..
Norua · 1 points · Posted at 19:26:22 on February 14, 2016 · (Permalink)
It only looks like order to you because that's the only universe math can describe. But it's still a human qualification.
[deleted] · 1 points · Posted at 21:39:45 on February 14, 2016 · (Permalink)
CHECKMATE ATHEISTS
SpeedyVT · 2 points · Posted at 04:01:17 on February 14, 2016 · (Permalink)
3
2
1
Atheists suddenly attack your statement.
Kaserbeam · 2 points · Posted at 05:50:27 on February 14, 2016 · (Permalink)
well, he was objectively wrong...
Bronze_Bull · 1 points · Posted at 03:54:22 on February 14, 2016 · (Permalink)
burn it
a_rucksack_of_dildos · 1 points · Posted at 04:14:27 on February 14, 2016 · (Permalink)
No. There are an infinite number of operators in the universe. This doesn't mean anything
ezequien · 0 points · Posted at 03:59:31 on February 14, 2016 · (Permalink)
Math are the only real rules of the universe. If there is a god, I'd imagine math would be his/her laws. No right or wrong, just rules.
iamPause · 0 points · Posted at 04:19:46 on February 14, 2016 · (Permalink)
Jebbediahh · 0 points · Posted at 04:45:10 on February 14, 2016 · (Permalink)
Isn't it weird that when we see order, we think it must be magic beyond order
JimBeamLean · 0 points · Posted at 04:54:22 on February 14, 2016 · (Permalink)
We created math. It has no connection to the universe. Based on the system we created, it might have some coincidences, but it could've been done differently. Why does everyone jump to universal grand claims over things like math that are totally just ideas made up by us?
ophello · 0 points · Posted at 08:57:58 on February 14, 2016 · (Permalink)
No, it means we use a decimal system. The relationship between 10 and 7 yields this result.
cynoclast · 10 points · Posted at 03:47:18 on February 14, 2016 · (Permalink)
It's a meaningless artifact of a base 10 system. Do the same math in hexadecimal.
Xamius · 6 points · Posted at 04:22:42 on February 14, 2016 · (Permalink)
wat
cynoclast · 7 points · Posted at 05:40:23 on February 14, 2016 · (Permalink)*
In hex:
1 ÷ 7 = 0.24924924924924
2 ÷ 7 = 0.49249249249248
3 ÷ 7 = 0.6db6db6db6db6c
4 ÷ 7 = 0.9249249249249
5 ÷ 7 = 0.b6db6db6db6db8
6 ÷ 7 = 0.db6db6db6db6d8
The pattern is a product of the number base, not magic or even math really.
You'll get different results in binary, octal, and base64. A really carefully chosen base system would either have none of these, or use them to highlight meaningful things.
Math can be done in any number base, arithmetic has to pick one.
[deleted] · 2 points · Posted at 07:49:38 on February 14, 2016 · (Permalink)
[deleted]
cynoclast · 2 points · Posted at 08:07:42 on February 14, 2016 · (Permalink)
10x01IAll represent "one".
666- decimal110 0110 0110- binary03146- octal0x29A- HexadecimalDCLXVI- Roman numerals*:- Base 64 (https://en.wikipedia.org/wiki/Uuencoding)If you had "six hundred, sixty six" oranges. It would be equally true to substitute one of those 'numbers' to tell someone how many oranges you had. The arabic numeral system is just an arbitrary choice of ten symbols.
An easy exercise is, count from 0 to 9, then call the next 'number'
Aand continue down the alphabet. That would be base 36. Where10represents "thirty six". Because it's a one in the 36es place, and a 0 in the 'ones' place.Kinda mind blowing, innit?
SavannahWinslow · 3 points · Posted at 02:21:54 on February 14, 2016 · (Permalink)
Magic is mystical; math is merely logical to those who understand.
Dr_WLIN · 6 points · Posted at 02:54:06 on February 14, 2016 · (Permalink)
If you think you "understand" then you clearly dont.
[deleted] · -1 points · Posted at 03:00:25 on February 14, 2016 · (Permalink)
[deleted]
Dr_WLIN · 6 points · Posted at 03:10:18 on February 14, 2016 · (Permalink)
Im saying the more you learn, the more you learn that you really dont understand.
SavannahWinslow · 6 points · Posted at 03:26:58 on February 14, 2016 · (Permalink)
If you don't understand it, you haven't "learned" it ... you've merely learned of its existence. That said, it's often true that the more you learn, the more you discover that there's even more to be learned. Perhaps that's what you really meant?
bluemtfreerider · 3 points · Posted at 04:01:41 on February 14, 2016 · (Permalink)
X-post /r/iamverysmart
Dr_WLIN · 3 points · Posted at 04:17:08 on February 14, 2016 · (Permalink)
No. There is always more to it. You never fully understand. You learn the sum of the parts, but not the parts.
I wouldnt even really say "learned", I think "memorized" is more fitting. Learning is not the same as understanding.
1+1=2 appears very simple and straightforward, go look at the mathematical proof of it.
Cum_Trumpster69 · 2 points · Posted at 03:10:09 on February 14, 2016 · (Permalink)
Is this a trick question?
SavannahWinslow · 1 points · Posted at 03:30:35 on February 14, 2016 · (Permalink)
It's obviously not a "trick" question. Perhaps rephrasing would help? A declarative statement of the issue would say that a person of average intelligence does NOT "understand" certain things in the same way that a person of high intelligence does.
sizzlelikeasnail · 4 points · Posted at 02:53:46 on February 14, 2016 · (Permalink)*
Not all of maths is logical. E.g, adding up all the numbers from 1 to infinity gives you -1/12. Sometimes maths makes no sense at all. The maths itself works. But thinking about it logically completely contradicts it. How can you add up infinite positive numbers and get a negative answer?
Edit: proof
It apparently appears in physics too
PeterQuincyTaggart · 5 points · Posted at 02:57:26 on February 14, 2016 · (Permalink)
Is there an ELI5 version of this or am I going to have that my field of study in order to get it?
sizzlelikeasnail · 5 points · Posted at 03:36:34 on February 14, 2016 · (Permalink)
Idk if an ELI5 is possible but the proof hurts my brain
Talono · 3 points · Posted at 04:28:23 on February 14, 2016 · (Permalink)*
There's a difference between "intuitive" and "logical."
The sum of all positive integers is counter-intuitive, not illogical. It only seems illogical becausepeople often forget that infinity is a man-made concept to make understanding things easier, not something that exists in nature. Same goes for zero, imaginary numbers, etc. (It really applies to all numbers, but that's harder for people to see :P)Edit: Here's an article that argues that the sum of positive integers doesn't equal -1/2 but only seems so due to mathematical semantics where "=" means closer to "associated with" rather than "equal to" http://physicsbuzz.physicscentral.com/2014/01/redux-does-1234-112-absolutely-not.html
Satans__Secretary · 0 points · Posted at 04:32:37 on February 14, 2016 · (Permalink)
Magick isn't mystical at all; it's just physics.
Jallorn · 1 points · Posted at 04:42:29 on February 14, 2016 · (Permalink)
It's more that if you have infinite possible combinations, as numbers do, there's going to be some patterns.
ScrithWire · 1 points · Posted at 04:47:32 on February 14, 2016 · (Permalink)
Math is inherently a pattern seeking discipline. Its like saying, "oooh, i lined up these tiles in order from smallest to largest, and a pattern emerged! The tiles go from smallest to largest!!! Omgsocoolapattern!"
But yea, i know what you mean, and i get that same feeling as you. :)
_Solution_ · 1 points · Posted at 04:49:14 on February 14, 2016 · (Permalink)
It's MathMagical
DevyatGrammovSvintsa · 1 points · Posted at 05:20:40 on February 14, 2016 · (Permalink)
It's just an artifact of our use of base 10.
AsianBarMitzvah · 1 points · Posted at 05:42:25 on February 14, 2016 · (Permalink)
lucian with deathcap
penis_in_my_hand · 1 points · Posted at 05:51:49 on February 14, 2016 · (Permalink)
You're wrong about that.
All parts of math are black magic.
Or rather, black magic is math. And if A = B then B = A.
dannyr_wwe · 1 points · Posted at 06:16:01 on February 14, 2016 · (Permalink)
Remember, a lot of the patterns that we see may simply be a result of using a base 10 number system. Other number systems would have different patterns, which means the patterns come from our ability to recognize them, not necessarily the numbers or operations themselves.
spacepepperoni · 1 points · Posted at 06:34:41 on February 14, 2016 · (Permalink)
Things like this are the closest I will come to believing in God. The beauty and order in math is worth study and worship.
noes_oh · 1 points · Posted at 06:59:09 on February 14, 2016 · (Permalink)
You and everyone else in the 12th century.
witeowl · 1 points · Posted at 07:57:41 on February 14, 2016 · (Permalink)
Must be white magic. After all, all the digits divisible by three are missing...
AndNowIKnowWhy · 1 points · Posted at 08:37:35 on February 14, 2016 · (Permalink)
I consider it the purest form of poetry.
[deleted] · 1 points · Posted at 08:51:18 on February 14, 2016 · (Permalink)
Or black math.
reexox · 1 points · Posted at 13:09:31 on February 14, 2016 · (Permalink)
"Math is the closest thing to magic" gets me through life
[deleted] · 1 points · Posted at 02:25:36 on February 14, 2016 · (Permalink)
Also prime spirals are pretty cool...
Legend_Zector · 1 points · Posted at 04:06:23 on February 14, 2016 · (Permalink)
"There's no such thing as magic - only math"
ifjnweu · -1 points · Posted at 03:12:07 on February 14, 2016 · (Permalink)
there's a billionth in one chance of this happening and us knowing about it. It's nice to think we realized it.
Tealwisp · 2 points · Posted at 03:40:51 on February 14, 2016 · (Permalink)
Considering that this is just divisions of seven, I feel like there's more than "a billionth in one" chance of knowing about it.
jvi · -35 points · Posted at 01:27:30 on February 14, 2016 · (Permalink)
makes you believe in intelligent design perhaps?
[deleted] · 33 points · Posted at 01:48:58 on February 14, 2016 · (Permalink)
Only if you're too lazy to read the mathematical proofs but still want to draw existential conclusions.
UnchainedMundane · 11 points · Posted at 02:31:18 on February 14, 2016 · (Permalink)
Mathematics was intelligently designed by humans, as a tool for measuring and understanding the world.
haldr · 10 points · Posted at 01:46:41 on February 14, 2016 · (Permalink)
No.
ihavetenfingers · 1 points · Posted at 01:50:00 on February 14, 2016 · (Permalink)
I see youve dreamt of cats too
theghostmachine · 1 points · Posted at 02:52:58 on February 14, 2016 · (Permalink)
Just because you can't understand it doesn't mean god did it. I've seen Penn and Teller catch bullets in their teeth, but I would never think they actually caught a bullet just because I can't figure out how they really did it.
CWSwapigans · 1 points · Posted at 02:59:15 on February 14, 2016 · (Permalink)
If this is a joke, lol.
If this is serious, lolololol.
[deleted] · 0 points · Posted at 02:53:00 on February 14, 2016 · (Permalink)
Lol!
FetchFrosh · 1411 points · Posted at 19:46:01 on February 13, 2016 · (Permalink)*
Similar to this, numbers divided by 5 in base 12 are repeating series of 2497. When you divide by 10 instead you get one other digit, and then a series of 2497. For anyone who doesn't know, base 12 works with 12 different digits as opposed to 10. Here's a quick summary:
Now, fractions feel weird when you make them, because you get stuff like this:
Now when we start getting into some the 5 and 10 fractions, we will get that 2497 I mentioned:
mediumhydroncollider · 1706 points · Posted at 21:40:59 on February 13, 2016 · (Permalink)
I have a feeling your father was a calculator
CIearMind · 343 points · Posted at 22:01:14 on February 13, 2016 · (Permalink)
Overwatch?
RealRedLanderV · 178 points · Posted at 22:51:58 on February 13, 2016 · (Permalink)
Don't you mean great, strong and powerful woman?
CIearMind · 47 points · Posted at 23:11:11 on February 13, 2016 · (Permalink)
That didn't work on Nyssa :(
cayal3 · 7 points · Posted at 02:14:35 on February 14, 2016 · (Permalink)
It's amazing how much this phrase is leaking.
Atlas001 · 2 points · Posted at 02:46:42 on February 14, 2016 · (Permalink)
I don't get it, can someone explain?
cayal3 · 11 points · Posted at 02:48:51 on February 14, 2016 · (Permalink)
Do you watch Arrow?
One of the characters - Felicity Smoak - has kind of taken over the show (blame tumblr) and they are keen on telling us how she is a great, strong & powerful woman as she deals with being in a wheelchair.
Atlas001 · 3 points · Posted at 03:02:31 on February 14, 2016 · (Permalink)*
I only watched half the 1st season
Also, what's with the overwatch and calculators
joke? seems to be relatedAwela · 4 points · Posted at 03:03:45 on February 14, 2016 · (Permalink)
Spoilers ahead:
Her nickname is Overwatch and her father nickname is Calculator.
cayal3 · 2 points · Posted at 03:12:50 on February 14, 2016 · (Permalink)
Overwatch is her hero name and Calculator was a bad guy who turned out to be her dad. But I haven't heard any jokes regarding that.
Atlas001 · 2 points · Posted at 03:20:47 on February 14, 2016 · (Permalink)
i guess i meant reference, the one that started the "leak"
Theniallmc · 1 points · Posted at 12:42:25 on February 14, 2016 · (Permalink)
Except they dont at all but Reddit likes to complain
DrAjax0014 · 17 points · Posted at 01:27:19 on February 14, 2016 · (Permalink)
/r/arrow is leaking
bis1998 · 2 points · Posted at 05:42:25 on February 14, 2016 · (Permalink)
/r/arrow is leaking
Jacob_Mango · 1 points · Posted at 11:29:53 on February 14, 2016 · (Permalink)*
Oh wait. So this is where that leak from link /r/arrow. Oh lol.
Exodus2011 · 7 points · Posted at 01:15:10 on February 14, 2016 · (Permalink)
Fuck.
[deleted] · 4 points · Posted at 01:32:10 on February 14, 2016 · (Permalink)
Fuck.
thatjesushair · 8 points · Posted at 03:26:55 on February 14, 2016 · (Permalink)
Onlywatch...
bnh1978 · 6 points · Posted at 02:46:40 on February 14, 2016 · (Permalink)
Would have called her Oracle, but that was taken.
ItsBBA · 15 points · Posted at 23:48:58 on February 13, 2016 · (Permalink)
/r/arrow Is leaking.
curtmack · 7 points · Posted at 02:51:33 on February 14, 2016 · (Permalink)
Am I the only person who thought this was about the Blizzard game and not anything to do with Arrow?
Quartapple · 9 points · Posted at 03:12:24 on February 14, 2016 · (Permalink)
You're not alone.
OnlyWatch T_T
AdamMc66 · 3 points · Posted at 07:43:17 on February 14, 2016 · (Permalink)
My mind went to X-Com.
CIearMind · 1 points · Posted at 14:15:47 on June 14, 2016 · (Permalink)
It became so damn popular.
ToastyXD · 2 points · Posted at 04:32:13 on February 14, 2016 · (Permalink)
Can we please not call him the Calculator?
BrutalWarPig · 2 points · Posted at 06:32:38 on February 14, 2016 · (Permalink)
/r/Arrow is leaking ...... better breakout the speed weed
deadadventure · 3 points · Posted at 23:12:10 on February 13, 2016 · (Permalink)
Arrow
sirbruce · 1 points · Posted at 00:45:48 on February 14, 2016 · (Permalink)
That name is already taken.
torkel-flatberg · 5 points · Posted at 23:18:34 on February 13, 2016 · (Permalink)
80085
Skerries · 1 points · Posted at 11:15:41 on February 14, 2016 · (Permalink)
8008135
ead9450 · 3 points · Posted at 01:32:01 on February 14, 2016 · (Permalink)
And old grandpa Abacus
JackAceHole · 2 points · Posted at 02:08:18 on February 14, 2016 · (Permalink)
He was. You could always count on him.
mint-bint · 1 points · Posted at 22:46:59 on February 13, 2016 · (Permalink)
And your mother smelled of elderberries.
jrkirby · 1 points · Posted at 05:04:25 on February 14, 2016 · (Permalink)
You know, calculator actually used to be a profession. But it's unlikely that his father did that unless he's very old. So it's more likely his grandfather. Or great-grandfather. Or, since there were more female calculators, grandmother.
[deleted] · -1 points · Posted at 23:57:55 on February 13, 2016 · (Permalink)
...and your mother smelled of elderberries!
MyAssholeSmellsAwful · -1 points · Posted at 10:21:06 on February 14, 2016 · (Permalink)
Are you implying that his mother masturbates using a calculator?
CatMines · 95 points · Posted at 21:26:32 on February 13, 2016 · (Permalink)
This is a very interesting and well formatted response. It's cool to see the consequences of other number systems.
DuplexFields · 4 points · Posted at 01:26:15 on February 14, 2016 · (Permalink)
I really like how the number represented by the highest digit in a base has that property like nine, where you sum the digits to test for divisibility. If the digits of a hex number sum to 5, 10, or 15, it's divisible by 5.
awkwardIRL · 2 points · Posted at 01:54:40 on February 14, 2016 · (Permalink)
Now, I'm no good at math and other bases really give me trouble. This little tidbit though is enough to really help me out I bet
TwoFiveOnes · 3 points · Posted at 03:30:11 on February 14, 2016 · (Permalink)
Careful, it's only a different representation of numbers! The numbers themselves are quite the same.
confettibukkake · 16 points · Posted at 23:37:13 on February 13, 2016 · (Permalink)
Extremely cool. But I find it surprising that you'd say "fractions feel weird" in base 12. I always felt like we might be a little better off as a base 12 society, specifically because so many of those "common" fractions would be so much less unwieldy than they are in base 10.
arandombritishguy · 0 points · Posted at 03:26:54 on February 14, 2016 · (Permalink)*
I thought we were a base 12 society no? Our global time-keeping system orientates itself around base 12 for the exact reasons you've given.
We use 60 seconds to denote 1 minute. Where each minute is divided into 12 five second slices.
We use 60 minutes to denote 1 hour. Where each hour is divided into 12 five minute slices.
We use 24 hours in 1 day.
We use 12 months in a year.
The only weird one is weeks. Why the fuck do we use 7 day weeks? lol.
Everything else we count in as a society is in base 10 purely because of the unilateral ease of the concept (as the norm is to have ten fingers/toes, so the public at large find it easier to visualise/grasp when interacting with others).
edit: formatting
Starrystars · 8 points · Posted at 03:30:31 on February 14, 2016 · (Permalink)
Literally all of our other math is done in base 10 though. Also I'm fairly sure that the way we divide time is based off a base 60 system.
s_s · 5 points · Posted at 03:43:37 on February 14, 2016 · (Permalink)
Yep.
Take your right thumb and touch it to each of your finger tips on your right hand. Then, do it again using the next pad on each finger. Then do it again using the last pad on each finger. Congratulations, you counted to 12 like a Sumerian.
Now extend your fingers out on you left hand to indicate a complete cycle. Do that whole thing 5 times (one for each finger on your left hand) and you're counting in base 60.
TellMeYourBestStory · 1 points · Posted at 04:25:18 on February 14, 2016 · (Permalink)
Holy shit! Thank you.
arandombritishguy · 2 points · Posted at 03:47:36 on February 14, 2016 · (Permalink)
Yeah all our maths is in base 10 but I think that is from ease of use conceptually more than anything else.
After a quick google it seems our time system is a mix of base 12 and base 60, though more swiging towards the base 60. Seems to be a mish-mash of many past civilisations own particular systems! Never realised how interested I was in all this until this thread.
An intellectually stimulating askreddit, I like it!
Starrystars · 1 points · Posted at 03:59:05 on February 14, 2016 · (Permalink)
There isn't that much difference between bases conceptually, at least not when starting out. It's just much easier to count and show ten on our fingers than anything else.
arandombritishguy · 1 points · Posted at 04:36:31 on February 14, 2016 · (Permalink)
Makes sense. Especially back in the day before most people were literate/had an education. Much easier to be able to show what you mean than try and explain it.
Pun-Master-General · 2 points · Posted at 03:50:22 on February 14, 2016 · (Permalink)
Hence why we're a base 10 society in everything but time.
arandombritishguy · 1 points · Posted at 04:40:59 on February 14, 2016 · (Permalink)
Touché!
Though I would argue our timing system is the basis of our technological society (however, depending on the argument I could say the same of so many other things which are in base 10, like money).
Brings a new meaning to the saying "time = money" haha, maybe not after all lol.
Pun-Master-General · 2 points · Posted at 05:36:22 on February 14, 2016 · (Permalink)
I have to disagree on that. Our society in general rests pretty squarely on base ten, what with money, the majority of math and science, our natural counting, and just about everything else we do on a daily basis consisting of base ten. Even with time, we use base ten units. For it to be proper base 12, we would say that 9:00 is followed by A:00, then B:00, then 10:00 (which is what we would think of as 12:00).
Other bases are really only used for specialized applications, such as base twelve and base sixty being used for time, base two being used for computers, and base sixteen being used for colors.
arandombritishguy · 1 points · Posted at 17:05:57 on February 14, 2016 · (Permalink)
Yes that makes sense, good reasoning thanks!
Don't worry I don't really believe we are a base 12 society, I was more saying it for the sake of the discussion. It is very evident that we use base 10 in the majority of situations and in where it really matters. Everything that doesn't is the exception.
However, where you have changed my view is on time being in base 10 as opposed to base 12. We still use 10 digits in our timing system so you're right in that it is base 10. Pretty obvious once I think about it, thanks for that, I have thought for a while it is in base 12, not sure why, probably some rubbish I read somewhere on the interwebs which agreed with my world view, damn confirmation bias!
Also what I meant by time is the basis of our technological society is that without the precise measurement and understanding of how to describe time we wouldn't be able to have all the satellites, the internet or even a train timetable. Ie. without an agreed upon timing system, we wouldn't be able to live in the computational/technologically advanced civilisation in which we live today. Hence why I thought it reasonable to say our society is a base 12 society as we rely on our ability to describe time accurately. However I was wrong in that time is base 12 so the statement isn't correct. Thanks for enlightening me :).
saremei · 1 points · Posted at 13:18:56 on February 14, 2016 · (Permalink)
Weeks are based on the moon. Each phase is a week.
probablyhrenrai · 9 points · Posted at 22:43:12 on February 13, 2016 · (Permalink)
So now I have to ask... is there a general relation between bases and repeating fractions, and if so, what is it?
Change of base transformations have always fascinated me.
lukfugl · 9 points · Posted at 01:39:35 on February 14, 2016 · (Permalink)
I'm not 100% on this, so I won't be surprised to be corrected, and you should confirm before repeating it as fact (or maybe I'll confirm and edit), but...
I believe it has to do with relative primality of the base and the prime factors of the divisor (though not the divisor itself). E.g. 10 is not relatively prime with multiples of 2 or 5, fractions with only 2s and 5s in the factorization of the divisor will have finite decimal representations. But if the divisor includes a 3 or 7 (or larger prime) in the factorization, it will have a repeating decimal representation.
In base 12, 3 is not relatively prime to the base, so e.g. 2/3 has a finite doudecimal (aka dozenal) representation. But 5 and 12 are relatively prime, so 1/5 has a repeating representation.
I have a suspicion that the product of the distinct relatively prime factors plays into the period of the repetition, but it's not direct (see 1/3 in decimal, who's period is 1 not 3).
Edit: just fixed a typo in the last paragraph
arandombritishguy · 2 points · Posted at 03:06:16 on February 14, 2016 · (Permalink)
So is this why 1/3 in base ten gives a recurring decimal, but 1/5 in base ten is finite? It's just to do with the number of digits used in the numeral system you are dealing with, in our case, ten digits.
If so you just blew my mind, that is really cool way of explaining positional notation. Just explain it in terms of relative 'primeness' to the base used and it makes SO much more sense to me. Holy fuck thank you!
Shaunisinschool · 4 points · Posted at 01:53:22 on February 14, 2016 · (Permalink)
When people start talking about other bases and the like when it pertains to math a part of me knows they're part alien. Space type
[deleted] · 5 points · Posted at 00:10:23 on February 14, 2016 · (Permalink)
I don't understand this but I am extremely uncomfortable with base 12 now
Dr_WLIN · 3 points · Posted at 02:58:01 on February 14, 2016 · (Permalink)
Base 12 is the Devil! Bobby Boucher.
notafishtoday · 5 points · Posted at 01:11:41 on February 14, 2016 · (Permalink)
The diminished chord of math!
ZarquonsFlatTire · 5 points · Posted at 00:59:25 on February 14, 2016 · (Permalink)
Forget sobering up to reread this, anyone got some peyote? I think this guy just pointed out the universe's lace undergarments creeping out.
TheBiznoid · 2 points · Posted at 02:15:42 on February 14, 2016 · (Permalink)
2497 was an old password for my iPod
Somebodys · 2 points · Posted at 05:03:17 on February 14, 2016 · (Permalink)
I'm a filthy math casual. You made my brain stop working. I also now feel dumb.
hapiscan · 2 points · Posted at 05:08:04 on February 14, 2016 · (Permalink)
I'm really intrigued with Base 12 :O What do you use it for? Why did you learn it? Did you? Is it really hard?
FetchFrosh · 2 points · Posted at 11:04:45 on February 14, 2016 · (Permalink)
I was looking for a problem that I could write Python code for that would push my beginner programming skills, and also require that I learn something new, since it's easy enough to put into code something you already know well, but much harder when you just learned it. So I made a code that would switch base 10 to base 12, then modified it to switch between any two bases.
hapiscan · 2 points · Posted at 15:48:59 on February 14, 2016 · (Permalink)
Neat... I'll be trying to learn more about it, I hope it's not that difficult. Also, good luck with your learning, it's never enough! :D
ChickenBrad · 1 points · Posted at 02:49:01 on February 14, 2016 · (Permalink)
makes a lot of sense now why Greeks preferred a base 6 system. Although there's things we can do that they couldn't. I wonder if a base 12 system would have both worlds?
Xcodist · 1 points · Posted at 03:18:47 on February 14, 2016 · (Permalink)
For anyone that may be a little confused: I found this
theBCexperience · 1 points · Posted at 03:57:13 on February 14, 2016 · (Permalink)
What I want to know is who the hell ever took the time to sit down and think that hard about numbers in base 12? Like specifically base 12.
Diabolik_killer · 1 points · Posted at 04:46:05 on February 14, 2016 · (Permalink)
[8] I think this just melted my mind
lnkofDeath · 1 points · Posted at 04:48:08 on February 14, 2016 · (Permalink)
Is there a perfect base numbering system? I think I understand the gravity of such a question.
For general things base ten doesn't break down. But for larger or smaller things it's sort of 'unfocused'? Or inaccurate, like .333x3.
Is base twelve producing a clearer description of reality? Does it matter if we go higher or lower in base systems? Is there a base system that would be clearer than ever needed?
In simple terms I guess I'm asking if reality is 1080p, base ten is 480p and base twelve is 720p. Does this increase linearly, or logarithmicly by each base? And what base would produce 1200p clarity but would be too accurate for reality?
Is this the wrong way to think of base numbering systems? Also slightly confused on how prime numbers would effect any of this.
Dimpl3s · 1 points · Posted at 05:02:35 on February 14, 2016 · (Permalink)
Just wanna say, the division aspect us why there are 12 inches in a foot instead of 10. It makes the fractions easier
streamburger · 1 points · Posted at 05:48:48 on February 14, 2016 · (Permalink)
I love you.
danbronson · 1 points · Posted at 08:24:58 on February 14, 2016 · (Permalink)
What I get from this is that base 12 is even more beautiful than I'd previously thought because not only do most common fractions fit into it elegantly, the fractions that base 10 has an advantage on still have a predictable, attractive appearance when interpreted in base 12.
One day this planet will be taken over by an alien race that uses base 12. I genuinely feel we're at a disadvantage, mathematically.
[deleted] · 1 points · Posted at 09:02:47 on February 14, 2016 · (Permalink)
Yeah, this is the whole point of imperial units.
googolplexbyte · 1 points · Posted at 14:22:45 on February 14, 2016 · (Permalink)
Boo! Base 12 is over inflated.
Get rid of the unnecessary 2 and go for base 6.
Kids have hard enough times tables already.
JakkuScavenger · 1 points · Posted at 14:36:20 on February 14, 2016 · (Permalink)
That's why base 60 is best!
gr770 · 1 points · Posted at 17:47:46 on February 14, 2016 · (Permalink)
For those confused a bit by the use of A and B for the base 12
A=X = 10
B=E = 11
randomlylostperson · 1 points · Posted at 02:27:29 on February 14, 2016 · (Permalink)
This reminds me of microtonal music and adding extra scale degrees
Michael_Pitt · 1 points · Posted at 07:31:28 on February 14, 2016 · (Permalink)
How?
Lord_Stag · 1 points · Posted at 03:01:07 on February 14, 2016 · (Permalink)
I didn't understand any of this.
Nikwoj · 0 points · Posted at 01:24:24 on February 14, 2016 · (Permalink)
5/7 funnest fact ever
chocopouet · 196 points · Posted at 19:40:09 on February 13, 2016 · (Permalink)
Ok, I have to ask. Is there any mathematical reason to that? And any mathematical application ?
Addarash1 · 354 points · Posted at 20:00:12 on February 13, 2016 · (Permalink)*
Try using long division with something like 1/7, and it would give different remainders that carry over for every new digit (10/7 gives 3, 30/7 gives 2, 20/7 gives 6...). But the only nonzero remainders that you can have when dividing by 7 are 1, 2, 3, 4, 5 and 6, and these are all cycled through and then continually repeated. Therefore something like 2/7 simply starts off at a different point in the sequence (you would begin with 20/7 instead of 10/7).
A number like 1/3, however, only observes one possible remainder (1 from doing 10/3) when using long division, and doesn't have all the possible nonzero remainders when dividing by 3 occur (1 and 2). This is why 1/3 and 2/3 don't show similar behaviour.
For more information or an alternate explanation this site may be useful.
Edit: As for applications, I don't actually know of any other than being a nice trick for being accurate to as many decimal places as you like if you don't have a calculator but have the digits memorised. Wikipedia does tell me it has use in cryptography, though...no idea how true that is.
chocopouet · 10 points · Posted at 20:25:41 on February 13, 2016 · (Permalink)
Super clear answer, thanks a lot :p
MattieShoes · 16 points · Posted at 01:43:28 on February 14, 2016 · (Permalink)*
You remember long division with a remainder, from like 3rd grade or whatever?
1/7 = 0, remainder 1 (0)
Now in order to turn remainders into digits, you add a zero and do it again
1 becomes 10, and 10 / 7 gets 1, remainder 3 (0.1)
3 becomes 30, and 30/7 gets 4, remainder 2 (0.14)
2 becomes 20, and 20/7 gets 2, remainder 6 (0.142)
6 becomes 60 and 60/7 gets 8, remainder 4 (0.1428)
4 becomes 40 and 40/7 gets 5, remainder 5 (0.14285)
5 becomes 50 and 50/7 gets 7, remainder 1 (0.142857)
Remainder 1 is where we started from, so the whole sequence repeats.
Now some things about this...
So these magic numbers are related to cyclic numbers, which connects to a bunch of math that fancy pants mathemeticians like Euler have been exploring since the 1700's at least.
There's a wiki page for cyclic numbers -- https://en.wikipedia.org/wiki/Cyclic_number
heap42 · 2 points · Posted at 23:21:17 on February 13, 2016 · (Permalink)
It is 'because' of the Modulo operator... \Forall x x mod 7 is only a small set of numbers(by definition of mod it is 1-6). Anyways each of the numbers 1-6 have these numbers 28.... in their first digits. so you get that.
chocopouet · 1 points · Posted at 23:48:12 on February 13, 2016 · (Permalink)
Thks
SurprisedPotato · 2 points · Posted at 01:12:56 on February 14, 2016 · (Permalink)
Yes! Fermat (yes, that Fermat) noticed and proved a remarkable pattern - if you raise a number to the power of a bigger prime, then divide the result by that prime, the remainder will always be the original number.
This is now called Fermat's Theorem (not to be confused with the more famous Fermat's Last Theorem)
This means if you write down successive powers if a number a, and take the remainder on division by p, the remainders start to repeat after p-1. They might repeat earlier, but if do, the number if different remainders will always be a factor of p-1.
When you work out the decimal expansion of 1/p, you are basically working out different powers of 10 and their remainders when you divide by p. The trendiness get coded into the decimal digits.
So, 1/7 has digits .142857, repeating every 6, because the powers of 10 have remainders 1, 3, 2, 6, 4, 5; reiterating every 6.
Every possible remainder is there, and when you work out 2/7, you just start the pattern in a different place.
1/11 must repeat every 10 digits, but in fact repeats every 2.
1/13 must repeat every 12 digits, but in fact repeats every 6. Some of 2/13, 3/13, and so on will share the same six digits that 1/13 has, the rest will share between them a different set of six digits.
And so on with other prime fractions: 1/17, 1/19, 1/23, etc. They each have a repeating decimal that repeats after some factor of 16,18, 22, etc places.
As for practical applications:
Fermat's Theorem forms the basis of RSA cryptography, so it's immensely useful. I won't go into the details here, instead I'll site you how it can be used as a way to test a number to see if it's prime.
Suppose we're wondering if 21 is prime. We could start looking for factors, and that works very well for 21. It might not work very well for a number with ten thousand digits, so here's another way.
We could work out the decimal expansion of 1/21. If 21 is prime, that must repeat after 20 digits (or done factor if 20, maybe 10 or 5 or 4 or 2 or 1). Instead, it repeats after 6 digits: 1/21 is 0.047619047619... This proves that 21 isn't prime, because the remainder of 1021 when you divide by 21 isn't 10.
skratch · 1 points · Posted at 05:48:04 on February 14, 2016 · (Permalink)
One application that my dad taught me was that if you want to get a quick approximation of pi , you can just use 22/7, which comes out to 3 +
Easy 3.14 if you're doing rough estimates. Had no idea about the repeating pattern though, neat.
ArcusImpetus · 1 points · Posted at 00:25:12 on February 14, 2016 · (Permalink)
Because 999999/7=142857, 1=0.999999 9999999 999999
ThirdFloorGreg · 0 points · Posted at 22:54:23 on February 13, 2016 · (Permalink)*
1/7= 0.14+0.0028+0.000056+0.00000112+0.0000000224....
1/7=2*7/100+4*7/10000+8*7/1000000+16*7/100000000+32*7/10000000000...
1/7=7(2/102 +4/104 +8/106 +16/108 +32/1010 ...)
1/7=7(21 /102*1 +22 /102*2 +23 /102*3 +24 /102*4 +25 /102*5...)
1/7=7* the sum of 2n /102n from n=1 to infinity.
Bigsam411 · 582 points · Posted at 20:10:43 on February 13, 2016 · (Permalink)
But I thought 5/7 is 1 or "perfect"
RepostThatShit · 1103 points · Posted at 20:26:27 on February 13, 2016 · (Permalink)
Someone left the door to the patio open and now the goddamn dog is dredging up old memes out of the bin in the toilet again.
1337ndngrs · 86 points · Posted at 20:45:30 on February 13, 2016 · (Permalink)
Why do you have a bin in your toilet?
fortyeightD · 154 points · Posted at 20:55:48 on February 13, 2016 · (Permalink)
In some parts or the world the sewerage system cannot handle toilet paper so there is a bin in the toilet. Also in most places the sewerage system cannot handle tampons and pads.
Also some memes are so dank and smelly you wouldn't want to put them in the bin in the kitchen.
1337ndngrs · 13 points · Posted at 21:24:27 on February 13, 2016 · (Permalink)
Cool to know, but I meant to imply he actually had a trash bin in the bowl of his toilet as a joke.
chilly-wonka · 19 points · Posted at 21:39:31 on February 13, 2016 · (Permalink)
I figured as much, but more seriously I'm assuming OP is british or something - they call the whole bathroom "the toilet."
othergallow · 6 points · Posted at 23:56:45 on February 13, 2016 · (Permalink)
What is American for a room a toilet but no bath or shower?
chilly-wonka · 4 points · Posted at 00:07:37 on February 14, 2016 · (Permalink)
We still call it a bathroom, or a restroom if you're feeling fancy or prudish.
[deleted] · 0 points · Posted at 11:30:09 on February 14, 2016 · (Permalink)
Wrong. It's a bathroom if there's a bath or shower in it. It's a restroom otherwise
Stickit · 1 points · Posted at 13:57:00 on February 14, 2016 · (Permalink)
Well, yes, but people still call it a bathroom. Signs in restaurants say "Restroom" and people still say "I'm going to go to the bathroom" at least some of the time.
[deleted] · 1 points · Posted at 13:58:53 on February 14, 2016 · (Permalink)
Yes and colloquially speaking that's OK.
But to say that the difference between the terms is about being fancy or prudish is silly
jchabotte · 3 points · Posted at 03:13:06 on February 14, 2016 · (Permalink)
a "half-bath" or in olde days: Water Closet
SteveMcQwark · 3 points · Posted at 04:15:36 on February 14, 2016 · (Permalink)
Or washroom.
Kruegr · 1 points · Posted at 03:22:11 on February 14, 2016 · (Permalink)
Usually a half bath or powder room if its just a toilet and sink.
Live_Z_Or_Die · 1 points · Posted at 08:02:11 on February 14, 2016 · (Permalink)
The john.
Matti_Matti_Matti · 1 points · Posted at 03:33:42 on February 14, 2016 · (Permalink)
No, they call the whole toilet room the toilet. The room with a bath is the bathroom. A room with a bath and a toilet is a bathroom, but they can use the toilet without needing a bath, or vice versa, or both.
chilly-wonka · 2 points · Posted at 05:06:35 on February 14, 2016 · (Permalink)
When saying "they call the whole bathroom" I was using American lingo, and a room with a toilet and no bath is called a bathroom here. If you want to be technical, it's a "half-bath," that's what you'll see in real estate listings, but literally no one calls it that. A bathroom without a bath is still a bathroom... we're totally divorced from the origins of the word.
It's cool to know the British difference though. So if you just need to pee, but you're going to a room that has a bath in it, you still say I'm going to the bathroom?
Matti_Matti_Matti · 2 points · Posted at 20:22:06 on February 14, 2016 · (Permalink)
"I'm going to the loo" or "I'm going to the toilet."
Or "I'm going for a waz" or similar euphemism.
shiguoxian · 1 points · Posted at 02:47:40 on February 14, 2016 · (Permalink)
I thought that you were referring to the toilet bowl. Where I'm from, toilet = washroom/bathroom.
jashaszun · 2 points · Posted at 01:32:37 on February 14, 2016 · (Permalink)
I'm still wondering why the bin is in the toilet and not just in the bathroom.
Teddybomb · 1 points · Posted at 23:23:25 on February 13, 2016 · (Permalink)
Lady trash is the biggest issue when flushing
Tarantulasagna · 1 points · Posted at 02:09:52 on February 14, 2016 · (Permalink)
Mum I want to be a bin man
[deleted] · 1 points · Posted at 02:41:46 on February 14, 2016 · (Permalink)
[deleted]
fortyeightD · 2 points · Posted at 02:59:02 on February 14, 2016 · (Permalink)
To me, toilet can mean the porcelain throne or the room where you find the porcelain throne.
rallyaroundus · 1 points · Posted at 03:09:20 on February 14, 2016 · (Permalink)
Also sewage.
MobileMeT · 1 points · Posted at 03:17:39 on February 14, 2016 · (Permalink)
How does the sewage handle the whole bin as opposed to just the paper products?
[deleted] · 1 points · Posted at 04:44:03 on February 14, 2016 · (Permalink)
Is sewerage actually a word? I've always just heard it as sewage, but my phone knows the word sewerage.
fortyeightD · 1 points · Posted at 05:01:15 on February 14, 2016 · (Permalink)
IIRC it's called sewage when it's on your property and sewerage after it leaves your property.
7a7p · 1 points · Posted at 04:53:08 on February 14, 2016 · (Permalink)
That's a bin in a bathroom, though, right? Is it actually in the toilet?
Nollege_gaming · 1 points · Posted at 05:08:06 on February 14, 2016 · (Permalink)
Also in some parts of the world the bathroom is called the toilet, and a bun is a garbage can. I feel like it's normal to have a garbage can in your bathroom. Goodnight.
jenga_sm · 1 points · Posted at 10:21:56 on February 14, 2016 · (Permalink)
Easy! Poop on the beach.
fortyeightD · 12 points · Posted at 20:53:47 on February 13, 2016 · (Permalink)
In some parts or the world the sewerage system cannot handle toilet paper so there is a bin in the toilet. Also in most places the sewerage system cannot handle tampons and pads.
gnorty · 3 points · Posted at 22:44:52 on February 13, 2016 · (Permalink)
my toilet system in the UK cannot handle toilet paper tubes, toothepaste boxes, disposable razors etc. That in itself is not a problem, but my wife cannot handle loads of shit on the floor of the bathroom, so we have a bin
RepostThatShit · 1 points · Posted at 03:31:00 on February 14, 2016 · (Permalink)
I don't really use it myself, it's just for tampons and whatever mysterious things women throw away in there.
SpaceMonkey_Mafia · 1 points · Posted at 05:31:26 on February 14, 2016 · (Permalink)
Someone's single.
workaholic_alcoholic · 1 points · Posted at 06:14:24 on February 14, 2016 · (Permalink)
Why do you not? What do you do with used razors or empty shampoo bottles? Walk them out to the kitchen? Fuck that. Throw them in the trash in the bathroom.
[deleted] · 1 points · Posted at 23:50:05 on February 13, 2016 · (Permalink)
Read the comment again, he only has a bin in the toilet that's out on the patio.
2T2T · -6 points · Posted at 20:55:55 on February 13, 2016 · (Permalink)
You'll find out if you ever grow up, move out of your parents basement and get a human (non Anime ) girlfriend.
1337ndngrs · 5 points · Posted at 21:23:30 on February 13, 2016 · (Permalink)
I meant it as a joke, implying that he actually placed a trash bin in the bowl of his toilet but sure, personal attacks are cool too.
ananori · -6 points · Posted at 21:42:01 on February 13, 2016 · (Permalink)
It was meant as a joke as well but looks like it hit home, eh?
xmrsmoothx · 5 points · Posted at 23:30:36 on February 13, 2016 · (Permalink)
That is absolutely not an old meme.
UndeadBread · 4 points · Posted at 02:33:31 on February 14, 2016 · (Permalink)
It's been around at least a couple of weeks.
xmrsmoothx · 1 points · Posted at 02:58:44 on February 14, 2016 · (Permalink)
Yeah, like I said, not old. Old memes would be ones that are more than a few years old.
UndeadBread · 2 points · Posted at 03:02:40 on February 14, 2016 · (Permalink)
Anything more than a year old is practically prehistoric in the world of internet memes.
xmrsmoothx · 3 points · Posted at 03:11:11 on February 14, 2016 · (Permalink)
The hell it is, I've been memeing for seven plus years, 5/7 is practically a newborn.
dan4334 · 2 points · Posted at 05:34:11 on February 14, 2016 · (Permalink)
It's already been flogged to death by reddit. It wasn't even that funny to start with.
xmrsmoothx · 1 points · Posted at 05:41:25 on February 14, 2016 · (Permalink)
That still doesn't make it old. It's just worn-out and shitty to begin with.
[deleted] · 1 points · Posted at 11:32:23 on February 14, 2016 · (Permalink)
Wow, five plus years? That's a long time
ceelo_purple · 1 points · Posted at 08:48:37 on February 14, 2016 · (Permalink)
Welcome to my homepage! I kiss you!
[deleted] · 0 points · Posted at 00:37:02 on February 14, 2016 · (Permalink)
[deleted]
xmrsmoothx · 4 points · Posted at 01:04:59 on February 14, 2016 · (Permalink)
It's clearly not dead, judging by the amount of people that use it.
an_obscene_username · 2 points · Posted at 06:24:17 on February 14, 2016 · (Permalink)
ever heard of "beating a dead horse"?
thgril · 1 points · Posted at 02:18:04 on February 14, 2016 · (Permalink)
Dammit Moon Moon
boogswald · 1 points · Posted at 12:46:38 on February 14, 2016 · (Permalink)
Your toilet is on your patio?
eyehateq · 0 points · Posted at 02:21:07 on February 14, 2016 · (Permalink)
Poor colby :(
OC4815162342 · 5 points · Posted at 01:32:54 on February 14, 2016 · (Permalink)
Can someone explain this to me please
Bigsam411 · 15 points · Posted at 01:44:05 on February 14, 2016 · (Permalink)
http://imgur.com/gallery/6xkzh
Its fake apparently but it is very funny.
an_obscene_username · 4 points · Posted at 06:23:03 on February 14, 2016 · (Permalink)
if by funny you mean "the imaginary arguments every redditor wishes they had because it has every current circlejerk topic in it" then sure why not.
mikey_says · 5 points · Posted at 01:47:19 on February 14, 2016 · (Permalink)
OH MY GOD SO FUCKING FUNNY EVERY TIME
tkookookachoo · 2 points · Posted at 03:31:58 on February 14, 2016 · (Permalink)
I don't get it :(
Bigsam411 · 2 points · Posted at 03:39:54 on February 14, 2016 · (Permalink)
check one of the other replies to my post. I linked someone to the context.
Average_Sized · 2 points · Posted at 10:20:09 on February 14, 2016 · (Permalink)
STOP THIS MEME ALREADY
Shmeeku · 1 points · Posted at 06:39:57 on February 14, 2016 · (Permalink)
I know this is a joke, but there is actually such a thing as a "perfect number." The first few are 6, 28, and 496, so 5/7 isn't perfect in the mathematical sense.
[deleted] · 3 points · Posted at 07:13:43 on February 14, 2016 · (Permalink)
I figured this out while taking a test, I ended up failing the test cause I sat there trying all the fractions of 7.
[deleted] · 5 points · Posted at 22:55:46 on February 13, 2016 · (Permalink)*
[deleted]
Random832 · 1 points · Posted at 07:56:43 on February 14, 2016 · (Permalink)
Just put \ before each *.
Jelmo_Jurnas · 2 points · Posted at 23:05:32 on February 13, 2016 · (Permalink)
I rate this comment 0.714285714285...
Flight714 · 2 points · Posted at 00:54:25 on February 14, 2016 · (Permalink)
Ahh, that makes sense...
Yep, there's a pattern here all right, let me guess...
What the fuck, Seven? What do you call that?
Not gettin' fooled by your bullshit this time.
siamthailand · 1 points · Posted at 02:53:27 on February 14, 2016 · (Permalink)
7 * 2 = 14 * 2 = 28 * 2 = 56. It become 57 because 1 is carried.
Random832 · 1 points · Posted at 08:14:01 on February 14, 2016 · (Permalink)
Obviously the math gets harder as it goes on, but it checks out.
And now I'm about to blow your mind:
TheWookieeMonster · 2 points · Posted at 01:08:50 on February 14, 2016 · (Permalink)
That's neat I always thought 7 was kind of fucked.
My_Perfect_Boy · 2 points · Posted at 01:43:03 on February 14, 2016 · (Permalink)
Reminds me a lot of musical modes...
SpectralMornings · 1 points · Posted at 14:00:40 on February 14, 2016 · (Permalink)
That can't be a coincidence right?
HauckPark · 2 points · Posted at 20:48:35 on February 13, 2016 · (Permalink)
Huh. Could musical modes be related to this in some way?
bag_of_oatmeal · 1 points · Posted at 22:15:59 on February 13, 2016 · (Permalink)
Neat.
freenarative · 1 points · Posted at 23:05:10 on February 13, 2016 · (Permalink)*
deadbird17 · 1 points · Posted at 00:05:28 on February 14, 2016 · (Permalink)
Cool, seems like it would be worth memorizing the series.
pm_me_ur_lil_titties · 1 points · Posted at 00:23:42 on February 14, 2016 · (Permalink)
Just thought I'd point out the chain of 7, 14, 28 (then 5; not sure what to do with that) .ie 7 doubled, then doubled again.
Not sure what that means, with my limited maths knowledge, but thought it was interesting.
Like the fact that the digits of all multiples of nine always add up to nine. [18 (1+8), 27(2+7)... 108(1+0+8), 117(1+1+7)...]
LuxDeorum · 1 points · Posted at 01:12:25 on February 14, 2016 · (Permalink)
I had a student discover this independently while doing homework. I was amazed
TehTurk · 1 points · Posted at 01:14:37 on February 14, 2016 · (Permalink)
Is there a name with numbers that run like this?
Appetite_TDE · 1 points · Posted at 01:27:14 on February 14, 2016 · (Permalink)
I cant be bothered to check but do other prime numbers behave similarly?
EDIT: I checked and nope
smc5230 · 1 points · Posted at 01:27:27 on February 14, 2016 · (Permalink)
Not sure if its a typo or not but 5/6 begins with .71 and according to looking at the numbers in the previous one 6/6 should begin with .42 but begins with the .85.
TigerlillyGastro · 1 points · Posted at 01:28:34 on February 14, 2016 · (Permalink)
And the decimals of ninths are .1111... .2222... .333... etc.
So, 9/9 is .999999.... which we all know is actually 1.
tomai443 · 1 points · Posted at 01:29:12 on February 14, 2016 · (Permalink)
This was my first thought. Glad to see others picked up on this.
chewyrunt · 1 points · Posted at 01:47:28 on February 14, 2016 · (Permalink)
If you look deeper, you can see that the repeating '142857' can be formed by successively doubling 14 and dividing by 100:
I once tried to generalize this pattern to any fraction and it turned out to be the binomial theorem (I think).
Random832 · 2 points · Posted at 08:24:38 on February 14, 2016 · (Permalink)
It's because 14/98 = 1/7.
FallenAege · 1 points · Posted at 01:52:27 on February 14, 2016 · (Permalink)
And 22/7 is used to approximate pi.
Edit: For the curious, it's 3.1428571428571428571428571428571428
bluehaught · 1 points · Posted at 01:55:29 on February 14, 2016 · (Permalink)
in addition, 142857x[1-6] will produce the same effect 142857x2=285714 142857x3=428571 142857x4=571824 142857x5=718245 142857x6=824517
but it gets better than that: 142857x7=999999
think thats cool? 142+857=999 14+28+57=99
and even more... 1428572 =20408122449 and 20408+122449=142857
and there's even more things about 142857 that i havent remembered from years of using this as a conversation starter because im a nerd
Joe59788 · 1 points · Posted at 02:07:58 on February 14, 2016 · (Permalink)
Neat.
bagelbomb · 1 points · Posted at 02:09:48 on February 14, 2016 · (Permalink)
I discovered that exact pattern years ago. And this works for any number that isn't a factor or multiple of 7. For example, 1256 divided by 7 is 179.42857... (The whole number increases regularly but there's always the same pattern at some point.)I checked with my mathematician granddad and he says it isn't a new discovery but it's still interesting.
AkirIkasu · 1 points · Posted at 02:14:21 on February 14, 2016 · (Permalink)
Yes, but did you know that the same is true of 3?
vpustote · 1 points · Posted at 02:18:16 on February 14, 2016 · (Permalink)
This is true of all decimals. They repeat same digits starting from another digit. For instance. 1/17 is .0588235294117647.
If you put those same 16 repeating digits in order you can know the next repeating number start point. 2/17 is .1176470588235294.
3/17 is the next lowest number which is .1764705882352941
ajprax · 1 points · Posted at 02:19:47 on February 14, 2016 · (Permalink)
There are powers of 2 hidden in the decimals of 1/7.
plug that last line into wolfram alpha
[deleted] · 1 points · Posted at 02:20:07 on February 14, 2016 · (Permalink)
Why weren't these the Lost numbers?
FunkeTown13 · 1 points · Posted at 02:32:18 on February 14, 2016 · (Permalink)
And now to wait for a group of people that will be impressed by my recitation of fractions of 7 up to 8 decimal places...
well_golly · 1 points · Posted at 02:41:00 on February 14, 2016 · (Permalink)
It's like some kind of Phillip Glass rule.
like_a_squeezel · 1 points · Posted at 02:41:19 on February 14, 2016 · (Permalink)
Sounds like modes to me.
BrawlKarter · 1 points · Posted at 02:41:52 on February 14, 2016 · (Permalink)
So the missing numbers are all divisible by 3, why is that?
IZ3820 · 1 points · Posted at 02:45:04 on February 14, 2016 · (Permalink)
Interestingly, 7/22 is 3.142857142857...
Mavioso23 · 1 points · Posted at 02:46:31 on February 14, 2016 · (Permalink)
Cyclical modular group theory perhaps ?
Greatgat · 1 points · Posted at 02:50:22 on February 14, 2016 · (Permalink)
So what's between the 14 and the 57? Infinity? But it seems like it repeats, right? Infinite numbers can't repeat. Right?
I mean the first series seems to be 14 and then anything after has 14 preceded by 57. So would 14 be the 'first' and then 57 for everything after is the end of the loop?
I may not be making much sense here.
DasNative · 1 points · Posted at 02:52:58 on February 14, 2016 · (Permalink)
My head hurts
jank321 · 1 points · Posted at 03:13:47 on February 14, 2016 · (Permalink)
Winner winner chicken dinner
username2065 · 1 points · Posted at 03:15:18 on February 14, 2016 · (Permalink)
interesting
MobileMeT · 1 points · Posted at 03:15:47 on February 14, 2016 · (Permalink)
5/7 = 1.0 what're you talking about?
LeonardSmallsJr · 1 points · Posted at 03:22:47 on February 14, 2016 · (Permalink)
It kind of bugs me that the rotating digits are 142857, yet the first digit if each line is 142578. So close to perfection!
[deleted] · 1 points · Posted at 03:26:29 on February 14, 2016 · (Permalink)
Does this relate to musical scales?
Alarid · 1 points · Posted at 03:31:50 on February 14, 2016 · (Permalink)
What about 7/7? Don't leave me in suspense!
[deleted] · 1 points · Posted at 03:32:05 on February 14, 2016 · (Permalink)
This reminds me of the message buried deep in Pi at the end of the novel Contact.
kiddo51 · 1 points · Posted at 03:38:05 on February 14, 2016 · (Permalink)
1 4 2 8 5 7
4
2
8
5
7
antsugi · 1 points · Posted at 03:52:51 on February 14, 2016 · (Permalink)
13 has a similar one, only that the pattern is longer
jeanduluoz · 1 points · Posted at 03:55:24 on February 14, 2016 · (Permalink)
Oh I remember 6th grade too
WeirderQuark · 1 points · Posted at 03:59:27 on February 14, 2016 · (Permalink)
Yes! I only noticed this late last year when I realised that the only fractions I didn't know decimal for between 1/2s and 1/12s was 1/7s, so to improve my mental math game I went to memorise 1/7 through 6/7 and realised this pattern.
goat18 · 1 points · Posted at 04:02:41 on February 14, 2016 · (Permalink)
I discovered this on my own. The numbers in the decimals are also the multiples of seven.
1/7 = 0.14 28 57 142857...
14 = 2*7
28 = 4*7
56 = 8*7
112 = 16*7 (the 1 is added to the 56 making it 57, and the 2 has 2 added to it from the next iteration)
etc.
I tried to play around with other numbers for a little while to see if I can get something useful out of it but didn't get very far. I basically ended up deriving a formula for 1/7.
1Rab · 1 points · Posted at 04:09:18 on February 14, 2016 · (Permalink)
This turned me on.
MrMi10s · 1 points · Posted at 04:17:03 on February 14, 2016 · (Permalink)
Tyy
Futurist110 · 1 points · Posted at 04:21:30 on February 14, 2016 · (Permalink)
Dude ... you just totally blew my mind! ;) Well done! ;)
MJawn · 1 points · Posted at 04:26:28 on February 14, 2016 · (Permalink)
1/81 is pretty neat in a similar vein
Trizizzle · 1 points · Posted at 04:27:31 on February 14, 2016 · (Permalink)
TOok me a good ten minutes but wow.
Krissam · 5743 points · Posted at 19:10:21 on February 13, 2016 · (Permalink)
There's exactly 10! seconds in 6 weeks.
Ervin_Pepper · 3154 points · Posted at 19:55:50 on February 13, 2016 · (Permalink)
6 weeks in seconds = 6 * 7 * 24 * 60 * 60 = 6 * 7 * (8 * 3) * (3 * 2 * 10) * (1 * 3 * 4 * 5) = 6 * 7 * 8 * 9 * 2 * 10 * 1 * 3 * 4 * 5 = 10!
jillyboooty · 1156 points · Posted at 21:46:07 on February 13, 2016 · (Permalink)
That's the most concise explanation possible.
KNueve83 · 43 points · Posted at 01:50:29 on February 14, 2016 · (Permalink)
Explain like I'm 3?
DonkeyD13K · 60 points · Posted at 03:20:55 on February 14, 2016 · (Permalink)*
Coming from an idiot to facepalmingly figuring this out... remember that the symbol for times is x and also * and sometimes just a tiny dot. next look at the law/rule/formula stating that n! = n*(n-1) * (n-2) * (n-3) So in this case starting from 10! and not n! the math goes 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 which = 3,628,800 = 6 weeks in seconds.
now knowing what you know lets work backwards.
6 weeks * 7 days * 24 hours * 60 minutes * 60 seconds = 3,628,800.
Now look at those big numbers 24, 60, and 60. those can be factored, and factoring is basically what times what gives you that number.
Look at it again
6 Weeks * 7 days * 24 hours * 60 minutes * 60 seconds = 3,628,800
After factoring
6 * 7 * (8 * 3) * (3 * 2 * 10) * (1 * 3 * 4 * 5) = 3,628,800
You can get 24 with (8 * 3)
and you can get 60 with (3 * 2 * 10)
and also another way to get 60 with (1 * 3 * 4 * 5)
So look! if you now notice we have all the numbers leading up to 10.
6 * 7 * (8 * 3) * (3 * 2 * 10) * (1 * 3 * 4 * 5) = 3,628,800.
looking closer into this equation There is no 9 but there are three 3's. with 3 * 3 = 9 we can take two of the 3's out in this equation and represent it as 9.
After rearranging our equation :
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 = 3,628,800.
Bringing us back to our first representation of 10!
SoulofZendikar · 12 points · Posted at 05:58:29 on February 14, 2016 · (Permalink)
Get this man a chocolate bar.
I read through all of that just to find out on the last line what the ! in n! or 10! means.
But at least this guy friggin' taught it.
NC-Lurker · 7 points · Posted at 08:47:13 on February 14, 2016 · (Permalink)
The others didn't, because that's part of the question. They explained the answer, assuming you already understood the question.
ihateshen · 5 points · Posted at 04:24:57 on February 14, 2016 · (Permalink)
this is a really good explanation (i think) but....
what?!?!?
DonkeyD13K · 2 points · Posted at 05:04:13 on February 14, 2016 · (Permalink)
Just formatted and edited for clarity!
HunterDigi · 2 points · Posted at 08:20:15 on February 14, 2016 · (Permalink)
and sometimes nothing at all xD
kyl12 · 2 points · Posted at 18:16:05 on February 14, 2016 · (Permalink)
Give that man a Reddit Gold!
jillyboooty · 32 points · Posted at 02:02:08 on February 14, 2016 · (Permalink)
Left part of equation is converting to seconds. Next part is breaking up some of the numbers into smaller factors (24=8*3). Next part is rearranging in (somewhat) order.
Related_TIL · 53 points · Posted at 04:02:39 on February 14, 2016 · (Permalink)
ELI a neonatal
vikingcock · 55 points · Posted at 04:22:08 on February 14, 2016 · (Permalink)
Math.
Related_TIL · 27 points · Posted at 04:29:29 on February 14, 2016 · (Permalink)
Oh. Thanks
tonycomputerguy · 15 points · Posted at 06:37:18 on February 14, 2016 · (Permalink)
This has summed up this entire post for me basically. Not sure why I expected to suddenly become a math genius by coming here.
[deleted] · -4 points · Posted at 11:22:30 on February 14, 2016 · (Permalink)
I really don't understand how people can be so fucking stupid they don't know basic multiplication.
[deleted] · 3 points · Posted at 11:36:32 on February 14, 2016 · (Permalink)
No need to be a cunt about it.
jillyboooty · 7 points · Posted at 04:37:26 on February 14, 2016 · (Permalink)
Googoogaga
Related_TIL · 5 points · Posted at 05:05:51 on February 14, 2016 · (Permalink)
gasps for air
Exaskryz · 10 points · Posted at 02:25:09 on February 14, 2016 · (Permalink)
That second to last part isn't really putting in order, but combining factors into what was missing. We had three threes but no nines, so it just took two threes and wrote it as a nine.
SoulofZendikar · 1 points · Posted at 06:00:58 on February 14, 2016 · (Permalink)
I think 3! means 1 x 2 x 3
So 10! means 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10.
Rearrange those numbers to be days of the week / hours of the day and so on.
dont_wear_a_C · 1 points · Posted at 07:35:04 on February 14, 2016 · (Permalink)
Michael Scott checking in!
The_purple_pear · 0 points · Posted at 02:52:49 on February 14, 2016 · (Permalink)
Many numbers.
MrFurrypants · 0 points · Posted at 03:07:53 on February 14, 2016 · (Permalink)
Numbers are fun!
Exaskryz · 10 points · Posted at 02:27:24 on February 14, 2016 · (Permalink)
I disagree. This is more concise. (And you can probably argue for an even more concise answer.)
non-suspicious · 10 points · Posted at 03:34:43 on February 14, 2016 · (Permalink)
I think most people who have had to endure a university math course solution manual would laugh at the post before yours considered as "the most concise explanation possible".
Kombat_Wombat · 19 points · Posted at 03:38:35 on February 14, 2016 · (Permalink)
"exercise left to reader"
non-suspicious · 11 points · Posted at 03:57:28 on February 14, 2016 · (Permalink)
"reduced to a previously solved problem"
AmericanBigDog · 1 points · Posted at 05:46:31 on February 14, 2016 · (Permalink)
1 week = 7 days 1 day = 24 hours 1 hr = 3600 seconds 6 * 7 * 24 * 3600 = 3628800 seconds
boldra · 1 points · Posted at 07:01:27 on February 14, 2016 · (Permalink)
The Babylonians liked 60 because it was easy to factor. That's why I have 360° degrees in a circle and lead to me putting 60 seconds in my minutes.
SadGhoster87 · 1 points · Posted at 07:08:17 on February 14, 2016 · (Permalink)
Other than "There's exactly 10! seconds in 6 weeks"
jillyboooty · 1 points · Posted at 07:27:24 on February 14, 2016 · (Permalink)
Not much of an explanation
najodleglejszy · 1 points · Posted at 07:55:38 on February 14, 2016 · (Permalink)
well he did say "in seconds".
my_password_is_1245 · 1 points · Posted at 08:18:37 on February 14, 2016 · (Permalink)
I prefer units for dimensional analysis.
6 weeks * (7days/week) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute)
from a mathematical quirk of an arbitrary division of units (minutes don't NEED to be 60 seconds), this can be rewritten as 10!.
blackNstoned · 1 points · Posted at 08:37:37 on February 14, 2016 · (Permalink)
I thought the ! was an exclamation till i read the next post that its for factorial
makethemake · 1 points · Posted at 02:56:57 on February 14, 2016 · (Permalink)
How is that an explanation to anyone who doesn't know what factorial means, and anyone who does doesn't need an explanation
peon2 · -5 points · Posted at 23:11:03 on February 13, 2016 · (Permalink)
6 weeks in 10 seconds= 10!
More concise, just shows less work
[deleted] · 6 points · Posted at 01:17:18 on February 14, 2016 · (Permalink)
Rephrasing a theorem doesn't prove it.
Example:
(This doesn't proof anything)
The aim of a proof is to communicate an understanding why a theorem is true by deriving it from other proven mathematical rules, axioms or by proving that if it isn't true, these proven rules or axioms would be broken.
A proper proof of eπi = -1 (which is called Euler's identity, and is one of the coolest facts I know) can be made by proving Euler's formula:
exi = (cos x + i sin x)
For when x = π, sin π = 0 and cos π = -1
A really elegant proof of Euler's formula can be found here, along with some others. If you understand the proof, it now should make sense to you that eπi = -1
Edit: Not necessarily meant directly to your reply, /u/peon2, I just had to insert it somewhere in the comment chain.
peon2 · 5 points · Posted at 01:30:16 on February 14, 2016 · (Permalink)
Ok glad to know you didn't waste any time typing that out for my silly joke. I've had to write out eulers proofs for several classes in the past and appreciate it's wonder. Was just making a dumb joke.
raddaya · 0 points · Posted at 02:11:36 on February 14, 2016 · (Permalink)
Nah, here's the best and most concise proof available.
6 weeks = 10! seconds. The proof is trivial and left to the reader.
[deleted] · 1 points · Posted at 02:17:43 on February 14, 2016 · (Permalink)
There should be a name for this... "proof by audience"?
[deleted] · 0 points · Posted at 04:00:23 on February 14, 2016 · (Permalink)
I think this is:
10 weeks in seconds = 6×7×24×60×60 = 3628800 = 10!
There really is no reason to the through the factorization. This is just a coincidence and it isn't too surprising imo
seth11111 · 0 points · Posted at 04:06:54 on February 14, 2016 · (Permalink)
really? even more than (10x9x8x7x6x5x4x3x2x1)/6/7/24/60/60.... uh im quickly realizing I dont' know how to write math anymore
ebbomega · -4 points · Posted at 23:32:30 on February 13, 2016 · (Permalink)
Proof, not explanation.
[deleted] · 2 points · Posted at 01:52:18 on February 14, 2016 · (Permalink)
Both in this case. It should be easy to figure out what each number represents, as they're neatly ordered: 6 weeks, 7 days per week, 24 hours per day, 60 minutes per hour, 60 seconds per minute.
deusset · 16 points · Posted at 01:52:00 on February 14, 2016 · (Permalink)
I'll be honest, the elegance of the proof is more exciting than the fact itself
[deleted] · 9 points · Posted at 06:56:58 on February 14, 2016 · (Permalink)
This is why physics teachers fail people who don't use units.
DonkeyD13K · 3 points · Posted at 02:58:47 on February 14, 2016 · (Permalink)
Why do you break it down in this way? 6 * 7 * 8 * 9 * 2 * 10 * 1 * 3 * 4 * 5 And this way?
I understand the first one but not the latter
DonkeyD13K · 7 points · Posted at 03:04:48 on February 14, 2016 · (Permalink)
OH Breaking it down is the explainationnnnnnnnnn... WOW lol
RAT_STINK · 3 points · Posted at 03:59:37 on February 14, 2016 · (Permalink)
WOW lol
[deleted] · 1 points · Posted at 04:25:27 on February 14, 2016 · (Permalink)
He excludes 9 so he puts 2 extra 3s
ranthria · 1 points · Posted at 01:18:26 on February 14, 2016 · (Permalink)
Thank you! I was trying to work it out in my head, but couldn't keep track of that many factors.
dabosweeney · 1 points · Posted at 02:48:31 on February 14, 2016 · (Permalink)
This is exactly what I wanted to see
ranma_one_half · 1 points · Posted at 03:01:18 on February 14, 2016 · (Permalink)
Is that not ten or were you just excited by ten?
blastpower5 · 4 points · Posted at 03:45:40 on February 14, 2016 · (Permalink)
https://en.m.wikipedia.org/wiki/Factorial
Also ten is a very exciting number.
ranma_one_half · 2 points · Posted at 04:37:00 on February 14, 2016 · (Permalink)
I was making a math joke. It seems it was !(very funny).
indigoflame · 1 points · Posted at 03:59:12 on February 14, 2016 · (Permalink)
Argh, I spent so long trying to figure out how to split up the factorization in a way that showed each time unit that you multiply. Now I see that the 9 could not be included in the factorization and had to be split into two 3's. Good on you for figuring it out :)
thatTigercat · 1 points · Posted at 04:01:21 on February 14, 2016 · (Permalink)
This guy proofs
diabolical-sun · 1 points · Posted at 05:41:02 on February 14, 2016 · (Permalink)
I get throwing it in there for the sake of the factorial, but it's so weird seeing you break down 60 = 3 * 4 * 5 * 1
Bolton_colton · 1 points · Posted at 06:14:26 on February 14, 2016 · (Permalink)
I had a much longer week than you...
TheMrShadySlim · 1 points · Posted at 06:17:31 on February 14, 2016 · (Permalink)
If you re-ordered the last part people would of caught that way faster. This is a crazy fact tho
pterrorgrine · 1 points · Posted at 06:51:32 on February 14, 2016 · (Permalink)
holy shit
trey82 · 1 points · Posted at 08:59:06 on February 14, 2016 · (Permalink)
Beautiful
NAN001 · 1 points · Posted at 11:46:05 on February 14, 2016 · (Permalink)
garblegarble12342 · 1 points · Posted at 12:38:09 on February 14, 2016 · (Permalink)
Hnngnngnnggggh maaath
JakkuScavenger · 1 points · Posted at 14:37:05 on February 14, 2016 · (Permalink)
Nice!
halorazer · 1 points · Posted at 03:36:03 on February 15, 2016 · (Permalink)
Oh god, this reminds me of the new Common Core standards.
[deleted] · 1 points · Posted at 02:00:02 on February 14, 2016 · (Permalink)
That's cool as f**k
[deleted] · 1 points · Posted at 02:36:27 on February 14, 2016 · (Permalink)
I don't know enough about the alphabet to dispute this statement.
CalebDK · 0 points · Posted at 04:30:07 on February 14, 2016 · (Permalink)
I'm so confused
[deleted] · 5835 points · Posted at 22:20:56 on February 13, 2016 · (Permalink)
[deleted]
Qqaim · 1876 points · Posted at 22:32:53 on February 13, 2016 · (Permalink)
In case you want to know, n! (pronounced n factorial) means n*(n-1)*(n-2)*(n-3)*....*2*1. So 10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800.
[deleted] · 1259 points · Posted at 01:01:58 on February 14, 2016 · (Permalink)
Also, really clever people leave out the
*1because it doesn't do anything. When we point this out to other people, we feel super clever and are happy for days!columbus8myhw · 715 points · Posted at 01:10:55 on February 14, 2016 · (Permalink)
Just make sure not to go too far and accidentally do "*0".
TheRoss23 · 892 points · Posted at 01:36:47 on February 14, 2016 · (Permalink)*
0! = 1, for those asking how, idk, but here's a numberphile
[deleted] · 395 points · Posted at 01:39:03 on February 14, 2016 · (Permalink)
0! = 1!, too
[deleted] · 612 points · Posted at 01:40:22 on February 14, 2016 · (Permalink)
0 != 1
[deleted] · 593 points · Posted at 01:42:06 on February 14, 2016 · (Permalink)
truesillyblanco · 61 points · Posted at 01:56:27 on February 14, 2016 · (Permalink)*
Ok, gotta step in here. ELI48, please.
Edit: Wow, reddit is really representing itself well tonight. Really, really good stuff. Thanks to each of you.
[deleted] · 110 points · Posted at 02:04:05 on February 14, 2016 · (Permalink)
Ok, step by step (read this more slowly if you think I'm going too fast):
0! = 1
This is a definition. You can read n! as: "How many different orderings can I pick from n objects"
So say you have 3 colored pieces of paper; at first you can choose any of the three, then there are only two left to choose from and the last one you have to take any way, so there are 3 * 2 * 1 ways to choose orderings from 3 pieces of paper.
That's basically what factorial does.
We define 0! as 1, i.e. if you have no pieces of paper, there is only one ordering: an empty ordering.
That covers 0! = 1
0! = 1!
There is only one ordering of one piece of paper:
1! = 1
but also: 0! = 1
therefore: 0! = 1! (which both equal 1)
Then we found our programmer: /u/Combustible_Baguette.
In programming, "!=" often means "not equals" (think of this symbol: ≠) and it is used to check the values of variables and such:
Consider this piece of made-up code:
It prints "x is not equal to 3", you can read it as a task list. First we give x the value of 4, then we raise the condition: "if x does not equal 3, then we print some text on screen".
A condition that holds in programming, evaluates to
true(which is a special word in a program to identify conditions that hold).The joke is that 0! = 1 holds, but in programming,
0 != 1also holds since 0 is not equal to 1, so it evaluates to thistrue:)GGritzley · 11 points · Posted at 06:58:51 on February 14, 2016 · (Permalink)
That was very in depth, I couldn't have said it better.
Fastriedis · 5 points · Posted at 15:52:50 on February 14, 2016 · (Permalink)
it better.
You're really lazy.
SplendidZebra · 3 points · Posted at 12:11:13 on February 14, 2016 · (Permalink)
this is great!
Scizors · 12 points · Posted at 01:57:54 on February 14, 2016 · (Permalink)
In some programming languages "!=" is used as a "not equal" operator. So if you put the statement "0 != 1" it would return true since 0 is not equal to 1.
mattmonkey24 · 3 points · Posted at 07:37:09 on February 14, 2016 · (Permalink)
Fun fact, it is also a tautology so whatever following statement will always execute
Plasma_000 · 2 points · Posted at 11:13:09 on February 14, 2016 · (Permalink)
But it becomes redundant. Just use while(true)
ImBi-Polar · 3 points · Posted at 02:06:58 on February 14, 2016 · (Permalink)
The "!" in programming is saying, "not equal to." He replies "true" because 0 !(not)= 1; That statement would be true because 0 and 1 are not equal...
_chadwell_ · 5 points · Posted at 06:09:20 on February 14, 2016 · (Permalink)
Technically. "!" means not, and "!=" means not equal to.
[deleted] · 4 points · Posted at 01:59:15 on February 14, 2016 · (Permalink)
!= means "different" in programming. The statement "0 is different from 1" is true
oneawesomeguy · 2 points · Posted at 02:26:37 on February 14, 2016 · (Permalink)
That's true but a better way to explain is that the exclamation point means opposite (kind of). So != means the opposite of equal.
[deleted] · 3 points · Posted at 02:33:51 on February 14, 2016 · (Permalink)
Yes, as you can also say
which would be false.
ELI48: == means equals, as = assigns variables (like x in math, except no one uses x as a variable)
saving_storys · 1 points · Posted at 04:58:07 on February 14, 2016 · (Permalink)
!= is not equal to
magpac · 3 points · Posted at 07:45:09 on February 14, 2016 · (Permalink)
I have to do this
Not equal to what?
[deleted] · 3 points · Posted at 08:21:10 on February 14, 2016 · (Permalink)
0 != 1
It reads as 'Zero isn't equal to one'
UnderNatural · 3 points · Posted at 03:54:40 on February 14, 2016 · (Permalink)
1
gamehelp16 · 3 points · Posted at 13:01:26 on February 14, 2016 · (Permalink)
Found the programmer.
LOLWATERUDOIN · 2 points · Posted at 06:18:45 on February 14, 2016 · (Permalink)
What's going on
[deleted] · 1 points · Posted at 14:28:26 on February 14, 2016 · (Permalink)
https://www.reddit.com/r/AskReddit/comments/45m1zl/whats_the_coolest_mathematical_fact_you_know_of/czz3il5 :)
chidedneck · 1 points · Posted at 04:09:27 on February 14, 2016 · (Permalink)
This statement is not 0 != 1.
Plague_Bears · 1 points · Posted at 04:27:02 on February 14, 2016 · (Permalink)
1
marakpa · 0 points · Posted at 04:31:39 on February 14, 2016 · (Permalink)
WHAT THE FUCK
You blew my mind.
jakx102 · 5 points · Posted at 04:37:52 on February 14, 2016 · (Permalink)
Found the programmer
mumblinmad · 4 points · Posted at 04:06:21 on February 14, 2016 · (Permalink)
/r/programmerhumor
recalcitrantJester · 1 points · Posted at 05:03:46 on February 14, 2016 · (Permalink)
Q.E.D.
Extruded_Chicken · 1 points · Posted at 05:42:39 on February 14, 2016 · (Permalink)
O! m8
ClearlyChrist · 1 points · Posted at 06:51:00 on February 14, 2016 · (Permalink)
Oh my fucking god
danbronson · 1 points · Posted at 08:28:23 on February 14, 2016 · (Permalink)
0 = 1, motherfucker!
PacoTaco321 · 1 points · Posted at 13:56:35 on February 14, 2016 · (Permalink)
0! + 0! = 2sin (pi/2)
naughty_ottsel · 1 points · Posted at 16:22:58 on February 14, 2016 · (Permalink)
Unless you #define false true
jdman929 · 0 points · Posted at 01:50:29 on February 14, 2016 · (Permalink)
1=1
AlpineKnot · 4 points · Posted at 01:59:28 on February 14, 2016 · (Permalink)
1 == 1
unproperNoun · 0 points · Posted at 08:55:45 on February 14, 2016 · (Permalink)
(limx→∞(0!+(0!/n)n)((√(0-(0!)))*((0!+0!)arccos0)) +0! = 0
dj0 · 2 points · Posted at 02:04:43 on February 14, 2016 · (Permalink)
0! = 1!!
That last one was just for exclamation
limasxgoesto0 · 2 points · Posted at 03:40:56 on February 14, 2016 · (Permalink)
0! = eπ*i * -1
[deleted] · 2 points · Posted at 14:07:08 on February 14, 2016 · (Permalink)
Cancel out the exclamation marks because they're on both sides of the equation
0
!= 1!0 = 1
/r/shittyaskmath
balls_of_wisdom · 1 points · Posted at 09:24:43 on February 14, 2016 · (Permalink)
Cancelling the factorial marks on both sides we get proof that 0 = 1. Checkmate Mathematicians.
Cajus · 1 points · Posted at 12:01:10 on February 14, 2016 · (Permalink)
wait what
ShootToThrill · 1 points · Posted at 15:51:16 on February 14, 2016 · (Permalink)
TIL that 0=1 if you yell it.
FLYGUYBAU5 · 10 points · Posted at 01:44:29 on February 14, 2016 · (Permalink)
Now how's that even work?
[deleted] · 29 points · Posted at 01:59:36 on February 14, 2016 · (Permalink)*
Going from n! to (n-1)! is the same as dividing by n.
5! = 5*4*3*2*1 = 120. 5!/5 = 120/5 = 24 = 4*3*2*1=4!.
1! is simple because it's 1. 0! would then be 1!/1 = 1/1 which is also 1.
FriskyTurtle · 13 points · Posted at 02:39:29 on February 14, 2016 · (Permalink)
Hunh. I've never seen it argued this way. I always went for the combinatorial argument.
Bonezmahone · 1 points · Posted at 05:06:34 on February 14, 2016 · (Permalink)
Is combinatorial argument 5!=5*4! :. 5!/5=4! ?
FriskyTurtle · 2 points · Posted at 05:10:49 on February 14, 2016 · (Permalink)
It's the n! counts the number of ways to permute n objects. With zero objects, there is one and only one permutation.
BenTheHokie · 3 points · Posted at 04:20:42 on February 14, 2016 · (Permalink)
And I just assumed it was for mathematical convenience so that Taylor series and Maclaurin series (and others) worked out in a nice, little, easily written summation.
camelCaseIsDumb · 1 points · Posted at 22:59:51 on June 8, 2016 · (Permalink)
It is just for convenience.
[deleted] · 8 points · Posted at 01:58:46 on February 14, 2016 · (Permalink)*
[deleted]
Physics_Cat · 3 points · Posted at 02:10:43 on February 14, 2016 · (Permalink)
Little typo there: you wrote
What you meant is:
Viking_Lordbeast · 4 points · Posted at 06:04:57 on February 14, 2016 · (Permalink)
Think of a factorial more like "how many ways can I arrange these certain number of things?" So if you have 4 things, you can make 4! (24) different combinations of them.
How many ways can you group 0 things together? There's only one way: a big pile of nothing.
case_O_The_Mondays · 1 points · Posted at 03:23:17 on February 14, 2016 · (Permalink)
This video has several great explanations.
https://youtu.be/Mfk_L4Nx2ZI
inherendo · 1 points · Posted at 04:29:45 on February 14, 2016 · (Permalink)
Factorial is actually permutations on a set of size n. How many ways can you order the empty set? 1 therefore 0!=1
taboojump · 4 points · Posted at 02:23:13 on February 14, 2016 · (Permalink)
Because how many ways can you group zero of something! One
brunhilda1 · 3 points · Posted at 02:34:43 on February 14, 2016 · (Permalink)
(-1/2)! = sqrt(pi)
mc_hambone · 2 points · Posted at 02:38:57 on February 14, 2016 · (Permalink)
0 != 1
jaskamiin · 2 points · Posted at 03:36:05 on February 14, 2016 · (Permalink)
I did a short blog post using calculus to show why that's true:
insoucianc · 1 points · Posted at 02:26:03 on February 14, 2016 · (Permalink)
There's only one way not to choose.
_Iv · 1 points · Posted at 02:40:44 on February 14, 2016 · (Permalink)
0 != 1
Xaxxon · 1 points · Posted at 02:46:31 on February 14, 2016 · (Permalink)
Error on line 1: got an rvalue (0!) where an lvalue was expected.
PotatoFruitcake · 1 points · Posted at 02:46:53 on February 14, 2016 · (Permalink)
Explain pls
24basketballs · 1 points · Posted at 02:49:26 on February 14, 2016 · (Permalink)
Yh my old teacher explained this to me but I forgot! It has always frustrated me. Can anyone tell me why 0! = 1 ?
oORocketOo · 1 points · Posted at 08:23:51 on February 14, 2016 · (Permalink)
An analogy which I think will help you understand better why 0! =1 is looking at each element as a card and thinking of factorial as "the number of different shuffles I can do to those cards".
For example, we have 2 different elements, let's look at them as 2 cards stacked on top of each other. The different shuffles we can do are:
1: don't shuffle
2: switch the two cards
No other option other than that.
For 1 element, how many ways are there to shuffle? Only one, which is:
1: don't shuffle
No matter what you try to do with that card, you cannot shuffle a single card.
For 0 elements it's a similar situation. No matter what you do, you can't shuffle 0 cards. Therefore the only shuffle is:
1: don't shuffle.
24basketballs · 1 points · Posted at 17:59:04 on February 14, 2016 · (Permalink)
Sweet, I like that analogy. So is n(n-1)(n-2) etc not completely true as a definition for factorials, but instead gives us an easy way to calculate them? Or is 0! More of a exception?
oORocketOo · 1 points · Posted at 18:27:34 on February 14, 2016 · (Permalink)
both are true. i'll give you a simple example.
you have two cards, how many ways are there to shuffle them?
the answer is 2, which is also 2!.
now if we add a 3rd card, how many ways are there to shuffle them?
you can go and count each and every one of the possibilities, but that's boring. instead let us look at all of the different positions the 3rd card can be at.
for each one of the positions of the 3rd card, the other two cards can be shuffled between them (we won't know which order they're in).
so we have 3 positions for the 3rd card and for each such position we have 2 possibilities for the other cards (the number of ways you can shuffle 2 cards). so all in all we get that the total number of possibilities is the number of possibilities for the 3rd card times the number of ways to shuffle 2 cards, which is 3*2, or more accurately 3*2! which is 3!
this can be broadened for an arbitrary number n.
you have n cards, how many ways are there to shuffle them?
n possibilities for the top card times the number of ways to shuffle a deck of (n-1) cards, meaning n*(n-1) which is n!
24basketballs · 1 points · Posted at 02:14:56 on February 15, 2016 · (Permalink)
I like your examples. Thanks for taking the time to explain brah!
ShoutBasil · 1 points · Posted at 02:50:09 on February 14, 2016 · (Permalink)
My teacher could never explain that well to me. How?
jpow0912 · 1 points · Posted at 03:04:10 on February 14, 2016 · (Permalink)
Wat
nicholas818 · 1 points · Posted at 03:25:56 on February 14, 2016 · (Permalink)
What's "(-1)!"?
jam11249 · 1 points · Posted at 00:05:44 on February 15, 2016 · (Permalink)
The best way to answer that is infinity. If you want a more in depth answer look up the gamma function.
hahaha01357 · 1 points · Posted at 04:24:35 on February 14, 2016 · (Permalink)
ELI5?
Valyrian_Tinfoil · 1 points · Posted at 06:11:15 on February 14, 2016 · (Permalink)
Wait.. Is this true?
Grazfather · 1 points · Posted at 07:47:56 on February 14, 2016 · (Permalink)
This used to piss me off in high school and my teacher couldn't give me a good explanation as to why.. other than that it would break perms/combs otherwise.
[deleted] · 1 points · Posted at 09:30:16 on February 14, 2016 · (Permalink)*
[deleted]
Phildudeski · 1 points · Posted at 11:05:03 on February 14, 2016 · (Permalink)
But it's still a relevant note for the thread. It's an interesting mathematic fact.
Siarles · 1 points · Posted at 16:11:55 on February 14, 2016 · (Permalink)
It's because n! is actually the number of ways you can arrange a series of n items. There's only one way to arrange zero items, because there are no items to arrange.
22fortox · 1 points · Posted at 16:27:36 on February 14, 2016 · (Permalink)
I first read this as zero does not equal one
semperlol · 1 points · Posted at 16:54:52 on February 14, 2016 · (Permalink)
Basically it's just for convenience, right?
ITSBULKINGSEASON · 1 points · Posted at 01:44:27 on February 14, 2016 · (Permalink)
Wouldn't 0! = 0?
14flash · 4 points · Posted at 02:21:26 on February 14, 2016 · (Permalink)
When you "expand" 0! you'll find that there are no terms in the sequence because you start with a number less than 1. This is what's known as an "empty product" which equals 1 (because this is the multiplicative identity). This is the same reason why doing a0 also equals 1 (when a =/= 0).
matap821 · 0 points · Posted at 01:59:12 on February 14, 2016 · (Permalink)
And 1.5! = sqrt(pi)
Markster94 · 1 points · Posted at 02:07:34 on February 14, 2016 · (Permalink)
I know it's square root, but I like to annoy everyone by pronouncing it 'squirt'.
hebo07 · 0 points · Posted at 02:14:31 on February 14, 2016 · (Permalink)
Yeah but 5! != 5!4!3!2!1 it equals to 5!=5*4*3*2*1 so mentioning that 0!=1 doesn't change anything because that's not how you define it.
Diaclaimer: i know it's joke i just felt a need to point it out for the ones not familiar with the math. Cheers
edit: formatting
[deleted] · 4 points · Posted at 01:48:20 on February 14, 2016 · (Permalink)
No problem, just divide by zero and you'll get your answer back. Right?
ruok4a69 · 1 points · Posted at 04:07:31 on February 14, 2016 · (Permalink)
But that would make the math so much simpler.
Givants · 1 points · Posted at 05:08:57 on February 14, 2016 · (Permalink)
It will brick your iphone
briantd · 1 points · Posted at 08:12:06 on February 14, 2016 · (Permalink)
Interestingly, though, 0! = 1.
lothpendragon · 0 points · Posted at 01:48:31 on February 14, 2016 · (Permalink)
Dude, you never go full retard.
[deleted] · 32 points · Posted at 01:32:26 on February 14, 2016 · (Permalink)*
[deleted]
HoldMyWater · 3 points · Posted at 02:34:57 on February 14, 2016 · (Permalink)
I think you're right.
And factorials are also defined for zero (0! = 1), so it should be:
10! = 10*9*8*7*6*5*4*3*2*1*1
[deleted] · -4 points · Posted at 01:56:35 on February 14, 2016 · (Permalink)
1! = 1
But also:
1! = 1 * 1 * 1 * 1
You don't break anything by adding * 1 to a formula, and if you have other constants, you can even leave it out. (3 * 1 = 3)
It will break the pattern, yes, but it's not invalid. And it saves you some time writing down the sequence (especially if you have slow handwriting or are low on ballpoint ink)
1! = 1
2! = 2 * 1
3! = 3 * 2 * 1
4! = 4 * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1
But we can also write:
1! = 2 - 1
2! = 2
3! = 3 * 2
4! = 24
5! = 5 * 24
These are all perfectly valid equations.
StillsidePilot · 6 points · Posted at 02:26:21 on February 14, 2016 · (Permalink)
That wasn't my point. I understand the multiplicative identity property. My purpose was that if you're trying to use a formula that works for ℤ+ you need to include the *1.
[deleted] · -2 points · Posted at 02:28:59 on February 14, 2016 · (Permalink)
I don't follow. There is absolutely no reason to include the *1 when you have other constants, other than that it looks pretty (for n > 1. Obviously you have 0!=1 and 1!=1).
[deleted] · 1 points · Posted at 02:31:28 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · -1 points · Posted at 02:53:19 on February 14, 2016 · (Permalink)
You were talking about *1 in all your comments; as in "multiplied by one". That can always be left out.
1! = 1 does not include a "*1", so there's nothing to leave out.
StillsidePilot · 3 points · Posted at 02:58:41 on February 14, 2016 · (Permalink)
Not in the formula it can't.
[deleted] · 0 points · Posted at 02:59:38 on February 14, 2016 · (Permalink)
What formula?
ToFitnsOrNotToFitns · 2 points · Posted at 03:25:17 on February 14, 2016 · (Permalink)
I don't know if you're honestly just missing his point or if you're being facetious, but this one (link because I don't know how to latex within reddit's reply box). Removing the *1 (i.e, making it i = 2 on the bottom instead of i = 1) would make that formula only work for > 1, instead of >= 1.
[deleted] · 1 points · Posted at 14:45:29 on February 14, 2016 · (Permalink)
I'm guessing you're all just misreading my comments on purpose...
Indeed this requires n > 1 (I pointed this out multiple times), but your link is just one of the many definitions of a factorial. I wasn't stating it can be left out in the definition; it can be left out in the sequence of integers I replied to. By the points on that comment, most people seem to agree.
ToFitnsOrNotToFitns · 1 points · Posted at 15:57:35 on February 14, 2016 · (Permalink)
No, actually I'm not. You asked what formula (rather facetiously, it appears from your current comment), and I answered. That is all.
[deleted] · 1 points · Posted at 02:32:06 on February 15, 2016 · (Permalink)
If you ignore the context of all other comments you had to read to get here, yes, you're right.
ToFitnsOrNotToFitns · 1 points · Posted at 12:52:57 on February 15, 2016 · (Permalink)
The context of you pretending that you didn't know what formula he was talking about repeatedly while he agreed that you could leave it out in the sequence of integers (also repeatedly)? If you wish to be a jackass, feel free to reply and feel like you've "won". I've better things to do with life then waste it on morons such as yourself. I'm out.
[deleted] · 1 points · Posted at 13:15:25 on February 15, 2016 · (Permalink)
lol wat..?
I'm not here to win anything, I was genuinely confused about why he thought you have to multiply by one. So I attempted to explain it several times that it's just a pattern in the sequence. You don't break anything by leaving it out.
If you really think I'm just trying to be an asshole, suit yourself. Just know that I only tried to help..
[deleted] · 4 points · Posted at 01:32:12 on February 14, 2016 · (Permalink)
/r/iamverysmart
tinamou63 · 2 points · Posted at 01:38:24 on February 14, 2016 · (Permalink)
calm down there Clark Bray. You and your "clever"-ness
Wolfy21_ · 2 points · Posted at 01:22:33 on February 14, 2016 · (Permalink)
Now. What about negative numbers factorial? -10! for example? Is it = (-11)*(-12) etc? Or can you not do negative factorials?
nrufl · 9 points · Posted at 01:27:01 on February 14, 2016 · (Permalink)
0! is defined to be 1. The most natural way of extending the factorial to other numbers (negative numbers, fractions, imaginary numbers, etc.) is the gamma function, but it has singularities at the negative integers (like 1/x does at zero).
Qonic · 4 points · Posted at 01:25:05 on February 14, 2016 · (Permalink)
You can only do factorials on natural numbers
Paradigmist · 6 points · Posted at 01:34:13 on February 14, 2016 · (Permalink)
There are actually several extensions of the factorial function, such as the Gamma function, that extend the domain to most complex numbers (except negative integers).
DrBubbles · 1 points · Posted at 01:33:11 on February 14, 2016 · (Permalink)
...and a natural number (while we'e explaining things) is any whole number that is greater than, but not equal to, zero.
Qonic · 1 points · Posted at 02:35:01 on February 14, 2016 · (Permalink)
zero is a natural number as well
[deleted] · 1 points · Posted at 04:20:21 on February 14, 2016 · (Permalink)
[deleted]
columbus8myhw · 2 points · Posted at 04:51:03 on February 14, 2016 · (Permalink)
It's not a European/American split, it's a person-to-person split.
rossk10 · 0 points · Posted at 01:47:44 on February 14, 2016 · (Permalink)
No, because that would create an infinite number no matter which negative integer you begin with
Paradigmist · 0 points · Posted at 01:53:09 on February 14, 2016 · (Permalink)
The Gamma Function can extend the factorial function to most complex numbers.
[deleted] · -3 points · Posted at 01:37:34 on February 14, 2016 · (Permalink)
Factorial can be defined recursively:
Example with n = 3:
This is also one of the very basic examples used to explain recursion to beginner programmers.
You might notice it is undefined for n < 0. You cannot use factorial on negative numbers.
Wolfy21_ · 1 points · Posted at 01:41:15 on February 14, 2016 · (Permalink)
Makes sense, thanks.
Paradigmist · 1 points · Posted at 01:53:13 on February 14, 2016 · (Permalink)
The Gamma Function can extend the factorial function to most complex numbers.
tom808 · 1 points · Posted at 01:39:00 on February 14, 2016 · (Permalink)
What about if you had a negative number (-n!) you would need the 1 to get the correct answer then? Also shouldn't it always be included for completeness?
Non mathematical person here so those may just have been totally stupid questions.
[deleted] · 1 points · Posted at 01:51:35 on February 14, 2016 · (Permalink)
I'm not a mathematician either, computer science though, so not that far off.
Factorial only applies to non-negative integers. We call these: "Natural numbers", because you can count natural things with it, like 4 sheep or 10 coins.
We define 0! equal to 1
n! can be defined as n * (n-1)!
This is called recursion. For 3! we get
3! = 3 * (3-1)! = 3 * 2!, so we look at 2!
2! = 2 * (2-1)! = 2 * 1!, so we look at 1!
1! = 1 * (1-1)! = 1 * 0!, so we look at 0!
0! = 1 (defined above)
we can complete the rest now:
1! = 1 * 1
2! = 2 * (1 * 1)
3! = 3 * (2 * (1 * 1))
3! = 3 * 2 * 1
... or:
3! = 3 * 2 = 6
If you want to explain factorial to someone, you'd probably include the * 1, but if you're doing a lot of homework or writing down a sequence like that multiple times, you will probably just leave it be. It's similar to leaving out 1*x when writing x. You still mean "one times the value of x" where 2x means "two times the value of x".
luciddr34m3r · 1 points · Posted at 06:11:08 on February 14, 2016 · (Permalink)
If you are doing a lot of homework it would be done on a calculator. If you are in a class where they want you to write it down and you skip 1! and get full credit, you have a terrible instructor.
luciddr34m3r · 1 points · Posted at 06:11:48 on February 14, 2016 · (Permalink)
Excluding 1! when showing your work is foolish. OP is super duper smart.
jam11249 · 1 points · Posted at 00:02:31 on February 15, 2016 · (Permalink)
There is a way of extending the factorial to allow things like (1/2)! called the Gamma function, but it has singularities at all of the negative integers so (-n)! isn't something you can really consider. The factorial is strictly only defined for non-negative integers, and the definition of the gamma function has nothing to do with a product representation, it's just that if you evaluate the gamma function at positive integers it agrees with the factorial.
Bobshayd · 1 points · Posted at 05:10:42 on February 14, 2016 · (Permalink)
It doesn't reveal the pattern of multiplying every number from 1 to n, or make it obvious that 1! fits the same pattern.
Bane1998 · 1 points · Posted at 06:42:55 on February 14, 2016 · (Permalink)
I don't know why you'd call that clever, leaving something out. The definition of factorial includes it (I believe), so leaving it out is probably doing a disservice, even if it happens to not matter in this example. I'm not a mathematician (and probably the furthest thing form it, so I could be wrong) but I have to imagine there comes a case where the *1 actually matters and so it's good to not ignore it.
[deleted] · 2 points · Posted at 14:26:36 on February 14, 2016 · (Permalink)
It's called the multiplicative identity:
There exist an integer 1 such that 1n = n
Combine that with the definition of factorial:
The product of a non-negative integer and all non-negative integers below it
And you get the factorial sequence excluding 1.
Knever · 1 points · Posted at 07:23:34 on February 14, 2016 · (Permalink)
I was just about to say that when I read that last *1.
EltaninAntenna · 1 points · Posted at 09:55:47 on February 14, 2016 · (Permalink)
It makes the sequence look neat. That's not "nothing".
klod42 · 1 points · Posted at 10:36:41 on February 14, 2016 · (Permalink)
When you learn maths to a little bit more advanced level, you get even more cleverer and you understand that 0! also belongs there, so you might want to actually write n * (n-1) * ... * 2 * 1 * 0!
randomguy186 · 1 points · Posted at 14:42:37 on February 14, 2016 · (Permalink)*
REALLY clever people point out that the traditional definition of factorial is really just so that small children can understand a tiny piece of it, and you've actually got to do calculus on complex numbers to properly define it and do things like (1/2)! = (-1/2)! = sqrt(pi)
[deleted] · 2 points · Posted at 14:47:40 on February 14, 2016 · (Permalink)
Nah, we're just working with natural numbers here, since we're discussing the number of seconds in 6 weeks. You aren't the first to point out that there are multiple variations of factorial, by the way. :)
TranshumansFTW · 2 points · Posted at 02:27:16 on February 14, 2016 · (Permalink)
I just taught this to a student yesterday. She preferred the other name of factorial, which is "bang". You get to say things like "10 BANG over 2 BANG = x", which is delightful when you're 13.
[deleted] · 1 points · Posted at 22:51:23 on February 13, 2016 · (Permalink)
A better definition is 0!=1, n!=n.(n-1)! This extends the above to zero and makes the gamma function just a little easier to intuit.
BrohanGutenburg · 96 points · Posted at 23:04:05 on February 13, 2016 · (Permalink)
Better for whom? Because your definition is MUCH harder for a non-mathematical person to understand.
LordCharco_iii · 6 points · Posted at 23:51:43 on February 13, 2016 · (Permalink)
Yeah, what the fuck are either of these.
Explain like I'm actually 5?
_SovietMudkip_ · 16 points · Posted at 23:56:45 on February 13, 2016 · (Permalink)
Multiply a number by every integer between itself and 0.
So 4! = 4 x 3 x 2 x 1 = 24
[deleted] · 0 points · Posted at 00:19:22 on February 14, 2016 · (Permalink)
And 0! = 1
n! = n(n-1)!
Hence, (n-1)! = n!/n
Substitute n as 1,
0! = 1!/1 = 1
pippinto · 14 points · Posted at 01:02:27 on February 14, 2016 · (Permalink)
Have you ever met a 5 year old?
CakeStak · 2 points · Posted at 23:57:50 on February 13, 2016 · (Permalink)
Multiply all the numbers up to that number together. E.g 3! = 1x2x3
Shit-Smear · 1 points · Posted at 00:06:14 on February 14, 2016 · (Permalink)
Word.
[deleted] · -4 points · Posted at 23:39:56 on February 13, 2016 · (Permalink)*
Pretty sure most people who finished high school can understand that.... I'm shit at math and I did
I guess they don't teach you about sequences in US highschool...
XJCM · 2 points · Posted at 00:17:02 on February 14, 2016 · (Permalink)
I went to 2 different high schools in the US, and both of them taught this
[deleted] · 0 points · Posted at 00:21:49 on February 14, 2016 · (Permalink)
Not sure why im being downvoted then lol
Azgurath · 2 points · Posted at 01:03:40 on February 14, 2016 · (Permalink)
Because you said
which isn't true.
[deleted] · 0 points · Posted at 01:09:36 on February 14, 2016 · (Permalink)
I guess that can be read in a negative way, I've got experience with 3 different systems and they are all different enough in regards to what subjects are taught... I added that bit in after a few downvotes.
BrohanGutenburg · 0 points · Posted at 23:42:52 on February 13, 2016 · (Permalink)
That doesn't mean it explains how to do it. Let's say I didn't know what "10!" meant (which is the situation here). So I ask you how to do it. If you tell me "well 0!=1 and n!=n.(n-1)!" or whatever, that wouldn't tell me how to solve the problem at all
pudgycaveman · 5 points · Posted at 23:57:47 on February 13, 2016 · (Permalink)
It tells you exactly how to solve the problem. It is a recursive function. You just have to apply it repeatedly.
You want to find out what 10! is. OK, let's apply the definition. n is not 0, so n! is not 1 (because, remember, from the definition, 0! =1). Therefore, let's go with n! = n*(n-1)!. So, 10! = 10*(10-1)! = 10*9!. Now, you need 9!. Apply the same definition again. 9! = 9*(9-1)! = 9*8!. So, 10! = 10*9! = 10*9*8!. Keep applying the definition recursively, and you'll reach:
10! = 10*9*8*7*6*5*4*3*2*1*0!
Now, the definition says that 0! = 1. So:
10! = 10*9*8*7*6*5*4*3*2*1*1.
BrohanGutenburg · 0 points · Posted at 02:21:26 on February 14, 2016 · (Permalink)
It explains exactly how to solve the function if you're math literate. Most people aren't.
pudgycaveman · 1 points · Posted at 05:29:36 on February 14, 2016 · (Permalink)
Nope, you do not have to be exactly math-literate to understand factorials and the factorial notation/definition! :-) That's the beauty of a recursive definition: you don't really overthink it - just keep applying the definition over and over until you reach a terminating condition. In this case, the terminating condition is: 0! = 1. You don't go further down to think about -1!, -2! etc.
Recursive functions are atypical in that they are used in their own definitions, so it could be a little tricky to wrap your head around them initially.
[deleted] · -4 points · Posted at 00:00:52 on February 14, 2016 · (Permalink)*
In the UK educational system (which IMO is very inefficient) you learn in year 10 how to work out sequences:
You learn that "n"= whatever value you assign to it.
So if 10=n, "well 0!=1 and n!=n.(n-1)!" becomes: "well 0!=1 and 10!=10*(10-1)!"
Well, I guess they don't teach you that in the US, but this is coming from someone who doesn't know how to turn a fraction into a decimal (which is year 8 stuff) and has trouble with simple division...
AwesomePocket · 3 points · Posted at 00:21:43 on February 14, 2016 · (Permalink)
No, I think most people are taught factorials in the US by the end of high school. In my area, advanced students learned it in middle school
TheLastSparten · -4 points · Posted at 23:25:10 on February 13, 2016 · (Permalink)
It's a much more concise way of saying the same thing. And it doesn't take that much logical reasoning to see that they're the same.
[deleted] · 1 points · Posted at 23:06:36 on February 13, 2016 · (Permalink)
I like this definition because I like recursion
Scypherdebater · 5 points · Posted at 23:19:04 on February 13, 2016 · (Permalink)
I like this definition because recursion.
[deleted] · 1 points · Posted at 23:21:36 on February 13, 2016 · (Permalink)
I Recursion
M1nusbarca · 1 points · Posted at 01:03:04 on February 14, 2016 · (Permalink)
I
1100101000 · 1 points · Posted at 01:29:45 on February 14, 2016 · (Permalink)
Reminds me of this comment.
[deleted] · 1 points · Posted at 01:54:32 on February 14, 2016 · (Permalink)
cries
HoldMyWater · 1 points · Posted at 02:38:59 on February 14, 2016 · (Permalink)
I'M TRAPPED IN INFINITE RECURSION! HELP!
[deleted] · 1 points · Posted at 01:32:06 on February 14, 2016 · (Permalink)
I'm sure you'll be ecstatic to know that the "B." in the name "Benoit B. Mandelbrot" is short for "Benoit B. Mandelbrot".
Tibetzz · 1 points · Posted at 23:23:20 on February 13, 2016 · (Permalink)
That's better if youre a programmer, not if youre a layman.
museum_of_dust · 1 points · Posted at 01:38:26 on February 14, 2016 · (Permalink)
That's a pretty cool factorial to know.
[deleted] · 1 points · Posted at 02:32:28 on February 14, 2016 · (Permalink)
♫3,628,800 seconds♪
♪How do you measure, measure a week?
setfire3 · 1 points · Posted at 02:44:15 on February 14, 2016 · (Permalink)
no, it's bang. There's exactly 10 bangs seconds in 6 weeks. talk about horrible sex life.
duffmanhb · 1 points · Posted at 02:59:20 on February 14, 2016 · (Permalink)
Na dude... I'm pretty sure his formula is just proving that there are only 10 seconds a weak in which I'm happy :(
bogidyboy · 1 points · Posted at 03:12:06 on February 14, 2016 · (Permalink)
sigh
Thanks
AbigailLilac · 1 points · Posted at 03:50:00 on February 14, 2016 · (Permalink)
I had to Google that yesterday.
GryffindorGhostNick · 1 points · Posted at 03:51:13 on February 14, 2016 · (Permalink)
In written format, to explain how something is read, you write (read....) And not (pronounced...)
So your comment should read "n!( read n factorial)...."
Qqaim · 2 points · Posted at 09:24:46 on February 14, 2016 · (Permalink)
Thanks, did not know that. I'm more of a math person than an English person ;)
Simon_Hans · 1 points · Posted at 06:36:05 on February 14, 2016 · (Permalink)
Somehow I could never grasp this when my teacher explained it in math class, but now I understand it and can not believe how simple it is. Thanks for the succinct explanation, it's great to understand it even when I don't think I'll ever actually have a need to use it.
boldra · 1 points · Posted at 06:59:13 on February 14, 2016 · (Permalink)
Is n!! = n! * (n-1)! * (n-2)! * ... ?
Qqaim · 2 points · Posted at 09:23:55 on February 14, 2016 · (Permalink)
It's not, no. n!! (read n double factorial) = n*(n-2)*(n-4)*...*(2). Depending on n is odd or even, the multiplication either ends with 2 or 1. Similarly, n!!! = n*(n-3)*(n-6)*...*3. Again, the last number can change depending on what you started with.
Thornsten · 1 points · Posted at 07:18:54 on February 14, 2016 · (Permalink)
Pronounced "n bang" tyvm..
SalamanderSylph · 1 points · Posted at 11:39:08 on February 14, 2016 · (Permalink)
Or called n shriek depending on how old your lecturer is
TheHornyToothbrush · 1 points · Posted at 11:50:31 on February 14, 2016 · (Permalink)
Yeah see no one knows what that means.
BASEDME7O · 1 points · Posted at 23:04:28 on February 14, 2016 · (Permalink)
Shut the fuck up lol
Fexmeif · 1 points · Posted at 22:17:49 on February 15, 2016 · (Permalink)
Late for the party, but when I was in sixth grade I read a book called "Number's devil" (I think? Unsure of English title) that called factorial the "boom" numbers, because they so easily "exploded " into big numbers.
I really enjoyed that book and to this day I often call factorial "boom" in my head.
lulubuttersnips · 1 points · Posted at 15:13:52 on February 24, 2016 · (Permalink)
But
Z_Coop · 1 points · Posted at 01:16:47 on February 14, 2016 · (Permalink)
Even knowing this, I still read "n!" As an enthusiast person saying N!
StFluffy · 0 points · Posted at 01:35:10 on February 14, 2016 · (Permalink)
n* (n-1)* (n-2)* ....* (n-(n-1))
Just to keep the n-form. :)
Qqaim · 2 points · Posted at 09:27:20 on February 14, 2016 · (Permalink)
Why would you, though? (n-(n-1)) is always equal to 1, and 1 reads much easier and shows better what is meant.
StFluffy · 1 points · Posted at 15:14:19 on February 14, 2016 · (Permalink)
It was premature commenting. My thought process was to contribute not going past zero, staying solely in the natural numbers. You are right 1 reads better.
TomasTTEngin · 8 points · Posted at 00:03:21 on February 14, 2016 · (Permalink)*
So some weeks you might spend two seconds being enthusiastic? In Russia this level of jubilance is considered a sign you are losing your mind.
[deleted] · 2 points · Posted at 01:50:08 on February 14, 2016 · (Permalink)
It's the last second before you pass out, blackout drunk. It is assumed that this happens on both Friday and Saturday.
arbitrageME · 3 points · Posted at 02:47:48 on February 14, 2016 · (Permalink)
seems reasonable: We just have to find every number between 2 and 10:
6 weeks = 6 weeks * 7 days per week = 42 days
1 day = 2 * 3 * 4 hrs = 24 hrs
1 hr = 5 * 8 * 9 * 10 = 3600 sec
that's all of them
The_Thylacine · 5 points · Posted at 22:32:37 on February 13, 2016 · (Permalink)
I just won $10!
DeaconFrostedFlakes · 2 points · Posted at 00:53:01 on February 14, 2016 · (Permalink)
Intercourse approximately once every six weeks...ten seconds per encounter...yes. Yes, this math checks out.
fudgepop01 · 2 points · Posted at 02:49:40 on February 14, 2016 · (Permalink)
so new measurement of time - the enthusiastic second:
1 enthusiastic second = 8640 seconds
AKA: 1440 minutes, or 60 hours, or 2.5 days. o3o
thomasry · 1 points · Posted at 00:22:25 on February 14, 2016 · (Permalink)
This is fascinating - is it always the same 10 seconds? Or does it change for every set of 6 weeks? Are they all together, or spread out?
[deleted] · 2 points · Posted at 01:50:36 on February 14, 2016 · (Permalink)
It's random. They can be any day. Except Mondays.
Delicious_Nipples · 1 points · Posted at 01:38:57 on February 14, 2016 · (Permalink)
I only get about ten seconds of enthusiasm in 6 weeks.
TheSovietGoose · 1 points · Posted at 01:43:58 on February 14, 2016 · (Permalink)
I can relate to that so well.
ranaadnanm · 1 points · Posted at 01:48:12 on February 14, 2016 · (Permalink)
Thank you for making me laugh :)
[deleted] · 1 points · Posted at 01:48:14 on February 14, 2016 · (Permalink)
As an adult I can confirm I'm enthusiastic for about ten seconds every six weeks.
quasive · 1 points · Posted at 01:48:24 on February 14, 2016 · (Permalink)
In my school textbook, in the section on factorials, it read something like:
“5 factorial is 5 * 4 * 3 * 2 * 1, and can be represented by writing 5!”
They treated the exclamation point as punctuation, which I think is the wrong thing to do, because I spent a frustrating while wondering how 5 differs from 5, and why the book was so damned excited about it.
10KeyFrog · 1 points · Posted at 01:49:03 on February 14, 2016 · (Permalink)
Obviously that guy isn't married if he's having sex 10 times in a 6 week span.
laschke · 1 points · Posted at 01:56:01 on February 14, 2016 · (Permalink)
Jeb!
Grizzly_Berry · 1 points · Posted at 01:58:25 on February 14, 2016 · (Permalink)
They're on Friday when you finaly take your shoes off til Monday.
nomadofwaves · 1 points · Posted at 02:20:36 on February 14, 2016 · (Permalink)
Had sex. Still counts.
Rivet_39 · 1 points · Posted at 02:34:47 on February 14, 2016 · (Permalink)
Sounds like my sex life.
mikes_username_lol · 1 points · Posted at 02:55:39 on February 14, 2016 · (Permalink)
Must have been married for a while and not last very long.
Gurip · 1 points · Posted at 02:55:51 on February 14, 2016 · (Permalink)
you dont have to be mathematical person, you just need to be done with 6th grade math,
4Sken · 1 points · Posted at 03:46:17 on February 14, 2016 · (Permalink)
office lyfe
PrivilegeCheckmate · 1 points · Posted at 03:47:07 on February 14, 2016 · (Permalink)
Employed and married with kids. Math checks out.
[deleted] · 1 points · Posted at 04:04:34 on February 14, 2016 · (Permalink)
Sad to hear about your sex life
thegreatestajax · 1 points · Posted at 04:04:49 on February 14, 2016 · (Permalink)
OP is married.
Tobikage1990 · 1 points · Posted at 04:05:11 on February 14, 2016 · (Permalink)
True, I am enthusiastic about something for maybe 10 seconds in a week.
ruok4a69 · 1 points · Posted at 04:06:06 on February 14, 2016 · (Permalink)
Welcome to my sex life.
No, really, sit down and have a drink.
patrickkellyf3 · 1 points · Posted at 04:20:50 on February 14, 2016 · (Permalink)
There are about 10 seconds in six weeks where I'm enthusiastic? Sounds about right.
senshisentou · 1 points · Posted at 04:30:03 on February 14, 2016 · (Permalink)
Huh, now I wonder how mathematicians feel about Jeb!.
Pardonme23 · 1 points · Posted at 05:02:43 on February 14, 2016 · (Permalink)
I'm waiting to see someone pronounce it like that in the wild
jesuisunnomade · 1 points · Posted at 05:42:56 on February 14, 2016 · (Permalink)
How sad. I have 11 enthusiastic seconds in a week.
RobinBankss · 1 points · Posted at 06:32:29 on February 14, 2016 · (Permalink)
We call that Marriage.
Happy Valentine's Day.
Harry-Littlewood · 1 points · Posted at 07:14:17 on February 14, 2016 · (Permalink)
Sounds like my sex life..
Taburn · 1 points · Posted at 07:20:02 on February 14, 2016 · (Permalink)
In high school on a math unit test I thought the answers were boring, so I put an exclamation mark after them. The next unit was factorials...
hamclammer · 1 points · Posted at 08:05:30 on February 14, 2016 · (Permalink)
Le epic
danbronson · 1 points · Posted at 08:27:48 on February 14, 2016 · (Permalink)
Holy shit you're right. It's exact to the second.
skelebone · 1 points · Posted at 12:51:45 on February 14, 2016 · (Permalink)
Just pay attention over the next six weeks. One of those enthusiastic seconds will come, and when you feel it you will say "Ah! There it was"
madkeepz · 1 points · Posted at 13:53:09 on February 14, 2016 · (Permalink)
no wonder the rest of em fucking suck
Xicotencatl86 · 1 points · Posted at 18:39:46 on February 14, 2016 · (Permalink)
I like to quote this as:
Want to know something cool? The exact number of seconds in a week is 10!
TheNumberMuncher · 1 points · Posted at 20:06:37 on February 14, 2016 · (Permalink)
As someone in a long term relationship, this is correct.
hypervelocityvomit · 1 points · Posted at 09:53:28 on February 15, 2016 · (Permalink)
r/bandname??? Almost.
OZONE_TempuS · 432 points · Posted at 19:27:12 on February 13, 2016 · (Permalink)
3,628,800 for anyone wondering.
bear__attack · 14 points · Posted at 00:03:11 on February 14, 2016 · (Permalink)
This number doesn't flow quite as well as in song
Neospector · 3 points · Posted at 02:09:06 on February 14, 2016 · (Permalink)
Five hundred twenty-five thousand six hundred minutes
Divotus · 1 points · Posted at 03:17:43 on February 14, 2016 · (Permalink)
Is there an easy way of calculating this?
Felix_Tholomyes · 1 points · Posted at 03:33:34 on February 14, 2016 · (Permalink)
For low factorials such as 10! the easiest way is to simply compute 109...21 sequentially.
However for very large factorials it can be useful to employ the gamma function or Stirling's approximation.
abcedarian · 1 points · Posted at 03:37:52 on February 14, 2016 · (Permalink)
That's not very catchy... Let's try minutes in a year.
CanYouDigItHombre · 1 points · Posted at 14:56:14 on February 14, 2016 · (Permalink)
But what is 10!? I thought it'd be a 1 and a lot of 0's after it like a 1 trillion
[deleted] · -9 points · Posted at 19:39:19 on February 13, 2016 · (Permalink)
[removed]
[deleted] · -1 points · Posted at 20:36:01 on February 13, 2016 · (Permalink)
What? How?
175gr · 338 points · Posted at 21:38:10 on February 13, 2016 · (Permalink)
Unless you get a leap second. That doesn't happen very often though.
VoteLobster · 492 points · Posted at 22:15:23 on February 13, 2016 · (Permalink)
I hear once every 4 seconds.
skysurf3000 · 369 points · Posted at 23:45:12 on February 13, 2016 · (Permalink)
except every 100 seconds, except every 400 seconds.
diMario · 12 points · Posted at 08:08:48 on February 14, 2016 · (Permalink)
This only is true for metric leap seconds.
Imperial leap seconds come about every twelfth full revolution of the minute hand, unless it is divisible by a baker's dozen dozens (13*12), with the exception that every third or fifth time this happens (third time for the second half of the century, fifth for the first half) gets skipped. If you are in the Southern Hemisphere, swap the third and fifth times around unless you are in New Zealand, where they shift the year a count of 24 into the future before applying the rule as if in Northern Hemisphere.
skysurf3000 · 6 points · Posted at 08:20:33 on February 14, 2016 · (Permalink)
Highly relevant https://www.youtube.com/watch?v=-5wpm-gesOY&ab_channel=Computerphile
diMario · 3 points · Posted at 08:33:55 on February 14, 2016 · (Permalink)
That was amusing. Well, sort of. I'm a bit of a code welder myself and I completely sympathize with this guys frustration.
MattieShoes · 13 points · Posted at 02:01:04 on February 14, 2016 · (Permalink)
In seriousness, about once every 50 million seconds, or once every φ years. Now I bet that's not a place you'd expect the golden ratio to show up...
repetitionofalie · 6 points · Posted at 02:58:14 on February 14, 2016 · (Permalink)
Can you explain the golden ratio bit?
MattieShoes · 1 points · Posted at 13:34:00 on February 14, 2016 · (Permalink)*
The golden ratio is called φ (phi).
It has a value of ~1.618 and goes on forever, like pi.
1 + 1/φ = φ
1 / 1.618... = 0.618...
The golden ratio shows up in a bunch of places. If you know the fibonacci sequence (where each successive value is the sum of the previous two)
1, 1, 2, 3, 5, 8, 13, 21
the ratio of a number to the number before it converges on phi.
1/1 = 1
2/1 = 2
3/2 = 1.5
5 / 3 = 1.6666...
8 / 5 = 1.6
13 / 8 = 1.625
21 / 13 = 1.(615384)...
Of course, that means the ratio of the number to the number after it converges on (φ-1).
The fibonnaci sequence shows up in nature all over the place, which means approximations of the golden ratio show up all over the place.
The golden ratio is also in logarithmic spirals, which are also found everywhere, like the arms of the milky way, hurricanes, most animals with spiral shells, etc.
Some people have noticed that the golden ratio shows up in all sorts of other places... some almost certainly by chance, but the argument is that we humans tend to find that ratio aesthetically pleasing. The number of female honey bees to male honey bees in a hive is generally φ. The number of kilometers per mile is ~φ. 1920x1200 monitors have a ratio of ~φ. Our eyes appear about φ times wider than they are tall. 3x5 notecards are ~φ. Some measurements in the mona lisa approximate φ. The Vitruvian Man is supposed to have φ in it. The Parthenon in Greece is φ times wider than it is tall. And so on...
The leap seconds thing happening to happen every 1.6 years or so on average since the early 70s... Pure chance, but I thought it was funny.
sarcbastard · 6 points · Posted at 07:07:21 on February 14, 2016 · (Permalink)
There is a god, and he's just fucking with us
MightyButtonMasher · 5 points · Posted at 10:51:50 on February 14, 2016 · (Permalink)
"I really like this number, so I'll just use it for any constant I don't have something else for."
Actionmaths · 8 points · Posted at 00:09:00 on February 14, 2016 · (Permalink)
So like when people talk to you they have to say a word every 4 seconds? That must be annoying
kongu3345 · 1 points · Posted at 05:37:02 on February 14, 2016 · (Permalink)
It's kind of like birthdays for people born on February 29th.
Colopty · 1 points · Posted at 12:48:19 on February 14, 2016 · (Permalink)
That's a weird issue to have with your hearing, have you consulted a doctor?
13pr3ch4un · 1 points · Posted at 05:35:07 on February 14, 2016 · (Permalink)
Or use the actual time of a day which is a 23 hours 56 minutes or so
suckmypenisfukmygoat · 1 points · Posted at 07:35:17 on February 14, 2016 · (Permalink)
But are leap seconds an actual thing? We just lump them all together and make a leap day. As opposed to adding a second every 4 seconds.
Krissam · -3 points · Posted at 21:42:01 on February 13, 2016 · (Permalink)
around 1% of the time.
PoisonousPlatypus · 5 points · Posted at 22:12:52 on February 13, 2016 · (Permalink)
0.11538461538% of the time actually.
jimmy011087 · 7 points · Posted at 01:10:34 on February 14, 2016 · (Permalink)
42 (6x7) days with 24(3x8) hours in. Each hour has 60 minutes (10x3x2) and each minute 60 seconds (5x4x3)
Leaves the sum (6x7)(3x8)(10x3x2)(5x4x3)
2 of the 3's multiplied makes a 9 so:
(6x7x9x8x10x2x5x4x3x1)
Reorder:
(1x2x3x4x5x6x7x8x9x10)
Magic!
dinoswithjetpacks · 3 points · Posted at 02:09:56 on February 14, 2016 · (Permalink)
This would make a good math joke.
"How many seconds are there in 6 days? 10!"
ZergUser · 2 points · Posted at 13:17:22 on February 14, 2016 · (Permalink)
A math teacher should totally write this on the board for extra credit. "Jimmy asks, 'How many seconds are there in 6 weeks?' Sally replies, '10!'" Is Sally right or wrong?
blh1003 · 3 points · Posted at 02:32:47 on February 14, 2016 · (Permalink)
Jeb!
lukesvader · 3 points · Posted at 12:14:53 on February 14, 2016 · (Permalink)
I like your enthusiasm!
Krissam · 2 points · Posted at 12:21:33 on February 14, 2016 · (Permalink)
I've had a lot of replies that looked like jokes, but yours was the first one to actually make me giggle :)
TexanInExile · 2 points · Posted at 01:39:30 on February 14, 2016 · (Permalink)
Alright, now someone create a watch that counts up to 10!
9000_HULLS · 0 points · Posted at 02:46:12 on February 14, 2016 · (Permalink)
/r/nocontext
Enjoyer_of_Cake · 2 points · Posted at 01:54:52 on February 14, 2016 · (Permalink)
To explain it away, 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 (drop the one as it doesn't change anything).
60 seconds in a minute, so remove 6 x 10.
9 x 8 x 7 x 5 x 4 x 3 x 2
60 minutes in an hour so remove 5 x 4 x 3.
9 x 8 x 7 x 2
24 hours in a day, so remove 8 x 3 (split 9 into 3 x 3).
3 x 7 x 2.
7 days in a week.
3 x 2.
6 weeks.
ahf95 · 2 points · Posted at 02:06:10 on February 14, 2016 · (Permalink)
In math, you can't divide by 0, but you can divide by 0!
I'm sorry, I'll leave now.
MattieShoes · 1 points · Posted at 01:54:51 on February 14, 2016 · (Permalink)
Ooh, that's a good one! I had never heard that one.
asaltandbuttering · 1 points · Posted at 02:05:18 on February 14, 2016 · (Permalink)
A similar coincidence is that there are pi*107 seconds in a year to reasonably high precision.
AIMpb · 1 points · Posted at 02:07:24 on February 14, 2016 · (Permalink)
and 11! seconds in 66 weeks!
[deleted] · 1 points · Posted at 03:00:42 on February 14, 2016 · (Permalink)
From now on I will type, "Just give me 10! seconds and I'll get it done, guaranteed."
chesterjosiah · 1 points · Posted at 03:05:16 on February 14, 2016 · (Permalink)
This is really cool! To more easily see where each of the 9 factors come into play:
BenjiG19 · 1 points · Posted at 03:06:22 on February 14, 2016 · (Permalink)
Jeb! seconds in how many weeks?
K3R3G3 · 1 points · Posted at 03:50:18 on February 14, 2016 · (Permalink)
That's awesome. And the square root of 10! is approximately 1905, the year Einstein published all those wild papers. Coincidence? I think not.
LaconianStrategos · 1 points · Posted at 03:53:45 on February 14, 2016 · (Permalink)
So what does Jeb! equal?
Liquidies · 2 points · Posted at 04:26:10 on February 14, 2016 · (Permalink)
Base 26: Jeb
Base 10: 13219
13219!= (Windows calculator overflowed, used Wolfram Alpha) 4.41838200273788544277250000924454430222679211619135 × 1048739
drdeadringer · 1 points · Posted at 03:54:59 on February 14, 2016 · (Permalink)
I'm now expecting this to show up in a novel by Vernor Vinge.
[deleted] · 1 points · Posted at 03:55:57 on February 14, 2016 · (Permalink)
What does 10! equal? Ten to the power of something?
[deleted] · 1 points · Posted at 15:07:46 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 2 points · Posted at 16:37:21 on February 14, 2016 · (Permalink)
Woah, that's cool! Thanks for explaining :)
And I wonder why 0! is 1
[deleted] · 3 points · Posted at 20:41:51 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 2 points · Posted at 21:03:08 on February 14, 2016 · (Permalink)
That helps a bit, thank you very much!
nicholas818 · 1 points · Posted at 04:08:53 on February 14, 2016 · (Permalink)
You should word it more ambiguously:
[deleted] · 1 points · Posted at 04:26:43 on February 14, 2016 · (Permalink)
Why are you so excited!
Trizizzle · 1 points · Posted at 04:29:56 on February 14, 2016 · (Permalink)
Thought it was just a really enthusiastic 10... This took me forever
Kstewart708 · 1 points · Posted at 04:41:53 on February 14, 2016 · (Permalink)
Jeb! = Jeb • Je • J
phillyphan2323 · 1 points · Posted at 05:40:55 on February 14, 2016 · (Permalink)
That's all well and good, but why is 10 all excited?
GuruMeditationError · 1 points · Posted at 06:00:39 on February 14, 2016 · (Permalink)
But there's only one Jeb!
_brodre · 1 points · Posted at 06:30:27 on February 14, 2016 · (Permalink)
i like this one the best.
punkin_spice_latte · 1 points · Posted at 07:13:17 on February 14, 2016 · (Permalink)
So to figure out the number of seconds in any number of weeks it would be (10!/6)*n
kigid · 1 points · Posted at 08:06:07 on February 14, 2016 · (Permalink)
I like this one because it's the only one I almost understand.
Jdrawer · 1 points · Posted at 08:11:20 on February 14, 2016 · (Permalink)
And approximately Pi x 107 secs/year
unproperNoun · 1 points · Posted at 08:16:25 on February 14, 2016 · (Permalink)
Don't believe him? Let's break it down!
Six weeks in seconds is
But lets break that down into factors
And reorganize it smallest to largest
And simplify
Meanwhile Ten factorial is (and let's do the same process here)
And wouldn't you know it it's the same answer
Random832 · 1 points · Posted at 08:27:35 on February 14, 2016 · (Permalink)
I stole this from a TIL thread about this:
10! = 71 52 34 28
[deleted] · 1 points · Posted at 09:00:46 on February 14, 2016 · (Permalink)
why are you shouting 10 at me?
GaBeRockKing · 1 points · Posted at 09:12:52 on February 14, 2016 · (Permalink)
I like approximating the number of seconds in a year as pi*107.
It's more than 99.5% accurate, so that's good enough for me :)
Baltimore_ · 1 points · Posted at 09:52:03 on February 14, 2016 · (Permalink)
And 10! = 7!*6!
randomperson1a · 1 points · Posted at 10:07:40 on February 14, 2016 · (Permalink)
To give some help, 10! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10.
lets ignore the * 1.
6 * 10 = 60 seconds, or 1 minute. 3 * 4 * 5 = 60 seconds as well, 60 * 60 = 3600 seconds, or 1 hour.
We're left with (1 hour) * 2 * 7 * 8 * 9
Well 9 = 3*3, so we have 8 * 9 is the same as 8 * 3 * 3 = 24 * 3, in other words (1 hour) * 24 * 3 = 24 hours * 3 = 3 days.
3 days * 2 * 7 = 6 days * 7, or 7 days * 6, so 1 week * 6, so 6 weeks.
suburban_hyena · 1 points · Posted at 10:25:24 on February 14, 2016 · (Permalink)
i like
PhysicalSweats · 1 points · Posted at 11:44:06 on February 14, 2016 · (Permalink)
I found that out when it was a question at a math competition.
rpetre · 1 points · Posted at 12:22:30 on February 14, 2016 · (Permalink)
I like to think this is what the 42 joke in HHG2G refers to (6 weeks = 42 days).
Krissam · 1 points · Posted at 12:24:42 on February 14, 2016 · (Permalink)
Actually, Douglas Adams has stated the number was chosen at random.
texruska · 1 points · Posted at 13:11:28 on February 14, 2016 · (Permalink)
Similarly, there are 11! seconds in 66 weeks and 12! seconds in 792 weeks and so on
axisdelasal · 1 points · Posted at 14:22:48 on February 14, 2016 · (Permalink)
10! = 6 * 7 * 24 * 60 * 60 = 6 * 7 * 2 * 3 * 4 * 60 * 60 = 2 * 3 * 4 * 6 * 7 * 5 * 4 * 3 * 2 * 3 * 10 = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10
JakkuScavenger · 1 points · Posted at 14:39:21 on February 14, 2016 · (Permalink)
And there's 52! unique ways to shift a standard deck of cards, which is a number so big, that if you shifted one deck of cards every second since the Big Bang, you still wouldn't have made much progress in all the unique ways it can be shifted.
randomguy186 · 1 points · Posted at 14:52:21 on February 14, 2016 · (Permalink)
Nifty! I wonder if the Babylonians knew that?
trophymursky · 1 points · Posted at 20:29:20 on February 14, 2016 · (Permalink)
not if there's a leap second somewhere in the 6 weeks.
MechanicalPotato · 1 points · Posted at 10:21:58 on February 15, 2016 · (Permalink)
You should really say ten factorial somewhere in your comment... I thought you were really bad at punctuation there...
(not a math guy)
musicmast · 1 points · Posted at 01:27:15 on February 14, 2016 · (Permalink)
someone explain?
[deleted] · -1 points · Posted at 01:48:46 on February 14, 2016 · (Permalink)
[deleted]
musicmast · 2 points · Posted at 01:52:13 on February 14, 2016 · (Permalink)
"10!"? Is the exclamation mark a typo?
BoldElDavo · 1 points · Posted at 01:55:39 on February 14, 2016 · (Permalink)
It's a factorial, which means it multiplies by all the integers from 1 to 10.
musicmast · 1 points · Posted at 01:57:17 on February 14, 2016 · (Permalink)
oh ok. Didn't realize that was the meaning of the exclamation mark.
K3R3G3 · 1 points · Posted at 03:59:30 on February 14, 2016 · (Permalink)
https://www.reddit.com/r/AskReddit/comments/45m1zl/whats_the_coolest_mathematical_fact_you_know_of/czyr7kq
[deleted] · 1 points · Posted at 01:54:22 on February 14, 2016 · (Permalink)
I think there's more than ten seconds in six weeks
[deleted] · 1 points · Posted at 01:56:22 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 02:02:52 on February 14, 2016 · (Permalink)
What
[deleted] · 1 points · Posted at 02:05:43 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 02:06:15 on February 14, 2016 · (Permalink)
Oh,I thought it had to do something with Jeb Bush
legalilegali · 1 points · Posted at 02:03:31 on February 14, 2016 · (Permalink)
Not everyone knows what a factorial is. Come on.
Israe12 · 0 points · Posted at 04:07:08 on February 14, 2016 · (Permalink)
yes ofcourse almost 8 seconds in a week :P
jfb1337 · 87 points · Posted at 11:56:53 on February 14, 2016 · (Permalink)
Graham's number, the biggest number ever used in a mathematical proof, is bigger than any number you could ever imagine.
It's defined using Knuth's Up Arrow Notation:
a↑b = ab = a*a*a...*a (b times), repeated multiplication
a↑↑b = aaaa...a (b times), repeated exponentiation
a↑↑↑b = a↑↑a↑↑a↑↑a...↑↑a (b times), repeated ↑↑
In general, a↑↑↑...↑ (n arrows) = a↑nb = a↑n-1a↑n-1a...↑n-1a (b times)
To put this in context, 3↑3 = 33 = 27.
3↑↑3 = 333 = 7625597484987. This is over 50 times the distance to the sun in m 3↑↑↑3 = 3↑↑3↑↑3 = 3↑↑7625597484987 = 3333...3 (7625597484987 times). If we wanted to write this out in full, with each 3 taking up 1 cm of paper, this would take us about halfway to the sun. And actually expanding it down would be a HUGELY insane number. Which hasn't even scratched the surface of Graham's number yet.
3↑↑↑↑3 = 3↑↑↑3↑↑↑3 = 3↑↑3↑↑3↑↑3...↑↑3, the number of times being that HUGE number which takes us halfway to the sun just to write down the power stack. Wolfram alpha can't handle this number. There are no analogies I can think of to help comprehend this number. This number is called g1. We're getting closer to Graham’s number, but we're still a long way off.
What is g2? It's 3↑↑↑↑...↑3, but how many arrows are there? There are g1 of them. When only using 4 arrows, we got an insanely huge incomprehensible number. Now we're using that many arrows. This number is HUGE.
And g3 is just 3↑g23. Which is WAY bigger than g1 and g2.
In general, g(n) = 3 ↑g(n-1) 3.
And, finally, Graham's number = g64. If you wanted to write this down, and you could write every digit in one Planck volume (the smallest possible volume in the universe, equal to 4.22×10-105 m3, you wouldn't have enough space to write it all down. In fact, if you replaced every planck volume with another universe, and used every planck volume in THOSE universes to write down Graham's number, you STILL wouldn't have enough space.
In fact, the ONLY thing bigger than Graham's number is the weight of your mum.
[deleted] · 13 points · Posted at 23:31:17 on February 14, 2016 · (Permalink)
Take a look at TREE(3), or SCG(13). In comparison Graham's number looks almost as small as your penis
hypervelocityvomit · 8 points · Posted at 12:24:13 on February 15, 2016 · (Permalink)
A = π rekt
Hyboe · 5 points · Posted at 15:31:39 on March 11, 2016 · (Permalink)
Thanks Day[9]
yomamaso__ · 1 points · Posted at 21:25:16 on February 18, 2016 · (Permalink)
Grahams number explained. https://m.youtube.com/watch?v=1N6cOC2P8fQ
PowerfulComputers · 258 points · Posted at 02:54:03 on February 14, 2016 · (Permalink)
You can write any repeating decimal, like 0.789789789... as a fraction with the repeating part over the same number of 9's: 789/999. That also implies that 0.9999 repeated is 9/9 = 1.
spirituallyinsane · 93 points · Posted at 02:59:11 on February 14, 2016 · (Permalink)
Well, I'll be durned. You're right. I never noticed that before. Please accept .999... upvotes.
TaohRihze · 3 points · Posted at 07:53:46 on February 14, 2016 · (Permalink)
Nobody got time to make repeated upvotes these days, just give 1 and be done with it.
chevymonza · 1 points · Posted at 15:02:53 on February 14, 2016 · (Permalink)
It took some powerful computers to get that.
somadIcanteven · 5 points · Posted at 03:18:36 on February 14, 2016 · (Permalink)
Moreover, the existence of repeating decimal expansions for a number completely characterizes whether it can be written as a ratio of two integers.
1/2 = .5 = .5000000000... is repeating
sqrt(2) = 1.41421356237... is known to be non-repeating because we know sqrt(2) is irrational
AmadeusMop · 6 points · Posted at 23:56:20 on February 14, 2016 · (Permalink)
1/2 is also equal to 0.4999999..., which is repeating as well.
hypervelocityvomit · 3 points · Posted at 11:01:13 on February 15, 2016 · (Permalink)
0.999999... = 9/9
4.999999... = 4 + 9/9 = 45/9
.4999999... = 45/90 = duh 1/2
Shortest proof I've seen yet.
[deleted] · 5 points · Posted at 06:58:41 on February 14, 2016 · (Permalink)
I often heard that 0.9999999... equals 1 but I never heard the explanation until now!
Grug16 · 14 points · Posted at 09:41:09 on February 14, 2016 · (Permalink)
Here's how it was explained to me:
1/3 = 0.3333333...
2/3 = 0.6666666...
1/3 + 2/3 = 1.
0.3333333... + 0.6666666... = .9999999...
.9999999... = 1;
biggerfisch · 4 points · Posted at 07:40:08 on February 14, 2016 · (Permalink)
This isn't so much an explanation as it is a side effect.
hypervelocityvomit · 2 points · Posted at 10:55:52 on February 15, 2016 · (Permalink)*
Long division shows how it works:
The multiples of 999 are basically multiples of (1000-1), so their magic is to chop the 1000s digit off, and reinsert it as the units digit. After 3 iterations, the old result reappears, so we know that the digits obtained so far will repeat forever.
Good. Now we know that 789/999 equals .789789789... But what about other numbers?
They will scroll through just like 789 did, so we can draw the same conclusion:
0.(3-digit number repeated ad inf.) = (3-digit number) / 999.
For other period lengths, just take
0.(n-digit number repeated ad inf.) = (n-digit number) / (10n - 1).
It'll take a different number of iterations to scroll the period through, but otherwise, it'll work the same.
luckypech · 2978 points · Posted at 20:27:07 on February 13, 2016 · (Permalink)
The Banach–Tarski paradox: Given a solid ball, there exists a decomposition of the ball into a finite number of disjoint subsets, which can be put back together in a different way to yield two identical copies of the original ball.
chocapix · 3510 points · Posted at 21:07:24 on February 13, 2016 · (Permalink)
What's an anagram of Banach-Tarski?
Banach-Tarski Banach-Tarski.
Schohns · 1532 points · Posted at 22:04:22 on February 13, 2016 · (Permalink)
Hah I like that one! Reminds me of this:
What does the B. in Benoît B. Mandelbrot stand for?
Benoît B. Mandelbrot.
Sipczi · 741 points · Posted at 00:50:53 on February 14, 2016 · (Permalink)
Recursion is cool.
jimmy_the_jew · 113 points · Posted at 02:13:45 on February 14, 2016 · (Permalink)
Very very sneaky sir...
IndoorForestry · 34 points · Posted at 03:38:48 on February 14, 2016 · (Permalink)
For another sneaky fun thing, google "recursion".
EDTa380 · 24 points · Posted at 04:59:19 on February 14, 2016 · (Permalink)
Did you mean "recursion?"
MooGrowl · 26 points · Posted at 05:42:55 on February 14, 2016 · (Permalink)
To understand recursion you must first, understand recursion.
Derf_Jagged · 29 points · Posted at 02:35:45 on February 14, 2016 · (Permalink)
I'm incredibly confused how you posted this without an edit...
ShoggothEyes · 60 points · Posted at 02:37:50 on February 14, 2016 · (Permalink)
I think if you edit within a few minutes, it doesn't show as an edit.
UndeadBread · 39 points · Posted at 02:58:12 on February 14, 2016 · (Permalink)
The infamous ninja edit.
Derf_Jagged · 10 points · Posted at 03:04:48 on February 14, 2016 · (Permalink)
That makes more sense. I was thinking along the lines that when you are posting something it generates your unique comment ID and he found it in the source code and pasted it in his link... But that works too =)
-WPD- · 3 points · Posted at 06:42:57 on February 14, 2016 · (Permalink)
I thought he was some kind of reddit wizard.
Sipczi · 3 points · Posted at 08:42:30 on February 14, 2016 · (Permalink)
Correct, it took me a few seconds, but I believe it's a 2 minutes window.
jeremymeyers · 9 points · Posted at 04:28:42 on February 14, 2016 · (Permalink)
In order to understand recursion, we must first understand recursion.
Turtlebelt · 6 points · Posted at 05:24:29 on February 14, 2016 · (Permalink)
You bastard, you forgot your base cases! You've gotten us all stuck in an infinite loop.
Sipczi · 6 points · Posted at 08:47:25 on February 14, 2016 · (Permalink)
Actually, if you click 12462 times, it will do something... different.
Turtlebelt · 4 points · Posted at 10:47:46 on February 14, 2016 · (Permalink)
That's just your finger falling off...
Problem119V-0800 · 2 points · Posted at 06:10:06 on February 14, 2016 · (Permalink)
⊥
JoXand · 6 points · Posted at 06:46:12 on February 14, 2016 · (Permalink)
Recursion? Did you mean recursion?
IronOhki · 2 points · Posted at 11:15:07 on February 14, 2016 · (Permalink)
That's my favorite Google easter egg because that's my favorite Google easter egg.
hypervelocityvomit · 4 points · Posted at 09:58:51 on February 15, 2016 · (Permalink)
The first rule of Tautology Club is Rule #1 of Tautology Club.
Es_el_moose · 9 points · Posted at 02:14:28 on February 14, 2016 · (Permalink)
Amazing link, should click, much happy.
ktkps · 2 points · Posted at 04:40:03 on February 14, 2016 · (Permalink)
I would have upvoted twice for regression...but...
Come_along_quietly · 2 points · Posted at 05:13:49 on February 14, 2016 · (Permalink)
To understand recursion one must understand recursion.
becomingknown · 2 points · Posted at 05:20:48 on February 14, 2016 · (Permalink)
Well done sir.
[deleted] · 2 points · Posted at 06:49:03 on February 14, 2016 · (Permalink)
Ah you fucking snake bitch!
kingfrito_5005 · 2 points · Posted at 08:31:11 on February 14, 2016 · (Permalink)
Whoa, I didnt know reddit would let you do that, that IS cool.
realist_konark · 2 points · Posted at 13:19:25 on February 14, 2016 · (Permalink)
This must be sent to best of Reddit!
----_____---- · 2 points · Posted at 13:55:53 on February 14, 2016 · (Permalink)
Hold my proof, I'm going in!
Siarles · 1 points · Posted at 16:27:11 on February 14, 2016 · (Permalink)
Did you mean: recursion
chemicaldecay · 1 points · Posted at 10:17:03 on February 14, 2016 · (Permalink)
Genius. I read a book by this author - Sipczi - once. Some mathematical philosopher who spent his entirety writing about where said Recursion begins.
[deleted] · 36 points · Posted at 00:22:31 on February 14, 2016 · (Permalink)
More like Benoît BALLS Mandelbrot
Jacob2040 · 17 points · Posted at 00:00:15 on February 14, 2016 · (Permalink)
What does GNU mean?
GNU's not UNIX!
[deleted] · 6 points · Posted at 01:02:58 on February 14, 2016 · (Permalink)
PHP: PHP Hypertext Preprocessor
My favourite acronym
HiddenKrypt · 3 points · Posted at 02:43:06 on February 14, 2016 · (Permalink)
Backronym, actually. It was originally "Personal Homepage Tools". It started as a small set of perl scripts to let Lerdorf make his homepage be a little more dynamic. After people started asking for copies of the 'program', and started expanding it / asking Lerdorf to add features, it became a preprocessor language supporting a name change. These days it's closer to a general purpose programming language than a preprocessor, so I would suggest they update the acronym again.
OneTripleZero · 1 points · Posted at 03:07:26 on February 14, 2016 · (Permalink)
I'm happy you were that guy so I didn't have to be :)
HiddenKrypt · 2 points · Posted at 03:20:24 on February 14, 2016 · (Permalink)
I love being that guy
rekenner · 5 points · Posted at 05:53:25 on February 14, 2016 · (Permalink)
WINE Is Not an Emulator.
dotcomaphobe · 3 points · Posted at 03:56:26 on February 14, 2016 · (Permalink)
You're a day-glo pterodactyl.
STAAAAAALIN · 3 points · Posted at 09:29:35 on February 14, 2016 · (Permalink)
You're a badass fucking fractal.
Yserbius · 3 points · Posted at 05:50:47 on February 14, 2016 · (Permalink)
There's a type of Jewish biscotti called "mandelbroit". I had a box of some the other day and asked my wife if they were made out of other mandelbroits and does that mean it's a mandelbroit set. She just gave me this strange look while I spent five minutes laughing at myself.
Same look my dad gave me earlier tonight when we drove past Dijsktra St. and I mentioned how it's easy to find the shortest way to get here.
Problem119V-0800 · 4 points · Posted at 06:12:30 on February 14, 2016 · (Permalink)
But nobody does, because going to Dijkstra street is considered harmful.
Valiantful · 1 points · Posted at 01:35:19 on February 14, 2016 · (Permalink)
I didnt get this for a second.
Ltbsd · 1 points · Posted at 13:32:03 on February 14, 2016 · (Permalink)
Not even for a second?
PM_ME_UR_THROW_AWAYS · 1 points · Posted at 01:47:15 on February 14, 2016 · (Permalink)
Unfortunately, it's not a joke that PHP stands for PHP Hypertext Preprocessor
Greghole · 1 points · Posted at 01:57:25 on February 14, 2016 · (Permalink)
I always assumed it stood for Badass.
JamesTheJerk · 1 points · Posted at 02:56:26 on February 14, 2016 · (Permalink)
It's like that old zip virus.
Savir5850 · 1 points · Posted at 03:13:34 on February 14, 2016 · (Permalink)
These are all over the place in Linux. There's software called 'Wine' that stands for 'Wine is not an Emulator'. It's not an Emulator.
SlowBeans · 1 points · Posted at 03:14:03 on February 14, 2016 · (Permalink)
The operating system GNU is also a recursive acronym : GNU is Not Unix.
Glitch29 · 1 points · Posted at 05:02:23 on February 14, 2016 · (Permalink)
http://dilbert.com/strip/1994-05-18
[deleted] · 1 points · Posted at 05:37:48 on February 14, 2016 · (Permalink)
In college when people used to use "slash" as a conjunction, someone asked my friend what it meant. She said, "I always thought it stood for the slash in between and/or."
And/and/and....or/or/or.
WoooaahDude · 1 points · Posted at 06:44:12 on February 14, 2016 · (Permalink)
For Web developers: PHP stands for PHP Hypertext Processor.
chewrocka · 1 points · Posted at 08:09:08 on February 14, 2016 · (Permalink)
The Rs in George R.R. Martin's name both stand for "R.R. Martin'. That makes his name endlessly recursive so one can never mystically bind him.
Christopher135MPS · 1 points · Posted at 08:48:44 on February 14, 2016 · (Permalink)
Dilbert has a great comic about this;
http://dilbert.com/strip/1994-05-18
jooblethedark · 1 points · Posted at 10:38:05 on February 14, 2016 · (Permalink)
What does the R in RIP stand for? RIP in peace.
splitcroof92 · 1 points · Posted at 16:27:22 on February 14, 2016 · (Permalink)
The P in PHP actually stands for PHP
ectish · 1 points · Posted at 02:54:30 on February 15, 2016 · (Permalink)
What is E.T. short for?
he's got little legs
Emmkay67 · 1 points · Posted at 06:19:01 on February 15, 2016 · (Permalink)
Balls
Ganjisseur · 0 points · Posted at 06:16:49 on February 14, 2016 · (Permalink)
Balls.
[deleted] · 9 points · Posted at 03:18:46 on February 14, 2016 · (Permalink)
I don't get it.
markneill · 7 points · Posted at 03:43:00 on February 14, 2016 · (Permalink)
Banach-Tarski says you can take the different parts of something, and rearrange them to make a different but identical copy of something.
An anagram is the rearrangement of the letters in a word to make a new word.
So a Banach-Tarski anagram would be a rearrangement that results in a different but identical word.
kendebater · 5 points · Posted at 01:21:41 on February 14, 2016 · (Permalink)
That was not a good joke. That was a great joke.
[deleted] · 1 points · Posted at 03:13:34 on February 14, 2016 · (Permalink)
What that even a joke?
[deleted] · 1 points · Posted at 05:23:50 on February 16, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 05:49:13 on February 16, 2016 · (Permalink)
Haha I watched it. I was making a Comedy Bang! Bang! joke.
DoWhile · 6 points · Posted at 02:16:54 on February 14, 2016 · (Permalink)
Anti-joke answer:
A brackish ant.
JuntaEx · 4 points · Posted at 00:47:23 on February 14, 2016 · (Permalink)
:( I feel stupid
Sergeanttoasty · 3 points · Posted at 04:00:26 on February 14, 2016 · (Permalink)
What do you call a Banach Analytic Manifold?
BanAnaMan
jmezfm · 3 points · Posted at 07:02:42 on February 14, 2016 · (Permalink)
One of my favorite math professors told us this joke after explaining the Banach-Tarski paradox to us. I remember a solid 10 seconds of silence before the class burst out laughing. Thanks for the reminder on that one, happy memory.
[deleted] · 2 points · Posted at 04:18:23 on February 14, 2016 · (Permalink)
this is my new favorite joke.
staytaytay · 1 points · Posted at 03:04:00 on February 14, 2016 · (Permalink)
Jeez that's clever
bon_voyage_felicia · 1 points · Posted at 04:23:09 on February 14, 2016 · (Permalink)
Banach Banach cheese cheese Tarski Tarski please please.
[deleted] · 1 points · Posted at 04:45:34 on February 14, 2016 · (Permalink)
This kind of stuff only works if everything is continuous vs. discreet. Zeno's paradox is another example of this.
We know that matter and energy are discreet (and maybe space is too). So this isn't something that would actually work in practice.
Maybe I'm missing something.
NamelessNamek · 1 points · Posted at 06:09:07 on February 14, 2016 · (Permalink)
Eli5
RobinBankss · 1 points · Posted at 06:39:00 on February 14, 2016 · (Permalink)
Satan Bar Hick is what I found
moonrocks · 1 points · Posted at 12:35:09 on February 15, 2016 · (Permalink)
u win this round nerdlinger...
Kitty-Kat-Katarina · 1 points · Posted at 05:34:37 on February 14, 2016 · (Permalink)
That was literally the most retarded joke I've ever heard. I'm fascinated with it
YourBrothersMother · 641 points · Posted at 21:41:18 on February 13, 2016 · (Permalink)
I watched the vsauce video about it and it still confuses me
tedgag · 538 points · Posted at 23:59:11 on February 13, 2016 · (Permalink)
Link for the uninitiated
Not_Pablo_Sanchez · 715 points · Posted at 01:46:03 on February 14, 2016 · (Permalink)
Could you click it for me?
flyZerach · 27 points · Posted at 05:34:25 on February 14, 2016 · (Permalink)
Instructions unclear; got educated.
tedgag · 33 points · Posted at 01:53:27 on February 14, 2016 · (Permalink)
Well if you have RES, it pretty much clicks itself!
Datduckdo · 195 points · Posted at 02:05:50 on February 14, 2016 · (Permalink)
TL;DW: infinity does what it wants bitch
GodlessPerson · 5 points · Posted at 12:40:43 on February 14, 2016 · (Permalink)
Too Long; Didn't Weed?
FourBox · 5 points · Posted at 13:43:47 on February 14, 2016 · (Permalink)
Too long; Didn't Watch
[deleted] · 65 points · Posted at 01:49:33 on February 14, 2016 · (Permalink)
Wtf did I just watch
GGABueno · 33 points · Posted at 04:31:05 on February 14, 2016 · (Permalink)
The best channel on YouTube.
pigi5 · 2 points · Posted at 08:05:24 on February 14, 2016 · (Permalink)
God, I love his voice.
fitcheroo · 1 points · Posted at 08:45:47 on February 14, 2016 · (Permalink)
I enjoy his videos but the dramatic pauses and slowing down of speech for emphasis gets kinda redundant and irritating after 2-3 videos.
judgej2 · 5 points · Posted at 09:42:33 on February 14, 2016 · (Permalink)
If your experience was anything like mine, about an hour's worth of vsauce videos.
PunsAndRoses · 17 points · Posted at 02:01:27 on February 14, 2016 · (Permalink)
I was lost at the Diagonal part. Why does he say that it is different from any other number on the list. Why couldn't it have been randomly generated in the original list?
Redingold · 40 points · Posted at 02:49:39 on February 14, 2016 · (Permalink)
Well, it can't be the first number, since it's different in the first decimal place.
It can't be the second number, because it's different in the second decimal place.
Indeed, it can't be the nth number on the list for any n, because by the nature of its construction, it differs from the nth number of the list in the nth decimal place.
So it's not in the list.
SakuraDragon · 5 points · Posted at 03:09:09 on February 14, 2016 · (Permalink)
I had the same question, so thanks for your simple explanation. This is one of the things that makes me realize I could never even begin to fathom infinity.
[deleted] · 2 points · Posted at 04:01:45 on February 14, 2016 · (Permalink)
I still don't get it... ohhhhh wait. I just realized, ok. There's just another infinity you've got to throw in.
So I was gonna say, how don't you know it wasn't randomly generated like guy said. But you are literally going through the infinite list that was generated and changing the numbers.
I know he says we shouldn't consider infinity weird or strange, but goddamned if it isn't weird and strange.
Tsu_Dho_Namh · 1 points · Posted at 07:32:18 on February 14, 2016 · (Permalink)
Some of the weirder points of infinity are explained well by the full version of the Hilbert Hotel.
First you can fit a new guest in the hotel. Then you find rooms for a bus containing an infinite number of guests. Then an aircraft carrier with an infinite number of buses, each with an infinite number of guests. And finally, an algorithm that allows you to move hotel guests around to make room for an infinite number of aircraft carriers, each with an infinite number of buses, each with an infinite number of passengers.
And then the hotel is full, but can still make room for uncountably infinitely more people.
etherkiller · 1 points · Posted at 06:27:43 on February 14, 2016 · (Permalink)
Why couldn't the first number reappear on the list with a different number in the first digit? Sure, the odds against it are near infinite, but still non-zero. When we're talking about an infinite list, isn't that basically one?
bleachisback · 3 points · Posted at 07:13:24 on February 14, 2016 · (Permalink)
We're not making a number where the first digit is different from the first number and then making a second number where the second digit is different from the second number. We're making one number where the first place is different than the first number, the second place is different than the second number, the third place is different than the third number, and then continuing until we reach the "last" number and the "last" place. Therefore, our new number is one which each place has an original number which doesn't match, and vice verse.
In your situation, if you consider that the 250,000,000,000,000th number is identical to the first number, except that its first decimal place is one more than the first number, the new number's 250,000,000,000,000th decimal place will be different.
thevoiceless · 1 points · Posted at 18:48:11 on February 14, 2016 · (Permalink)
But the list is infinite, so aren't you really just describing a way to generate another number? It seems like the only way a number "couldn't" be in the list is if it couldn't be generated by that algorithm
Redingold · 1 points · Posted at 20:52:15 on February 14, 2016 · (Permalink)
It is a way of generating another number, and that number can't be on the list because it's not the same as any of the numbers on the list.
Remember, the point is that it doesn't make sense. It's a reductio ad absurdum argument. The list is impossible, it can't exist, and this number that we can generate explains why - the list is supposed to be complete, and yet we have a number that cannot be on it, so the list must not exist.
Im_A_Nidiot · 7 points · Posted at 01:51:18 on February 14, 2016 · (Permalink)
Good god, that was a lot.
jakielim · 5 points · Posted at 02:06:45 on February 14, 2016 · (Permalink)
But we are initiated.
KrisKorona · 1 points · Posted at 02:46:25 on February 14, 2016 · (Permalink)
Aren't we Bruce?
Idontdeservethiss · 4 points · Posted at 03:24:43 on February 14, 2016 · (Permalink)
I think this video is a perfect example of when I personally find math fascinating, but realize that I would never be good at it.
lola_fox · 3 points · Posted at 02:57:28 on February 14, 2016 · (Permalink)
that just really hurt my brain
CarlSagansturtleneck · 2 points · Posted at 03:16:49 on February 14, 2016 · (Permalink)
So can I rip up dollar bills and create more dollar bills?
shennanigram · 2 points · Posted at 04:41:50 on February 14, 2016 · (Permalink)
I don't get it, isn't the paradox just saying infinity is still infinity when we add to it?
-WPD- · 3 points · Posted at 06:44:26 on February 14, 2016 · (Permalink)
More that infinity is still infinity if we subtract from it, but simplifying it greatly, yes.
DavidPastrnak · 2 points · Posted at 16:46:40 on February 14, 2016 · (Permalink)
Not at all, really. I haven't watched the video, but the point of the theorem is that there are certain types of sets of points in 3-d space where it doesn't make sense to assign them a volume.
The idea is that you start with a ball of volume 1, and you break it up into five or so pieces in this crazy way. If those pieces each have a volume, then when you move each piece around, its volume shouldn't change. But if you move your pieces around in the right way, then you can put them back together and get two balls, each of which is volume 1. So the total volume of your pieces should be 2. But when you started the total volume of your pieces was 1. So 2=1, a contradiction.
You get a contradiction because you assumed you could say those crazy pieces had "volume". The point of the theorem is that it doesn't make any sense to assign a volume to those pieces you broke the original ball into.
buzzbros2002 · 1 points · Posted at 03:14:50 on February 14, 2016 · (Permalink)
Holy shiz that was fun.
0raichu · 1 points · Posted at 04:08:22 on February 14, 2016 · (Permalink)*
jworsham · 1 points · Posted at 04:13:21 on February 14, 2016 · (Permalink)
Excuse me, I need to pick up my brain off the walls because my head just exploded...
[deleted] · 1 points · Posted at 04:20:07 on February 14, 2016 · (Permalink)
Bah nasssshhhhhh!
[deleted] · 1 points · Posted at 04:23:42 on February 14, 2016 · (Permalink)
countable just means having an injection into the natural numbers.
BobTehCat · 1 points · Posted at 07:31:04 on February 14, 2016 · (Permalink)
Replying to check out in the morning
TinyNuggins · 1 points · Posted at 07:43:36 on February 14, 2016 · (Permalink)
Funny that he puts 1/2 in between 1 and 2 on his number line.
Ucantalas · 1 points · Posted at 07:59:06 on February 14, 2016 · (Permalink)
...this crazy math ball voodoo is why the Church used to burn scientists.
sephrinx · 1 points · Posted at 08:04:59 on February 14, 2016 · (Permalink)
So, by rotating the sphere, it magically increases in mass? Just because you apply an arbitrary label to points on the sphere doesn't mean that it exists. Those points would, exist, but there would be nothing there, just a small gap between the other points.
I don't get it. When you "fill in" from infinity, you can't just pull mass out of nowhere, that "infinity" that you are pulling from is not infinite, it is a finite object with defined and limited definitions.
I don't see how that paradox makes sense. It does not seem to be physically valid.
As for the hadron collider creating "more" particles, don't the collisions convert the energy into new mass? I thought that was the entire point of the experiment, to create new particles from the sheer amounts of energy from the collision of the particles.
DavidPastrnak · 1 points · Posted at 16:58:09 on February 14, 2016 · (Permalink)
I haven't watched this video, but it seems like it is more confusing and overwhelming than it needs to be.
The point of the theorem has nothing to do with physically being able to duplicate two balls. That's how people like to try to sell it, because it's shocking and sexy, but that's not at all why mathematicians care about it. Its to show that there are certain types of sets in 3-D space where it doesn't make sense to say they have a "volume."
The idea is that you start with a ball of volume 1, and you break it up into five or so pieces in this crazy way. If those pieces each have a volume, the sum of their volumes should add up to 1. When you move each piece around, its volume shouldn't change. But if you move your pieces around in the right way, then you can put them back together and get two balls, each of which is volume 1. So the sum of the volumes of your pieces should be 2. But when you started the total volume of your pieces was 1. So 2=1, a contradiction.
You get a contradiction because you assumed you could say those crazy pieces had "volume". The point of the theorem is that it doesn't make any sense to assign a volume to those pieces you broke the original ball into.
physchy · 1 points · Posted at 08:05:45 on February 14, 2016 · (Permalink)
Wouldn't that sphere have to be infinitely dense?
Artren · 1 points · Posted at 09:30:46 on February 14, 2016 · (Permalink)
I read that in Kevin's voice from The Office. I've been watching too much of The Office.
saadahmad96 · 1 points · Posted at 10:22:45 on February 14, 2016 · (Permalink)
But we are initiated, aren't we?
DaGranitePooPooYouDo · 1 points · Posted at 10:57:14 on February 14, 2016 · (Permalink)
I can't stand type and style of narration. It's so common on Youtube.
SurprisedPotato · 1 points · Posted at 10:59:49 on February 14, 2016 · (Permalink)
I clicked the link and watched it twice
Cajova_Houba · 1 points · Posted at 11:39:18 on February 14, 2016 · (Permalink)
I like how he explains that the infinity is rather something size-like than a number, but I don't like the "different sizes of infinity". I personaly prefer to think of infinity as a name, or concept. So yes, inf+1 is still inf, but not bigger nor smaller infinity, just infinity.
DavidPastrnak · 1 points · Posted at 17:10:38 on February 14, 2016 · (Permalink)
"Different sizes of infinity" is an important concept in math, but it might mean something different than you think.
In math, you say that two sets have the same cardinality (i.e., "size") if you can create a one-to-one correspondence between the things in those sets. For example, the set {3, 4 ,5} has the same cardinality as the set {6, 7, 9}, because you can say 3 corresponds to 6, 4 corresponds to 7, and 5 corresponds to 9. The word we use to describe this cardinality is "three". The set {1, 2} has cardinality "two", which isn't as big as three because when you try to create your one-to-one correspondence between {1, 2} and {3, 4, 5}, you'll always have something in {3, 4, 5} left over which doesn't correspond to an element of {1,2}.
You can do this with infinite sets. The even numbers have the same cardinality as all integers because for each integer n, you can assign it to 2n.
The set of real numbers is "bigger" than the set of integers because if you try to create this one-to-one correspondence between the integers and real numbers, then you'll always have a bunch of real numbers left over.
(It doesn't stop there, though. There are sets which are "bigger" than the real numbers in the same way. There are actually infinitely many sizes of infinity...)
TheTurnipKnight · 1 points · Posted at 13:33:53 on February 14, 2016 · (Permalink)
So... When dealing with infinity everything is possible?
Also it's actually pronounced "Banah". "CH" is the same as "H".
[deleted] · 146 points · Posted at 23:18:27 on February 13, 2016 · (Permalink)
Good, because it doesn't make sense. It's a paradox.
kaladyr · 155 points · Posted at 01:27:49 on February 14, 2016 · (Permalink)*
.
uhhguy · 13 points · Posted at 03:07:46 on February 14, 2016 · (Permalink)
My mind just thinks 'limited atoms' and shuts off as I try to understand this, mathematically it's cool as hell.
kaladyr · 6 points · Posted at 03:29:55 on February 14, 2016 · (Permalink)*
.
uhhguy · 3 points · Posted at 03:39:21 on February 14, 2016 · (Permalink)
Mind is spinning all over again! Thank you!
MaraschinoPanda · 5 points · Posted at 03:33:23 on February 14, 2016 · (Permalink)
Well, it is notable because it is provable in ZFC but not in ZF. So in a sense the weirdness of the result could be an argument against including the axiom of choice.
kaladyr · 1 points · Posted at 03:36:32 on February 14, 2016 · (Permalink)*
.
pjf18222 · 3 points · Posted at 04:38:07 on February 14, 2016 · (Permalink)
Yeah no what
kaladyr · 1 points · Posted at 04:54:45 on February 14, 2016 · (Permalink)*
.
Drews232 · 1 points · Posted at 03:12:36 on February 14, 2016 · (Permalink)
Maybe they should write down its measurements on a Post It before breaking it down, then they'll have enough information to know you can only make one ball out of it when they resurrect it.
Rlysrh · 1 points · Posted at 12:37:02 on February 14, 2016 · (Permalink)
Oh my god thank you. I watched that whole video, came out feeling like a dumbass and you've explained the whole thing in a short paragraph.
TheLittleGoodWolf · 1 points · Posted at 12:38:23 on February 14, 2016 · (Permalink)
I think the issue I have with it is that he mentions a countable infinity, which to me seems to go against the definition of an infinity. Not that I would understand a mathematical infinity but expressed with just words an infinity has no end (at least how I see it). Since it has no end it can't have a definite size or volume or anything really, any definite characteristic becomes irrelevant.
In the end all this reminds me of is that story of some Greeks (I think it was Greeks) who argued that time and distance doesn't exist. If I recall correctly the example used was the race between the hare and the turtle and how if you divided time into small enough increments they both traveled at the same speed. I don't remember enough keywords to find it again though.
GuSec · 1 points · Posted at 13:36:50 on February 14, 2016 · (Permalink)
Countable infinite just means that you can enumerate all elements using the natural numbers, not that a counting process where each step takes a finite time will also complete within finite time (which it obviously won't as you say). The real numbers are not countably infinite in number because you can't assign each real a natural number, they are simply too many and the amount of them all is a larger, non-countable, infinity.
Which is a cool mathematical fact in itself.
kaladyr · 1 points · Posted at 18:39:32 on February 14, 2016 · (Permalink)*
.
Vidyogamasta · 1 points · Posted at 15:31:05 on February 14, 2016 · (Permalink)
Tell me if I'm misunderstanding something, but wouldn't this only work for an object with infinite density? Basically the "paradox" is a fancy way of saying infinity × 2 = infinity.
kaladyr · 1 points · Posted at 18:32:08 on February 14, 2016 · (Permalink)*
.
[deleted] · 1 points · Posted at 00:00:18 on February 16, 2016 · (Permalink)
Yes it's provable within ZFC, where things like "Sphere" and "decompose the ball" do not mean what everyone thinks they mean.
Damarusxp · 1 points · Posted at 03:23:18 on February 14, 2016 · (Permalink)
But how does that preserve the original amount of energy?
kaladyr · 2 points · Posted at 03:30:47 on February 14, 2016 · (Permalink)
Energy?
Damarusxp · 1 points · Posted at 10:05:46 on February 14, 2016 · (Permalink)
Sadly the Wikipedia article of the paradox doesn't mention the word energy even once. I'm pretty sure this goes against the law of conservation of energy. I can see how the new matter might be created from energy, as we're dealing with subatomic particles anyways, but how do you get the overall energy level before the process to be doubled afterwards (as you now have the original object twice)?
no_nick · 2 points · Posted at 11:05:17 on February 14, 2016 · (Permalink)
The 'ball' in this case is an abstract notion, not a physical object. Physics doesn't factor into this.
kaladyr · 1 points · Posted at 18:27:43 on February 14, 2016 · (Permalink)*
.
Damarusxp · 1 points · Posted at 18:29:51 on February 14, 2016 · (Permalink)
Alright, I got that wrong then.
zacker150 · 0 points · Posted at 20:23:56 on February 14, 2016 · (Permalink)
Say you have two particles collide in a particle accelerator. Their energy comes from their speed going from .9c to zero.
thektulu7 · -1 points · Posted at 07:20:39 on February 14, 2016 · (Permalink)
So basically take a solid ball, do magic to it so it exists in another dimension where size doesn't matter, cut it up, then do more magic to bring it back to our dimension and put it back together again, twice. Got it.
kaladyr · 3 points · Posted at 07:46:45 on February 14, 2016 · (Permalink)*
.
thektulu7 · 1 points · Posted at 15:40:50 on February 14, 2016 · (Permalink)
The "not measurable" part is what sounds like magic to me.
lambdaknight · 5 points · Posted at 03:44:10 on February 14, 2016 · (Permalink)
It's not really a paradox, but rather a thing-that-is-pretty-unintuitive-and-seems-like-it-should-be-wrong. Unfortunately, mathematicians got tired of calling it the Banach-Tarski thing-that-is-pretty-unintuitive-and-seems-like-it-should-be-wrong.
[deleted] · 2 points · Posted at 13:17:34 on February 14, 2016 · (Permalink)
I think that is generally what paradox refers to in math. From https://en.wikipedia.org/wiki/Category:Mathematics_paradoxes :
lambdaknight · 2 points · Posted at 22:38:27 on February 14, 2016 · (Permalink)
As a mathematician studying mathematical logic, I've always been taught that a "paradox" is a statement that is contradictory. The most famous example being the liar's paradox: "This statement is false." If the statement is false, then that statement is true then the statement is false then the statement is true... A more important example is Russel's paradox: "Let R be the set of all sets that are not members of themselves." If R is not a member of itself, then the definition dictates it must contain itself, and so on. Paradoxes are a huge part of mathematical logic and they are pretty rigorously defined (as are most things in mathematical logic).
Now, outside of mathematical logic, then you get into the usage of paradox as an "unintuitive result", which is fine. My problem with the Banach-Tarski paradox is that is a problem INSIDE of mathematical logic (specifically set theory), so it's odd for them to call it a paradox when that term has a rigorous definition inside of mathematical logic.
[deleted] · 1 points · Posted at 15:27:42 on February 15, 2016 · (Permalink)
I only know Zeno's paradox(the one with the tortoise) in calculus and the birthday paradox in stochastics, and both aren't contradictory. I don't know about mathematical logic though.
lambdaknight · 2 points · Posted at 20:33:47 on February 15, 2016 · (Permalink)
Zeno's paradox is sort of iffy. The "paradox" there is that you shouldn't be able to reach the end point, but you obviously can. Now, Zeno didn't have the mathematical tools to discuss limits, so it was contradictory to him. To us, not so much.
Birthday paradox is straight up an unintuitive result.
[deleted] · 1 points · Posted at 23:53:14 on February 15, 2016 · (Permalink)
"The sphere can be divided into parts and reassembled into two copies of the original sphere" would be a false statement under elementary geometry, but becomes a true statement given higher level concepts like the axiom of choice.
It's a matter of English interpretation and what fundamental ideas one understands. The statement is false for all practical purposes, using everybody's grade-school definitions of "sphere, divide into parts" etc... So, for most people, it is an oddly true/false statement. i.e. a paradox. For mathematicians it's a matter of definitions and axioms.
I agree that technically it is most likely not a paradox, just a weird result that we don't yet know how to interpret.
lambdaknight · 1 points · Posted at 17:20:29 on February 16, 2016 · (Permalink)
What I'm fundamentally getting at is that in mathematical logic, the word "paradox" has a more strict meaning. Yeah, the Banach-Tarski paradox is a "paradox" in the common usage, but it isn't really a "paradox" in the mathematical logic usage and the Banach-Tarski paradox is fundamentally a result in mathematical logic, which is why it is weird.
PS: We know exactly how to interpret it; it's just intuitive. Just like it's easy to interpret the well-ordering principle being equivalent to the axiom of choice, but it is highly unintuitive.
[deleted] · 1 points · Posted at 16:20:27 on February 18, 2016 · (Permalink)
Of course. Though it's interesting to think about, in a philosophical sense, what it means for mathematics if the results are actually not applicable to reality.
lambdaknight · 1 points · Posted at 17:59:15 on February 18, 2016 · (Permalink)
Well, mathematics is a language and like any language, it can be used to describe impossible things. A good example is a non-intersecting Klein bottle is impossible in reality, but there are all sorts of mathematics describing such a beast.
In the case of the Banach-Tarski paradox, part of the decomposition relies on non-measurable sets, i.e. sets with an undefined volume, in order to get the two spheres. Things with undefined volume are not a realistic thing. In a sense, this is similar to those proofs that 1=2 that depend on dividing by zero at one step.
[deleted] · -4 points · Posted at 01:47:07 on February 14, 2016 · (Permalink)
Paradoxes make me think math is just a bunch of mumbo-jumbo.
popisfizzy · 3 points · Posted at 02:41:16 on February 14, 2016 · (Permalink)
It's not an actual paradox. A lot of times, a mathematical result is called a paradox if it contradicts intuition in a significant way. In the Banach-Tarski paradox, it seems that just doing rotations and translations should not affect the volume in the way it does. The flaw in intuition is that the sets one does these rotations and translations on can not have a volume assigned to it, which is a somewhat-surprising result.
[deleted] · 1 points · Posted at 23:57:17 on February 15, 2016 · (Permalink)
"The flaw in intuition is that the sets one does these rotations and translations on can not have a volume assigned to it"
That's less a flaw in intuition and more a flaw in description, would you say? Most people when presented the banach-tarski paradox are not thinking about infinite sets, they're thinking about a ball of play-dough and a knife. This is equivalent to changing the axioms of the system without informing the listener.
It's not mumbo jumbo because in all likelihood it'll turn out to be useful somewhere.
popisfizzy · 1 points · Posted at 10:07:57 on February 16, 2016 · (Permalink)
That's just misunderstanding mathematical terminology. A ball, in mathematics, is a particular type of infinite set satisfying some property. I don't believe I've ever heard someone who knows what they're talking about every imply in a serious manner that the Banach-Tarski theorem can apply to reality.
It essentially boils down to the fact that without having an understanding of the terminology and jargon of a field, you're bound to misinterpret what's said.
[deleted] · 1 points · Posted at 16:19:22 on February 18, 2016 · (Permalink)
Hence the "mumbo jumbo"
awyissmfbreadcrumb · 3 points · Posted at 03:15:59 on February 14, 2016 · (Permalink)
I feel like I understand it better every time I watch it again. Ive seen the video well over 10 times and I feel as if I have a pretty clear understanding of it.
releasethepr0n · 2 points · Posted at 03:58:03 on February 14, 2016 · (Permalink)
I felt sleepy watching it. Which made me feel dumb.
shennanigram · 2 points · Posted at 04:42:11 on February 14, 2016 · (Permalink)
I don't get it, isn't the paradox just saying infinity is still infinity when we add to it?
Patsastus · 1 points · Posted at 09:46:30 on February 14, 2016 · (Permalink)
I guess it's saying if you divide infinity into a finite number of disjoint infinite parts, you can make an exact equal of the original infinity by combining only some of the parts, because infinity. I got lost on how the countability of infinity mattered in any of the steps.
[deleted] · 1 points · Posted at 04:51:03 on February 14, 2016 · (Permalink)
I'm confused as to how this is different from Zeno's arrow paradox.
https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Arrow_paradox
DavidPastrnak · 1 points · Posted at 07:29:11 on February 14, 2016 · (Permalink)
I haven't watched the video, but from what other people have said, it seems like they might be covering a lot more detail than they need to for you to get the gist of what theorem is saying.
I wrote this for another comment in this thread:
It shows that it doesn't make sense to assign a volume to certain sets.
Suppose you said that every subset of 3-d space could be assigned a volume. Volume should satisfy a couple properites:
If you move a set around (rotate/translate) it should still have the same volume
If a set is broken up into smaller sets, then the volume of the whole set should be the sum of the volumes of the parts.
The theorem shows that this is impossible, because when you start with a ball of volume 1, you break it up into a finite number of parts whose volumes should add up to one. But now when you move those parts around, their volumes shouldn't change, so the total volume should still be 1. But when you put them back together, you now have two balls, whose total volume is 2. So 1=2.
The reason we get a contradiction is that we assumed we could assign a volume to any set we wanted in a consistent way, which turns out to be impossible. The point is that while it makes sense to assign a volume to the balls before they've been dismantled and after they've been put together, it doesn't make sense to assign a volume to the sets you break them up into.
I should add that there are other, easier theorems which also show that there are "nonmeasurable sets" (basically sets to which you can't assign a volume or length), but the Banach-Tarski paradox is especially compelling because you only need finitely many pieces and finitely many rotations/translations of the pieces.
Erekai · 1 points · Posted at 07:44:52 on February 14, 2016 · (Permalink)
Loved that video, but it completely blew my mind. Same with his recent deck of cards one, about 52! So crazy.
FrozenInferno · 1 points · Posted at 07:45:34 on February 14, 2016 · (Permalink)
I don't think he did a very good job of explaining it to be honest, which I'll just chalk up to the seeming complexity of the subject matter.
u56i67 · 0 points · Posted at 03:10:34 on February 14, 2016 · (Permalink)
Take a line from 0 to 1. It is one unit long. Take a line from 0 to 2. It is 2 units long.
Every single point on the line from 0 to 1 can be mapped to a unique point on the line from 0 to 2. To go from any point on line one (say, 0.514528) simply multiple it by two (to get 1.029056, for example) and 100% of the points in line 1 can be mapped to a unique point on line two. To go from any point on line 2 to a point on line 1, simply divide it by two. Now, if 100% of the points of line 1 can be mapped to a unique point on line 2 and 100% of the points on line 2 can be mapped to a unique point on line 1, it what sense is S1 = {number of points on line 1} different from S2 = {number of points on line 2}?
Despite line 2 being twice the length as line 1, we say that S1 and S2 have the same cardinality. There are an infinite number of points in each and both of those infinities are of the same "size." Or, less formally, this kind of infinity is still that same kind of infinity regardless of whether we multiply or divide by 2. Infinity*2 = infinity/2 = infinity.
You can do the same thing with 3-dimensional objects, you just need a more complicated function to map between the two, which is what that vsauce video took so long to develop. Note that this only works with mathematical objects. Real objects are finite(ish).
-Reddit_Account- · 327 points · Posted at 22:10:10 on February 13, 2016 · (Permalink)
This seems true, but it isn't appliable because we can't really cut infinitely complex objects, bacause åtomic theory.
[deleted] · 791 points · Posted at 01:24:33 on February 14, 2016 · (Permalink)*
[deleted]
LordoftheSynth · 183 points · Posted at 03:11:03 on February 14, 2016 · (Permalink)
I always end up with some extra quarks left over and I'm not sure why.
daphth · 19 points · Posted at 05:48:09 on February 14, 2016 · (Permalink)
That's quite strange.
LordoftheSynth · 15 points · Posted at 05:50:52 on February 14, 2016 · (Permalink)
Maybe I missed something on the top or bottom.
daphth · 11 points · Posted at 05:58:32 on February 14, 2016 · (Permalink)
Wait, I hadron for this...
LordoftheSynth · 10 points · Posted at 06:24:36 on February 14, 2016 · (Permalink)
What a charming pun.
ameya2693 · 2 points · Posted at 13:17:35 on February 14, 2016 · (Permalink)
The level of puns in this thread keeps going up.
ToxethOGrady · 2 points · Posted at 14:16:44 on February 14, 2016 · (Permalink)
are you calling me a boson?
Strangely_quarky · 1 points · Posted at 01:51:01 on May 15, 2016 · (Permalink)
hi
goatonastik · 1 points · Posted at 06:33:49 on February 14, 2016 · (Permalink)
You could say it's quite quarky.
JoXand · 3 points · Posted at 06:47:56 on February 14, 2016 · (Permalink)
They always give you extra in case you lose them.
Nerfi · 2 points · Posted at 13:39:36 on February 14, 2016 · (Permalink)
You can't lose them, if you need another one just put a pair in different rooms.
Gripey · 2 points · Posted at 10:25:07 on February 14, 2016 · (Permalink)
Uncertainty in a nutshell.
IamASynthCourser · 1 points · Posted at 06:11:50 on February 14, 2016 · (Permalink)
Greetings fellow "human".
CarcajouIS · 0 points · Posted at 07:16:57 on February 14, 2016 · (Permalink)
It's the spare parts. Don't lose them.
phobiac · 5 points · Posted at 03:12:31 on February 14, 2016 · (Permalink)
Nah, you've got to build with LIGO.
RandomPratt · 4 points · Posted at 05:34:35 on February 14, 2016 · (Permalink)
So... you're saying that by using åtomic theory, we can prove that the universe started out flat, but became a different shape altogether over time?
-Reddit_Account- · 2 points · Posted at 03:54:51 on February 14, 2016 · (Permalink)
It autocorrected, but your post in convincing me to keep it up.
[deleted] · 89 points · Posted at 02:00:19 on February 14, 2016 · (Permalink)
Just because something isn't applicable in physics doesn't make it useless in mathematics at all.
dontcareitsonlyreddi · -30 points · Posted at 05:40:25 on February 14, 2016 · (Permalink)
nobody said it wasn't shitbag
[deleted] · 25 points · Posted at 06:31:33 on February 14, 2016 · (Permalink)
You just called someone a shitbag over a discussion of the banach-tarski theorem. Consider getting a good nights' sleep, possibly while listening to some Rachmaninov on youtube
[deleted] · 10 points · Posted at 06:26:24 on February 14, 2016 · (Permalink)
Soluz · 1 points · Posted at 13:02:54 on February 14, 2016 · (Permalink)
Noone claimed it was useless.
ameya2693 · 0 points · Posted at 13:20:18 on February 14, 2016 · (Permalink)
Yet....well, technically, ever. But, we can cut them infinitely small enough to be able to map the object, in which case, replication is possible. It's impractical as fuck to do it with complex objects, but not impossible. Just need to have the computing capability to map all the points uniquely and tag them and categorise them and, then, replicate it.
DavidPastrnak · 5 points · Posted at 07:16:36 on February 14, 2016 · (Permalink)
Even if balls were made of some abstract, continuous fluid instead of atoms, it would be impossible to physically apply the theorem because it depends on the axiom of choice. It is impossible even to concretely describe which points are in which set.
The point of the theorem is not that you could physically do this, but that there are certain types of sets for which it is impossible to assign a volume in a coherent way. But that doesn't sound as interesting to most people.
SirSoliloquy · 2 points · Posted at 08:12:00 on February 14, 2016 · (Permalink)
I'm glad I read this, because I could never figure out why in the world such an obviously-never-applicable claim about the ball could be at all useful.
Now that I know it doesn't actually have anything to do with the theoretical ability to duplicate theoretical objects, it finally makes sense why anyone would care.
Consequence6 · 1 points · Posted at 08:41:41 on February 14, 2016 · (Permalink)
Also: There are some scientists who think this actually happens when smashing subatomic particles together. Sometimes you end up with more particles than you start with, this is one proposed reason as to why.
DISCLAIMER: I know nothing about this, i just watched the Vsauce video posted above.
MrRandomSuperhero · 22 points · Posted at 23:53:05 on February 13, 2016 · (Permalink)
I feel like that is the copout of the theory.
It splits everything down infinitely, then postulates that because the gaps after the split are infini-small they can be filled without loss of data or without being unmathematical.
It is true, but if you handle things like that you can dublicate anything once you split it down infini-small.
mongoosefist · 29 points · Posted at 00:27:32 on February 14, 2016 · (Permalink)
Well it's a little more complex than that and deals with some rather specific definitions, but basically it holds for any manifold I believe. The property of manifolds are what makes it possible, and its quite easy to find counter examples where Banach Tarsky doesn't work
Coequalizer · 8 points · Posted at 03:23:41 on February 14, 2016 · (Permalink)
It's possible because of set theory and the existence of non-measurable sets.
dregaus · 2 points · Posted at 10:09:29 on February 14, 2016 · (Permalink)
None of this makes any sense to me, but it's turning me on in a weird way.
ClintonCanCount · 6 points · Posted at 03:27:31 on February 14, 2016 · (Permalink)
One can interpret Banach-Tarski as a statement about the importance of Measurable Sets; that is, you have to be careful how you cut if you want things to reassemble cleanly.
21stGun · 2 points · Posted at 23:47:40 on February 13, 2016 · (Permalink)
Yeah, but is universe infinite?
[deleted] · -6 points · Posted at 01:51:30 on February 14, 2016 · (Permalink)
[deleted]
UScossie · 8 points · Posted at 02:41:36 on February 14, 2016 · (Permalink)
The Planck length doesn't technically define the minimum finite distance possible in the universe, if it did we would observe the universe as being pixilated or granulated, which experimentally we have been unable to do, and instead what we see is a universe that is continuous. The Planck length minimum is a side effect of the uncertainty principle which mathematically creates a black hole with a schwarzchild radius of a Planck length when trying to observe anything on that small of a scale, and the more you try to "zoom in" the larger the black hole becomes. So basically a Planck length is the theoretical limit on observation, but not the minimum distance across which action can take place (the propagation of a photon for example).
Adm_Chookington · 5 points · Posted at 03:31:25 on February 14, 2016 · (Permalink)
This is a completely incorrect misunderstanding of what the Planck length is.
EnoCrux · 1 points · Posted at 04:59:53 on February 14, 2016 · (Permalink)
What about string theory?
tadair919 · 1 points · Posted at 08:30:27 on February 14, 2016 · (Permalink)
Think waves vibrating at lower and lower frequencies. You can never find the lowest energy frequency.
mjbat7 · 1 points · Posted at 12:39:37 on February 14, 2016 · (Permalink)
If only there were some shady sub-atomic particles we could scratch up
-Reddit_Account- · 1 points · Posted at 12:59:42 on February 14, 2016 · (Permalink)
While they might be solid objects, you would still need an infinitely fine cut and an (uncountable) infinite amount of time to define every point on it's surface.
fknprob · 1 points · Posted at 13:39:48 on February 14, 2016 · (Permalink)
well, it actually is.
that fact is quite important in understanding measure and probability theory. and i assume you know that probability theory is very much applicable.
-Reddit_Account- · 1 points · Posted at 13:53:22 on February 14, 2016 · (Permalink)
Yeas, of course.
I miss worded my comment a bit; I meant I don't think you can apply on a physical object in a physical environment.
Teblefer · 1 points · Posted at 16:55:09 on February 14, 2016 · (Permalink)
If the universe is truly continuous, then it is completely applicable, just not in atomic chunks.
skysurf3000 · 14 points · Posted at 23:52:55 on February 13, 2016 · (Permalink)
I would like to add that the process of separating the ball into two is only made by rotations of the subsets. (Otherwise this is just saying something about cardinality)
ngwoo · 13 points · Posted at 00:28:42 on February 14, 2016 · (Permalink)
But if the ball is hairy they'll both have cowlicks
theyeshman · 0 points · Posted at 02:53:23 on February 14, 2016 · (Permalink)
So meta.
ngwoo · 1 points · Posted at 03:23:34 on February 14, 2016 · (Permalink)
Mathemeta
theyeshman · 1 points · Posted at 03:38:19 on February 14, 2016 · (Permalink)
*Mathemetacs
FTFY
aol_cd · 11 points · Posted at 21:26:22 on February 13, 2016 · (Permalink)
I was under the impression that it could any object of the right sort of complexity.
[deleted] · 5 points · Posted at 22:30:51 on February 13, 2016 · (Permalink)*
[deleted]
overconvergent · 7 points · Posted at 02:50:57 on February 14, 2016 · (Permalink)
No, Banach-Tarski does not hold in R or R2.
175gr · 1 points · Posted at 22:12:07 on February 13, 2016 · (Permalink)
I imagine if you can map it to a ball in a reversible way, you can do that, double the ball, and then reverse the process for each ball.
[deleted] · 7 points · Posted at 23:40:50 on February 13, 2016 · (Permalink)
This relies on the axiom of choice.
fiat_sux2 · 1 points · Posted at 05:35:16 on February 14, 2016 · (Permalink)
This should be higher!
And note for non-mathematicians. The axiom of choice is not necessarily true, so neither is the Banach–Tarski paradox.
almightySapling · 4 points · Posted at 06:22:32 on February 14, 2016 · (Permalink)
No axiom is "necessarily" true. In a more serious mathematical discussion, your comment would be fine, but I feel like in a thread like this, people will just read your comment and think "oh, so it's not really true" and dismiss it outright.
The important thing to note is that BT follows from choice, and pretty much all analysis is done with choice.
fiat_sux2 · 1 points · Posted at 19:28:43 on February 17, 2016 · (Permalink)
Bollocks. No layman would dispute the Peano axioms. The axiom of choice is only even understandable to hardcore mathematicians, so don't even bother asking a layman if he thinks it's true or not. But more often than not, if you explain the implications (for example, the Banach–Tarski paradox), this will be consider by said layman as evidence against the Axiom of Choice.
Which is appropriate.
That doesn't make it a "fact".
almightySapling · 1 points · Posted at 22:47:15 on February 17, 2016 · (Permalink)
If they could be proven true, they wouldn't be axioms. We made them axioms strictly because we are so damn sure of their "truth". That doesn't make them necessarily true, and there are quite a number of mathematicians that reject PMI (an extreme minority, but they do exist).
It's not about whether you "think" something is true. Mathematically speaking, it is consistent with the other axioms that pretty much everyone thinks should hold, and we use it to do a lot of math. In particular...
the field of mathematics in which the entire statement of BT is formulated assumed Choice as a default. In this realm, it absolutely is a fact. It's not an opinion, or a hypothesis, or a conjecture. It's a theorem.
fiat_sux2 · 1 points · Posted at 23:24:01 on February 17, 2016 · (Permalink)
You're missing the point. A "mathematical fact" is something that every reasonable person can agree fits with their reality. The Peano axioms do meet that criterion, the axiom of choice does not. If you want to be pedantic about things, nothing is true, but honestly, that's a nihilist view.
Or more precisely, you could say, "Given the Peano axioms (which basically every reasonable person agrees with), the following are mathematical facts.., and if you further accept the axiom of choice (which many academics agree with, but basically no one else), then this clearly absurd ridiculous thing is also true..."
But if you start citing the Peano axioms as the context in which you are replying to this post, people are going to wonder why you bothered because basically no one disputes them. If you do the same for axiom of choice then it will be seen as a useful clarification.
almightySapling · 1 points · Posted at 23:55:13 on February 17, 2016 · (Permalink)
Well for starters, the Peano Axioms are not the ones being discussed. The Zermelo-Frankel axioms of set theory are.
And if you want to define "mathematical facts" to be those things that "every reasonable person agrees with" then you suddenly have bullshit like 0.99... not equal to 1. Fortunately, your definition of fact is not the standard.
A mathematical fact is something that has been proven from mathematical axioms. It is a fact that the Banach-Tarski paradox follows from the axioms of ZFC, which many people (that is, most current mathenaticians) agree with.
Also, you keep using phrasing that suggests the axioms are "debated" in some philosophical sense (which ones are true, which are false). While that certainly does happen in some areas, and while it may be the case that most mathematicians have some sense of which axioms they personally agree with, it is not a mathematical question to ask "is choice 'true'?" All that matters is that it is independent from, and equiconsistent with, ZF. In some areas, Choice is useful or "obvious" and in those areas it is taken as true. In other areas, it isn't.
And in the area of (set-theoretic) geometry, the context in which Banach-Tarksi is stated, Choice is assumed. To say Banach-Tarksi is not a fact is the mathematical equivalent to a straw man: you have changed the terms and assumptions to make your argument true, but you are no longer working in the context as the people you are saying are wrong.
Rabid_Lemming · 3 points · Posted at 02:18:03 on February 14, 2016 · (Permalink)
Happy Valentine's Day!
http://www.lukesurl.com/archives/comic/380-picking-up-the-pieces
[deleted] · 2 points · Posted at 02:52:48 on February 14, 2016 · (Permalink)
I was thinking of this earlier today, remembering seeing it at least a year ago. Then I saw OPs comment and was weirded out because I had just looked up the comic. And then I saw you post it... it's a weird day.
trump_did_nineeleven · 2 points · Posted at 23:23:33 on February 13, 2016 · (Permalink)
Link: https://youtu.be/s86-Z-CbaHA
ahmadsarvmeily · 3 points · Posted at 21:45:07 on February 13, 2016 · (Permalink)
I thought this didn't work because 1D points can't make up a 3D object, since they lack dy and dz components?
MegaGoomy · 2 points · Posted at 00:07:03 on February 14, 2016 · (Permalink)
Maybe I'm just stupid, but to me this seems like infinity/x=infinity
Miserable_Fuck · 4 points · Posted at 01:52:14 on February 14, 2016 · (Permalink)
More like xfinity=shit
attomsk · 0 points · Posted at 01:59:16 on February 14, 2016 · (Permalink)
Yeah I was just thinking the same. Isn't this just another property of infinite sets?
overconvergent · 3 points · Posted at 02:53:34 on February 14, 2016 · (Permalink)
No, this is something more complicated. This is not just saying that a ball and two balls have the same cardinality as sets. The pieces the ball is cut into are not stretched or distorted in any way when reconstructing the two balls - they are only rotated.
ranaadnanm · 1 points · Posted at 01:51:47 on February 14, 2016 · (Permalink)
I have read about it before that it's not a paradox in itself since it is a proven fact but I may be wrong. Would you be able to provide an explanation for the layman, preferably with colourful illustration and diagrams?
Edit: Got my explanation in one of the links below.
[deleted] · 1 points · Posted at 02:27:38 on February 14, 2016 · (Permalink)
Vsauce did an interesting video that further explains this paradox.
southbayrider2 · 1 points · Posted at 02:42:17 on February 14, 2016 · (Permalink)
I googled this before, insane
workethicsFTW · 1 points · Posted at 03:01:55 on February 14, 2016 · (Permalink)
This is something similar - (http://m.youtube.com/watch?v=dmBsPgPu0Wc)
[deleted] · 1 points · Posted at 03:27:21 on February 14, 2016 · (Permalink)
Didn't the guy who figured this out get like a million dollars or was that something else
ReuBQ · 1 points · Posted at 03:40:26 on February 14, 2016 · (Permalink)
VSAUCE!
[deleted] · 1 points · Posted at 03:46:05 on February 14, 2016 · (Permalink)
I always knew there would be something I would learn about that is a mathematic or scientific fact that my brain is just not ready for. Thank you for confirming.
drkitteh · 1 points · Posted at 03:55:35 on February 14, 2016 · (Permalink)
Wouldn't that violate conservation of matter?
iamonthatloud · 1 points · Posted at 04:18:08 on February 14, 2016 · (Permalink)
ELi5:?
KnowledgeGreaterThan · 1 points · Posted at 04:27:06 on February 14, 2016 · (Permalink)
Here's a really cool v-sauce video that explains exactly what you're talking about.
UniformCompletion · 1 points · Posted at 04:43:59 on February 14, 2016 · (Permalink)
Not to be a party pooper, but I think this result should be stated more modestly: there exists a decomposition of the set of points of the unit ball, and rotations+translations of these pieces, that produces the set of points of two disjoint unit balls.
I phrase it this way because I don't believe that there is any definition of a decomposition, that is compatible with any of the usual geometric structure we usually associate with the unit ball (metric, topology, measure, etc.), that is also compatible with Banach-Tarski.
In my opinion, Banach-Tarski, while fascinating, is really a theorem about the bad behavior of the operation take the points, and only the points.
For example, a 2011 paper of Alex Simpson has argued that Banach-Tarski fails when we acknowledge that sets of points come equipped with certain topological information (specifically, they should be treated as something called a sublocale).
Imperium_Dragon · 1 points · Posted at 05:03:38 on February 14, 2016 · (Permalink)
Um, what?
Lightfail · 1 points · Posted at 05:25:23 on February 14, 2016 · (Permalink)
ELI5?
ammoprofit · 1 points · Posted at 05:43:44 on February 14, 2016 · (Permalink)
Watched this explanation on YouTube and it was hilarious. Just shows how screwy our perception of the universe really is.
penis_in_my_hand · 1 points · Posted at 05:53:01 on February 14, 2016 · (Permalink)
dafuq
NotInVan · 1 points · Posted at 05:55:20 on February 14, 2016 · (Permalink)
...Assuming you take the Axiom of Choice.
[deleted] · 1 points · Posted at 06:01:44 on February 14, 2016 · (Permalink)
This covers it. Thanks Vsauce.
http://youtu.be/s86-Z-CbaHA
websnarf · 1 points · Posted at 06:51:40 on February 14, 2016 · (Permalink)
Assuming the axiom of choice, of course.
shadowlightfox · 1 points · Posted at 07:00:16 on February 14, 2016 · (Permalink)
I, too, watch vsauce.
factsbotherme · 1 points · Posted at 07:06:17 on February 14, 2016 · (Permalink)
Saw this done with a chocolate bar
-Goonzilla- · 1 points · Posted at 07:11:16 on February 14, 2016 · (Permalink)
What amazes me specifically about the this paradox is that it mathematically proves it is possible, but we cannot mathematically or scientifically prove that it is possible (or that it could happen). It's literally questioning the boundaries of nature. I just learned about it today so it's very cool to see this post!
MrLime11 · 1 points · Posted at 08:26:02 on February 14, 2016 · (Permalink)
I think Vsauce did a video with this paradox being explained in it.
usurp_slurp · 1 points · Posted at 09:07:49 on February 14, 2016 · (Permalink)
Is this the mathematics behind the cause of the global financial crisis?
GregoryGoose · 1 points · Posted at 09:36:18 on February 14, 2016 · (Permalink)
I don't think that actually applies to real world objects. It's just a mathematical proof that infinity divided by 2 equals infinity times two.
romulusnr · 1 points · Posted at 09:40:12 on February 14, 2016 · (Permalink)
Some math is just made up to allow for impossibilities to be possible. I could say it's possible for me to become a billionaire without working, by inventing a conceptual imaginary universe in which a billion dollars is not made of money and where work isn't really work but simply an exertion of energy and then thus prove that I can be a billionaire without working. But that shit don't have any bearing on anything real.
[deleted] · 1 points · Posted at 11:11:09 on February 14, 2016 · (Permalink)
Oh I wish I could believe or understand that!
itisike · 1 points · Posted at 12:16:46 on February 14, 2016 · (Permalink)
Only if you accept the axiom of choice.
random314 · 1 points · Posted at 14:53:55 on February 14, 2016 · (Permalink)
I put that in Google translate and it seems to have trouble translating it to English.
iNinjaNic · 1 points · Posted at 15:36:44 on February 14, 2016 · (Permalink)
There is a thing called the Axiom of Choice. It is one of the fundamental "rules" for maths. Some mathematicians do not like this Axiom because they think it is too "powerful". They often point to this paradox as an example!
sotek2345 · 1 points · Posted at 17:45:59 on February 14, 2016 · (Permalink)
Good math trick, but I would love to see them try to do it in a machine shop. She conservation of energy might have something to say about that.
aaronod · 1 points · Posted at 01:09:26 on February 14, 2016 · (Permalink)
I am a total maths dunce but would this have anything to do with quantum particles supposedly appearing to be in two places at the same time? Or am I way off?
That_One_Dood · 1 points · Posted at 02:01:13 on February 14, 2016 · (Permalink)
I'm pretty sure this has no real world application and is just mental gymnastics BUT IANAM.
[deleted] · 1 points · Posted at 03:07:54 on February 14, 2016 · (Permalink)*
[deleted]
UniformCompletion · 2 points · Posted at 04:32:06 on February 14, 2016 · (Permalink)
No. The (finitely many) pieces are rearranged using translations and rotations in space, not arbitrary set maps. This is a much deeper result.
[deleted] · 1 points · Posted at 12:47:29 on February 14, 2016 · (Permalink)*
[deleted]
UniformCompletion · 1 points · Posted at 17:27:17 on February 14, 2016 · (Permalink)
DavidPastrnak · 2 points · Posted at 07:07:06 on February 14, 2016 · (Permalink)
It's way more than that. It shows that it doesn't make sense to assign a volume to certain sets.
Suppose you said that every subset of 3-d space could be assigned a volume. Volume should satisfy a couple properites:
If you move a set around (rotate/translate) it should still have the same volume
If a set is broken up into smaller sets, then the volume of the total set should be the sum of the volumes of the parts.
The theorem shows that this is impossible, because when you start with a ball of volume 1, you break it up into a finite number of parts whose volumes should add up to one. But now when you move those parts around, their volumes shouldn't change, so the total volume should still be 1. But when you put them back together, you now have two balls, whose total volume is 2. So 1=2.
The reason we get a contradiction is that we assumed we could assign a volume to any set we wanted in a consistent way, which turns out to be impossible. The point is that while it makes sense to assign a volume to the balls before they've been dismantled and after they've been put together, it doesn't make sense to assign a volume to the sets you break them up into.
[deleted] · 0 points · Posted at 12:46:29 on February 14, 2016 · (Permalink)*
[deleted]
buenotaco55 · 1 points · Posted at 14:26:45 on February 14, 2016 · (Permalink)
he means a finite number of parts. this isn't a statement about cardinality--its a statement about measure.
DavidPastrnak · 1 points · Posted at 16:31:44 on February 14, 2016 · (Permalink)
I meant finite number of parts. The issue here is not cardinality, which is the idea of sets have the same "number of elements." You can show that by assigning to each element of one set an element in another set. It is relatively trivial to show one ball of points has the same cardinality as two balls of points; you could ask an undergraduate math major to do it for homework.
The idea of the B-T theorem is that you are trying to come up with an idea of "volume" for sets of points in 3-d space. This is supposed to measure not "how many points are there," but "how much space does this set of points take up". This works for some sets, but if you try to do it for all possible sets in 3-d space, then you get a contradiction.
ManualNarwhal · 0 points · Posted at 02:03:49 on February 14, 2016 · (Permalink)
Paradox solved: Any such process would require an infinite amount of energy. An infinite amount of energy would have nowhere to go/be transferred to/produce no work. Therefore there is no possibility of Banahch-Tarski existing in our world.
stratdog25 · 0 points · Posted at 02:31:47 on February 14, 2016 · (Permalink)
Awesome!! I came here for Banach Tarski. I recently asked a math professor for the 10 second definition: if a sphere is comprised of 2000 points but is defined by 1000 points, you could theoretically decompose the sphere and rebuild it as two spheres defined by 1000 points.
OsrsNeedsF2P · -1 points · Posted at 02:57:14 on February 14, 2016 · (Permalink)
No. That's wrong.
Munninnu · 1518 points · Posted at 19:36:23 on February 13, 2016 · (Permalink)*
How big is the number of possible permutations when shuffling a 52 cards deck.
Specifically the example to give us the faintest perception of how ridiculously big 52 Factorial is.
EDIT: u/LotharWilhelm reported that this video gives us a visualization of what Scott Czepiel wrote in the original link I gave. It starts at 14:00 though.
EDIT II: In this video posted by another redditor the guy uses a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
EmpireOfTheTsun · 968 points · Posted at 23:16:03 on February 13, 2016 · (Permalink)
If you shuffle a standard 52 card deck, there's a very real chance that nobody in the history of the world has ever created such a combination of cards.
MattGeddon · 436 points · Posted at 23:41:07 on February 13, 2016 · (Permalink)
That's true an it absolutely blows my mind when you consider the amount of of hands of online poker, blackjack etc. are played every day
ulyssessword · 438 points · Posted at 03:29:48 on February 14, 2016 · (Permalink)*
Fun fact #2: computer card games require special, stronger randomization. Most "random numbers" in a computer are one of 232 specific numbers (between 00000000000000000000000000000000 and 11111111111111111111111111111111) that are chosen randomly. This is about 4 billion different ways the cards can be mixed, which means that 99.9999999999999999999999999999999999999999999999999999999999% of all possible card orders will never be seen in a poorly coded card game.
(Gambling websites have figured this out, and they do a good job of randomizing now.)
EDIT: That means that if you could see six cards and know which order they were in, you would have a very, very good chance of being able to figure out the rest of the deck.
2074red2074 · 66 points · Posted at 03:53:16 on February 14, 2016 · (Permalink)
Wouldn't it be a lot better to simply randomly select each card as it appears?
ulyssessword · 54 points · Posted at 04:48:48 on February 14, 2016 · (Permalink)
There would need to be some extra chaos thrown in for that to be useful. Computers are completely deterministic, and will come up with the same results given the same inputs.
In a bad card shuffling algorithm, the inputs are "one of 232 numbers, selected randomly" and the shuffling algorithm. It doesn't matter if that same random number is used in multiple places in the code, the inputs are the same so the outcome would be the same too.
In contrast, in a good card shuffling algorithm, the inputs are something like "one of 2256 numbers, selected randomly" and the shuffling algorithm.
blaziken311 · 14 points · Posted at 05:59:12 on February 14, 2016 · (Permalink)
Why not request entropy from the user in the form of keyboard mashing to shuffle the cards? I remember this kind of entropy is necessary to set up a key ring in arch Linux or something along those lines.
[deleted] · 47 points · Posted at 06:46:48 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 5 points · Posted at 07:12:27 on February 14, 2016 · (Permalink)*
[deleted]
christian-mann · 29 points · Posted at 07:31:54 on February 14, 2016 · (Permalink)
Actually for really secure shit they tend to use atmospheric noise and Geiger counters.
ProfessorPaynus · 8 points · Posted at 07:42:28 on February 14, 2016 · (Permalink)
Mine's in the shop
christian-mann · 2 points · Posted at 07:32:51 on February 14, 2016 · (Permalink)
But keyboards, network I/o times, disk read times, etc. are all good sources of entropy.
[deleted] · 1 points · Posted at 09:01:14 on February 14, 2016 · (Permalink)
Nu uh
[deleted] · 1 points · Posted at 14:50:34 on February 14, 2016 · (Permalink)
Ive also heard images of lava make really great strong entropy
blueandroid · 8 points · Posted at 09:51:53 on February 14, 2016 · (Permalink)
There's a bit of a counterintuitive problem when hashing "good" randomness together with other inputs, especially those provided by an attacker, and even more so if they'll have an opportunity to observe, or make a guess at, the "good" random number when providing their input. Say one random number generator is seeded by the system clock only, and another is seeded by the system clock hashed with a number I provide. To attack the first, I need to guess the exact system time. To attack the second, I can choose my input in a way that attacks a whole range of possible system times. All I have to do is take the range of likely system times, run the hashing algorithm against every number in that range myself using as many various inputs as I have time to try until I find an input that results in low entropy. Even simpler example. Imagine we need a random number from 1-100, and we have a hashing algorithm which, say, multiplies numbers together, then discards all but the two least significant digits, and adds 1. You have two fair 10-sided dice you can use to get a number from 1-100. You can either use just your dice alone, or you can use your dice and the hashing algorithm with another input that I provide. If I also roll fair dice, the output will look pretty random, but if I'm malicious and just put in 100 every time, the algorithm will cause the "random" number to always be 1. This is obviously a very weak example just for the sake of illustration. The upshot is that allowing an attacker who knows (or can guess at) your hashing algorithm to control any of its inputs lets them erode your entropy, and hashing can not add entropy. Usually hashing destroys entropy, and the more complex your hashing algorithm, the more likely it will throw out a bunch of entropy by accident. This is why many people in the crypto community advocate just reading raw bytes off of /dev/urandom for random numbers. Doing randomness in user space is almost always buggy and is frequently attackable.
tyrico · 12 points · Posted at 09:20:48 on February 14, 2016 · (Permalink)
Pokerstars uses user input AND quantum randomness as entropy sources for their shuffle:
https://www.pokerstars.com/poker/room/features/security/
TheNightCaptain · 10 points · Posted at 08:17:04 on February 14, 2016 · (Permalink)
Could you not have a deck and randomly select a number between 1 and 52 from the order of the current deck to form the first card of the new deck then 1-51 for the next card for the 2nd card of the new deck and so on?
meneldal2 · 1 points · Posted at 02:51:43 on February 15, 2016 · (Permalink)
The problem is not the shuffling algorithm, it's how you generate the randomness in the first place. If you use many common methods, you can guess the state of the generator with a few values of the output and then no matter what shuffling algorithm you're using it won't help.
Good random numbers generators have a huge amount of different states which makes inferring them from some data too hard (if you need to see 30+ cards, it's probably not very useful) and with no way to predict their initial value.
2074red2074 · 11 points · Posted at 04:57:18 on February 14, 2016 · (Permalink)
You haven't answered my question. You've just explained why it's better to have a good randomization algorithm, which is what I'd call a "no shitter"
Why is it better to determine the order of all 52 cards at once, rather than randomly selecting one card from the pool of remaining cards every time a card is revealed?
__kojeve · 28 points · Posted at 05:00:15 on February 14, 2016 · (Permalink)
When he says:
What he means is that there's no such thing as "randomly selecting" to a computer. Selecting them one at a time will never be any more random than computing the entire deck because there's no randomness involved.
2074red2074 · 3 points · Posted at 05:07:46 on February 14, 2016 · (Permalink)
My original point was that that would allow any theoretical deck arrangement to exist.
However, if the randomization seed was determined by a nearly random method, such as a very specific measurement of how long an action takes to reach the server, wouldn't that allow true randomization?
dJe781 · 29 points · Posted at 05:14:59 on February 14, 2016 · (Permalink)
True randomness cannot be achieved because <what he said>.
For real.
Ripred019 · 1 points · Posted at 13:59:12 on February 14, 2016 · (Permalink)
That's not true. True randomization can't be programmed as of now. There are such things as hardware random number generator which rely on circuit noise. There's also random.org which uses atmospheric noise, I think. That allows for "true randomness" until someone figures out how to perfectly model both of those phenomena.
18scsc · 1 points · Posted at 21:02:18 on February 19, 2016 · (Permalink)
I'm no physics major, but I think this site gives true random numbers. It measures the timing of radioactive decay and uses that as seed.
http://www.fourmilab.ch/hotbits/
2074red2074 · 0 points · Posted at 05:17:44 on February 14, 2016 · (Permalink)
So if they determined the seed based on a measurement (in nanoseconds) of how long it took the user to submit an action to the server, there would be some way to predict that? Because there's shit like wind patterns, rainfall, etc. that effect how long that measurement would be.
__kojeve · 7 points · Posted at 05:28:12 on February 14, 2016 · (Permalink)
The amount of time a signal takes is not random either. It may or may not be a good seed, but it doesn't solve the problem of determinism.
Look at it this way, throwing the cards in the air is also deterministic, it's just that the number of inputs are invariably more complicated than any computer such that the pseudo-randomness generated by the individual movement of the cards over a body of air is functionally indistinguishable from true randomness. That doesn't mean that it is truly random, however.
2074red2074 · 1 points · Posted at 05:36:18 on February 14, 2016 · (Permalink)
But what I'm saying is that it would be as random as you can get without bringing a Geiger counter into it.
Gripey · 3 points · Posted at 10:29:31 on February 14, 2016 · (Permalink)
Randomness for computers is a really hard problem. just saying.
distactedOne · 2 points · Posted at 07:33:51 on February 14, 2016 · (Permalink)
Because if you don't add in any extra source of randomness, these aren't actually different things.
An RNG with only 232 states, by itself, can only produce 232 outcomes, no matter whether it produces the deck all at once or one card at a time.
2074red2074 · 1 points · Posted at 07:34:27 on February 14, 2016 · (Permalink)
I was assuming that a new seed would be used for each card.
aezart · 0 points · Posted at 07:46:10 on February 14, 2016 · (Permalink)
That's actually less random. Generally, an RNG should only be seeded once per program execution.
2074red2074 · 1 points · Posted at 08:29:52 on February 14, 2016 · (Permalink)
The seed itself would need to be randomized for each card, ideally through a "true" randomization process like ping times. Then it would be truly random, but have 52! permutations from only 52 seeds.
[deleted] · 0 points · Posted at 23:22:52 on February 14, 2016 · (Permalink)
False assumption that ping times are random. They run off other computer hardware, emitting packets only on some multiple of their clock or the network fabric (ie 100mb).
2074red2074 · 0 points · Posted at 02:13:13 on February 15, 2016 · (Permalink)
Just because they have to be a multiple of something does not mean they aren't random. There are too many factors involved to predict what a ping time will be with certainty.
ulyssessword · 1 points · Posted at 05:08:15 on February 14, 2016 · (Permalink)
They are mathematically identical. Let's say that the random number is 3134212345 (converted to base 10 to be smaller).
You shuffle the 52 card deck in pattern 3134212345, draw the top card, then shuffle the 51 cards in pattern 3134212345 again, draw the top one, and repeat until you have drawn all 52 cards. Every time that 3134212345 is the random number and you use the re-shuffle algorithm, the draw order will be exactly the same.
Contrast that to shuffling once. You shuffle the 52 card deck in pattern 3134212345, draw the top card, then draw the new top card, and so on. This will be different than the results from the re-shuffle algorithm with 3134212345, but it will be identical to every other one-shuffle that is seeded with 3134212345.
2074red2074 · 4 points · Posted at 05:15:46 on February 14, 2016 · (Permalink)*
I was assuming that each card would be randomized using a different algorithm
EDIT seed. A different seed.
ulyssessword · 1 points · Posted at 05:26:56 on February 14, 2016 · (Permalink)
As long as it still uses the same seed, it would be the same outcome every time.
The 52card algorithm with seed 3134212345 would have a certain output. Removing the top card and plugging the new deck into the 51card algorithm with seed 3134212345 would then have its output. same with the 50card and the 49card and so on until the 2card algorithm.
If the inputs are the same, then the outputs are the same. Picking a new seed for each card would be difficult, as most computers don't have true (hardware) random number generators.
2074red2074 · 2 points · Posted at 05:37:06 on February 14, 2016 · (Permalink)
The client computer shouldn't be the one determining anything for online gambling.
wral · 1 points · Posted at 06:08:50 on February 14, 2016 · (Permalink)
you could just use some time as seed + something secret with no problem.
pandas_ok · 1 points · Posted at 09:17:24 on February 14, 2016 · (Permalink)
what? generate random numbers between 1 and 52 twice. mix and match. boom, shuffled. (card x goes to slot x_n for all x for all n)
tyrico · 1 points · Posted at 09:20:37 on February 14, 2016 · (Permalink)
Pokerstars uses user input AND quantum randomness as entropy sources for their shuffle:
https://www.pokerstars.com/poker/room/features/security/
themuffinking · 10 points · Posted at 06:09:21 on February 14, 2016 · (Permalink)*
Yes. The comment above yours isn't quite right. It's fine to output one 32-bit number at a time - because you're really only picking one of 52 cards, anyway - what matters is the internal state of your random number generator. Your generator's internal state completely determines its output.
If your random number generator only has 32 bits of internal state, then it can only be in 232 possible states - so it will start to repeat itself after only ~4 billion steps, in the best case. Even worse, that series of 4 billion outputs is the only one it can ever produce.
If you have a better pseudorandom number generator with 256 bits of internal state, then it can be in 2256 possible states. log(52!)/log(2) = 225.5810 is less than 256, so this would (potentially) be enough to make a good random shuffle algorithm that could potentially generate any deck.
Consider a random number generator with only one bit of internal state. Its output might look like this:
389421, 9351177, 389421, 9351177, 389421, 9351177,...
which would obviously make it hard to generate different decks of cards.
tl;dr For a much clearer explanation, see Wikipedia's article on PRNGs.
qevlarr · 5 points · Posted at 09:21:35 on February 14, 2016 · (Permalink)*
Computers use pseudo-random number generators with a truly random seed as input. Care must be taken with how many different possible seeds there are, relative to the number of possibilities you want to pick from using the PRNG. The seed being too short is only one of many pitfalls. Another would be using modulo arithmetic creating a bias to smaller outcomes (under certain conditions).
Grappindemen · 2 points · Posted at 08:07:44 on February 14, 2016 · (Permalink)*
Ignore the top reply. You're right. At least for texas hold'em poker, and other card games that do not use the entire deck.
With 10 players, there are 25 cards being drawn, for a total of 52!/27! combinations. Very significantly less combinations.
It's still better not to use the naive algorithm, as /u/ulyssessword points out. However, not completely permuting the deck at the start, but selecting one-by-one would improve the naive algorithm.
Note that the order of permutations of a whole deck exceeds 264 (e.g. a 64-bit seed), but for just 25 cards, the number of combinations is significantly smaller than 264. That means that, assuming you refresh your seed sufficiently often, 64 bits is enough for one-card-at-a-time, but not for shuffling the whole deck.
2074red2074 · 2 points · Posted at 08:28:27 on February 14, 2016 · (Permalink)
8 bits would actually be enough for one at a time, because the seed for the card is itself random, you only need 52 possible seeds, so 11111111 is enough.
Grappindemen · 2 points · Posted at 08:51:25 on February 14, 2016 · (Permalink)
No, unless you want to reseed between individual cards (which doesn't make sense).
Given a seed, e.g. 10011101, the sequence of random number drawn will be identical. So on 10011101, the first card is 8h, then 4c, then Ah, etc. Such a sequence exists for every seed. Since you have 256 sequences, on average, there's about 5 sequences that start with any arbitrary card. And, with two cards, you have almost certainly enough info to deduce the seed.
2074red2074 · 2 points · Posted at 09:26:40 on February 14, 2016 · (Permalink)
My whole point was that you would be reseeding between cards. Because each seed will always lead to the same sequence, 52! seeds must be possible to have the same amount of randomness as a shuffled deck of cards. If you have a true random component determine the seed for each card, then only 52 seeds are needed.
Grappindemen · 2 points · Posted at 09:45:39 on February 14, 2016 · (Permalink)
The problem is that the only proper seed uses external unpredictable data (e.g. hash of system time, hash of temperature readings, dedicated noise machines etc.) I'm not sure you can find a source of random data that fluctuates sufficiently fast to extract so many unique seeds. If you don't give the clock a chance to change, or the temperature readings a time to update, then the seed remains the same over multiple cards.
2074red2074 · 2 points · Posted at 10:23:37 on February 14, 2016 · (Permalink)
If you use, for example, the time in ticks between actions submitted to the server, it's totally random. Not client-side manipulation can account for variance in data reaching a satellite.
oliverbtiwst · 1 points · Posted at 06:22:59 on February 14, 2016 · (Permalink)
that is the same thing as having log(52!) bits of state, just spread out over a longer series of operations. (selecting 1/52 cards then 1/51 etc.)
2074red2074 · 0 points · Posted at 06:27:36 on February 14, 2016 · (Permalink)
Well if you know the randomization software, then you need 52! possible values for the seed for every theoretical arrangement to be possible. Instead, some truly random thing (Geiger counter, times for a ping,etc.) could determine a new seed for each card, so only at least 52 possible values need exist, or 000000-111111. Way less than 52!
I say determine it as each card comes up so you don't have to do this 52 times.
oliverbtiwst · 1 points · Posted at 06:37:52 on February 14, 2016 · (Permalink)
Of course you can encode the values from 0 to 52 in a small amount of bits and rewrite to that memory to change it... But when we talk about bit count we aren't talking about software memory used to run the algo, but the number of total bits to encode the problem size (from a mathematics perspective).
2074red2074 · -1 points · Posted at 06:53:25 on February 14, 2016 · (Permalink)
Having 52! possible seeds would require 256-bit processing.
a_persian · 0 points · Posted at 04:06:42 on February 14, 2016 · (Permalink)
No, because as the deck shrunk it would become less and less random.
2074red2074 · 2 points · Posted at 04:31:00 on February 14, 2016 · (Permalink)
How do you figure that?
yokhai · 2 points · Posted at 05:01:49 on February 14, 2016 · (Permalink)
He didn't mean to say would, he means to say should. You can't random a new card each time, because they are supposed to represent a physical deck. So you actually have to created 52 "objects" and shuffle them using a randomizer, or else you would create a virtual game that in no way resembles physical poker/blackjack
2074red2074 · 2 points · Posted at 05:04:58 on February 14, 2016 · (Permalink)
You can reduce the pool as it comes up. Pick one random card from the 52, then pick one from the remaining 51, then one from 50, etc.
yokhai · 1 points · Posted at 05:29:17 on February 14, 2016 · (Permalink)
Then you'd have 51 incrementally smaller shuffles instead of a single shuffle. That's computationally irresponsible.
2074red2074 · 1 points · Posted at 05:35:16 on February 14, 2016 · (Permalink)
But more random, because there are a (comparatively) low number of possible arrangements.
yokhai · 1 points · Posted at 05:38:47 on February 14, 2016 · (Permalink)
But would be reshuffling the deck after each deal, which is illegal in the rules of most card games. I forgot to mention that point.
2074red2074 · 2 points · Posted at 05:46:38 on February 14, 2016 · (Permalink)
That's to prevent cheating by the dealer. And technically, the deck was never truly shuffled and never even existed before each card was revealed. Kind of a false equivalency.
yokhai · -1 points · Posted at 05:49:28 on February 14, 2016 · (Permalink)
There are very strict rules in place to make sure the digital games do not operate with behavior that violate the rules of the physical game.
2074red2074 · 2 points · Posted at 05:51:25 on February 14, 2016 · (Permalink)
So how would this be addressed if there was never a deck or determined order of cards? Because technically the order of the cards never changed because it never even existed.
yokhai · 0 points · Posted at 05:59:03 on February 14, 2016 · (Permalink)
"Existed" is philosophical construct that shouldn't be used in this conversation. Electrons are real, so the representation of the cards are real. Trying to reduce the problem by saying "but they aren't even real" is rather pointless.
To answer the question you asked, a player would probably never notice, as far as they are concerned, they are getting random cards out of a pool of cards. It would have to be discovered on the shoulders of whatever regulating body performed inspections of the software companies. If they found out the algorithms were doing something "shady" there would be fines, probably.
But that's not the point. If I were running a gambling application, I wouldn't want to add an extra 50 shuffles into each game. That's a lot of computing power, especially having to re-seed each time. You are also diluting the value of your seeds, but I'm sure that point is probably mathematically irrelevant.
2074red2074 · 1 points · Posted at 06:04:39 on February 14, 2016 · (Permalink)
I'm not saying that the fact that there are no physical cards is the issue. I'm saying that there was never a deck to reshuffle. In card games, your options are shuffling the deck once or reshuffling. In online card games, there is a third option, which is randomly determining exactly one spot in the arrangement of the theoretical deck, which means that each card is shuffled once, and the order of cards can't be changed because the cards have no order.
What I'm saying is that it is entirely a philosophical debate whether or not this would even be considered reshuffling.
yokhai · 0 points · Posted at 06:15:15 on February 14, 2016 · (Permalink)
I don't think you understand data structures and how digital objects are stored in memory.
You can make a Graph of cards, that contain no explicit order, and randomly assign the order at your choosing, which is what I think you are referring to. Or you can created a List of cards, which have an explicit order, indexed at 0.
These algorithm use graph theory to do the shuffling once, which what another user was talking about when they mentioned "programmers are getting very good at this stuff", and then once the order of the deck is solve, the digital objects are arranged in a list, to be drawn from.
So think of taking a deck of cards, and spreading them all over the table, face down, and "shuffling" them by mixing them all up in pile, that's graph shuffling; difficult and clumsy for humans, very very efficient for computers. Then the pile is pulled together to form the deck. That's exactly what a computer does, but digitally, and its orders of magnitude faster than trying to digitally perform a riffle shuffle.
2074red2074 · 1 points · Posted at 06:22:26 on February 14, 2016 · (Permalink)
Neither of these are what I'm talking about. I mean you have a list of cards with an explicit order (organised by suit and the rank) and you remove one of them at random each time a card is revealed. So if you know the first fifty cards that were revealed, you still have no way of predicting which card will be next, even if you knew exactly how the software that determined the card worked. You would need to know both how a seed becomes a card and how that seed is determined, which ideally would also be random and based on something impossible to predict, like a Geiger counter or something.
This also means that the deck is never shuffled. At no point is there even a known order of the cards. There is no virtual order being stored anywhere.
yokhai · 1 points · Posted at 08:08:22 on February 14, 2016 · (Permalink)
Again, that would like pulling a random card from the middle of the deck and using it to play, which is against the rules of the physical game, so there are strict policies in place to insure that the software isn't doing that. They take a list of cards, shuffle that list, and pull one at a time off the top of the list.
The randomness in each game isn't the mathematical problem. I don't care how random the deck is in a single game. It's the randomness across ALL games, which is the point of the original commenter. So running your RNG 50x more than normal would severely dilute your seeds over millions of games, assuming you only have a 4 billion seed count. You'd actually reduce the fidelity of randomness across your games. But that whole point is mute. It doesn't change the game itself, it's only a comment about the uniquiness of the games played.
2074red2074 · 1 points · Posted at 08:26:25 on February 14, 2016 · (Permalink)
Oh, so you're running on the assumption that a seed is never used more than once. Well, considering that in this case every possible arrangement of cards can exist, that's more random.
Firehed · 1 points · Posted at 08:36:48 on February 14, 2016 · (Permalink)
Not necessarily, it's just shuffling by selecting one card at (cryptographically secure) random at a time.
e.g.
Then draw from the deck normally with
deck.pop()or similar.Technically you only need six bits of entropy per card in the deck (26 == 64 > 52) so depleting the system entropy pool is unlikely to be a problem. And it's only O(n), which (skimming SO) seems like it's on par with most shuffle implementations.
Could you do it in a more clever way? Almost certainly. But trying to get it down to O(log(n)) will likely obfuscate what's going on (bad for auditing crypto/security-related code), and you already know n is never going to be more than 52 for a one-deck game so the runtime practically doesn't matter anyway.
Disclaimer: I know enough crypto to know that this shouldn't be totally fucked up, and more importantly know enough about crypto to get work peer reviewed. I don't work for a gambling approval board or anything, so don't assume that example would pass any sort of audit.
rawling · 1 points · Posted at 08:23:05 on February 14, 2016 · (Permalink)
Picking one card at random at a time is the Fisher-Yates shuffle, which is the goto shuffling algorithm.
SirPseudonymous · 0 points · Posted at 05:38:21 on February 14, 2016 · (Permalink)
In most modern casinos, that's basically what blackjack is now, actually. They introduced autoshufflers that reshuffle cards back in right away and use high deck counts, in order to eliminate card counting (which revolves around knowing the ratio of high cards in the deck, which increase the likelihood of the dealer busting, and thus the likelihood of the player winning the hand on account of they can stop before 17+ in a hot deck while the dealer can't) and reduce the potential for dealer error/curtail any accusations that the dealer is cheating (but mostly it's a card counting countermeasure; people being aware of dynamically shifting odds in a casino game really pisses them off).
yokhai · 3 points · Posted at 05:42:25 on February 14, 2016 · (Permalink)
They don't reshuffle the deck in the middle of the game. They use high deck counts 8-12 decks shuffled together, then swap the shoe at 30% of the cards remaining.
If you see a casino reshuffling dealt cards back into the shoe, contact your local Games Board, they should be breaking most laws.
joshu · 9 points · Posted at 05:22:58 on February 14, 2016 · (Permalink)
I believe you are thinking about https://www.cigital.com/papers/download/developer_gambling.php - your explanation is not close to correct.
You are talking about stdlib's rand(), which is not "most." Anyone who cares about randomness is using something else. Which is all the crypto on your system, which is almost certainly your majority consumer of randomness.
ulyssessword · 4 points · Posted at 05:40:06 on February 14, 2016 · (Permalink)
Would this be better:
The standard implementation of a "random number" in a computer is one of 232 numbers, although the large majority of applications dependent on randomness use different standards that are more secure.
joshu · 5 points · Posted at 05:57:49 on February 14, 2016 · (Permalink)
not really. the shuffle problems were deeper than that: they used the current time as a seed (guessable and much, much smaller than 232) and didn't use yates-fisher shuffling.
Mosethyoth · 2 points · Posted at 10:16:36 on February 14, 2016 · (Permalink)
When I programmed a Black Jack my programm selected a random card then a random slot in the deck and assigned the card to it. It repeated this with with all remaining cards and empty slots until every card was in the deck.
I think that randomization should have allowed for completely random decks. The key wasn't to create a random value high enough to create a deck seed but to eliminate any possibility for a pattern to form by handling every single associaton as random as it is possible within the game's rules.
t014y · 1 points · Posted at 06:00:01 on February 14, 2016 · (Permalink)
What is the weaker method for shuffling cards in a computer? The only way I can think to do an algorithm based shuffle in the computer is to go though each card and randomly place it into a position in the new deck. This method should allow for any possibly because on the last step there will only be 52 positions the card could go into, well within the range of a standard random method.
Ex. Fist card taken will go into the only position avaliable in the new deck. Second card goes on top or on bottom. 3rd goes 1 of 3. And so on until the last card has 1 of 52 spots to go into.
If this is the weaker shuffle can you explain why?
I do understand that random is not really random but it seems your claim is that the weaker shuffle would be unable to configure the deck into most of the configurations. I'm trying to figure out what shuffling method you would use to have this problem, short of a static list of preconfigured decks that are randomly chosen from.
TimHallman · 1 points · Posted at 07:19:55 on February 14, 2016 · (Permalink)
The guy is confused and doesn't realize that the fisher-yates shuffle can give you all of those permutations despite using random numbers between 0 and max_int. One weaker shuffle would be to pick a random number between 1 and 52 for each of the 52 cards, instead of using fisher-yates.
t014y · 1 points · Posted at 07:31:09 on February 14, 2016 · (Permalink)
So going straight to 1 of 52 for fist card then 1 to 52 minus the last value and so on. That sounds harder to program but I still don't see why you wouldn't have the chance of getting every combination.
TimHallman · 1 points · Posted at 09:40:35 on February 14, 2016 · (Permalink)
It don't think it's 'minus the last value' - but I'm not sure I understand you. See this: http://www.i-programmer.info/programming/theory/2744-how-not-to-shuffle-the-kunth-fisher-yates-algorithm.html
t014y · 1 points · Posted at 23:10:13 on February 14, 2016 · (Permalink)
That is what I was looking for. Maybe it's just me but, even without the flaws mentioned in the article, the idea of shuffling this way is not intuitive. In general when I program I try and simulate the real life method. But I see the concern now.
TimHallman · 1 points · Posted at 07:15:33 on February 14, 2016 · (Permalink)
You only need a random number between 1 and 52, 52 times to do the fisher-yates shuffle. How do you think a poorly coded game would be coded so that all of those orders wouldn't be possible?
edit: Other than something like simply not shuffling the deck?
blackNstoned · 1 points · Posted at 08:52:10 on February 14, 2016 · (Permalink)
Can you explain why is it 232? I understand the digital signal is either 0 or 1 (binary) so thats 2 possibilities but what is 32? There ar 52 cards in a set a cards
Madagoscar · 1 points · Posted at 12:21:20 on February 14, 2016 · (Permalink)
Assume you can shuffle the deck of cards once per second. every Billion Years, take one step forward. Every time you complete a lap around the earth, take a drop of water out of the ocean. Every time you drain all the oceans, put a piece of paper on the ground. By the time the stack of paper reaches the sun, you'll have finished less than 1% of all possible shuffles.
Ltbsd · 1 points · Posted at 13:42:43 on February 14, 2016 · (Permalink)
I would just pick a random number between 1 and 52 for the top card, between 1 and 51 for the second card, etc.… then you don't need a special system for it.
Geminii27 · 1 points · Posted at 13:43:56 on February 14, 2016 · (Permalink)
Only if you used a single randomly generated number to determine the entire order of the pack. Instead, generate 51 random numbers and use each one to choose what the next card in the pack will be out of the unpicked cards.
(Yes, this assumes access to a source of sufficient randomness.)
Ripred019 · 1 points · Posted at 14:05:56 on February 14, 2016 · (Permalink)
Why not pick a random seed 32-bit int, shuffle the deck once. That's one of four billion options. Now pick a new random seed, shuffle again. Now it's ~1.6 x 1019. Keep doing this a few times and you're good. It would help tremendously if the order of the seeds made a difference i.e. if the first seed was 1 and the second seed was 4, you get a different deck than if the first seed was 4 and the second seed was 1. Isn't this basically what people do? We don't just shuffle a deck perfectly in one shuffle, we repeat our actions for a little while to get a good shuffle.
Unless of course the algorithms they use today achieve the same outcome, but are much more efficient.
chevymonza · 1 points · Posted at 14:28:11 on February 14, 2016 · (Permalink)
Decades ago, I learned of a mathematical formula that you could use as a card trick: Take a deck, divide into three piles, face down. Turn over the top cards on the first and third decks; plug the card numbers into the formula and you get the middle card.
Something like that. It's been so long I forget the details, but as a kid I was blown away.
InfieldTriple · 11 points · Posted at 03:13:26 on February 14, 2016 · (Permalink)
Well since non virtual decks are all arranged in a given fashion when you open the pack, some permutations are more likely.
dj0 · 9 points · Posted at 02:13:09 on February 14, 2016 · (Permalink)
I did the math on this one day and I got ridiculous numbers like if everyone that has ever lived made a deck every second for a billion years that would be like 0.00001% of all combinations
[deleted] · 24 points · Posted at 03:52:40 on February 14, 2016 · (Permalink)
52!/(number of people that ever lived)(number of seconds in a billion years)
8.07x1067/1.07x1011 x 3.15x1016 = 2.39x1040.
That's 27 orders of magnitude smaller than 52!. "0.00001%" is quite a bit off. Either remember to carry your 22 zeros next time or stop making shit up.
Schrodingers_cock · 6 points · Posted at 04:24:37 on February 14, 2016 · (Permalink)
Stephen Fry described it as a thousand suns, each with a thousand planets, each with a billion people, shuffling a thousand decks a second since the big bang would just now have started to repeat.
[deleted] · 1 points · Posted at 16:11:19 on February 14, 2016 · (Permalink)
I'm pretty sure too that a solitaire hand can be played in a second. Every card is in order with aces on top and so forth. Kinds at the bottom.
thuktun · 17 points · Posted at 01:51:28 on February 14, 2016 · (Permalink)
I think you mean permutation. Combination is order-independent, IIRC.
EmpireOfTheTsun · 1 points · Posted at 08:53:42 on February 14, 2016 · (Permalink)
Absolutely right, I even typed permutation before posting, but changed my mind because permutation is a pretty scary word to budding mathematicians who are interested in learning cool facts. I guess I should have had a little more faith! If people are interested, check out this simple page from one of the best sites for explaining mathematical concepts.
[deleted] · 1 points · Posted at 02:34:06 on February 14, 2016 · (Permalink)
[deleted]
felix_dro · 4 points · Posted at 03:29:33 on February 14, 2016 · (Permalink)
Every complete deck in the history of the world had had the same combination, almost certainly none have had the same permutation
Antithesys · 23 points · Posted at 02:19:29 on February 14, 2016 · (Permalink)
This is one of those things that is mathematically true but not necessarily practically true.
For instance, a new deck has the cards arranged a certain way that is common to all new decks. So if you give it one standard shuffle, chances are you're not the first person to shuffle a new deck in precisely that way. So if n people have achieved that shuffle, then a subset of n will have also achieved the next shuffle, and so on.
If for instance you shuffle a new deck three standard times and then deal a game of Klondike solitaire, you may not have been the first person to do that. If you and your card-shuffling forbears play that game optimally, even if you don't win the game, you may retrieve the cards in the same fashion. If you do win the game -- and this goes for many solitaire games -- you'll have reorganized the cards into suits and your next few shuffles will also not be unique.
If you have a situation where a professional dealer is shuffling new decks on a regular basis, it is likely that he has created the same arrangements of cards over and over again. I don't know much about how casinos deal with new decks, I imagine there are machines that shuffle in ways that don't produce similar results.
108241 · 6 points · Posted at 03:34:25 on February 14, 2016 · (Permalink)
Odds are even higher of repeating if playing at certain casinos.
http://www.nj.com/news/index.ssf/2012/08/golden_nugget_suing_card_manuf.html
[deleted] · 11 points · Posted at 02:17:03 on February 14, 2016 · (Permalink)*
To put this into perspective: 52! (52 factorial - 52 * 51 * 50 * 49...*3 * 2 * 1) = 80658175170943878571660636856403766975289505440883277824000000000000 (8.06*1067)
Let's say that every country in the world sells 750 billion packs of cards every year - with 196 countries, that's 1.47*1014.
Let's say that they do this for 5,000 years, and that every single deck they produce gets shuffled 1,000,000 (1 million) times. That number is 7.35*1023.
If you divide 52! by 7.35*1023, you get 1.097*1044 . Meaning you would need every country in the world to produce 750 billion packs of cards every year for 5000 years and shuffle each deck 1 million times 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times to cover all the possibilities of orders of cards.
This is assuming that every shuffle gets you a completely new order, which probably wouldn't happen, so the number is even higher, but you can't really calculate that I don't think.
[deleted] · 1 points · Posted at 03:42:46 on February 14, 2016 · (Permalink)
I don't see how you did this. Did you mean perhaps dividing the 52! By 7.35*1023?
[deleted] · 3 points · Posted at 04:43:42 on February 14, 2016 · (Permalink)
whoops yea i said that backwards
CitricBase · 9 points · Posted at 02:45:47 on February 14, 2016 · (Permalink)
"Very real chance" is a misleading way of saying it. You're more likely to win a dozen lottery jackpots at the same time than to randomly produce a card order that has previously existed...
Drecifer · 5 points · Posted at 03:19:06 on February 14, 2016 · (Permalink)
It's almost a guarantee
Xaxxon · 5 points · Posted at 02:53:51 on February 14, 2016 · (Permalink)
very real chance is an odd way to put it.
It's almost a certainty it's never happened before. It is massively improbable it's happened before.
[deleted] · 1 points · Posted at 23:40:41 on February 14, 2016 · (Permalink)
That's assuming everyone shuffles perfectly randomly and evenly.
Xaxxon · 1 points · Posted at 23:45:40 on February 14, 2016 · (Permalink)
That's really only a problem with a brand new deck..
But if you're not talking about random patterns, then the whole thing is uninteresting. If you pick the order of the cards, then there's really nothing mathematically to say about it.
johnnybravo1014 · 2 points · Posted at 03:08:31 on February 14, 2016 · (Permalink)
It's more likely to be a unique order than one ever done before actually.
PotatoFruitcake · 2 points · Posted at 03:12:14 on February 14, 2016 · (Permalink)
More like there is an astronomically small chance that you make a combination that's been done before.
HookDragger · 1 points · Posted at 03:50:00 on February 14, 2016 · (Permalink)
And if you perfectly shuffle a deck 8 times... It's in its original order
su5 · 1 points · Posted at 03:53:49 on February 14, 2016 · (Permalink)
Almost certainly without even a slightly reasonable doubt, assuming a true shuffle.
And this includes all arrangements generated by a computer
scottevil110 · 1 points · Posted at 05:49:49 on February 14, 2016 · (Permalink)
I don't think it's just a very real chance. Isn't it all but certain that no one ever has?
EmpireOfTheTsun · 1 points · Posted at 08:55:41 on February 14, 2016 · (Permalink)*
Yep! But I'm anticipating my comments will be analysed in 1,000,000,000,000 years by space historians, so I want them to be future-proof.
BornInTheRSA · 1 points · Posted at 11:25:01 on February 14, 2016 · (Permalink)
Not only a chance, it's practically impossible (only technically an infinitely small possibility) that anyone ever had such a deck.
i_killed_hitler · 0 points · Posted at 03:27:02 on February 14, 2016 · (Permalink)
I call bullshit on that. It depends on how many shuffles you make. It's certainly possible if you only shuffle 1 or 2 times. I think most people learn to cut the deck in a similar way and shuffle the 2 sides together, plus we've seen each other shuffle so we emulate how others do it. I'm not saying it's common or uncommon, but to say that no one has ever shuffled a deck in the exact same sequence as anyone else on the planet, as this is how I often hear it said, is b.s. I think 3-5 shuffles is probably sufficient to meet that criteria though.
musicninja · 2 points · Posted at 04:12:56 on February 14, 2016 · (Permalink)
The statement is assuming a truly random shuffle, which I've heard is generally considered to be around 7 times.
ChickenBrad · 0 points · Posted at 04:25:03 on February 14, 2016 · (Permalink)
I used to be a poker dealer and I've seen some weird shit.... really weird shit. Like the same two people getting KK and AA in a no limit game on back to back hands... and the kings beat the aces both times. I once asked for 222 on the first 3 cards and it came out. I once saw a hand where the only card that could help someone win was the 10 of spades, and another player announced he folded it already, the dealer thought the hand was over and had fouled the cards and had to reshuffle. The next card was the 10 of spades (only 47 to 1 chance, but misdeals in a spot like that are like 10,000 to 1 at least).
However I've yet to see or hear of anyone who has shuffled a deck of cards and had it come out perfectly in order the way it started (or even close).
the_timps · 0 points · Posted at 08:35:09 on February 14, 2016 · (Permalink)
But cards aren't truly randomly shuffled. And most decks of cards start from a sequence as new, or as the result of a game. So likely a huge portion of "shuffles" are pulling from a smaller subset of possible outcomes and the chances of a collision are exponentially higher.
EmpireOfTheTsun · 1 points · Posted at 08:49:39 on February 14, 2016 · (Permalink)
Yes, there are certain patterns that can occur, but variables such as shuffle type and frequency mean that these patterns become much less predictable as the number of shuffles increases, not to mention changing order of cards in use (e.g. while playing a card game).
What's really interesting is your claim of "true" randomness. It's a very interesting topic.
As a very big TL;DR: A lot of things we consider random aren't random. For everything else, we aren't sure.
the_timps · 1 points · Posted at 09:03:46 on February 14, 2016 · (Permalink)
There's surprisingly a lot of studies out there on shuffling cards. Many types of shuffling involve little randomness.
There's a little over here: https://www.math.hmc.edu/funfacts/ffiles/20001.1-6.shtml A few other pages in there with other shuffle math.
But while there ARE a huge number of potential decks combinations that isn't what is going on. That's the difference between probability on paper and in reality.
"true" I only meant as plain English speech to describe the situation. It's not a mathematical paper, it's a Reddit post ;)
Mikeismyike · -9 points · Posted at 01:58:45 on February 14, 2016 · (Permalink)*
I doubt that factoid is true when taking online poker sites into consideration for sequences of cards already obtained.
Nicko265 · 7 points · Posted at 02:10:19 on February 14, 2016 · (Permalink)
Did you look at the link OP posted?
The number of permutations of 52 cards is astronomical. There is 99.999% chance two people have never had the same.
Mikeismyike · 1 points · Posted at 06:27:26 on February 14, 2016 · (Permalink)
Yeah I saw the video. But if you include digital decks of cards along with considering the matching birthday problem it seems like it isn't too outrageous for there to have been a match at some point.
[deleted] · 6 points · Posted at 02:34:26 on February 14, 2016 · (Permalink)*
[removed]
Mikeismyike · 1 points · Posted at 06:17:04 on February 14, 2016 · (Permalink)
I was talking about having every single combination of cards completed, I was talking about the probability of a shuffled deck matching any one combination cards previously made.
When you take the large amount of online poker tables and combine it with the matching birthday problem it seems to me that we're getting much closer to a reasonable result rather than the comparable improbability of being able to walk through a solid wall because all the atoms lined up.
dj0 · 3 points · Posted at 02:14:20 on February 14, 2016 · (Permalink)
52! is almost incomprehensibly large.
LotharWilhelm · 81 points · Posted at 23:22:09 on February 13, 2016 · (Permalink)
Look up the YouTube channel Vsauce. He just did a great video on math magic and how big 52! is. It's enormous
Munninnu · 11 points · Posted at 23:42:22 on February 13, 2016 · (Permalink)
Maybe this one. But it starts at 14:00.
vicarwin · 1 points · Posted at 15:38:53 on February 14, 2016 · (Permalink)
Still not bigger than a deck of 53 cards.
[deleted] · 7 points · Posted at 22:54:02 on February 13, 2016 · (Permalink)
on my last calculator, the highest factorial product it would display, using scientific notation, was 69! that's 69! 70! and above it would just show an error.
[deleted] · 4 points · Posted at 03:52:53 on February 14, 2016 · (Permalink)
Most calculators have a max value of 10100 - 1
69! ≈ 1.711 * 1098
70! ≈ 1.199 * 10100
IAmScare · 13 points · Posted at 21:01:53 on February 13, 2016 · (Permalink)
Example/Explanation in Video Form for those that want it: https://www.youtube.com/watch?v=uNS1QvDzCVw
Shortdood · 11 points · Posted at 22:02:42 on February 13, 2016 · (Permalink)
came here to say this. crazy
AroundtheTownz · 2 points · Posted at 22:28:00 on February 13, 2016 · (Permalink)
came to indeed say. crazy
justtoreplythisshit · 3 points · Posted at 01:08:01 on February 14, 2016 · (Permalink)
Michael is awesome!
Here's the video marked at the relevant spot.
Munninnu · 3 points · Posted at 01:10:08 on February 14, 2016 · (Permalink)
TIL: you just right click and choose "copy video URL at current time", right?
justtoreplythisshit · 2 points · Posted at 01:27:14 on February 14, 2016 · (Permalink)
Yeah. Also, if you're on a PC, below the video where it says "Share", you can check the box "Start at: ", write the timestamp and it'll give you your marked link.
But right click > "copy video URL at current time" works faster if you want the timestamp to be exactly where it's playing at the moment.
16FootScarf · 6 points · Posted at 22:57:07 on February 13, 2016 · (Permalink)
I read this in a previous post, but the number of combinations in a 52 card deck is larger than the number of atoms in the solar system.
Munninnu · 1 points · Posted at 23:06:47 on February 13, 2016 · (Permalink)
I had read "more possible arrangements of cards than there are atoms on Earth", but still, this is an example I find difficult to visualize.
The example above on the other hand made me think more than once that it couldn't be true.
ngwoo · 2 points · Posted at 00:38:28 on February 14, 2016 · (Permalink)
I find the most relatable way of explaining it is just that every time you shuffle a deck (perfectly), you're statistically seeing a configuration of cards that no human ever has seen or will see again.
That evokes thoughts of there being an absolutely huge number of configurations, and still hugely understates how many there are.
16FootScarf · 1 points · Posted at 07:42:20 on February 14, 2016 · (Permalink)
A quick Google search for number of atoms in the solar system puts it near 1057. While the number of arrangements in a deck of cards is 8x1067.
badlymannered · 1 points · Posted at 08:55:42 on February 14, 2016 · (Permalink)
Atoms in a galaxy is a better approximation
zxcvbnmmssdh · 2 points · Posted at 23:22:09 on February 13, 2016 · (Permalink)
Assuming it too you 1 second to create each unique permutation it would take 1.9e50 time the age of the universe
SquidgyTheWhale · 2 points · Posted at 23:51:35 on February 13, 2016 · (Permalink)
I usually hear it said as, every time you shuffle a deck of cards, the odds are overwhelming that the sequence you end up with has never occurred before.
jtp8736 · 2 points · Posted at 01:18:02 on February 14, 2016 · (Permalink)
This is my favorite description of this concept:
http://czep.net/weblog/52cards.html
SolsKing · 2 points · Posted at 03:29:38 on February 14, 2016 · (Permalink)
That reminded me of a recent video by Vsauce about Math Magic!
Munninnu · 1 points · Posted at 03:31:47 on February 14, 2016 · (Permalink)
Yes, that is exactly the link I have written about in the comment you just read. m(_ _)m
SolsKing · 2 points · Posted at 03:33:41 on February 14, 2016 · (Permalink)
Oops, you didn't mention it was from Vsauce so I thought it was another video.
Munninnu · 1 points · Posted at 03:39:33 on February 14, 2016 · (Permalink)
It's okay. It has already been mentioned few times in this thread.
algag · 2 points · Posted at 03:31:40 on February 14, 2016 · (Permalink)
My 7th grade algebra teacher did her thesis on how many perfect shuffles it would take to rearrange a deck to its original position.
comradeda · 2 points · Posted at 03:46:22 on February 14, 2016 · (Permalink)
And yet sometimes we get the same hands twice in a row. I suck at shuffling, and I don't think my shuffling constitutes close to "true-random".
Munninnu · 1 points · Posted at 03:51:31 on February 14, 2016 · (Permalink)
But, how do you know it's exactly the same hand without recording it? And how can you achieve something like that, unless you first arrange all cards in the same exact order before shuffling?
comradeda · 2 points · Posted at 05:59:15 on February 14, 2016 · (Permalink)
I can't. But if we see familiar hands, we just say someone fucked up and shuffle again. Usually by this point we're quite sloshed and wearing only most of our clothes.
I_too_amawoman · 2 points · Posted at 04:30:46 on February 14, 2016 · (Permalink)
Isn't there a fact about being more possibilities of shuffling than atoms in the galaxy? What am I getting wrong
Munninnu · 2 points · Posted at 04:36:29 on February 14, 2016 · (Permalink)
More permutations than there are atoms on Earth, I think it was.
Mekfal · 2 points · Posted at 09:44:50 on February 14, 2016 · (Permalink)
If I'm remembering correctly earth has around 1x1050 atoms, while the amount of permutations is around 8x1067.
Yep, Check this out
Darkrell · 2 points · Posted at 07:05:55 on February 14, 2016 · (Permalink)
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
That is the amount of possible combinations
There have been less seconds in the universe since time started than there are combinations of a simple card deck
Munninnu · 1 points · Posted at 13:31:52 on February 14, 2016 · (Permalink)
In this video posted by another redditor the guys says at the end:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
hutcho66 · 2 points · Posted at 07:12:18 on February 14, 2016 · (Permalink)
Learnt this from one of the greatest shows ever: https://m.youtube.com/watch?v=SLIvwtIuC3Y
DreVilla · 2 points · Posted at 07:20:46 on February 14, 2016 · (Permalink)
This comment has officially blown my freakin mind...
Munninnu · 2 points · Posted at 13:33:30 on February 14, 2016 · (Permalink)
In this video posted by another redditor the guys says the same with a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
ScrewAttackThis · 2 points · Posted at 09:52:08 on February 14, 2016 · (Permalink)*
Huh, if we had 9 billion people each shuffling a deck of cards simultaneously 1 time per second it would still take 2.842x1050 years.
That's 6.26x1040 times longer than the Earth is old.
e: I meant to use the population of Earth, but brain farted a bit. So let's just pretend Earth is a little more crowded.
Munninnu · 1 points · Posted at 13:34:10 on February 14, 2016 · (Permalink)
In this video posted by another redditor the guys says the same with a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
user5577 · 2 points · Posted at 11:52:37 on February 14, 2016 · (Permalink)
It's really haunting the end of that video. The chance of being born and experiencing conciousness is so astronomically rare, and here we are, using our time well.
AuroraDark · 2 points · Posted at 14:00:12 on February 14, 2016 · (Permalink)
That visualisation is absolutely mind blowing.
Munninnu · 3 points · Posted at 14:03:01 on February 14, 2016 · (Permalink)
In this video posted by another redditor the guys says the same with a different example:
"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."
AuroraDark · 3 points · Posted at 14:08:00 on February 14, 2016 · (Permalink)
My brain is melting. Thanks for sharing!
Crixomix · 2 points · Posted at 17:00:10 on February 18, 2016 · (Permalink)
How nuts is that? Think of all the times people have played cards. It's a very small chance any poker game has EVER been played with the same shuffle.
hil2run · 1 points · Posted at 02:14:50 on February 14, 2016 · (Permalink)
Most card games do not rely on the entire deck being drawn. Pragmatically the entire ordering of the deck is irrelevant. Even in long-hand hold'em with 8 players you'll only see 21 cards.
Munninnu · 1 points · Posted at 02:19:05 on February 14, 2016 · (Permalink)
Well, yes. But it doesn't make Factorial 52 any smaller. The point was how unimaginably big Factorial 52.
drkitteh · 1 points · Posted at 04:01:15 on February 14, 2016 · (Permalink)
What you're missing here is that a shuffle of a deck of cards doesn't randomize the entire deck. Odds are, a lot of shuffles have been repeated, just a very small subset of them.
Munninnu · 1 points · Posted at 04:06:20 on February 14, 2016 · (Permalink)
Wait a moment, what I'm missing from what?
The point is not about cards, the point is about Factorial 52, whether you have cards or numbers. Cards are only mentioned because they are 52.
Also what does it mean that shuffles have been repeated? Because that doesn't change the fact that factorial 52 is still a gigantic number, and that was the point.
drkitteh · 2 points · Posted at 04:23:06 on February 14, 2016 · (Permalink)
Sorry, I overreacted because this fact is always followed by "so every shuffle you make is unique!"
Munninnu · 2 points · Posted at 04:29:01 on February 14, 2016 · (Permalink)
That I do not believe myself, though it has been said a lot.
Also when a deck is new, the cards are always in the same position, with ordered suits and colors. So since every deck that has been shuffled, has been actually shuffed at least once from the very same starting position, and many dealers may just shuffle decks for 3-4 seconds, we can safely say that some permutations most likely have been obtained more than once.
BurningPlaydoh · 1 points · Posted at 07:11:48 on February 14, 2016 · (Permalink)
Psssh, 52! aint shit compared to 5252 .
dimview · 1 points · Posted at 03:16:16 on February 14, 2016 · (Permalink)
By the way, it's rather easy to calculate approximate value of 52! on the back of the envelope.
Just calculate 54!, then divide by 53 * 54.
son_of_sandbar · 1 points · Posted at 04:30:25 on February 14, 2016 · (Permalink)
When people say any newly shuffled deck is probably new, do they take into account the birthday problem? I don't know how relevant that is but I'm curious.
Munninnu · 1 points · Posted at 04:36:44 on February 14, 2016 · (Permalink)*
What's the birthday problem?
EDIT: ah, okay. So maybe here there might be an answer.
Also, as I was saying earlier, when a deck is new, the cards are always in the same position, with ordered suits and colors. So since every deck that has been shuffled, has been actually shuffed at least once from the very same starting position, and many dealers may just shuffle decks for 3-4 seconds, we can safely say that some permutations most likely have appeared more than once.
The point was only that factorial 52 is so huge that precaution must be taken before thinking about it.
PlasmicDynamite · 1448 points · Posted at 21:21:47 on February 13, 2016 · (Permalink)
Tetration is the iteration that follows exponentiation.
n a = aaaa... with an n number of a's.
Also, it is referred to as "a to the superpower of n"
[deleted] · 391 points · Posted at 01:09:59 on February 14, 2016 · (Permalink)*
You can go on forever, these are hyperoperations (H_0 = increment by one, H_1 = addition, then multiplication, exponentiation...)
I quite like the number 65536. Many programmers will immediately see it as 216 (ie. the number of values of a 2-byte variable) but the cool thing is that since
65536 = 216
16=24
therefore
65536 = 2222 = 4 2
But since 4=2 2
65536 = 2 2 2
Therefore we now go up to pentation, which I don't have Reddit-notation for (Knuth's arrows would be used)
65536 = pent(2, 3)
Which I just find to be pretty cool
Edit: I've quickly implemented the definition on Wikipedia into a few languages, though only tested the Haskell version. Here. Will probably crash your stack with even small values though, and passing a negative n will cause infinite recursion Edit Edit: See here for a cleaner and quicker Haskell version
Edit 2: Currently have
h 5 2 3running, literally no idea how long it will take, about to try a poor first year CS attempt at determining its asymptotic complexity in terms of n, a, bEdit 3: Apparently it's complexity may be in terms of itself
Edit 4: Total time to execute was 11 minutes
[deleted] · 14 points · Posted at 02:41:13 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 12:50:48 on February 14, 2016 · (Permalink)
WaitButWhy is a great site to spend a few hours on (the articles on the Fermi paradox and AI are particularly interesting)
bacondev · 9 points · Posted at 04:20:02 on February 14, 2016 · (Permalink)
Currently computing 2 ↑↑↑ 4. Wish me luck.
cisnotation · 2 points · Posted at 00:32:29 on February 15, 2016 · (Permalink)
Day9
TajunJ · 8 points · Posted at 06:30:16 on February 14, 2016 · (Permalink)
I'm just going to leave this here.
[deleted] · 5 points · Posted at 06:09:42 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 2 points · Posted at 12:33:32 on February 14, 2016 · (Permalink)
Good point, I was so set on copying the wikipedia definition exactly I forgot that pattern matching lent itself better here. Do you know why it is that pattern matching performs better? It certainly looks nicer but I thought it would have the same runtime
[deleted] · 3 points · Posted at 01:08:31 on February 15, 2016 · (Permalink)*
[deleted]
Alekzcb · 1 points · Posted at 16:56:55 on June 11, 2016 · (Permalink)*
The signature should be
otherwise
his subject to overflow errors.On another note, although this isn't as "pure", it's a good idea to explicitly define
hfor n<=3, since it's easy to do so and will cause fewer stack overflows:EDIT: Changed the first parameter to
Int(as if I could cope withnthat big!)doobyrocks · 4 points · Posted at 06:24:07 on February 14, 2016 · (Permalink)
Which terminal are you using?
[deleted] · 2 points · Posted at 12:40:39 on February 14, 2016 · (Permalink)
The shell is zsh + oh-my-zsh + powerline (specific package is python2-powerline-zsh in the Arch User Respository). Terminal is just xfce4-terminal
ppxeppxe · 3 points · Posted at 04:52:58 on February 14, 2016 · (Permalink)
Would love to see your bash prompt definition, if that's bash that is...
[deleted] · 1 points · Posted at 12:41:09 on February 14, 2016 · (Permalink)
It's zsh + oh-my-zsh + powerline (specific package is python2-powerline-zsh in the Arch User Respository)
ppxeppxe · 1 points · Posted at 16:17:23 on February 14, 2016 · (Permalink)
Sweet, thanks!
bluefirecorp · 3 points · Posted at 05:09:56 on February 14, 2016 · (Permalink)
Not just programmers, but network admins too.
AmadeusMop · 3 points · Posted at 05:15:01 on February 14, 2016 · (Permalink)
You'd want to type
↑, which is rendered as ↑.[deleted] · 2 points · Posted at 01:35:05 on February 14, 2016 · (Permalink)
I thought after exponentiation it was power tower. I like learning the abstract names of concepts.
WeirderQuark · 2 points · Posted at 04:12:09 on February 14, 2016 · (Permalink)
Is H_n(2,2) always 4 for every positive integer n?
TumblrTheFish · 3 points · Posted at 07:47:37 on February 14, 2016 · (Permalink)
yes, it is. I had the proof for it in my senior thesis, but I really don't want to dig that up. Its' a pretty simple proof by induction though.
kodek64 · 2 points · Posted at 08:17:29 on February 14, 2016 · (Permalink)
Cool prompt! Is that a powerline skin?
[deleted] · 1 points · Posted at 12:41:38 on February 14, 2016 · (Permalink)
Yeah it's just python2-powerline-zsh in the AUR with oh-my-zsh and near default config
InbredDucks · 2 points · Posted at 09:23:29 on February 14, 2016 · (Permalink)
Hmm yes
HolyGarbage · 2 points · Posted at 11:05:34 on February 14, 2016 · (Permalink)
If you like this, Look up the number G64, or Grahm's Number.
GreySummer · 2 points · Posted at 11:22:23 on February 14, 2016 · (Permalink)
This might be the coolest nerdy thing I've ever seen on reddit !
bobbertmiller · 2 points · Posted at 12:23:57 on February 14, 2016 · (Permalink)
alt 24 = ↑. So 3↑3 or 3↑↑↑↑3 is possible to write on reddit. The ASCII set involves a lot of quite useful characters, including →, –(compared to the shorter - –) or bullet points •►.
-Mountain-King- · 2 points · Posted at 16:05:12 on February 14, 2016 · (Permalink)
And here's the relevant xkcd for Knuth's up-arrow notation (the alt-text, specifically, is a riff on it.
StaleTheBread · 1 points · Posted at 14:51:51 on February 14, 2016 · (Permalink)
Does 2 [hyperoperation] always equal 4?
2+2=4
2*2=4
2^2=4
2[hyper-4]2=4
...?
fyreskylord · 1 points · Posted at 19:42:38 on February 14, 2016 · (Permalink)
If anyone wants to read more about hyperoperations and their applications, there's a wonderful explanation of them here- http://waitbutwhy.com/2014/11/1000000-grahams-number.html
He also talks about Graham's Number, which is IMO one of the most fascinating little bits of math ever.
zanderkerbal · 1 points · Posted at 23:00:32 on February 14, 2016 · (Permalink)
10^10
\^ for ^
everyoneknowsabanana · 1 points · Posted at 15:14:45 on March 2, 2016 · (Permalink)
How is your terminal so pretty?!!
[deleted] · 1 points · Posted at 18:53:41 on March 7, 2016 · (Permalink)
For future reference: Unicode 2191 is ↑
noggin-scratcher · 72 points · Posted at 23:17:58 on February 13, 2016 · (Permalink)
Quick formatting trick to share: if you want to have a superscript letter immediately followed by a non-superscript letter you can put brackets around the bit you want superscripted.
So
^(n)arenders as naPlasmicDynamite · 7 points · Posted at 23:24:07 on February 13, 2016 · (Permalink)
I was actually wondering how to do that. Thanks!
soinspirationaletc · 2 points · Posted at 02:51:21 on February 14, 2016 · (Permalink)
thanksdude
[deleted] · 535 points · Posted at 22:47:40 on February 13, 2016 · (Permalink)
[removed]
RickAScorpii · 292 points · Posted at 00:18:37 on February 14, 2016 · (Permalink)*
Maybe not Batman then.
billwoo · 16 points · Posted at 01:35:23 on February 14, 2016 · (Permalink)
Being rich is a superpower.
Gehalgod · 5 points · Posted at 02:13:54 on February 14, 2016 · (Permalink)
Rich 50 is middle class 38.
jaan42iiiilll · 3 points · Posted at 01:43:17 on February 14, 2016 · (Permalink)
nananana a-n!
fourcornerview · 3 points · Posted at 03:16:04 on February 14, 2016 · (Permalink)
He can cry himself to sleep, that's gotta count for something...
[deleted] · 2 points · Posted at 12:20:49 on February 14, 2016 · (Permalink)
Yes but that batman sure is full of sodium.
The_Archagent · 2 points · Posted at 18:21:57 on February 14, 2016 · (Permalink)
Batman's superpower is money.
Avcdo · 7 points · Posted at 23:20:56 on February 13, 2016 · (Permalink)
Sodium sodium sodium sodium sodium sodium sodium sodium batman!
AllGloryToSatan · 3 points · Posted at 23:40:30 on February 13, 2016 · (Permalink)
naaaaaaaa batman batman!!
HobbitFoot · 2 points · Posted at 23:31:44 on February 13, 2016 · (Permalink)
I love the Leader!
NotKrankor · 2 points · Posted at 01:59:32 on February 14, 2016 · (Permalink)
BATMA TO THE SUPERPOWER OF N, BATMAN
[deleted] · 2 points · Posted at 02:14:38 on February 14, 2016 · (Permalink)
Nananananananananananananananana BATMAN!!
AfterShave997 · 2 points · Posted at 05:00:30 on February 14, 2016 · (Permalink)
No idea why people upvote posts like these.
timndime · 1 points · Posted at 09:43:51 on February 14, 2016 · (Permalink)
Q: What was Beethoven's favorite fruit?
A: BaNANANA BaNANANA
zanderkerbal · 1 points · Posted at 23:01:12 on February 14, 2016 · (Permalink)
nananananananabatman
JackFlynt · 7 points · Posted at 23:08:53 on February 13, 2016 · (Permalink)
ISomewhat related and really cool article.
Accio_Cake · 7 points · Posted at 00:03:47 on February 14, 2016 · (Permalink)
Read that article so many times and I still cannot take it all in.
brokenplasticshards · 5 points · Posted at 00:07:00 on February 14, 2016 · (Permalink)
So what do you call ... a a aa with an n number of a's? "a to the second superpower of n"? Can't you go on forever like this?
Icepick823 · 13 points · Posted at 00:22:43 on February 14, 2016 · (Permalink)
I don't know if there's an exact name, but there are notations that compress stacks of stacks of exponents.
https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
brokenplasticshards · 1 points · Posted at 00:23:55 on February 14, 2016 · (Permalink)
TIL. Thanks!
PlasmicDynamite · 1 points · Posted at 00:35:49 on February 14, 2016 · (Permalink)
a and n are just variables. You can go on forever with any sequence.
life-change · 6 points · Posted at 01:43:43 on February 14, 2016 · (Permalink)
Tetration reminds me of Graham's number which makes my head hurt.
nicholas818 · 2 points · Posted at 05:57:49 on February 14, 2016 · (Permalink)*
Didn't Graham's Number use arrow notation? Like OP's example, aaaa... with an n number of a's, would be a↑↑n.
And with this method, WE CAN GO DEEPER. a↑↑↑n = a↑↑a↑↑a↑↑a... with n a's. a↑↑↑↑n = a↑↑↑a↑↑↑a↑↑↑a... with n a's.
For Graham's number, you start with 3↑↑↑3 (already pretty huge), but that describes the number of arrows between two 3's. And THAT number describes the number of arrows between two 3's. Recurse 62 more times any you have Graham's Number.
Edit: More about Graham's Number.
[deleted] · 5 points · Posted at 02:07:33 on February 14, 2016 · (Permalink)*
The problem of calculating ba for non-integer b is an open one although its results are not very useful. It is also very interesting that ∞x is actually a real-valued monotonic function in [e-e, e1/e] with all derivatives approaching positive infinity at the top of the domain.
nicholas818 · 1 points · Posted at 06:04:23 on February 14, 2016 · (Permalink)
I understood some of those words.
[deleted] · 1 points · Posted at 11:43:16 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 1 points · Posted at 15:08:16 on February 14, 2016 · (Permalink)
The first identity you stated is incorrect so the second identity doesn't apply. ba = aaa...} b times. Exponentiation is right-associative meaning the tower is evaluated from the top down. Strangely, this function is presently defined only for integer and infinite b. The problem is that there is no known functional square root f(f(x)) = ex otherwise it would be easy to exponent a number, say, two-and-a-half times.
cManks · 6 points · Posted at 01:26:36 on February 14, 2016 · (Permalink)
4 years of a math and computer science degree and I've never come across this before.
PlasmicDynamite · 11 points · Posted at 01:27:44 on February 14, 2016 · (Permalink)
That's because it's really unnecessary in most cases.
no_myth · 2 points · Posted at 02:21:18 on February 14, 2016 · (Permalink)
I've heard "power tower". Also I was super disappointed to find out I wasn't the first to come up with this.
RisingWaterline · 1 points · Posted at 01:03:05 on February 14, 2016 · (Permalink)
Can I do this on a TI-84?
[deleted] · 2 points · Posted at 02:28:53 on February 14, 2016 · (Permalink)
Yes, if you write a program, not by default.
Njallstormborn · 1 points · Posted at 01:24:21 on February 14, 2016 · (Permalink)
"because exponentials weren't enough fun"
skyler_on_the_moon · 1 points · Posted at 02:04:49 on February 14, 2016 · (Permalink)
I remember discovering this on my own and thinking I had invented it for several years, because I didn't know what it was called so I couldn't google it.
Atario · 1 points · Posted at 11:01:50 on February 14, 2016 · (Permalink)
A guy I knew in college came up with it too, and he called it "macho" (with a corresponding "wimpo" function which was just incrementation).
beenoc · 1 points · Posted at 02:23:52 on February 14, 2016 · (Permalink)
I learned about this from a question that asked "What number can you write that is a bigger number than the amount of carbon atoms you just laid on the paper?" (was either reddit or What If XKCD.) The answer was 99, or 9999999999 . I'm pretty sure that's more than the amount of atoms in the known universe, considering every calculator I can find just returns "infinity" after 9999.
cowgod42 · 1 points · Posted at 04:28:16 on February 14, 2016 · (Permalink)
Try Python. I just used it to compute 97:
It took a few seconds, but it worked. I have no idea how to check the accuracy though.
[deleted] · 1 points · Posted at 02:30:28 on February 14, 2016 · (Permalink)
Obligatory link to the large numbers wikia, which is pretty comprehensive on the subject.
Page on Tetration
philly_fan_in_chi · 1 points · Posted at 02:43:38 on February 14, 2016 · (Permalink)
REALLY cool article:
http://www.scottaaronson.com/writings/bignumbers.html
SmellYaLater · 1 points · Posted at 02:45:08 on February 14, 2016 · (Permalink)
Get out here with your power tower.
DrPaprika0192 · 1 points · Posted at 03:09:48 on February 14, 2016 · (Permalink)
Relevant... smbc?
cecilx22 · 1 points · Posted at 03:19:26 on February 14, 2016 · (Permalink)
edit just saw that someone else posted this. Still a good read.
In case you haven't read it... http://waitbutwhy.com/2014/11/1000000-grahams-number.html
BlindProphet_413 · 1 points · Posted at 03:22:48 on February 14, 2016 · (Permalink)
Relevant SMBC
Clementinesm · 1 points · Posted at 03:23:01 on February 14, 2016 · (Permalink)
And multiple tetrations is called penetration. And multiple penetrations is called sextations. ;)
scharfes_S · 1 points · Posted at 03:31:48 on February 14, 2016 · (Permalink)
Relevant SMBC
canoe123 · 1 points · Posted at 04:20:10 on February 14, 2016 · (Permalink)
Going further, repeated tetration is called "penetration".
Repeated penetration is known as sexation.
[deleted] · 1 points · Posted at 04:21:06 on February 14, 2016 · (Permalink)
aaaaaaaaaaaaa
cfmcg · 1 points · Posted at 05:38:04 on February 14, 2016 · (Permalink)
Would that mean there's such thing as a quadration and it would be "a to the superduperpower of n"?
Yserbius · 1 points · Posted at 05:54:11 on February 14, 2016 · (Permalink)
Isn't that similar to Knuth Notation, where "A ! B = AAAA..."? And "A !! B = A ! (A ! B)" which is how Graham's Number (largest number known to have any sort of use in mathematics, it's the answer to a geometry problem) is calculated?
xkcd1234 · 1 points · Posted at 06:15:06 on February 14, 2016 · (Permalink)
this is somewhat a cool relevant fact that relates to tetration... https://en.wikipedia.org/wiki/Goodstein's_theorem
[deleted] · 1 points · Posted at 07:37:19 on February 14, 2016 · (Permalink)
Use knuth up arrow notation. Its better
Bobius · 1 points · Posted at 08:31:31 on February 14, 2016 · (Permalink)
Related watching - Day9 explaining Knuth up arrow notation and Graham's number. Make sure you watch right to the end.
dbonx · 1 points · Posted at 08:46:35 on February 14, 2016 · (Permalink)
That looks like to the super-duper power
thatinternetguyagain · 1 points · Posted at 08:47:19 on February 14, 2016 · (Permalink)
Is this on any level connected to Tetris? (Disclaimer: I just woke up...Why am I trying to understand this?)
Alpha3031 · 1 points · Posted at 09:45:23 on February 14, 2016 · (Permalink)
Up arrow notation is useful if you don't have the formatting options.
33 = 333 = 3327 = ARMN*
* A really massive number
break_main · 1 points · Posted at 11:43:51 on February 14, 2016 · (Permalink)
Thats not a math fact, your just naming a thing.
Hey guys pentation is tetrating something over and over. Lets call the product superduperpower. Cool fact huh?
[deleted] · 1 points · Posted at 14:28:56 on February 14, 2016 · (Permalink)
So Superman flight = flightflightflightflight
[deleted] · 1 points · Posted at 23:34:19 on February 13, 2016 · (Permalink)
[deleted]
SpiraliniMan · 6 points · Posted at 01:05:32 on February 14, 2016 · (Permalink)
No, grahams number uses arrow notation (which is similar) and is vastly larger
[deleted] · 1 points · Posted at 23:47:25 on February 13, 2016 · (Permalink)
It's called hyper-operations, actually.
[deleted] · 0 points · Posted at 00:21:36 on February 14, 2016 · (Permalink)
How huge the tetration of googol would be ?
Tallest9 · 3 points · Posted at 01:23:27 on February 14, 2016 · (Permalink)
3 10
Rehovak · 876 points · Posted at 20:19:10 on February 13, 2016 · (Permalink)
If you glue two Möbius Strips together, topologically it creates a Klein Bottle.
chilly-wonka · 235 points · Posted at 22:02:02 on February 13, 2016 · (Permalink)
What is a klein bottle?
New_World_Era · 304 points · Posted at 22:28:04 on February 13, 2016 · (Permalink)
It's basically analogous to a mobius strip. It's getting a tube to "twist" (or invert) before connecting. It only works in 4-D without crossing itself, but it's 3D shadow forms a bottle
SirSoliloquy · 92 points · Posted at 08:22:20 on February 14, 2016 · (Permalink)
One day, I swear I'm going to take the time to figure out how the hell 4D math works.
[deleted] · 15 points · Posted at 08:34:36 on February 14, 2016 · (Permalink)*
[removed]
Alpha3031 · 36 points · Posted at 09:33:51 on February 14, 2016 · (Permalink)
For "live" in n dimensions, I wish we lived in n+1 dimensions.
simsalaschlimm · 1 points · Posted at 16:57:15 on February 14, 2016 · (Permalink)
but 2 doesn't really work, does it? So we're at the bare minimum. A bit more would be nice!
Alpha3031 · 1 points · Posted at 04:33:40 on February 16, 2016 · (Permalink)
We could be at the bare maximum* too, as far as we know. *Well, it doesn't sound right, but what else am i supposed to say?
Royal-Ninja · 2 points · Posted at 03:11:30 on February 28, 2016 · (Permalink)*
S(A(G64, G64)) dimensions?
That's the Busy Beaver function with the number of whatever Ackermann's function is with Graham's Number as both arguments.
[deleted] · -5 points · Posted at 09:36:03 on February 14, 2016 · (Permalink)
n+1 = o
n-1 = m
in "no" dimensions?
pantofla · 9 points · Posted at 09:36:36 on February 14, 2016 · (Permalink)
We live in 4 special dimensions :-D
Artillect · 3 points · Posted at 15:46:17 on February 14, 2016 · (Permalink)
No we don't. We live in 3 spatial dimensions and 1 of time.
doublethump · 9 points · Posted at 17:58:54 on February 14, 2016 · (Permalink)
Give the guy a break, he's trying to be cute
pantofla · 6 points · Posted at 02:50:21 on February 15, 2016 · (Permalink)
And they're all special to me.
zazu2006 · 8 points · Posted at 13:22:53 on February 14, 2016 · (Permalink)
Multi dimensional math is easy. But i'll be damned if I can understand what a hypercube or a klein bottle should "look" like.
[deleted] · 14 points · Posted at 15:16:48 on February 14, 2016 · (Permalink)*
[deleted]
leadingthenet · 2 points · Posted at 19:16:56 on February 14, 2016 · (Permalink)
Amazing! This is the first time I was actually able to visualise it.
sirius4778 · 4 points · Posted at 22:52:59 on February 15, 2016 · (Permalink)
I hate to break it to you but you didn't visualize it. It's impossible for us to visualize it but you came close to visualizing its shadow
[deleted] · 1 points · Posted at 14:53:33 on February 19, 2016 · (Permalink)
I'm out.
darkekniggit · 330 points · Posted at 22:02:38 on February 13, 2016 · (Permalink)*
A 3d shape with only one surface.
Edit: 4D, actually. At least for a true Klein bottle.
mirjak · 97 points · Posted at 22:46:40 on February 13, 2016 · (Permalink)
A Klein bottle is 4d
tormenting · 23 points · Posted at 02:04:00 on February 14, 2016 · (Permalink)
It's a 2D manifold which can be embedded in a 4D Euclidean space (but not a 3D Euclidean space). Technically doesn't make it 4D, but nobody really cares anyway.
ClintonCanCount · 13 points · Posted at 03:47:56 on February 14, 2016 · (Permalink)
I care. This AskReddit is making me, as a mathematician, both happy at people learning fun facts, and angry at people who think they know things but are wrong.
Thanks for being right!
D-d-d-d-d-danger · 1 points · Posted at 05:49:45 on February 14, 2016 · (Permalink)
If you're a mathematician, then the ability to count is probably useful.
Raijinili · 3 points · Posted at 11:59:29 on February 14, 2016 · (Permalink)
Not as useful as you might think.
ClintonCanCount · 1 points · Posted at 14:03:14 on February 14, 2016 · (Permalink)
Combinatorics comes up lots of places, thank you very much
SidusObscurus · 1 points · Posted at 14:48:10 on February 14, 2016 · (Permalink)
Generating functions are literally black magic and voodoo.
Raijinili · 1 points · Posted at 09:19:42 on February 15, 2016 · (Permalink)
Combinatorics, graph theory, and algebraic topology are only three fields out of many that a mathematician can specialize in.
ClintonCanCount · 1 points · Posted at 12:32:08 on February 15, 2016 · (Permalink)
you know for some reason I am very aware of that
ClintonCanCount · 3 points · Posted at 14:03:00 on February 14, 2016 · (Permalink)
I can only count on a highly theoretical level.
TwoFiveOnes · 1 points · Posted at 20:00:29 on February 14, 2016 · (Permalink)
Please, not even! All you combinatorists do is say "at least" or "at most" cough cough Ramsey numbers cough
darkekniggit · 9 points · Posted at 22:49:53 on February 13, 2016 · (Permalink)
Yeah, I guess it'd have to be for the intersection to happen. I stand corrected!
johnnymo1 · 29 points · Posted at 23:47:21 on February 13, 2016 · (Permalink)
A Klein bottle itself is 2d. But if you want to embed it without self-intersection, you need a 4d ambient space.
Of course, I think you were still answering correctly in the spirit of the post you were responding to, but I think it's a point worth making anyway.
[deleted] · -16 points · Posted at 00:45:16 on February 14, 2016 · (Permalink)*
[deleted]
NullRad · 13 points · Posted at 00:48:44 on February 14, 2016 · (Permalink)
But no volume. It is like the black hole of containers.
[deleted] · -15 points · Posted at 00:52:09 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 13 points · Posted at 01:48:05 on February 14, 2016 · (Permalink)
Thats not an actual klein bottle. A true, mathematically correct klein bottle doesnt actually pass through itself, and can't actually exist in our universe.
johnnymo1 · 11 points · Posted at 01:58:18 on February 14, 2016 · (Permalink)
It also has no definable notion of "inside" and "outside," so it has no volume.
johnnymo1 · 3 points · Posted at 01:07:11 on February 14, 2016 · (Permalink)
Sure. Dimensionality is determined by how many coordinates it takes to specify a point on the figure.
[deleted] · -8 points · Posted at 01:09:35 on February 14, 2016 · (Permalink)*
[deleted]
johnnymo1 · 6 points · Posted at 01:12:58 on February 14, 2016 · (Permalink)
That's great and all, but this thread is about mathematics. Mathematically, a Klein bottle is a two-dimensional object, which can be embedded without self-intersection in a space of at least 4 dimensions. Even a square is 3d by your criterion because we can't make an infinitely thin square in real life, but that's missing the point spectacularly.
[deleted] · -19 points · Posted at 01:13:55 on February 14, 2016 · (Permalink)
[deleted]
johnnymo1 · 8 points · Posted at 01:15:17 on February 14, 2016 · (Permalink)*
No, you're ignoring what I'm saying and defining all terminology so that you are right.
Literally the first sentence of the wikipedia article for "Klein bottle." You can complain about the definition of "dimension" all you want, but it turns out mathematicians don't care.
[deleted] · -17 points · Posted at 01:20:14 on February 14, 2016 · (Permalink)*
[deleted]
SpartansATTACK · 6 points · Posted at 06:56:00 on February 14, 2016 · (Permalink)
Oh my god, you are unimaginably dense.
johnnymo1 · 10 points · Posted at 01:24:29 on February 14, 2016 · (Permalink)
No. I'm not guessing at what the wikipedia article means. I know what two-dimensional manifold is. It's a second-countable, Hausdorff topological space such that every point has a neighborhood which is homeomorphic to an open set in R2 (equivalently, all of R2 or an open ball in R2 ). A Klein bottle satisfies this. Hence, it is two-dimensional. The image you linked is a projection of a Klein bottle embedded in three-dimensional space, but the definition of a Klein bottle does not require that it be embedded in any higher space 3d space. It is a space in its own right, which is two-dimensional because every sufficiently small piece looks like two-dimensional Euclidean space.
TwoFiveOnes · 5 points · Posted at 04:06:48 on February 14, 2016 · (Permalink)
A Klein Bottle is this: [0,1]×[0,1]/((0,x)~(1,x) , (x,0)~(1-x,1)), and nothing else. It is a two-dimensional topological manifold, as is easily seen by explicitly presenting charts.
[deleted] · -16 points · Posted at 01:26:45 on February 14, 2016 · (Permalink)
[deleted]
johnnymo1 · 14 points · Posted at 01:34:28 on February 14, 2016 · (Permalink)
Once again, failing to distinguish between "the mathematically defined entity known as a Klein bottle" and "a neat math-inspired desk ornament." No one is talking about making Klein bottles in real life here (well, except you). This is a thread about mathematics.
You continue to try to lay some kind of pithy smackdown while failing to make any substantive argument that might refute why, for instance, Wikipedia might refer to a Klein bottle as "a two-dimensional manifold."
SidusObscurus · 1 points · Posted at 14:40:15 on February 14, 2016 · (Permalink)
A Klein bottle is a 2D surface embedded in 4-space. With self-intersection, you can depict any lower dimension object into a space as small as it's minimum dimension.
What's the difference? The simplest example is the Mobius Strip. This is a 2D object embedded in 3D. Why and how? Well it identifies edges by wrapping around. Imagine a square. The side edges are considered boundaries while the top and bottom edges are identified with reverse orientation. Therefore you can express the object in 2D without losing any information. However, to draw a real object with these properties, you need to draw in a 3D space.
Klein bottle is the same. It's a 2D object with more complicated identified edges. If you draw it in 2D, you have lots of identified edges. If you draw it in 2D you have fewer overlaps, but in the minimal case you still need that bottle neck overlap. In 4D you can draw it without overlap.
Doesn't change the fact that it is a 2D surface area type object.
[deleted] · 3 points · Posted at 23:35:17 on February 13, 2016 · (Permalink)
How?
Deadringer14 · 8 points · Posted at 02:44:55 on February 14, 2016 · (Permalink)
AFAIK, at some point the bottle has to go inside itself (because the inside is the same surface as the outside) but the only way you can do that in 3d space is to create an intersection or join. In 4d space, as difficult as it is to conceptualise, there is a way for the bottle to go inside of itself without creating a join
ihavetenfingers · 3 points · Posted at 10:36:05 on February 14, 2016 · (Permalink)
How the fsck does that even work
Deadringer14 · 5 points · Posted at 10:48:19 on February 14, 2016 · (Permalink)
Like I said, it's hard to think about it because we live in a 3D space but the gist of it is that extra dimension allows the bottle to kind of circumvent itself, if that makes any sense. Maybe it's a bit easier to think about it in 2d-3d. If I have a circle on a sheet of paper and I put the tip of my pencil on the outside of the circle, there's no way for me to move the pencil inside the circle without going over it, which is against the rules. But, if I can use 3 dimensions, I can just lift the pencil off the paper and then put it on the inside of the circle. I have gone from the inside to the outside, without crossing over. It's the same concept with the Klein bottle, just this time using the 4th dimension
ihavetenfingers · 2 points · Posted at 10:52:29 on February 14, 2016 · (Permalink)
Thank you, great example! Made me get how it works really quick.
Then i tried to carry the same concept over from 3d-4d and now my head hurts :(
SidusObscurus · 2 points · Posted at 14:56:50 on February 14, 2016 · (Permalink)
Think of in terms of things that are easier to conceptualize: Mobius Strip and 2D to 3D.
In 3D we can construct a Mobius Strip. But a Mobius strip is a 2D manifold, so we can write a 2D definition of a Mobius strip, we just have to identify the top and bottom boundaries of a square. Over the arrows we wrap around and our direction moves to the opposite. Every identification like this is an intersection with another dimension above 2D. Essentially wrapping over infinity, and when we do flipping over to swap direction, then connecting again; the wrapping over infinity is what requires us to move up a dimension to draw the object.
Exactly the same thing applies for a Klein Bottle (a 2D manifold embedded) in 4D space. In 4D we can draw it with no intersections, in lower dimensions we can draw it by wrapping stuff around and creating intersections (essentially points that are identified).
ZombyTed · 1 points · Posted at 06:12:44 on February 14, 2016 · (Permalink)
The wiki page has a good gif that made the 4D aspect make sense for me.
eviltreesareevil · -4 points · Posted at 03:12:05 on February 14, 2016 · (Permalink)
No!! A klein bottle is technically 3D, but it has to exist in a 4D space. Similar to how a mobius strip is 2D, but has to exist in a 3D space. (Paper may be 3D, but an actual mobius strip is theoretically 2D.)
[deleted] · -1 points · Posted at 02:37:02 on February 14, 2016 · (Permalink)
[deleted]
mirjak · 3 points · Posted at 03:44:18 on February 14, 2016 · (Permalink)
That's just a representation of one. A real Klein bottle wouldn't have the intersection.
chilly-wonka · 2 points · Posted at 22:04:14 on February 13, 2016 · (Permalink)
Isn't a moibus strip already that?
12_more_minutes · 9 points · Posted at 22:41:23 on February 13, 2016 · (Permalink)
Mobius is a 2d object with 2 surfaces, bent through the 3rd dimension, to create a 3d object with 1 surface.
Klein is a 3d object with an inside and an outside (2 surfaces), bent through the 4th dimension, to create a 4d object with 1 surface.
1 surface here means that you can take a pen and drag it around - without picking it up - to cover the whole object. Ad a contrast to this, on a regular piece of paper, you have to pick up the pen to start drawing on the backside.
skysurf3000 · 2 points · Posted at 00:04:20 on February 14, 2016 · (Permalink)
Not sure if I should say "as a consequence", but it is also an example of a closed surface which has no "inside".
12_more_minutes · 1 points · Posted at 01:29:58 on February 14, 2016 · (Permalink)
Right - because it only has one side! You could also say it has no outside,which is pretty trippy because you're clearly looking at something. It's super cool stuff.
darkekniggit · 11 points · Posted at 22:10:01 on February 13, 2016 · (Permalink)
Well, not really. There's no "inside" to a möbius strip. There is in a Klein bottle.
TehSuckerer · 1 points · Posted at 13:14:57 on February 14, 2016 · (Permalink)
It's a 2D shape that has to be embedded in at least 4 dimensional space, actually.
JackFlynt · 12 points · Posted at 22:59:09 on February 13, 2016 · (Permalink)
https://en.m.wikipedia.org/wiki/File:Klein_bottle.svg
Funk I want to learn glassblowing or something just to make one now. I don't care that it wouldn't be accurate, it looks awesome anyway.
[deleted] · 8 points · Posted at 01:44:10 on February 14, 2016 · (Permalink)
[removed]
JackFlynt · 3 points · Posted at 04:09:11 on February 14, 2016 · (Permalink)
HE ACTUALLY SHIPS TO AUSTRALIA!!! That's amazing, cool things never ship to Australia! I can't hug you over the internet but if I could, I would.
JshWright · 3 points · Posted at 02:04:37 on February 14, 2016 · (Permalink)*
Allow /u/cliffstoll to explain... https://www.youtube.com/watch?v=AAsICMPwGPY
I someday hope to be as excited about something as Cliff Stoll is about... everything...
bigbiff121 · 1 points · Posted at 08:19:52 on February 14, 2016 · (Permalink)
I don't understand the "edges" example, can someone explain to me how sewing them together makes an "edge-less" object?
ThePharros · 2 points · Posted at 04:45:36 on February 14, 2016 · (Permalink)
This video isn't primarily about a klein bottle's mathematical properties per say, but is still one of my favorite videos of it nonetheless.
[deleted] · 2 points · Posted at 04:57:13 on February 14, 2016 · (Permalink)
Imagine a funnel, whose thinner top end is extended, then curved to cut through the wall of the cone itself and merge with the wide end of the funnel.
IDontLikeItILoveIt · 2 points · Posted at 06:49:09 on February 14, 2016 · (Permalink)
This thing: http://www.map.mpim-bonn.mpg.de/images/4/43/Klein_bottle.png
bornfreediefree · 2 points · Posted at 07:41:04 on February 14, 2016 · (Permalink)
it was on the front page of /r/pics yesterday or today, I think.
Jdrawer · 1 points · Posted at 08:22:27 on February 14, 2016 · (Permalink)
The loopy cousin of the Klein stein, who has earned the title of "The best way to drink at work."
Seifty · 1 points · Posted at 09:54:37 on February 14, 2016 · (Permalink)
What is a Möbius Strip?
Rehovak · 1 points · Posted at 16:40:14 on February 14, 2016 · (Permalink)
It's a strip with only one side. Basically take a long piece of paper, twist it once, and tape it to it's other end. If you drag your finger along it, it'll eventually end up at the same place it started!
judgej2 · 1 points · Posted at 09:57:31 on February 14, 2016 · (Permalink)
A bottle with one surface - the inside is the outside. It is a real thing and can be constructed. Trying to buy one is a pain though, just not enough are made.
autiethoughts · 1 points · Posted at 10:11:42 on February 14, 2016 · (Permalink)
https://youtu.be/AAsICMPwGPY
der_iraner · 1 points · Posted at 10:49:15 on February 14, 2016 · (Permalink)
http://youtu.be/AAsICMPwGPY
This video explains it very well. I like that he is so passionate about Klein bottles.
legoman1237 · 1 points · Posted at 11:26:43 on February 14, 2016 · (Permalink)
A 4D version of a cylinder
Raijinili · 1 points · Posted at 12:04:59 on February 14, 2016 · (Permalink)
This except that the part where it crosses itself isn't actually an intersection. Imagine being a ghost and putting your arms through your belly and shaking your own hand (though that's not a Klein bottle thing, that's just because we can't have a real one in 3-D space).
A Klein bottle only has one "side": Imagine being an ant and crawling from any point on the "inside" to the "outside".
[deleted] · 1 points · Posted at 14:12:33 on February 14, 2016 · (Permalink)
A doughnut with a 4d twist.
Ralvald · 1 points · Posted at 14:40:12 on February 14, 2016 · (Permalink)
http://youtu.be/AAsICMPwGPY
[deleted] · 1 points · Posted at 16:30:25 on February 14, 2016 · (Permalink)
A very small bottle
[deleted] · 1 points · Posted at 00:43:11 on February 14, 2016 · (Permalink)
It's 2 Möbius strips glued together
Supersnazz · 1 points · Posted at 02:35:20 on February 14, 2016 · (Permalink)
2 Möbius strips stuck together.
helloreddits456464 · 1 points · Posted at 03:10:39 on February 14, 2016 · (Permalink)
About two Möbius Strips
DigitalAssassin · 0 points · Posted at 06:43:35 on February 14, 2016 · (Permalink)
It is just like an up dog.
[deleted] · 2 points · Posted at 07:06:04 on February 14, 2016 · (Permalink)
What's an up dog?
DigitalAssassin · 1 points · Posted at 08:34:42 on February 14, 2016 · (Permalink)
Not much, what's up with you....
[deleted] · -17 points · Posted at 22:12:49 on February 13, 2016 · (Permalink)
[deleted]
chilly-wonka · 4 points · Posted at 22:16:17 on February 13, 2016 · (Permalink)
Oh I didn't know google existed, I guess that means reddit is redundant, why the fuck are you even here?
175gr · 27 points · Posted at 22:32:55 on February 13, 2016 · (Permalink)
If you glue one Möbius strip to itself you get a projective plane!
[deleted] · 4 points · Posted at 04:43:11 on February 14, 2016 · (Permalink)*
only if you do it backwards, otherwise it just creates a klein bottle.
DuplexFields · 1 points · Posted at 01:47:29 on February 14, 2016 · (Permalink)
Slice a bagel down the middle with a half-twist that meets up where you started. Which side is the one side of the Möbius bagel, the flat side or the curvy side?
[deleted] · 2 points · Posted at 04:49:36 on February 14, 2016 · (Permalink)
The "moebius" bagel contains two rotations (one for each times it winds around with the moebius cut).
Monkey_Xenu · 1 points · Posted at 03:23:13 on February 14, 2016 · (Permalink)
Sounds interesting, could you elaborate please? I have a studied projective geometry but not in much depth
Moufang_Loop · 1 points · Posted at 04:08:50 on February 14, 2016 · (Permalink)
In addition to having one face, a mobius strip has only one edge. If you glue together a disk and a mobius band along their edge, you get a projective plane.
EmpireOfTheTsun · 17 points · Posted at 23:11:27 on February 13, 2016 · (Permalink)
If you make a Möbius strip out of a road, you create a very pissed off chicken.
Rehovak · 7 points · Posted at 23:18:56 on February 13, 2016 · (Permalink)
Why did the chicken cross the Möbius strip? To get to the same side.
MonsignorSauerkraut · 5 points · Posted at 03:29:14 on February 14, 2016 · (Permalink)
https://youtu.be/AAsICMPwGPY
AliceTaniyama · 13 points · Posted at 00:25:51 on February 14, 2016 · (Permalink)
A mathematician named Klein
Thought the Möbius band was divine
Said he, "If you glue
The edges of two
You get a neat bottle like mine."
darkstarone · 4 points · Posted at 01:14:14 on February 14, 2016 · (Permalink)
They also make cool 3D printed bottle openers!
xereeto · 3 points · Posted at 03:49:33 on February 14, 2016 · (Permalink)
Topologists can't tell the difference between a coffee cup and a donut.
sun_worth · 2 points · Posted at 00:06:39 on February 14, 2016 · (Permalink)
If you take scissors and cut a Möbius strip in half along its centerline, you end up with a loop with two twists -- no longer a Möbius strip. If you cut it one third of the way from the edge you end up with two connected loops -- one a Möbius strip and the other a longer loop with two twists.
philly_fan_in_chi · 2 points · Posted at 02:49:55 on February 14, 2016 · (Permalink)
And using gluing/surgery, Klein bottles and spheres are sufficient to construct all other surfaces.
msstark · 2 points · Posted at 03:03:21 on February 14, 2016 · (Permalink)
I just googled Klein bottle, and it's awfully close to that sex-reassignment surgery diagram that was on front page a few weeks ago.
staytaytay · 2 points · Posted at 03:24:01 on February 14, 2016 · (Permalink)
Bisecting a mobius strip down the centre creates a double long strip with two half twists.
Repeating the exercise doesnt make an even longer strip, but instead creates two interlocked copies of the second strip at half width.
Weirder still, It is possible to make the two-half-twist strip into a longer strip, by cutting it 1/3 of the way across instead of halfway.
Spiralofourdiv · 2 points · Posted at 17:13:01 on February 16, 2016 · (Permalink)
Does it? I thought glueing the edge of a Mobius strip to another creates a real projective plane?EDIT: Glueing the edge of a Mobius strip to itself generates a real projective plane.
coolkid1717 · 4 points · Posted at 22:58:48 on February 13, 2016 · (Permalink)
That's not correct. If you extend the edges of a mobius strio so that they connect to each other it creates a Klein bottle.
Rehovak · 6 points · Posted at 23:06:48 on February 13, 2016 · (Permalink)
That's why I said topologically. Topologists don't care about the exact look of things, just their properties. You are right in that you would have to extend or stretch edges. There's a joke that topologists get their coffee cups and their donuts mixed up because topologically they are the same!
bobby8375 · 2 points · Posted at 02:48:29 on February 14, 2016 · (Permalink)
You weren't really clear. All you said was "glue two mobius strips together," and you didn't specify at all which parts of the two strips were to be glued together.
Rehovak · 1 points · Posted at 16:42:12 on February 14, 2016 · (Permalink)
Sorry! It's kind of hard to describe without pictures, but I'm terrible at drawing, it's why I chose Math! :P
bobby8375 · 3 points · Posted at 21:10:09 on February 14, 2016 · (Permalink)
When I think about gluing two mobius strips, all I can think of is: https://www.youtube.com/watch?v=wKV0GYvR2X8
jonhydude · 1 points · Posted at 02:05:49 on February 14, 2016 · (Permalink)
Also, if you tape two opposite mobius strips together and cut them in half, you get two intertwined love hearts.
abedneg0 · 1 points · Posted at 02:48:58 on February 14, 2016 · (Permalink)
If you cut a Möbius strip lengthwise, you get a longer Möbius strip that is twisted twice. If you then cut that Möbius strip lengthwise, you get two double-twisted Möbius strips interlinked. This is fun to do with paper an scissors.
[deleted] · 1 points · Posted at 03:33:38 on February 14, 2016 · (Permalink)
spazzes internally
_Psyki · 1 points · Posted at 05:19:07 on February 14, 2016 · (Permalink)
Also, if those Möbius Strips were not of the same chirality, when you cut down the centre line of each you will be left with two entwined hearts.
TomSwirly · 1 points · Posted at 05:40:11 on February 14, 2016 · (Permalink)
Ucantalas · 1 points · Posted at 08:04:17 on February 14, 2016 · (Permalink)
If you glue three Mobius Strips together, it creates a mess.
233C · 1 points · Posted at 09:27:30 on February 14, 2016 · (Permalink)
Anybody who has never done this, please try:
Make a comfortably wide Möbius strip.
Cut is along its middle line and see what you got (1 trip, 2 strips? are they Möbius strips or not?)
Than cut it again, along its middle line.
be amazed.
[deleted] · 1 points · Posted at 10:12:36 on February 14, 2016 · (Permalink)
Nice! I knew about both objects, but not about this fact. Pretty neat :)
Embusen4 · 1 points · Posted at 12:13:27 on February 14, 2016 · (Permalink)
Who else remember that awesome crazy guy from numberphile?
baraxador · 1 points · Posted at 12:17:28 on February 14, 2016 · (Permalink)
I watched that video yesterday...
bruzdnconfuzd · 1484 points · Posted at 21:50:44 on February 13, 2016 · (Permalink)*
12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
...aaaand so on.
EDIT: for those confused mobile users, the 2 at the end of each starting number is supposed to be an exponent. Sorry for the confusion - I'm not a witch!
Osimonbinladen · 501 points · Posted at 00:25:54 on February 14, 2016 · (Permalink)
You can also choose how high the numbers go by shrinking the length of one value.
111 * 11111 = 1233321
1111 * 11111111 = 12344444321
The highest number in the result is the length of the shorter value. It then occurs one plus the difference in lengths of the numbers times.
PSLWORK · 66 points · Posted at 03:52:09 on February 14, 2016 · (Permalink)
what the fuck
PhotonicFlow · 8 points · Posted at 04:22:56 on February 14, 2016 · (Permalink)
Multiplication of numbers is basically a convolution of their digits. This fact is most obvious when all digits are 1s.
YukarinVal · 2 points · Posted at 04:12:41 on February 14, 2016 · (Permalink)
I'm sorry, but I still don't get this part. ;_;
Osimonbinladen · 8 points · Posted at 05:09:57 on February 14, 2016 · (Permalink)
It was hard to word, so I'll give an example.
1111 * 111111 = 123444321
The length of the first one is 4, the length of the second is 6.
This means that the highest number is 4 (the shorter of the two). The number is repeated 3 times because 6 - 4 + 1 = 3. (the length of the longest - the length of the shortest + 1)
YukarinVal · 1 points · Posted at 11:34:02 on February 14, 2016 · (Permalink)
Oh, now I get it. Thanks for explaining.
Jdrawer · 1 points · Posted at 08:27:29 on February 14, 2016 · (Permalink)
Could you restate the last sentence for me in relation to the distance between the 0th leftest digit and the most central digit?
PropertyOfMatter · 590 points · Posted at 23:25:13 on February 13, 2016 · (Permalink)*
FTFY
scrubmaster9001 · 14 points · Posted at 02:07:32 on February 14, 2016 · (Permalink)
F2 TY
justtoreplythisshit · 6 points · Posted at 01:12:07 on February 14, 2016 · (Permalink)*
FTFY
once-and-again · 6 points · Posted at 02:15:02 on February 14, 2016 · (Permalink)
English text is nonabelian.
(Also, you lost the s.)
BadBoyJH · 3 points · Posted at 04:19:05 on February 14, 2016 · (Permalink)
FTFY
(Written as "a^(4)nd so on")
PropertyOfMatter · 2 points · Posted at 05:31:18 on February 14, 2016 · (Permalink)
Thanks dude
IAMA_dragon-AMA · 1 points · Posted at 02:17:03 on February 14, 2016 · (Permalink)
UnchainedMundane · 5 points · Posted at 03:02:12 on February 14, 2016 · (Permalink)
there was no reason to capture those groups
IAMA_dragon-AMA · 1 points · Posted at 03:16:02 on February 14, 2016 · (Permalink)
I do so out of habit. Parentheses are wonderful, so long as they're properly matched.
PropertyOfMatter · 5 points · Posted at 03:42:39 on February 14, 2016 · (Permalink)
I think there's an XKCD for this....
pasqualy · 21 points · Posted at 23:54:11 on February 13, 2016 · (Permalink)
Sort of breaks down after 111111111112 = 123456790120987654321 though. Pretty cool up to that point though
bruzdnconfuzd · 11 points · Posted at 00:31:18 on February 14, 2016 · (Permalink)
Wow - what an interesting dose of perspective! The trick I cited above I learned back in maybe 4th or 5th grade just for shiggles. Obviously I've remembered it since then. But I never thought to keep pushing it until the rule breaks. I had always just assumed, but even today I got to learn even more about it. Thanks, and not in some sarcastic or ironic way - this was surprisingly enlightening.
siamthailand · 5 points · Posted at 03:29:05 on February 14, 2016 · (Permalink)
Actually it doesn't break at all. What he's doing wrong is that he's doing it in base10. When you encounter a number greater than 9 it can't be represented by a single digit in base 10 so it fucks up everything.
So just use a higher base it will work. :)
pasqualy · 1 points · Posted at 04:00:35 on February 17, 2016 · (Permalink)
You (and others) are correct about just moving to a higher base system to extend this pattern further. However, no matter what finite number you use as a base, there will be a point at which this pattern stops being obvious (i.e. "breaks", if you decompose the digits, you can probably see the pattern again but it's not immediately obvious as it is before that point).
If you can find a finite base where this works for an arbitrarily long string of 1s, I would be very interested in a proof.
siamthailand · 1 points · Posted at 04:10:36 on February 17, 2016 · (Permalink)
I am not quite sure what the first part means, but proving your second part would be rather trivial. While I am not sure how to write proofs, but what you're simply doing is shifting 1111..s by 1 position and adding. This would always hold true for any base.
pasqualy · 1 points · Posted at 00:17:04 on February 18, 2016 · (Permalink)
The first part is essentially that if you start in one base system (i.e. base 10), you can follow the pattern of a string of x 1s squared being equal to 123...x...321 until you get to x > your base (i.e. x = 11 in my previous example). However, if you increase the base (say from 10 to 16), the pattern will once again hold for some strings that broke it in the old base. My point was that no matter how large you make the base, as long as it's a finite number (i.e. as long as it makes sense), there will be a string of 1s long enough to break the pattern. For example:
111111111112 = 123456790120987654321 in base 10 (pattern broken) but 111111111112 = 123456789ABA987654321 in base 16 (pattern works for the same string of 1s). Then you can increase the string to 11111111111111111 to break the pattern in base 16.
The second part was asking for if there is a specific base system where the 11...12 = 123...321 pattern will hold no matter how long you make the string of 1s.
siamthailand · 2 points · Posted at 00:25:02 on February 18, 2016 · (Permalink)
No, there can't be any such base, because for n 1s, it'll hold true in Base n+1. That will always be the case.
pasqualy · 1 points · Posted at 00:43:27 on February 18, 2016 · (Permalink)
That's what I thought, but I was hoping someone would bring up some cool, obscure bit of math to get around that somehow.
siamthailand · 1 points · Posted at 00:47:21 on February 18, 2016 · (Permalink)
Actually, once you do it on paper, you know, old school multiplication, you'll instantly see why it holds true and suddenly it'll lose its charm.
pasqualy · 1 points · Posted at 03:30:53 on February 18, 2016 · (Permalink)
I can see why it holds true. That doesn't really cause it to lose its charm for me, it just changes it from "charming due to mystery" to "charming due to neat math stuff".
LanguiDude · 2 points · Posted at 03:05:50 on February 14, 2016 · (Permalink)
Heh, "shiggles."
siamthailand · 6 points · Posted at 03:29:11 on February 14, 2016 · (Permalink)
Actually it doesn't break at all. You're doing it in base10. When you encounter a number greater than 9 it can't be represented by a single digit in base 10 so it fucks up everything.
So just use a higher base it will work. :)
bobthemighty_ · 3 points · Posted at 08:07:42 on February 14, 2016 · (Permalink)
It works if you write it out! 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 4 3 2 1. It just happens that you carry the 10 to the next digit (the nine), which also carries to the eight making it a 9, so you end up with 1234567900987654321
hypervelocityvomit · 2 points · Posted at 10:31:02 on February 15, 2016 · (Permalink)
Try 01010101010101010101012 = 01 02 03 04 05 06 07 08 09 10 11 10 09 08 07 06 05 04 03 02 01
EDIT: Which is what /u/siamthailand said in the other branch. Higher base are belong to us.
[deleted] · 11 points · Posted at 23:44:46 on February 13, 2016 · (Permalink)
11111111112 = 1234567900987654321 yuck
111111111112 = 123456790120987654321 errm
1111111111111111112 = 12345679012345678987654320987654321 ooh neat
Domriso · 2 points · Posted at 06:32:32 on February 14, 2016 · (Permalink)
So, after it hits "9" in the middle it just starts adding a new set of "123456789" into the middle? Interesting.
MissApocalycious · 5 points · Posted at 07:34:37 on February 14, 2016 · (Permalink)
If you had a number system that was a higher base than 10, it would be clearer what's going on.
For example, if you use hexadecimal (base 16, 0-1 plus a-f) you get things like:
1111111111111112 = 123456789abcdefedcba987654321
Domriso · 1 points · Posted at 17:16:42 on February 14, 2016 · (Permalink)
Yeah, hexadecimal does make more sense in this context.
hypervelocityvomit · 1 points · Posted at 10:34:55 on February 15, 2016 · (Permalink)
Hexadecimal numbers are c001 af.
bobthemighty_ · 3 points · Posted at 08:12:57 on February 14, 2016 · (Permalink)
It makes more sense to write it out before you figure it out, 12 ones would be: 1 2 3 4 5 6 7 8 9 10 11 12 11 10 9 8 7 6 5 4 3 2 1, then we just have to carry all the ones over to get 1234567901232098765432.
Domriso · 1 points · Posted at 17:16:25 on February 14, 2016 · (Permalink)
Interesting. That does make sense, thanks!
Jellooooo · 4 points · Posted at 00:35:09 on February 14, 2016 · (Permalink)
Pascal's Triangle.
hypervelocityvomit · 1 points · Posted at 10:39:06 on February 15, 2016 · (Permalink)
No, that's more like...
Jellooooo · 2 points · Posted at 14:40:51 on February 15, 2016 · (Permalink)
This is why I didn't pass math last year.
jux74p0se · 2 points · Posted at 01:24:58 on February 14, 2016 · (Permalink)
also very interesting to this is that these numbers from the generated sequence can be structured into Pascal's Triangle, which is then used to determine the coefficients of binomial expansions.
SleepWouldBeNice · 2 points · Posted at 03:43:09 on February 14, 2016 · (Permalink)
Man, this didn't work on mobile. Doesn't show the super scripts properly.
Busybodii · 2 points · Posted at 05:47:30 on February 14, 2016 · (Permalink)
Thank you. I couldn't figure out what kind of crazy math was happening and I thought people were just messing with non-math people. On mobile it looks like 12=1, 112=121, etc. That makes way more sense.
TheFuckingPizzaGuy · 1 points · Posted at 02:58:00 on February 14, 2016 · (Permalink)
I don't get it.
pickle_inspector · 1 points · Posted at 03:04:22 on February 14, 2016 · (Permalink)
I think it would be weirder if 111112 = 4763316229
garblegarble12342 · 1 points · Posted at 12:45:03 on February 14, 2016 · (Permalink)
or if it was like 3.5, that would be weird.
hypervelocityvomit · 1 points · Posted at 10:37:49 on February 15, 2016 · (Permalink)
"Did you know that 7 times pi is closer to an integer than 7 times 3.14?"
intensely_human · 1 points · Posted at 03:16:29 on February 14, 2016 · (Permalink)
what
amanager · 1 points · Posted at 04:38:38 on February 14, 2016 · (Permalink)
Crazier if you ad the "1s" together on the left and square it, the result will be the sum of the numbers on the right:
112 = 121 same as (1+1)2 = 4 (1+2+1)
1112=12321. Same as 32 = 9(1+2+3+2+1)
11112= 1234321 Same as 42= 16 (1+2+3+4+3+2+1)
hypervelocityvomit · 2 points · Posted at 10:43:53 on February 15, 2016 · (Permalink)
Both are actually the same:
(x+1)2 = x2 + 2x + 1
If x=10, this simplifies to (10+1)2 = 100 + 20 + 1, or 112 = 121
but if x=1, you get (1+1)2 = 1+2+1, or (1+1)2 = 1+2+1
Next one: (x2 + x + 1)2 = x4 + 2x3 + 3x2 + 2x + 1
x=10: (100+10+1)2 = 10000 + 2000 + 300 + 20 + 1, or 1112 = 12321
x=1: (1+1+1)2 = 1 + 2 + 3 + 2 + 1, or 32 = 9. Etc, etc. Until carries start to ruin it, that is.
Ryan949 · 1 points · Posted at 05:45:16 on February 14, 2016 · (Permalink)
Now comes the question of whether or not this works in other bases
MissApocalycious · 2 points · Posted at 07:35:39 on February 14, 2016 · (Permalink)*
It does.
In base 16, using hexadecimal:
1111111111111112 = 123456789abcdefedcba987654321
Ryan949 · 1 points · Posted at 08:26:28 on February 14, 2016 · (Permalink)
^ you dropped this
MissApocalycious · 1 points · Posted at 18:18:38 on February 14, 2016 · (Permalink)
Thanks, fixed. Copy/paste loses it, and I forgot that :)
StinkinFinger · 1 points · Posted at 05:59:29 on February 14, 2016 · (Permalink)
I don't get this one.
AsInOptimus · 1 points · Posted at 06:24:00 on February 14, 2016 · (Permalink)
I don't get it. :(
(I have such a love-hate relationship with math. I find it fascinating, and completely incomprehensible.)
tychozorente · 1 points · Posted at 07:04:41 on February 14, 2016 · (Permalink)
Ahh, that takes me back to choir practise.
phyllop23 · 1 points · Posted at 08:29:19 on February 14, 2016 · (Permalink)
I don't get this. Can I get an explanation please?
Guitarswithlegs · 1 points · Posted at 09:16:16 on February 14, 2016 · (Permalink)
This is how my choir teacher had us sing a scale, by order of the 1st, 2nd, 3rd etc. Note in the scale.
MediocreMatt · 1 points · Posted at 10:01:13 on February 14, 2016 · (Permalink)
Wait, what?
karma3000 · 1 points · Posted at 11:31:07 on February 14, 2016 · (Permalink)
This is the coolest and also the easiest for non PhDs to get.
t17dr · 1 points · Posted at 13:46:12 on February 14, 2016 · (Permalink)
all4hurricanes · 1 points · Posted at 14:31:55 on February 14, 2016 · (Permalink)
If you use lattice multiplication this makes a lot of sense. Since each box will only contain 1 the highest digit in the product will be number of boxes in the longest diagonal.
StaleTheBread · 1 points · Posted at 15:05:08 on February 14, 2016 · (Permalink)
I'm on mobile so all I see is:
12 = 1
112 = 121
1112 = 12321
Etc
bruzdnconfuzd · 2 points · Posted at 15:43:26 on February 14, 2016 · (Permalink)
Oh, gotcha. What your phone isn't showing you is that the 2 at the end of each first number is supposed to be an exponent. So the numbers should read 11-squared, 111-squared and so on. Apologies to the mobile redditors.
StaleTheBread · 1 points · Posted at 16:19:33 on February 14, 2016 · (Permalink)
I figured it out. The same happened when I posted a comment earlier.
KitAndKat · 1 points · Posted at 17:16:30 on February 14, 2016 · (Permalink)
This is also true in other bases, eg
In base-16: 11 x 11 = 121
Decimal equivalent: 17 x 17 = 289
In base-4: 11 x 11 = 121
Decimal equivalent: 5 x 5 = 25
For base n, it breaks down for n digits or more, i.e. 11 x 11 != 121 in base-2 because there is no 2 in base-2 notation. Similarly, won't work in base 10 for 1111111111 x 1111111111.
small_potatoes312 · 1 points · Posted at 18:00:10 on February 14, 2016 · (Permalink)
Can somebody explain what this is?
Redbird9346 · 1 points · Posted at 05:18:33 on February 15, 2016 · (Permalink)
In a similar vein, the powers of 11 produce rows of Pascal's triangle.
110 = 1
111 = 11
112 = 121
113 = 1331
114 = 14641
…beyond this point, we need to expand place values beyond 10.
115 = 1×105 + 5×104 + 10×103 + 10×102 + 5×101 + 1 = 161051
116 = 1×106 + 6×105 + 15×104 + 20×103 + 15×102 + 6×101 + 1 = 1771561
... and so on.
hypervelocityvomit · 1 points · Posted at 10:28:24 on February 15, 2016 · (Permalink)
iamnewsorry · 1 points · Posted at 00:44:03 on February 14, 2016 · (Permalink)
How
bruzdnconfuzd · -2 points · Posted at 00:45:56 on February 14, 2016 · (Permalink)
Ummm... because math?
Pi4zza · 2 points · Posted at 04:59:08 on February 14, 2016 · (Permalink)*
Uh well can you actually explain why? I'm curious. I don't understand this at all.
Edit: i'm on mobile and he explained thet the 2 is an exponent, i understand exponents. Nvm.
bruzdnconfuzd · 3 points · Posted at 14:42:18 on February 14, 2016 · (Permalink)
Sorry, I thought my previous answer was enough - it's just the way the math works out every time. Just like 2+2=4, 11x11=121, and 111x111=12321... it just is. But if you want a better visualization of how those numbers stack up, /u/t17dr shows it off really well in this comment below.
Pi4zza · 1 points · Posted at 01:05:37 on February 15, 2016 · (Permalink)
He edited his comment saying that the 2 at the end of each number is an exponent. I didn't see that because im on mobile, i actually inderstand this. My bad man.
[deleted] · 1799 points · Posted at 19:15:55 on February 13, 2016 · (Permalink)
The smallest uninteresting number is 14972. It's uninteresting because it currently appears in no number sequences (minus the sequence of natural numbers, of course).
The number gets bigger as people figure out new sequences with that number.
Learning_Curves · 1685 points · Posted at 20:37:11 on February 13, 2016 · (Permalink)*
If it's the first uninteresting number, then it is quite INTERESTING though.
EDIT: spelling
sim642 · 565 points · Posted at 22:21:50 on February 13, 2016 · (Permalink)
But if that makes it interesting the original argument which made it interesting doesn't apply anymore. Paradox!
[deleted] · 290 points · Posted at 22:55:41 on February 13, 2016 · (Permalink)
Quick, upvote this to the top of r/mildlyinteresting!
[deleted] · 11 points · Posted at 02:54:56 on February 14, 2016 · (Permalink)
No, put it on r/mildlyuninteresting!
reddit__scrub · 7 points · Posted at 06:39:49 on February 14, 2016 · (Permalink)
No, it belongs on /r/mildlyinteresting!
/s
thtrf · 4 points · Posted at 12:26:35 on February 14, 2016 · (Permalink)
Also exists r/notinteresting
Zulfiqaar · 2 points · Posted at 01:15:14 on February 14, 2016 · (Permalink)
But the number is not interesting at all..
[deleted] · 10 points · Posted at 01:41:22 on February 14, 2016 · (Permalink)
Well, it is. Mildly.
Pigswithwigs · 14 points · Posted at 03:02:21 on February 14, 2016 · (Permalink)
This is actually a pretty famous mathematical paradox. https://en.m.wikipedia.org/wiki/Interesting_number_paradox
ShiftyMcShift · 6 points · Posted at 04:22:39 on February 14, 2016 · (Permalink)
As stephen fry said, being socially interesting doesn't make it mathematically interesting.
overhead_albatross · 2 points · Posted at 07:20:43 on February 14, 2016 · (Permalink)
Came for the QI reference.
RedShirtSmith · 2 points · Posted at 02:54:01 on February 14, 2016 · (Permalink)
This is exactly how the numberphile video on it went.
DCdictator · 2 points · Posted at 00:02:29 on February 14, 2016 · (Permalink)
It's not a paradox, it's culturally interesting - not mathematically.
Inteli_Gent · 2 points · Posted at 08:20:55 on February 14, 2016 · (Permalink)
There are such things as non-mathematical paradoxes. Paradoxi? Paradoxes.
tsnErd3141 · 1 points · Posted at 03:25:09 on February 14, 2016 · (Permalink)
You don't prove like that!
...
Reductio ad absurdum
Hence, quod erat demonstrandum
[deleted] · 1 points · Posted at 03:51:27 on February 14, 2016 · (Permalink)
Not really. You just define an uninteresting number as a number that appears in just two sequences:
The sequence of natural numbers and the sequence of uninteresting numbers.
Although I'm not sure what set of sequences /u/HowdyDoodlyDoo is talking about, as 14972 also appears in the sequence of even numbers, which is a pretty obvious sequence to have in any collection of sequences.
kogasapls · 2 points · Posted at 07:42:01 on February 14, 2016 · (Permalink)
OEIS I assume
[deleted] · 1 points · Posted at 04:52:57 on February 14, 2016 · (Permalink)
That's not merely a paradox, that's a contradiction. Clearly we have not defined interesting consistently
sim642 · 1 points · Posted at 09:30:11 on February 14, 2016 · (Permalink)
Clearly the number being interesting leads to a contradiction but so does it being uninteresting because that leads to the same contradiction as the interesting case. Both cases are contradictory, thus a paradox.
amlaminack · 1 points · Posted at 07:05:17 on February 14, 2016 · (Permalink)
It's not a paradox. Just a contradiction. This means we must conclude that there is no least interesting number.
kogasapls · 1 points · Posted at 07:38:40 on February 14, 2016 · (Permalink)*
Russell's Paradox: Does the set of all sets which do not contain themselves contain itself?
Inteli_Gent · 1 points · Posted at 08:27:21 on February 14, 2016 · (Permalink)
I can't remember what it's called, but this reminds me of the paradox/thought experiment (not sure which it would be) that goes something like:
NOTE: Quotes are added to differentiate between ideas, not because I thought they were grammatically needed.
almightySapling · 1 points · Posted at 22:33:22 on February 13, 2016 · (Permalink)
Berry and Kolmogorov woukd like to see you.
[deleted] · 1 points · Posted at 06:14:01 on February 14, 2016 · (Permalink)
searched these comments just to find the kolmogorov complexity nerd i knew was hiding in here
PM_ME_UR_THROW_AWAYS · 6 points · Posted at 01:59:40 on February 14, 2016 · (Permalink)
I see Bertrand Russell is alive and well in you
Learning_Curves · 1 points · Posted at 03:18:54 on February 14, 2016 · (Permalink)
Oh, you mean it for this reference u/OKImHere made moments ago?
PM_ME_UR_THROW_AWAYS · 2 points · Posted at 08:36:28 on February 14, 2016 · (Permalink)
Actually, no, I was referring to this
nicholas818 · 1 points · Posted at 06:30:32 on February 14, 2016 · (Permalink)
"What if I add the sequence of (natural) numbers that aren't in any other sequence?"
zarraha · 8 points · Posted at 23:41:34 on February 13, 2016 · (Permalink)
It's not. Being the first uninteresting number isn't very interesting. It's half interesting (and thus only half qualifies as uninteresting). Paradox solved.
[deleted] · 3 points · Posted at 02:22:51 on February 14, 2016 · (Permalink)
It's not really a paradox either way. It's a joke proof that there are no uninteresting numbers, because if there are then there has to be a lowest uninteresting number, which immediately makes it interesting. And so on.
bald_and_nerdy · 3 points · Posted at 00:37:03 on February 14, 2016 · (Permalink)
So 14972 has at least 1 friend...
[deleted] · 3 points · Posted at 05:15:08 on February 14, 2016 · (Permalink)
A set of numbers not in sets? Fuck, what am I gonna do with all these turtles?
cmpalmer52 · 3 points · Posted at 05:46:05 on February 14, 2016 · (Permalink)
"All primes are odd" "No, 2 is prime" "That makes 2 the oddest prime of them all"
OKImHere · 2 points · Posted at 02:33:12 on February 14, 2016 · (Permalink)
You're suggesting it's some kind of Borryng number?
abedneg0 · 2 points · Posted at 02:47:31 on February 14, 2016 · (Permalink)
That's the core of the inductive proof that every number is interesting.
ChickenBrad · 2 points · Posted at 04:30:42 on February 14, 2016 · (Permalink)
but is there a pattern to the uninteresting numbers???
nicholas818 · 2 points · Posted at 06:27:48 on February 14, 2016 · (Permalink)
What if I add the sequence of (natural) numbers that aren't in any other sequence?
ImightbeBertrandRussel.
Concubicycle · 1 points · Posted at 04:31:12 on February 14, 2016 · (Permalink)
If I is the set of all numbers that belong to known sequences (except natural numbers), let U be a sequence of all elements of the negation of I. Now, all numbers are interesting.
Nerdican · 1 points · Posted at 05:46:28 on February 14, 2016 · (Permalink)
I argue that any interest it should recieve for being the first uninteresting number really belongs to the last interesting number, and thus the first uninteresting number remains uninteresting.
thestickystickman · 96 points · Posted at 19:28:53 on February 13, 2016 · (Permalink)
Wait, what does that mean?
[deleted] · 238 points · Posted at 19:36:22 on February 13, 2016 · (Permalink)
Things like square numbers and Fibonacci numbers are simple sequences, there are ones which are much more complicated.
The number 14972 is a number which isn't part of any number sequence created so far.
thestickystickman · 166 points · Posted at 19:51:07 on February 13, 2016 · (Permalink)*
So, it's not in any important sequences, then? Because it's in the arithmetic sequence Tn = 2n.
The_White_Light · 121 points · Posted at 23:38:33 on February 13, 2016 · (Permalink)
That's a cop-out. You can say that any number divisible by X is in the set of Xn and therefore is "interesting". The only exceptions are primes, but they're interesting already.
AlephOmega1 · 13 points · Posted at 05:29:03 on February 14, 2016 · (Permalink)
This entire idea is probably the most ill-defined thing I've seen in a while. Are you being serious? This is totally ridiculous on several accounts. First, there's no way to define when a sequence is interesting. Second, the even numbers are certainly interesting (for instance, they are the "largest" proper subgroup of Z). Third, the idea that some constant (the "smallest uninteresting number") should be defined in terms of human mathematical knowledge is totally antithetical to the central goals and philosophy of mathematics. As discussed above, it even leads directly to a paradox, in that "the least uninteresting number" is certainly an interesting property to have.
3holes2tits1fork · 23 points · Posted at 06:11:40 on February 14, 2016 · (Permalink)
I think you are taking the word "interesting" a bit too literally here. It's not uncommon for professions to take common words and derive a more specific meaning for their field. In this case, "interesting" just means it's apart of a sequence used in non-elementary mathematics. Useful is another way to look at it. There's no paradox if you understand that much. Getting picky because "interesting" means something else in other contexts isn't useful. Our legal system would fall apart if that were the case :)
db0255 · 1 points · Posted at 05:07:14 on February 15, 2016 · (Permalink)
Yeah, the term "interesting" would definitely be void-for-vagueness if it were part of mathematical US case law.
AlephOmega1 · -11 points · Posted at 06:18:39 on February 14, 2016 · (Permalink)
Interesting (lol) perspective
-Samba- · 2 points · Posted at 14:53:48 on February 14, 2016 · (Permalink)
Another example is the difference between a proof in science and a proof in mathematics. In science a proof is just overwhelming evidence to support the theory, while a mathematical proof is a logical certainty.
db0255 · 3 points · Posted at 05:05:26 on February 15, 2016 · (Permalink)
This is how I imagine the conversation at an average lunch goes for grad students in a college math department.
JhonnyWongStockings · -1 points · Posted at 00:29:16 on February 14, 2016 · (Permalink)
Yeah, totally. I was about to raise this point, but you raised it first.
algag · -8 points · Posted at 03:35:07 on February 14, 2016 · (Permalink)
Yeah, totally. I was about to raise this point, but you raised it first.
What a cop out /s ;)
NYpoliceMan · 2 points · Posted at 01:27:17 on February 14, 2016 · (Permalink)
He shows in the video that it WOULD show up if one of the articles in the number sequence went far enough to include those numbers as a result.
2074red2074 · 2 points · Posted at 03:57:06 on February 14, 2016 · (Permalink)
Sequences that include all real numbers, all numbers greater than a certain number, all numbers that don't fall into a certain sequence, etc. don't count.
DoctorSingh · 1 points · Posted at 02:56:41 on February 14, 2016 · (Permalink)
Someone call Nobel.
backtoss56 · 7 points · Posted at 03:00:52 on February 14, 2016 · (Permalink)
14972
I've been staring at that number
9 minus 7 is 2.
9 plus 4 and 1 minus 7 is 2.
So regarding 9 the answer is 2. The right side symbolizes negative while its left side is positive. However 9 cannot attain 2 without -7.
14972
Which draws the question, does 1+1=2? If so then 14972 can really be seen as (597)2.
9-7 = 2.
5+9-7 = 2.
But this is pointless because this number is special.
1+4+9-7=2
9-7 = 2.
With this number, we can break the rule of equality, in that by removing the positive side of 9, we keep equilibrium.
But we all know, this isn't the same. What happened to 1 and 4?
9 decided to drop 7, but became worried. How will he achieve 2? He called up his friends still on his speed dial, 1 and 4.
After a while, 9, 4, and 1 went out together. The resulting night, 9 was reminded of 7, as the resulting night equated to 14. 4 and 1 tried putting their heads together, but it wasn't the same. 14/5 was missing 2. But 9 met a number that was out of this world that night, she was more than just a number. She opened his world past just whole numbers, and suddenly, 2 didn't seem all that anymore. And on that day, 9 said fuck valentines day and went home.
GambitGamer · 6 points · Posted at 06:38:15 on February 14, 2016 · (Permalink)
This is what I needed. Thank you.
ny_rangers · 2 points · Posted at 06:39:18 on February 14, 2016 · (Permalink)
Well this was quite a ride
sephrinx · 2 points · Posted at 08:11:49 on February 14, 2016 · (Permalink)
It was Singed...
richardathome · 1 points · Posted at 20:21:22 on February 14, 2016 · (Permalink)
Thats Numberwang!
db0255 · 1 points · Posted at 05:12:32 on February 15, 2016 · (Permalink)
I mean, the only reason I agree is because I'm too lazy to check your logic. But it seems to check out.
_____D34DP00L_____ · 9 points · Posted at 01:28:51 on February 14, 2016 · (Permalink)
Why don't I just create a sequence that begins with that number?
-Mountain-King- · 3 points · Posted at 16:05:51 on February 14, 2016 · (Permalink)
Like, say, a sequence of numbers that don't appear in any other sequence.
LittleDinghy · 2 points · Posted at 15:32:27 on February 14, 2016 · (Permalink)
Because then it would be a sequence we already know, just shifted. That doesn't make the new sequence mathematically interesting.
Bibibis · 2 points · Posted at 04:03:25 on February 14, 2016 · (Permalink)
It's part of my brand new "Sequence of Uninteresting Numbers"™ now!
LtWorf_ · 1 points · Posted at 13:50:43 on February 14, 2016 · (Permalink)
Is this sequence empty?
hijinga · 2 points · Posted at 23:21:37 on February 13, 2016 · (Permalink)
But how do you decide its in a sequence? In a sequence of 56345 how do you decide its got 63 in it or its got 634 in it
[deleted] · 6 points · Posted at 23:23:26 on February 13, 2016 · (Permalink)
Essentially, it's a list compiled by these people: https://oeis.org/
once-and-again · 1 points · Posted at 02:30:58 on February 14, 2016 · (Permalink)
Sequence of numbers, not sequence of digits. "56345" isn't a sequence of numbers; it's just one number, equal to 5 × 59 × 191.
It's also apparently not a very interesting number, as it only pops up in a couple of obscure sequences involving Molien series, whatever the hell those are. (Beyond a reminder that I really should read generatingfunctionology sometime, I mean.)
Gadget_Smith · 1 points · Posted at 07:12:01 on February 14, 2016 · (Permalink)
so you're saying that 14972 doesn't exist within PI that we know of so far?
[deleted] · 1 points · Posted at 15:17:01 on February 14, 2016 · (Permalink)
That has nothing to do with it.
Gadget_Smith · 1 points · Posted at 16:45:37 on February 14, 2016 · (Permalink)
oh, well then I don't understand?
[deleted] · 1 points · Posted at 20:36:36 on February 14, 2016 · (Permalink)
It's a stupid "fact". Best to just drop it.
sephrinx · 1 points · Posted at 08:10:33 on February 14, 2016 · (Permalink)
So, is 14972 part of a sequence? What about 829938? 9320? Why is 14972, specifically, so special and different?
LtWorf_ · 1 points · Posted at 13:49:36 on February 14, 2016 · (Permalink)
I present to you the LtWorf_'s sequence.
a(n) = 7486*n
Now 14972 is part of a number sequence.
datorangeguy · 1 points · Posted at 23:09:32 on February 13, 2016 · (Permalink)
What about even numbers?
BiggerJ · 2 points · Posted at 07:19:32 on February 14, 2016 · (Permalink)
He was referring to the Online Encyclopedia of Integer Sequences, presumably because, like Wikipedia, archive.org's software collection and so forth, it will destroy your free time.
rcheu · 1 points · Posted at 03:14:12 on February 14, 2016 · (Permalink)
Literally just means it's not in oeis https://oeis.org/search?q=14972&language=english&go=Search
TobiTako · 1 points · Posted at 07:33:02 on February 14, 2016 · (Permalink)
I think it means that it's the first number that doesn't appear in OEIS (https://oeis.org/), which is the database of "meaningful" sequences found.
Obviously you are right in saying that any integer appears in infinitely many sequences.
elyisgreat · 35 points · Posted at 21:22:16 on February 13, 2016 · (Permalink)
There are no boring numbers.
DoWhile · 30 points · Posted at 02:20:55 on February 14, 2016 · (Permalink)
All positive integers are boring.
Proof by contradiction:
Suppose not. Let n be the smallest number that's not boring.
Whatever.
QED
elyisgreat · 2 points · Posted at 02:39:30 on February 14, 2016 · (Permalink)
That proof only works for non number-enthusiasts.
[deleted] · 5 points · Posted at 21:33:52 on February 13, 2016 · (Permalink)
He has a very similar speaking style to Brian Cox.
scrochum · 2 points · Posted at 02:24:36 on February 14, 2016 · (Permalink)
brian cox is a bit more breathy, like everything is so infinitely amazing it needs to be treated with reverence
passiveaggressiveMN · 2 points · Posted at 02:16:57 on February 14, 2016 · (Permalink)
I'm over here like
j3i4ls99a02le0dl30dx · 9 points · Posted at 00:11:26 on February 14, 2016 · (Permalink)
Sequence of even integers?
[deleted] · 13 points · Posted at 23:44:15 on February 13, 2016 · (Permalink)
This isn't really mathematics but empirical data from OEIS. I can make up a sequence containing any arbitrary integer.
DWdota · 1 points · Posted at 15:36:41 on February 14, 2016 · (Permalink)
Well, no.
[deleted] · 2 points · Posted at 15:54:59 on February 14, 2016 · (Permalink)
It is still no formal mathematical fact. The number is just a few years old.
As I said: I can make up a sequence containing any arbitrary number.
PM_ME_YOUR_FELINE · 6 points · Posted at 01:57:32 on February 14, 2016 · (Permalink)
no
14972 occurs at position 49091 in pi. This string occurs 1984 times in the first 200M digits of Pi.
MunchmaKoochy · 4 points · Posted at 00:57:53 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Interesting_number_paradox
ngwoo · 6 points · Posted at 00:33:31 on February 14, 2016 · (Permalink)
what about the sequence of numbers equal to 14972
it actually has a very prominant role in that sequence
Redingold · 3 points · Posted at 03:14:42 on February 14, 2016 · (Permalink)
For those wondering what this actually means, 14972 is, as of time of writing, the smallest number to not appear in any sequence in the Online Encyclopedia of Integer Sequences, which is a real thing that exists for some reason.
Note that the OEIS only lists so many values in each sequence, so it does appear in some sequences, just at points not listed in the OEIS.
Ojeihah8phoocahW · 2 points · Posted at 23:49:26 on February 13, 2016 · (Permalink)
If only Ramujan were here...
datorangeguy · 3 points · Posted at 23:15:39 on February 13, 2016 · (Permalink)
That's not true. In Trenton, Utah the zip code is 84338. If you convert that into hexadecimal, then (DEC)84338=(HEX)14972. Checkmate, mathematicians.
WaitForItTheMongols · 10 points · Posted at 02:10:03 on February 14, 2016 · (Permalink)
It's in Utah. That makes it even LESS interesting.
Timothy_Claypole · 1 points · Posted at 00:16:52 on February 14, 2016 · (Permalink)
You have just disproven mathematics!
MacAdler · 1 points · Posted at 01:29:27 on February 14, 2016 · (Permalink)
Interestingly enough, the last time I had check, that number was 12407. So I had to check now and the learnt that the number changes; and as for now it is indeed 14972.
YetAnotherDumbGuy · 1 points · Posted at 01:36:39 on February 14, 2016 · (Permalink)
Consider the set of all numbers that have never been considered... oh, wait, they all vanished!
PM_ME_MARDIGRAS_PICS · 1 points · Posted at 01:52:33 on February 14, 2016 · (Permalink)
You would think that it would be the lonliest number, rather than 1
farcicaldolphin38 · 1 points · Posted at 01:55:43 on February 14, 2016 · (Permalink)
That's quite the interesting fact
TheOnlyMego · 1 points · Posted at 02:12:45 on February 14, 2016 · (Permalink)
Sure it is. It's in the sequence of integers that do not appear in any integer sequence other than the natural numbers.
TheElectriking · 1 points · Posted at 02:25:31 on February 14, 2016 · (Permalink)
But it appears in the sequence of uninteresting numbers...
IAMA_dragon-AMA · 1 points · Posted at 02:35:28 on February 14, 2016 · (Permalink)
I can't remember if I saw this on a QI episode or heard about it from the No Such Thing As A Fish podcast.
EricTheEmu · 1 points · Posted at 02:55:56 on February 14, 2016 · (Permalink)
Is there not a sequence of uninteresting numbers?
KingGumboot · 1 points · Posted at 03:13:06 on February 14, 2016 · (Permalink)
I think I just created a paradox by creating a sequence of uninteresting numbers. Do I get to name it now?
nixcamic · 1 points · Posted at 03:27:07 on February 14, 2016 · (Permalink)
So if I create a sequence of interesting numbers....
acatcus · 1 points · Posted at 03:52:18 on February 14, 2016 · (Permalink)
What about the constant sequence where each term is 14972?
yossi_peti · 1 points · Posted at 04:08:22 on February 14, 2016 · (Permalink)
I realize this is a tongue-in-cheek answer, but 14972 does appear as one of the first numbers in 2 sequences on OEIS, which is admittedly fewer than I expected.
raias4 · 1 points · Posted at 04:24:28 on February 14, 2016 · (Permalink)
It's like two is the only even prime number, making it the oddest prime of all
alotofmangos · 1 points · Posted at 04:48:16 on February 14, 2016 · (Permalink)
So what sequence does 14971 appear in?
hex_rx · 1 points · Posted at 04:54:20 on February 14, 2016 · (Permalink)
Wait wouldn't this be found in the Pi sequence at some point?
CHiLLSpeaks · 1 points · Posted at 05:48:10 on February 14, 2016 · (Permalink)
It's even, though?
SidusObscurus · 1 points · Posted at 06:09:32 on February 14, 2016 · (Permalink)
But there is no uninteresting natural number?
Suppose for contradiction there is an uninteresting natural number.. Then there must be a first one. By nature of being the first of this type, that number is interesting. Contradiction, as was to be shown.
squrr1 · 1 points · Posted at 07:16:30 on February 14, 2016 · (Permalink)
Doesn't that make it the first member of the sequence of uninteresting numbers?
sherlip · 1 points · Posted at 07:21:13 on February 14, 2016 · (Permalink)
What about even numbers?
sluuuurp · 1 points · Posted at 08:08:19 on February 14, 2016 · (Permalink)
You should make it clear that your definition of interesting depends on the OEIS, not on any sense of the actual definition of the word "interesting".
bassinastor · 1 points · Posted at 08:08:46 on February 14, 2016 · (Permalink)
What do you mean? You can reach it counting by twos or fours.
romulusnr · 1 points · Posted at 09:43:04 on February 14, 2016 · (Permalink)
It is in the sequence of uninteresting numbers. :P
TeaDrinkingBanana · 1 points · Posted at 09:56:05 on February 14, 2016 · (Permalink)
Qi
saadahmad96 · 1 points · Posted at 10:27:14 on February 14, 2016 · (Permalink)
Even number sequence?
throwaway-user-name · 1 points · Posted at 13:10:23 on February 14, 2016 · (Permalink)
All numbers are interesting
https://en.m.wikipedia.org/wiki/Interesting_number_paradox
flexmuzik · 1 points · Posted at 14:21:53 on February 14, 2016 · (Permalink)
let mysuperawesomesequence = {14972, 29944, ...} = 14972k, k>=1
Not uninteresting anymore.
Dorocche · 1 points · Posted at 14:36:24 on February 14, 2016 · (Permalink)
What constitutes a sequence? Not even numbers?
EonesDespero · 1 points · Posted at 15:01:07 on February 14, 2016 · (Permalink)
And the sequence of powers of 14972? The sequence of even numbers?
What do you mean by a number sequence? What are the rules to be classified as one?
I think is a case of an ill-defined problem.
[deleted] · 1 points · Posted at 19:04:20 on February 14, 2016 · (Permalink)
It's the first number in the sequence of uninteresting numbers, right?
_rocketboy · 1 points · Posted at 20:22:15 on February 14, 2016 · (Permalink)
Proof that all numbers are interesting:
Assume that there is a maximum uninteresting number. Then it has a unique property, making it interesting. Contradiction.
Therefore, all numbers are interesting. QED.
meneldal2 · 1 points · Posted at 02:55:23 on February 15, 2016 · (Permalink)
How about making a series of uninteresting numbers?
eviltreesareevil · 1 points · Posted at 00:40:52 on February 14, 2016 · (Permalink)
What about the sequence of even numbers? That doesn't count, I guess?
[deleted] · 1 points · Posted at 01:02:34 on February 14, 2016 · (Permalink)
It appears in the sequence of numbers where the sum of their digits is a prime number. The list on the website simply isn't long enough.
Felix_Tholomyes · 1180 points · Posted at 20:36:25 on February 13, 2016 · (Permalink)
Almost all real numbers are irrational.
Very unintuitive to me
jmt222 · 335 points · Posted at 21:03:59 on February 13, 2016 · (Permalink)
Rational numbers are countable which essentially means we can associate to each one a natural number n where no two rationals are associated with the same natural number.
Let ε be a positive number that is as small as you would like. For the rational number r associated with 1, we "cover" r with the interval (r-ε/4,r+ε/4) which has length ε/2. For the rational number s associated with 2, we again cover it, but with an interval half as small, i.e. the interval (s-ε/8,s+ε/8) which has length ε/4. Continue in this way to cover all rational numbers. The total length of all the intervals in this cover is:
ε/2+ε/4+ε/8+ε/16+... = ε
So we can cover all rational numbers with a set that is as "small" as we would like. What I have described minus some very technical details is that the set of all rational numbers has measure 0, meaning they account for a "small" small subset of all real numbers. For rationals to be a "small" subset of real numbers, irrationals have to be a "large" subset of real numbers which is to say in the measure sense, almost all real numbers are irrational.
Completeness_Axiom · 292 points · Posted at 23:48:33 on February 13, 2016 · (Permalink)
As a maths student seeing this makes me feel right at home.
jenbanim · 164 points · Posted at 01:41:15 on February 14, 2016 · (Permalink)
I ε> real analysis
89to · 15 points · Posted at 02:42:06 on February 14, 2016 · (Permalink)
Are you kidding me? Seeing episilons give me nightmares from real and complex.
jenbanim · 23 points · Posted at 02:53:59 on February 14, 2016 · (Permalink)
I actually do physics, so I'll just steal your proofs and misuse them I just really wanted to make that joke.
illustribox · 6 points · Posted at 06:50:54 on February 14, 2016 · (Permalink)
Usage of Mathematica
jenbanim · 1 points · Posted at 12:38:39 on February 14, 2016 · (Permalink)
I use so much Mathematica :/
illustribox · 2 points · Posted at 12:50:59 on February 14, 2016 · (Permalink)
The Simplify function absolutely amazes me. That it decides reasonably what is most easily interpreted by a human is astonishing. Like all the other stuff I can guess at some algorithm to implement, but that one is just so open ended.
Am currently in a numerical methods class that uses Matlab. Screw Matlab. There are five distinct ways to pass functions to functions in that accursed language.
eskuvai · 3 points · Posted at 04:49:06 on February 14, 2016 · (Permalink)
accurate af
[deleted] · 2 points · Posted at 03:31:15 on February 14, 2016 · (Permalink)
Did we really see it much in complex? We're certainly using it for Real, but my hilarious memories of complex were not knowing a question on the test, so I just wrote "pi/2".
Got it back: "You're right, but you have no work, so no marks."
limasxgoesto0 · 2 points · Posted at 03:55:19 on February 14, 2016 · (Permalink)
Ironically, despite real being the "math student filtering class" it was the only one I got an A in. Really interesting stuff.
dfsgdhgresdfgdff · 1 points · Posted at 10:38:02 on February 14, 2016 · (Permalink)
Meta.
hypervelocityvomit · 1 points · Posted at 10:45:45 on February 15, 2016 · (Permalink)
That should be a shirt
Ravenchant · 5 points · Posted at 09:26:57 on February 14, 2016 · (Permalink)
Word has it, if you stand in front of a mirror quickly saying "epsilon is less than zero" three times, Cauchy appears and chides you.
mafftastic · 4 points · Posted at 03:50:42 on February 14, 2016 · (Permalink)
How do you make an analyst chuckle?
Let epsilon be less than 0.
Yeahdudex · 3 points · Posted at 03:59:17 on February 14, 2016 · (Permalink)
This thread makes me feel retarded.
don_truss_tahoe · 3 points · Posted at 15:05:18 on February 14, 2016 · (Permalink)
Or at least within an ball of radius r of home.
VioletCrow · 2 points · Posted at 06:37:04 on February 14, 2016 · (Permalink)
I often tell my friends, "When starting off a proof, just let epsilon be greater than zero. I don't care what you're trying to prove, you can't go wrong by doing this."
Mooptimus · 2 points · Posted at 07:55:29 on February 14, 2016 · (Permalink)
how many maths do you study?
Berlinia · 2 points · Posted at 08:26:46 on February 14, 2016 · (Permalink)
I'm missing the δ tho
channingman · 1 points · Posted at 10:15:40 on February 14, 2016 · (Permalink)
Could have been sequence conversion. Then he just needs an n in N.
Berlinia · 1 points · Posted at 10:25:17 on February 14, 2016 · (Permalink)
unless the sequence is in !R ^ n or we are looking at limits in closed sets
ShiftyMcShift · 1 points · Posted at 04:06:58 on February 14, 2016 · (Permalink)
"Yay! You guys are AWESOME!! Life is the best!!!", said Epsilon.
Imreallythatguybro · 1 points · Posted at 07:38:57 on February 14, 2016 · (Permalink)
As a math major, screw epsilon... that with real analysis makes me cry :(
[deleted] · 1 points · Posted at 04:33:38 on February 14, 2016 · (Permalink)
I once saw a guy wearing a t-shirt, in the gym no less, that said, "Let ε<0. Live a little." I legit lol'd.
coolpoop · 23 points · Posted at 21:37:28 on February 13, 2016 · (Permalink)
Even more interesting is getting the Cantor set which has measure 0 but is uncountable.
stackbab · 1 points · Posted at 10:04:02 on February 16, 2016 · (Permalink)
That's not surprising since even the set of all algebraic numbers is countable.
[deleted] · 3 points · Posted at 01:25:16 on February 14, 2016 · (Permalink)
Even more interesting: almost all continuous functions are nowhere differentiable. ( in two senses- topology and in measure).
flexmuzik · 1 points · Posted at 13:55:51 on February 14, 2016 · (Permalink)
Can you ELI engineering student with some undergrad math?
[deleted] · 1 points · Posted at 20:16:50 on February 14, 2016 · (Permalink)
Suppose you have a particle confined to a line. The particle gets hit randomly by other particles around it, causing it to move back and forth( Brownian motion). If you look at the trajectory of the particle, with time in the x axis and position in y, you will get some continuous function ( motion is continuous). Now we could ask the question: what is the probability that the particle's trajectory is one of a given collection of continuous functions? To assign such probabilities in general is a pretty hard problem. What can be proved is that with probability 1, the trajectory of the particle will be a function which is not differentiable anywhere. This is the 'measure theory' part.
Look at the set of all continuous functions on the interval [0,1]. If you have a continuous function on this interval, |f(x)| has a maximum, from basic calculus. If you have two functions f and g, you can talk of how "close" they are: the distance between f and g is the maximum of |f(X)-g(X)|. Now that you have a notion of distance, you can talk of limits of functions, etc. The collection of nowhere differentiable functions is large in the following sense: given any continuous function and a error bound, you can approximate it by a n.d function. Also, all functions close enough to a nowhere differentiable function are nowhere differentiable. This means that functions which are differentiable at atleast one point are sparse, just like the set of integers is sparse in the real line.
cream_of_BARF_soup · 3 points · Posted at 03:20:35 on February 14, 2016 · (Permalink)
A more intuitive explanation (for non-math people) would be that there is a method for creating a list that contains all the rational numbers. No such method exists for the irrational numbers. Any attempt to do so will result in a list that excludes nearly all irrational numbers.
unMasqed · 1 points · Posted at 02:07:31 on February 14, 2016 · (Permalink)
Saw epsilon. Had unpleasant flashbacks from Adv. Calc and Adv. Linear Algebra.
ITouchMyselfAtNight · 1 points · Posted at 06:45:36 on February 14, 2016 · (Permalink)
Which results in some infinities being larger than others.
[deleted] · 1 points · Posted at 08:11:11 on February 14, 2016 · (Permalink)
Coulant you construct such an argument for any set of numbers?
jam11249 · 1 points · Posted at 13:35:12 on February 14, 2016 · (Permalink)
Any countable set of numbers yes. But if you have an uncountable set this won't work. For example there is no way to cover the interval (0,1) by countably many subintervals so that the sum of their lengths is less than one.
This is really how we define "length" for sets that are messier than intervals.
[deleted] · 1 points · Posted at 13:37:14 on February 14, 2016 · (Permalink)
These words seem to make sense but I can't seem to pray what any of these sentences mean. Sorry.
I remember the days I used to think I was pretty smart.
flexmuzik · 1 points · Posted at 14:04:06 on February 14, 2016 · (Permalink)
I don't understand.
When you 'cover' an interval, there are many rational numbers that fall within it. So if you cover the interval around r = 1 (so 3/4 to 1 1/4 in your example), there are many rational numbers that fall within that range.
So for each epsilon term in the summation, you associate a large number of rationals.
jmt222 · 1 points · Posted at 14:31:56 on February 14, 2016 · (Permalink)
You are correct and we could actually change the process to skip those rationals already covered unintentionally in a previous step, but this does not actually gain you anything meaningful towards the result and so no effort is made to do this in proofs usually. The process still contains all rationals with an arbitrarily small cover so it follows that rationals have measure 0.
jux74p0se · 1 points · Posted at 01:17:30 on February 14, 2016 · (Permalink)
is this associated with the epsilon-delta proof of a limit? because it sounds exactly like that to me
dkjb · 2 points · Posted at 03:53:09 on February 14, 2016 · (Permalink)
It's not related. Epsilon (ε) is commonly used in proofs to represent some very small number.
jux74p0se · 1 points · Posted at 12:39:25 on February 14, 2016 · (Permalink)
Thanks for the clarification!
drinks_antifreeze · 1 points · Posted at 05:42:16 on February 14, 2016 · (Permalink)
Someone's studied Lesbesgue integration.
Crixomix · 0 points · Posted at 17:03:07 on February 18, 2016 · (Permalink)
Umm. No. The rationals are uncountably infinite. I didn't read the rest of your post so the rest may be correct. But rationals are definitely uncountably infinite. Because there's ALWAYS one more between the two you just counted.
jmt222 · 2 points · Posted at 23:30:51 on February 18, 2016 · (Permalink)
You are in error. A proof can be found in any basic analysis text or more easily found with an internet search.
Crixomix · 1 points · Posted at 02:06:18 on February 19, 2016 · (Permalink)
Maybe you and I have different definitions of countable. Countable is the whole numbers. You can go from one to the next, an infinite number of times.
Uncountable is rationals, or irrationals. You can pick any two, and never count from one to the next. Yes I have seen the diagonal proof. But no, that is a different kind of countable. In the same way a space filling curve is "two dimensional" technically. But it's really not a 2d object.
StillsidePilot · -14 points · Posted at 01:52:22 on February 14, 2016 · (Permalink)
What's the purpose of going out of your way to use a silly variable? No one thinks you're smarter for it. Just use x.
James697 · 11 points · Posted at 02:18:48 on February 14, 2016 · (Permalink)
Epsilons pretty much the standard symbol used when constructing proofs similar to this one.
jam11249 · 4 points · Posted at 13:36:31 on February 14, 2016 · (Permalink)
Standard mathematics notation isn't trying to be smart.
CaesarTheFirst1 · 193 points · Posted at 21:59:12 on February 13, 2016 · (Permalink)*
More than that! Most numbers aren't even computable!
A computable number is a number that can be generated by a finite program - to be precise, if you give it enough time, it'll calculate the number to however much accuracy you want. For example, 3 is computable, the program that prints 3.00000... (while(1) print 0) satisfies the requirements.
Even pi is computable, it can be shown that pi/4=1-1/3+1/5-1/7... so the program that calculates 1/(2n+1) and adds or subtracts it from our result and keeps updating the result computes pi to arbitary accuracy.
However, almost all numbers aren't computable (the amount of computable numbers is countable), the absurd thing is we never meet a noncomputable number, since we meet numbers in everyday life through equations, integrals, and the like, and all of those are computable.
Asdanf · 96 points · Posted at 01:29:31 on February 14, 2016 · (Permalink)
We do occasionally encounter noncomputable numbers, such as Chaitin's Constant. But it is true that we only ever "meet" describable numbers, and there are only countably many of those.
This can be seen from the fact that descriptions are countable. For instance, you can write each description in English, and then sort them by length and alphabetically. The real numbers aren't countable, so most real numbers cannot be described by a finite amount of English text.
It's impossible to provide even a single example of an indescribable number, and yet they constitute almost all real numbers.
sjalfurstaralfur · 9 points · Posted at 04:56:47 on February 14, 2016 · (Permalink)*
Help me out, I have some basic theory of comp sci experience but reading that was a huge mindfuck
So basically you make a bunch of random programs by spitting out random 1's and 0's, run that program, and the Chaitin constant is the chance that the program will halt, lets say under a Turing machine? And the chaitin constant is not computable?
NotInVan · 11 points · Posted at 06:00:30 on February 14, 2016 · (Permalink)
Pretty much.
And it's not computable because if one could compute it one could solve the Halting problem.
[deleted] · 2 points · Posted at 10:08:35 on February 14, 2016 · (Permalink)
And of course the Halting problem has been shown to be undecidable over Turing machines.
Geoffles · 6 points · Posted at 07:15:26 on February 14, 2016 · (Permalink)
So are indescribable numbers like the "dark matter" of mathematics?
siamthailand · 3 points · Posted at 03:25:55 on February 14, 2016 · (Permalink)
So they are lurking out there, but we can't see them?
almightySapling · 5 points · Posted at 06:38:32 on February 14, 2016 · (Permalink)
We can see them. Take a look at the real line. Most of it is noncomputable.
Bobius · 2 points · Posted at 08:29:17 on February 14, 2016 · (Permalink)
So what's "The smallest describable number with a description of at least fifteen words"?
Drop_the_gun · 2 points · Posted at 11:17:16 on February 14, 2016 · (Permalink)
that's probably not a good definition, since you can "describe" any integer number in one word simply by writing it down, for example :)
Bobius · 1 points · Posted at 18:03:50 on February 14, 2016 · (Permalink)
Not a word. What if I change the question to "The smallest describable number with a description of at least fifteen words in English"?
I mean 1,000 has plenty of descriptions, all at least 2 words - ten cubed, one thousand, a thousand etc.
Given there's a finite number of English words there's a finite number of 15 word sentences. Only some will make sense, so there's certainly only a finite number of such sentences!
Drop_the_gun · 1 points · Posted at 18:12:29 on February 14, 2016 · (Permalink)
doesn't work, since you can take descriptions arbitrarily large
your last condition worked if you also prescribed taking words in a finite dictionary, because there's finite combinations of any finite lenght
my point was that you should've excluded numbers :)
Bobius · 1 points · Posted at 18:13:44 on February 14, 2016 · (Permalink)
"The smallest positive integer not definable in under sixty characters."
Drop_the_gun · 1 points · Posted at 18:32:31 on February 14, 2016 · (Permalink)
that works (if your set of acceptable definitions is finite therefore you know that the set of positive integers definable in under sixty characters is non-empty)
Asdanf · 1 points · Posted at 07:06:17 on February 15, 2016 · (Permalink)
It's good to see other folks are interested in the Berry Paradox.
nyando · 2 points · Posted at 08:42:03 on February 14, 2016 · (Permalink)
Maaan I found out like a month ago that most numbers are transcendental, and I thought that was the end of it. Now this crops up. It's not in my degree, but shit like this is why I want to take more math classes.
Atario · 1 points · Posted at 11:09:59 on February 14, 2016 · (Permalink)
But English lets you cheat your way around this limitation. "A random indescribable number". There, I just described one.
Drop_the_gun · 3 points · Posted at 11:18:51 on February 14, 2016 · (Permalink)
No you didn't. There is a precise definition of "describing a number" in this context, and it means to be able to find approximations of the number with arbitrarely high precision.
[deleted] · 2 points · Posted at 14:36:46 on February 14, 2016 · (Permalink)
No you didn't. If you managed to describe it then it's not indescribable and therefore doesn't fit your description of it.
Karoal · 6 points · Posted at 00:01:31 on February 14, 2016 · (Permalink)
There is a very interesting book that goes over Alan Turing's paper which includes this topic, it's called The Annotated Turing by Charles Petzold if I remember correctly.
One of the ways which is cool to think about this is that every single real number can be represented by an (infinite!) sequence of numbers, with a decimal point somewhere.
For now let's only think about what happens for each number after the decimal point. You could map the position of the first digit after the decimal point to the number 1, the second position to 2 etc. For each position you have, there are 10 possible choices of digits. So the number of possible combinations of digits is multiplied by 10. Since this sequence of numbers is infinite, it is unreasonable that you could expect 'most' real numbers to be able to be computed by a machine!
the_noodle · 5 points · Posted at 02:03:57 on February 14, 2016 · (Permalink)
NOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
UnchainedMundane · 3 points · Posted at 03:01:32 on February 14, 2016 · (Permalink)
Do you need a glass of water?
ShoggothEyes · 4 points · Posted at 02:44:41 on February 14, 2016 · (Permalink)
This is obvious if you consider the fact that the real numbers are uncountably infinite, but programs are countably infinite (they are just made up of symbols one after another, after all).
interestme1 · 2 points · Posted at 06:27:02 on February 14, 2016 · (Permalink)
Isn't this likely to be a gap in our mathematical understanding? If they "exist" ( assuming you have to take the philosophical approach that math and numbers aren't abstractions but rather an actual expression of nature), and we can't get to them, this seems like we're up against a fundamental wall in knowledge or our computational methods are incomplete. Does the general math community favor the former or the latter?
CaesarTheFirst1 · 4 points · Posted at 07:07:57 on February 14, 2016 · (Permalink)
It's no issue, the real numbers are well defined by Dedekind cuts for instance.
interestme1 · 1 points · Posted at 02:43:30 on February 15, 2016 · (Permalink)
So wouldn't that be a form of computation? What I was trying to say before is that if you say most numbers aren't computable, that seems like a large gap in computation. If they're just not computable without using special tools that's not quite the same as what you initially said. Perhaps I'm misunderstanding though?
CaesarTheFirst1 · 1 points · Posted at 09:14:05 on February 15, 2016 · (Permalink)
I don't exactly see what is the issue with uncomputable numbers, you can still think of them as an infinite decimal, just one that has no freaking pattern (by pattern I don't mean something repeating, I mean something even stronger, no finite program can come up with the next term).
interestme1 · 1 points · Posted at 09:46:53 on February 15, 2016 · (Permalink)
So if there's no pattern whatsoever, that doesn't strike you as strange? Generally speaking if we can't predict something, that means our knowledge is incomplete not that it's inherently unpredictable. However there seems to be a swing lately for many communities, mostly in physics and computer science (because of things like the Halting problem and quantum mechanics), to take findings and proofs as hard evidence that nature is inherently unpredictable.
The philosophical implication of the universe taking on properties that are inherently unable to be computed is that there are knowledge limits built into the universe, there are things that we could never know. I personally find this a bit unlikely for various reasons (such as why the hell would there be?), thus the other conclusion is that our ability to compute, and thus make predictions about the next in the sequence, isn't sufficient.
Anyway, the original question was just a wayward fishing line hoping to ensnare a mathematician (or I suppose just math enthusiast) to enlighten me to potential reasons why my intuition may be mistaken.
CaesarTheFirst1 · 1 points · Posted at 09:59:15 on February 15, 2016 · (Permalink)
Oh silly me I didn't answer your question!
Not all Dedekind cuts can be generated by a finite program simply because there are only a countable amount of finite program.
Math has not issue with things being called uncomputable, if you removed the requirement that the program be finite then we could generate every number.
I'm not much into philosophy, sorry, but I don't see any problem with the existence of those numbers (of course I'm not talking about physics, in math we just invent stuff and look at their properties).
interestme1 · 1 points · Posted at 10:10:04 on February 15, 2016 · (Permalink)
Got ya, I suppose the answer may be that most Mathematicians share your sentiment. It's a bit like asking construction workers how a screw is made. They don't care, nor does it pose any problem to them if I told them it was made of some random concoction of metals that couldn't be known. They just need the screw to build a wall.
But, as for why it's a problem, it's a problem because Math is a tool that we expect to predict and represent the universe. If we find we can't do something, we should determine if we just don't have the right tool or if the universe doesn't allow us to do it. Not just for the philosophical implications, but so people actually pursue seeing if they can build a new and better tool that does what we couldn't before. Unknowable vs not known is an important distinction for pragmatic reasons as well.
CaesarTheFirst1 · 1 points · Posted at 10:15:49 on February 15, 2016 · (Permalink)
computable numbers have no bearing on physics if that's what you mean, there is never a need in physics for an exact number, just a close approximation (and for examples the rationals are well defined and dense).
interestme1 · 1 points · Posted at 10:22:20 on February 15, 2016 · (Permalink)
No didn't mean physics, same arguments apply for strictly mathematics and computation without using applications.
Stamboolie · 1 points · Posted at 11:23:06 on February 14, 2016 · (Permalink)
That is the most interesting thing I've heard in a long time. I've always had a thought with calculus and using infinities everywhere in physics that it could be done better. Is there such a thing as a computable calculus? One that uses only computable numbers?
CaesarTheFirst1 · 1 points · Posted at 18:28:50 on February 14, 2016 · (Permalink)
I'm afraid I don't know much about computable numbers except for the fact that they are countable. I do know one really cool fact though:
Although they are countable, they aren't effectively countable, that means that there isn't a finite program that generates a list of all computable numbers to arbitary accuracy (meaning: let f be a bijection from N to the countable numbers, then there isn't a finite program so that given M, and epsilon calculates f(1),f(2)..f(m) to accuracy of e after enough time. This can be proved by a neat cantor diagonal argument.
Stamboolie · 1 points · Posted at 10:53:05 on February 15, 2016 · (Permalink)
Thanks, I did some googling and it seems it is a thing - http://eccc.hpi-web.de/resources/pdf/ica.pdf https://en.wikipedia.org/wiki/Computable_analysis
google "computable analysis" for more. cheers
rmxz · 1 points · Posted at 02:48:45 on February 14, 2016 · (Permalink)
Don't we meet them all the time?
"This fence is 100ft long" is just a rough approximation of the noncomputable number that really describes the fence's length.
drownballchamp · 2 points · Posted at 03:29:24 on February 14, 2016 · (Permalink)
No. If you could measure it completely, down to the atomic level, you could find a finite number that describes that length exactly.
limukala · 1 points · Posted at 18:11:07 on February 14, 2016 · (Permalink)
When you get down to the atomic level atomic vibration, diffusion, sublimation, the uncertainty principle and all kinds of other things come into play, so you can't really have a 100% precise and accurate description of the length. It wouldn't be a non-computable number so much as a probabilistic length distribution though.
drownballchamp · 2 points · Posted at 23:48:11 on February 14, 2016 · (Permalink)
The uncertainty principle does not generally apply to things as large as atoms locked in matrices. And everything else only matters if you care about the length over time. You could definitely get a perfect snapshot of the fence length if you had a large enough electron microscope.
limukala · 1 points · Posted at 05:07:37 on February 15, 2016 · (Permalink)
It may not have a large effect on say a hydrogen atom, but it does have enough of an effect that you couldn't define the length of the fence to arbitrary precision, which is necessary for your argument.
rmxz · -2 points · Posted at 03:45:24 on February 14, 2016 · (Permalink)
Not really.
Remember there are all sorts of continuous phenomena too -- like the universe itself expanding, or gravity waves from distant black holes stretching and smushing the earth -- that will be changing the length of the fence so most of the time it'll be a non-computable length.
Captain-Griffen · 10 points · Posted at 23:02:59 on February 13, 2016 · (Permalink)
Select a random real. Probability of it being rational is 0.
jorellh · 1 points · Posted at 03:24:03 on February 14, 2016 · (Permalink)
only because countable infinity over uncountable infinity = 0
AcellOfllSpades · 5 points · Posted at 21:42:22 on February 13, 2016 · (Permalink)
Even weirder, almost all real numbers are undescribable. We have literally no way to pin down most real numbers (for a definition of "pin down" fairly close to the intuitive one)
Oussl · 1 points · Posted at 04:29:17 on February 14, 2016 · (Permalink)
In a fundamental sense, can a number that is undescribable truly be said to exist? Its existence is not a meaningful concept as an individual entity
AcellOfllSpades · 1 points · Posted at 04:30:28 on February 14, 2016 · (Permalink)
Nothing in mathematics exists. We made it all up. Mathematics is the study of abstract sets of rules and their logical consequences.
[deleted] · 3 points · Posted at 01:22:48 on February 14, 2016 · (Permalink)
More than that, in fact. Almost all are transcendental - you can't get them as roots of aimed polynomial with integer coefficient. ( the square root of 2 is irrational, but not transcendental).
Despite this, there are very few numbers that we know are transcendental. Pi and e are two of them.
Godd2 · 2 points · Posted at 02:59:15 on February 14, 2016 · (Permalink)
Even more, almost all are normal, but we only know of 3 examples, and we don't know if pi or e are normal.
(I guess I shouldn't say "even more", since there are non-transcendental normal numbers, but they are still pretty interesting)
Glitch29 · 3 points · Posted at 05:36:46 on February 14, 2016 · (Permalink)
Then there's the Frivolous Theorem of Arithmatic.
Almost all natural numbers are very, very, very large.
I'm still fairly irked at a certain Wikipedia editor for deleting the entry there, but it's not a battle I'm willing to reopen.
skysurf3000 · 2 points · Posted at 23:57:30 on February 13, 2016 · (Permalink)
If you want something even better: almost all real numbers are not definable...
This is actually the starting point of the best intuitive explanation I heard as to why the continuum hypothesis is independent of ZF.
[deleted] · 2 points · Posted at 02:53:17 on February 14, 2016 · (Permalink)
It follows that if you randomly choose any real number, the probability of it being 2 (e.g.) is equal to zero.
Atmosck · 2 points · Posted at 05:23:28 on February 14, 2016 · (Permalink)
Well, yeah. The rational numbers are countable, and the definition of "almost all" is everything except a measure zero set, and countable sets have measure zero.
canaryherd · 2 points · Posted at 08:35:03 on February 14, 2016 · (Permalink)
Almost all real numbers are transcendental
NbyNW · 1 points · Posted at 21:59:27 on February 13, 2016 · (Permalink)
Most numbers are transcendental, but we only know a handful of such numbers.
georgeo · 1 points · Posted at 23:39:30 on February 13, 2016 · (Permalink)
Almost all irrational numbers are transcendental.
sameth1 · 1 points · Posted at 01:45:07 on February 14, 2016 · (Permalink)
That's because there is an infinite number of irrational numbers.
Felix_Tholomyes · 2 points · Posted at 02:39:11 on February 14, 2016 · (Permalink)
There is an infinite number of rational numbers as well.
[deleted] · 1 points · Posted at 06:18:08 on February 14, 2016 · (Permalink)
Some are more infinite than others. Kinda like YOUR MOM
[deleted] · 1 points · Posted at 04:14:15 on February 14, 2016 · (Permalink)
Just like people.
TimHallman · 1 points · Posted at 07:23:34 on February 14, 2016 · (Permalink)
Add any rational number to an irrational number, or vice versa, and you get an irrational.
[deleted] · 1 points · Posted at 15:12:33 on February 16, 2016 · (Permalink)
-sqrt(2) + sqrt(2) = 0
TimHallman · 1 points · Posted at 16:11:09 on February 16, 2016 · (Permalink)
:|
spin81 · 1 points · Posted at 09:31:05 on February 14, 2016 · (Permalink)
This continues to blow my mind:
Between each two rational numbers is at least one irrational number and vice versa.
Irregulator101 · 1 points · Posted at 10:28:22 on February 14, 2016 · (Permalink)
I find it amusing that we can say things like "almost" and "most" to describe infinite sets of numbers. Gets into the cardinality of infinity which is super fascinating.
[deleted] · 1 points · Posted at 11:25:56 on February 14, 2016 · (Permalink)
Even much worse: Almost all real numbers cannot be computed by any kind of finite algorithm.
Vryl · 1 points · Posted at 15:04:07 on February 14, 2016 · (Permalink)
I like the fact that most numbers are uncomputable - that there are vastly more uncomputable numbers than computable ones.
CharizardUltra · 1 points · Posted at 15:55:56 on February 14, 2016 · (Permalink)
When I was a kid, when we said, Hmmm..., which in our language means both the normal Hmmm... and one, everyone said two. We would get up to some high number, and then just throw infinities like : Infinite times two, Superinfinity, Super Infinityjin, etc...
osadon · 1 points · Posted at 01:49:26 on March 14, 2016 · (Permalink)
The most interesting part is between every 2 rational numbers theres an irational number and between every 2 irational numbers theres a rational number, also theres more irational numbers than rational numbers.
OlorinTheGray · 1 points · Posted at 23:29:37 on February 13, 2016 · (Permalink)*
Weirder:
The natural numbers are all integers from 1 to infinity. The integers are, well, all integers from minus infinity to infinity...
Both sets are exactly the same size. What?
/edited for correctness. Thanks to /u/edrudathec for pointing it out.
edrudathec · 2 points · Posted at 01:12:55 on February 14, 2016 · (Permalink)
Whole numbers generally refer to non-negative integers.
OlorinTheGray · 2 points · Posted at 01:15:51 on February 14, 2016 · (Permalink)
Aaand that's when you realize that the incredibly simple, obvious translation does not mean what you think it does.
Going to correct it...
What I meant to say is that there are as many positive integers as integers in general.
heap42 · 0 points · Posted at 23:43:28 on February 13, 2016 · (Permalink)
Meh... i don't know if you can say 'almost all' when talking about infinity... after all there are infinitely many real numbers that are not rational.
Felix_Tholomyes · 5 points · Posted at 00:42:37 on February 14, 2016 · (Permalink)
'almost all' is a well defined concept https://en.wikipedia.org/wiki/Almost_all
heap42 · 0 points · Posted at 00:58:50 on February 14, 2016 · (Permalink)
oh.. i did not know that... but your title is still a bit misleading.
ophello · 0 points · Posted at 09:07:27 on February 14, 2016 · (Permalink)
I think it's completely intuitive. There are so many more of them.
[deleted] · 2581 points · Posted at 19:35:33 on February 13, 2016 · (Permalink)
There are different kinds of infinity, and some are larger than others
MrXian · 164 points · Posted at 21:50:17 on February 13, 2016 · (Permalink)
I liked this video on the subject.
https://www.youtube.com/watch?v=Uj3_KqkI9Zo
seventhaccount005 · 10 points · Posted at 22:42:27 on February 13, 2016 · (Permalink)
That "paradox" is not a paradox
Cogswobble · 71 points · Posted at 23:03:16 on February 13, 2016 · (Permalink)
But this is: http://i.imgur.com/ekvcNc0.jpg
Raszagal · 7 points · Posted at 00:59:08 on February 14, 2016 · (Permalink)
What am I missing?
ianban · 34 points · Posted at 01:14:20 on February 14, 2016 · (Permalink)
the pair o' docks /u/cogswobble posted a photo of, clearly.
analogkid01 · 2 points · Posted at 04:40:40 on February 14, 2016 · (Permalink)
So is this.
magpac · 1 points · Posted at 08:40:53 on February 14, 2016 · (Permalink)
No, that's a Pair of Docks, a paradox is when your GP meets your Proctologist.
InsomniacAndroid · -1 points · Posted at 03:19:15 on February 14, 2016 · (Permalink)
A paradox can also apply to something that's unintuitive, such as the Birthday Paradox.
Inteli_Gent · 1 points · Posted at 07:38:17 on February 14, 2016 · (Permalink)
"a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true."
Take my +1 lifebuoy!
MrXian · 0 points · Posted at 17:17:36 on February 14, 2016 · (Permalink)
Yes it is. The hotel is full, yet it still fits more guests.
Or is my idea of paradoxes wrong?
baconlover24 · 6 points · Posted at 01:47:56 on February 14, 2016 · (Permalink)*
Hidden.
KSKaleido · 3 points · Posted at 02:48:04 on February 14, 2016 · (Permalink)
I just feel bad for the housekeeper.
Inteli_Gent · 3 points · Posted at 07:39:18 on February 14, 2016 · (Permalink)
I'm sure they have infinite house keepers, so each one only has to clean a hundred rooms. Or a billion. Or one. Whatever.
BlLE · 1 points · Posted at 12:22:12 on February 14, 2016 · (Permalink)
Actually, each of the infinite housekeepers would have an infinite rooms to clean. Infinite is counterintuitive and this is why I avoided math and went straight to evolution & ecology.
Inteli_Gent · 1 points · Posted at 14:40:33 on February 14, 2016 · (Permalink)
That's not necessarily true. If the infinite of the rooms was the same infinite of the number of house cleaners, it would be one room per cleaner.
Also, I'm so drunk that I'm surprised I can read, so I may be wrong.
ChickenBrad · 3 points · Posted at 04:18:46 on February 14, 2016 · (Permalink)
This is interesting too, but builds on something deeper. https://www.youtube.com/watch?v=s86-Z-CbaHA
Romulus3799 · 2 points · Posted at 05:35:51 on February 14, 2016 · (Permalink)
Plot twist: the video is actually just The Fault in our Stars
Crixomix · 1 points · Posted at 17:03:47 on February 18, 2016 · (Permalink)
I knew I was a math nerd when that link was already purple :D
Hyperdistortia · 1 points · Posted at 01:40:29 on February 14, 2016 · (Permalink)
Oh, man. I'm binging on this channel's videos now. Subbed and all. Great video, btw.
kvn9765 · 0 points · Posted at 01:35:41 on February 14, 2016 · (Permalink)
A math video that's not a Numberphile ;(
https://www.youtube.com/watch?v=dDl7g_2x74Q
Inteli_Gent · 1 points · Posted at 07:43:44 on February 14, 2016 · (Permalink)
Eh. It didn't explain Gabriel's Horn at all. I saw it mentioned elsewhere and was hoping this video would actually give some kind of explanation, but it just said the surface is infinite, but the space it encloses is finite. Thus far, I'm not a fan.
crossanlogan · 1 points · Posted at 07:52:32 on February 14, 2016 · (Permalink)
gabriel's horn:
imagine talking a horn and extending the mouthpiece infinitely. past a certain point the volume you add becomes negligible (because by the end the sides of the horn are technically still apart, but infinitesimally close together), but you keep adding surface area because you keep adding "outside" of the horn.
repeat ad infinitum (literally), and you have a finite volume and an infinite surface area!
Inteli_Gent · 1 points · Posted at 08:13:06 on February 14, 2016 · (Permalink)
See, but that doesn't make sense to me, because even if the volume you add to the interior is negligible, it's still there. Even if it adds .000000000001cm3 to the volume, and 999,999,999m2 to the area, it's still adding both infinitely, so they would both be infinite.
EDIT: I know that's not right, but I don't understand the actual mathematical logic behind it, and that's what I got from your explanation.
justdavidt · 1 points · Posted at 15:52:17 on February 14, 2016 · (Permalink)
If you were consistently adding .000000000001cm3 to the sum, then it would approach infinity. However, we are adding smaller numbers each time. The sum of these values can be bounded above and below, hence it is finite.
Consider a sum where it begins with 1. I always half the previous term, and add that to the sum.
1 + 1/2 + 1/4 + ..
Its clear that this sum is larger than 1, and must be less than 2 (any partial sum will never be larger than 2). We then can conclude that the sum is finite.
Inteli_Gent · 2 points · Posted at 22:48:07 on February 14, 2016 · (Permalink)
But aren'the you also adding less to the area?
h4n4_LOL · 0 points · Posted at 03:23:08 on February 14, 2016 · (Permalink)*
the video fails to explain why you would even need the step n to 2n at all (and in all laer stages of the example). Becaus if there is a an infinite number of guests moving in you still can do n to n+1 and just reapeat the step infinite times. so m(n to n+1) (or n(n tp n+1) im not sure how to note that stuff). SO it fails to even explain in the sligthest that infinite =! infinte+1 and why. If you can write it like that sure it seem ok in and mathematical way but as soon as you remeber that n=infinte it doesnt make sence at all QQ (btw i get the fact that the video was probably not meant to explain what i said but i buffels my that no matter what simple source oyu wanna find to the topic of infinity most of them dont even can or try to explain the basic concept and just take it as giventhat you can use simple math on it. This buggs me in so many other fields of since too. Like Entropy in physics for example)
MrXian · 1 points · Posted at 17:15:39 on February 14, 2016 · (Permalink)
I kinda dislike the idea of a simple explanation for something as complex as infinity.
I'm not disagreeing with you, though.
thatJainaGirl · 1037 points · Posted at 23:20:17 on February 13, 2016 · (Permalink)
For the confused, this is the description I like:
Think of whole numbers. Every single one. 1, 2, 3, 4, 5, 6, 7... on and on and on. It doesn't stop. There are an infinite number of whole numbers. Now think of the number of not-whole numbers between 1 and 2. 1.1, 1.01, 1.02, 1.002, 1.0035... It keeps going on and on into infinity. So the number of whole numbers and the number of numbers are both infinite, but the number of numbers without the whole requirement is a larger infinity. Denser infinity, if you will.
Thanks, /u/thesoundandthefury.
ComplicatedAdvice · 25 points · Posted at 02:22:03 on February 14, 2016 · (Permalink)
Ooh, can I explain this one?
So there are actually two types of not-whole numbers. One type is rational numbers (they can be written as a fraction of whole numbers, like 1/4, or 3/7), and it actually includes all of the whole numbers, too (2 = 2/1 = 4/2). The other is irrational numbers. These numbers can't be written as a fraction, like the square root of 2, or pi. They have an infinite number of digits after the decimal point, and those digits never repeat.
So let's start with the rational numbers. The way you can tell if infinities are the same size is by seeing if you can matching up each number from one set with a number from the other set. If none are left over, those sets are the same time.
You can write all of the fractions like this:
2/2 =14/2 = 26/2 = 33/3 = 16/2 = 3If you start from the top left, you can zig zag along the diagonals and number them, skipping over the duplicates (which I've crossed out). So, in this case, we'd say that:
You'll hit every fraction eventually, so there are the same number of rational numbers as there are whole numbers.
Then there's the irrational numbers. Let's only look at the irrational numbers between 0 and 1. This one you have to prove the size of differently.
Let's assume that you have a list (which you can number) of all of the irrational numbers like:
1) 0.1238975209825983240982452...
2) 0.123579872456982734....
3 0.90752348974260825...
4) 0.32579829587234...
5) 0.23579872340981234...
If we have a list of all irrational numbers, then it's not possible to make a new irrational number. Therefore, if we make a new irrational number, there are more irrational numbers between 0 and 1 than there are whole numbers.
So let's just try to generate a new number and see if it's possible. We'll start with the first digit after the decimal, and keep an eye on the bolded digits in my list.
If we make sure that the first digit isn't 1, then it's not the same as the first number. So we'll start our number off as 0.2...........
Then the second digit. If we make sure that the second digit isn't 2, then it's not the same as the first number. So we'll continue the number to be 0.24..........
Then the third digit. If we make sure that the third digit isn't 7, then it's not the same as the third number, so now let's make our number 0.243........
If we make sure that the fourth digit isn't 7, then we know the new number isn't the same as the fourth number. So our number is now 0.2439........
And if the fifth digit isn't 9, then the new number isn't the same as the 5th number on our list. So we'll say our new number is 0.2438.....
If you continue with that pattern, then you know that your new irrational number isn't any of the numbers we listed yet, but we don't have any more whole numbers to number this irrational number with! Therefore, there are more irrational numbers between 0 and 1 than there are whole numbers!
[deleted] · 2 points · Posted at 15:06:37 on February 14, 2016 · (Permalink)
Relevant username?
ComplicatedAdvice · 1 points · Posted at 21:31:32 on February 14, 2016 · (Permalink)
Hahaha, no, I just forgot to change to the right account.
trevour · 1 points · Posted at 22:30:12 on February 15, 2016 · (Permalink)
This is a much more correct explanation than the guy you're replying to. It's all about whether the sets are listable or not, not about "density" or whatever that guy is talking about.
ComplicatedAdvice · 1 points · Posted at 02:34:32 on February 17, 2016 · (Permalink)
I mean, the denser infinity does make sense, mine's just more technically correct, and gets around the annoying gut feeling of "it's not possible for there to be more numbers between 0 and 1 than between 0 and infinity."
an7agonist · 378 points · Posted at 23:34:06 on February 13, 2016 · (Permalink)
Eh, that's not really true. There are as many whole numbers as there are fractions.
But the set of irrational numbers is larger than the set of whole numbers/fractions (uncountable vs. countable).
But where it gets interesting is, that in any arbitrarily small neighbourhood of an irrational number you'll find (countably) infinite many rational numbers!
IlanRegal · 5 points · Posted at 07:37:02 on February 14, 2016 · (Permalink)
Actually, it's "provable" that there are more numbers between 0 and 1 than there are in the whole set of natural numbers.
Imagine you take every single natural number, and you pair it up with a decimal number from 0 to 1, with each one being unique. For example:
1 ~ 0.49628… 2 ~ 0.76539… 3 ~ 0.11247… 4 ~ 0.99430… 5 ~ 0.00053… etc.
After doing this for all natural numbers, every single positive integer has been paired with a unique decimal number. Every single one.
Now, define a decimal number that is unique from all others in this set in at least one spot. This is done by taking the tenth column on the first decimal number, and incrementing it. Do the same for the hundredth column on the second number. And the thousandth column for the third, and so on. Take those new decimal places and put them into a brand new number. Here's what it looks like:
1 ~ 0.49628… 4 + 1 = 5 2 ~ 0.76539… 6 + 1 = 7 3 ~ 0.11247… 2 + 1 = 3 4 ~ 0.99430… 3 + 1 = 4 5 ~ 0.00053… 3 + 1 = 4 etc.
New number = 0.57344…
You now have a number that is unique from all others in the sequence, and it still counts as a real number between 0 and 1, but it has nowhere to go on the set. Every natural number is already paired up.
This proves that there are more numbers between 0 and 1 than there are natural numbers, because you can always find a new decimal number in a set like the one just described.
rawling · 1 points · Posted at 13:07:28 on February 14, 2016 · (Permalink)
thatJainaGirl's comment is deficient in that
Between the two of them, this doesn't prove that there are "more" reals than integers.
You're not contradicting an7agonist, you're just providing a proper proof to thatJainaGirl's point.
taedrin · 8 points · Posted at 02:55:15 on February 14, 2016 · (Permalink)
Or put in simpler terms, between any two different irrational numbers, you can always find a rational number, no matter how close they are to each other.
fortenforge · 12 points · Posted at 04:11:23 on February 14, 2016 · (Permalink)
That's true, but that's also true for rational numbers. This doesn't get to the heart of the issue at all.
[deleted] · 5 points · Posted at 04:46:16 on February 14, 2016 · (Permalink)
Yeah. It works with all numbers.
Someone's probably going to call me out and explain why I'm wrong...
JJ_The_Jet · 6 points · Posted at 05:54:38 on February 14, 2016 · (Permalink)
You are wrong to assume you are wrong. For any number in the reals and any open interval around said number, there exists a countably infinite number of rational numbers in said region.
Proof sketch: We know if the rationals are countable, thus we get countably. Also rationals are dense in reals. If we take any region around a point, we can find at least one real. We use that fact and induction to get infinite rationals.
fofbacon · 3 points · Posted at 06:36:44 on February 14, 2016 · (Permalink)
there are also a countably infinite number of algebraic numbers (sqrt(2)for instance, any number that is a root of a polynomial with rational coefficients) which are the majority of the irrational numbers you would think about.
klod42 · 3 points · Posted at 11:38:41 on February 14, 2016 · (Permalink)
Hey, that's cool, I never really thought of that. Transcendentals are the ones ruining the party.
antsugi · 2 points · Posted at 05:01:10 on February 14, 2016 · (Permalink)
That doesn't add up right. If you tack on another whole number, you get an infinity between it and the last. And as you continue to add number after number you will get another and another infinite, while in the process of building the whole number infinite
klod42 · 3 points · Posted at 11:34:06 on February 14, 2016 · (Permalink)
Infinite is infinite. Infinite number of infinities is still the same infinite. Comparing infinities isn't about what "feels" bigger. The idea is, since we can't just intuitively comprehend the sizes of the infinite sets, we compare them by trying to "connect" their elements.
For example, N is a set of natural numbers. N={1,2,3,4,5,6,...}. We call its size "countably infinite". Now, imagine a set 2N={2,4,6,8,10,...}, a set of even numbers. I can "connect" their elements with a simple function f(n)=2*n. So, we have pairs: (1,2), (2,4), (3,6), etc.
That function is a bijection: it covers all elements in both sets, and every element in one set has exactly one pair in the other set. We never run out of elements, so we call those sets equal in size. One such function is enough to prove that the two sets are equal.
You can make such bijections for whole and rational numbers as well, but not for irrational numbers.
[deleted] · 3 points · Posted at 00:49:00 on February 14, 2016 · (Permalink)*
[deleted]
ComplicatedAdvice · 16 points · Posted at 01:51:59 on February 14, 2016 · (Permalink)
They're the same size infinity! If you take a list of all the natural numbers, and multiply each of them by two, you end up with a list of every even number. Any time you can take one set and map it onto another set (pair up the members of the set, with none left over in either set), they're the same size. That still holds for sets with infinite numbers of members.
bobby8375 · 12 points · Posted at 02:06:07 on February 14, 2016 · (Permalink)
Watch out using that word "onto." It has a mathematical meaning in context of functions and set theory, synonymous with the more technical sounding term "surjective," meaning that every element of the codomain (the "y" part of the function f(x)=y, with "x" being the domain) has a corresponding element in the domain that maps to it. Or, if a function is defined from the set X to the set Y, then every possible y in the set Y has an x in the set X such that f(x) = y. If a function is surjective or "onto," then X is cardinality-speaking at least as big or bigger than Y.
Intuitively it is obvious that the natural numbers are at least as big if not bigger than the even numbers, so there of course exists an "onto" function from the naturals to the evens. What is a little less obvious is showing that your function, take a natural number and double it, is not only "onto" or surjective, but also injective or "one-to-one," (in graphical terms, an injective function passes the horizontal line test), and thus bijective, which would imply that the natural numbers and the even numbers have exactly the same size or cardinality.
ComplicatedAdvice · 7 points · Posted at 02:32:50 on February 14, 2016 · (Permalink)
Thanks for the clarification! I actually used "onto" specifically because I knew that the two sets mapped one-to-one, but I'd forgotten to mention that you needed to be able to map A onto B AND B onto A. :)
mattmonkey24 · 1 points · Posted at 16:38:34 on February 14, 2016 · (Permalink)
Onto and one-to-one aren't the same, just to make sure, and one doesn't imply the other
[deleted] · 3 points · Posted at 01:11:43 on February 14, 2016 · (Permalink)
Same size. There are as many even natural numbers as there are natural numbers. Also, there are as many integers (..., -2, -1, 0, 1, 2, ...) as there are natural numbers (0, 1, 2, ...). These are examples of countably infinite sets.
[deleted] · 2 points · Posted at 02:29:26 on February 14, 2016 · (Permalink)
It's true in another sense of size called natural density. You can look at the natural numbers as having natural density of 1 (in the natural numbers) and define the density as the limit of the number of numbers from the other set occurring in the natural numbers. So in this sense the even numbers are half the size of the natural numbers.
AndrasKrigare · 1 points · Posted at 00:47:08 on February 14, 2016 · (Permalink)
I think what he said is true; he never mentioned fractions. I assumed his "not-whole" numbers were referring to irrational numbers.
GeeJo · 11 points · Posted at 01:52:30 on February 14, 2016 · (Permalink)
The examples he gives of not-whole numbers are:
None of these are irrational, and can all be described as 1 + 1/x.
JJ_The_Jet · 2 points · Posted at 05:55:46 on February 14, 2016 · (Permalink)
Id like to see you type out a decimal representation of an irrational number.
GeeJo · 6 points · Posted at 06:01:03 on February 14, 2016 · (Permalink)
Who said that the examples had to be decimal representations? e, pi, and root 2 would have worked fine. Irrational numbers weren't even mentioned by OP, just "not-whole" numbers, which was the problem. It was just all-around a very unclear explanation of cardinality.
MadDogMike · 1 points · Posted at 07:54:19 on February 14, 2016 · (Permalink)
Although you could say that "not-whole numbers" is the set of all numbers that aren't whole, which includes all irrational numbers and and all fractions. The set of "whole numbers" is infinite, but the set of "not-whole numbers" is both infinite and larger than the set of "whole numbers".
I find that the easiest way to explain this concept without having to refer to irrational numbers is to compare the set of all whole numbers to the set of all even whole numbers. Both are infinite, but even common sense says that the set of only even whole numbers is smaller.
Ibbot · 2 points · Posted at 02:42:35 on February 14, 2016 · (Permalink)
It's still abundantly clear that he's referring to the set of all numbers that are not whole numbers, whether or not they are irrational.
Im_thatguy · 3 points · Posted at 07:08:33 on February 14, 2016 · (Permalink)*
The issue is that saying it's a larger infinity because there is an infinite amount of numbers between 1 and 2 is wrong. He pointed out there are also an infinite number of rational numbers between 1 and 2, but the set of rational numbers is the same size as the set of whole numbers which is a counter example to that logic.
Ibbot · 1 points · Posted at 09:59:33 on February 14, 2016 · (Permalink)
And even worse, what I said makes even less sense when you consider what the person I was replying to was replying to.
Chris_Nash · 1 points · Posted at 09:59:17 on February 14, 2016 · (Permalink)
So in short, it's our own definitions that apply this continuity, right?
Jdavidnew0 · 1 points · Posted at 20:33:27 on February 14, 2016 · (Permalink)
No. All whole numbers is a countable infinity in comparison to the uncountable infinity of all real numbers
an7agonist · 1 points · Posted at 20:53:10 on February 14, 2016 · (Permalink)
What do you mean? The real numbers have the same cardinality as just the irrational numbers (Card(Q x R) = Card(R\Q) = Card(R)).
ratwing · -7 points · Posted at 01:28:02 on February 14, 2016 · (Permalink)
outsider (of math) looking in. I always find it entertaining when people add exclamation points to the ends of sentences like yours. Yes, it is interesting, but no, you probably would not shout it if you were in a room full of people.
hydrohawke · 6 points · Posted at 03:17:31 on February 14, 2016 · (Permalink)
As a small addendum, Hazel is partially correct and partially incorrect in TFIOS. The set of numbers between 0 and 1 and the set of numbers between 0 and 2 are the same size.
[deleted] · 1 points · Posted at 09:36:54 on February 14, 2016 · (Permalink)
[deleted]
TheOldTubaroo · 3 points · Posted at 11:12:24 on February 14, 2016 · (Permalink)
Intuition isn't great for dealing with infinity. Let go back to whole numbers. We have 1, 2, 3, 4... Now just take half of those, the even numbers: 2, 4, 6, 8...
Now, you can pair each whole number x with an even number 2x. So we get pairs like (1, 2), (2, 4), (3, 6), (4,8)... So you know there's the same amount of even numbers as whole numbers, even though the even numbers are part of the whole numbers.
What's fun is taking this to the next level. We've just shown that 2×∞=∞, but what about ∞×∞? If you take the set of fractions between 0 and 1, you can prove that there are as many of these as there are whole numbers. So then you take all the fractions ever, so you have the fractions between 0 and 1, the ones between 1 and 2, and so on. We now have an infinite amount of infinite groups of numbers. How many are there over all? Exactly the same as the number of whole numbers.
hydrohawke · 1 points · Posted at 13:32:50 on February 14, 2016 · (Permalink)
Check out this video: http://m.youtube.com/watch?v=A-QoutHCu4o
brokething · 9 points · Posted at 00:23:06 on February 14, 2016 · (Permalink)
You are so close to being right. But all of your not-whole numbers are rational. And there are just as many rational numbers as there are integers, it's the same.
You can prove this by putting all of the rationals into a list going 1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1 ... This is called Cantor's Diagonal Argument.
But irrational numbers like pi and e are outside of that collection of numbers. And when you count all of the irrational numbers as well, you really do have more, a bigger infinity, than your 1,2,3 counting numbers.
[deleted] · 7 points · Posted at 00:39:13 on February 14, 2016 · (Permalink)
Also, if my memory is right, there are more real numbers between 0 and 1 than there are natural numbers.
Querce · 3 points · Posted at 05:18:56 on February 14, 2016 · (Permalink)
and there are as many numbers between 0 and 1 as there are between 0 and 2
oh_my_baby · 3 points · Posted at 01:26:58 on February 14, 2016 · (Permalink)
Right because the reals between 0 and 1 are uncountably infinite there is no one to one correspondence to the natural numbers. To be countably infinite there must be a one to one correspondence with the natural numbers (so obviously the natural numbers are countably infinite)
prickity · 4 points · Posted at 11:47:34 on February 14, 2016 · (Permalink)
This is an example of everyone on reddit upvoting a cool intuitive explanation that is actually completely mathematically wrong.
Garizondyly · 1 points · Posted at 03:57:40 on February 14, 2016 · (Permalink)
This is completely wrong...? You're perpetuating a common misunderstanding when people say "there are different sizes of infinity", sorry.
mloos93 · 1 points · Posted at 07:03:44 on February 14, 2016 · (Permalink)*
So, someone else may have said this, but the fractions infinite is the same size as the whole numbers infinite. Same as the all negative and positive numbers infinite with the only positive numbers infinite.
Where the infinites become different sizes is in set theory. In the whole, positive numbers infinity, you can group the numbers together in different ways, called subsets. These subsets, when you take all of them also create a set.
You know what, watch this video. It explains it better.
Edit: An actual video...
Wheres_The_Pepsi · 1 points · Posted at 07:23:21 on February 14, 2016 · (Permalink)
/r/bandnames
mhblm · 1 points · Posted at 00:19:21 on February 15, 2016 · (Permalink)
That's not quite correct; both of your example sets are countably infinite and have the same cardinality of aleph naught.
If you included irrational numbers you would have an uncountably infinite set with a larger cardinality of aleph one.
[deleted] · 1 points · Posted at 10:24:50 on March 8, 2016 · (Permalink)
No, the density has nothing to do with it. There are as many decimal numbers of finite length as there are integers, even though they're dense everywhere. What you want to talk about is the infinity of infinitely long decimal numbers, that is, numbers that you can't completely write down. Because they are so long there are a lot of choices for them. The integers are only finite in length, so there are fewer (but still infinite) choices.
cobbs_totem · 1 points · Posted at 03:54:42 on February 14, 2016 · (Permalink)
Accountably infinite vs Unaccountably infinite. Essentially, the first example we can map the whole numbers to every item in the infinite set. In the second example, we can't map a whole integer to every number in its infinite set.
TheOldTubaroo · 2 points · Posted at 11:15:30 on February 14, 2016 · (Permalink)
*countably, not accountably
Also there are several levels of uncountably infinite, beyond the number of reals. A still open question is where there's an infinity between countable and the size of the reals.
[deleted] · -1 points · Posted at 01:39:50 on February 14, 2016 · (Permalink)
[deleted]
108241 · 1 points · Posted at 03:26:41 on February 14, 2016 · (Permalink)
People are downvoting you since they think you're joking.
https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
[deleted] · 1 points · Posted at 04:04:27 on February 14, 2016 · (Permalink)
Or because it's a vaguely correct factoid perpetuated by people who saw one math video or one TIL post and don't understand that it only "equals" -1/12 in one sense so it's misleading if not outright incorrect to say it equals -1/12 as if it converged.
mrill · 0 points · Posted at 06:48:22 on February 14, 2016 · (Permalink)
That doesn't make any sense. It depends on what your defining one as. Both infinities are the same. They're both just ifinitely subdividing something. There is one cosmos and numbers are our way of subdividing objects and patterns into existence. An apple can be 'one' or it could be subdivided ifinitely into particles nonstop. After all there is an infinite amount of numbers between zero and 1. You can subdivide in that infinite amount into more infinity. So yeah both infinities are the same thing it just depends on scale and what you pick 'one' to be.
rawling · 1 points · Posted at 13:09:13 on February 14, 2016 · (Permalink)
You know this is a maths thread, right?
Dalfamurni · 0 points · Posted at 09:37:50 on February 14, 2016 · (Permalink)
Each digit is an infinity unto itself. It's infinitely precise at 1.000~repeating. Also, it might be better to say that between the numbers a and 2 there are an infinite number of decimal numbers. Between 1 and infinity, however, there are all of those decimal numbers for every digit. And between -infinity and infinity there are even more. Really you can even say that between 1 and infinity is an infinity, but between 2 and infinity is a smaller infinity.
Still, the best way to explain it is by just showing them two circles of differing sizes. Each is an infinite loop, but one is smaller than the other. Both have infinite points, but somehow one has less points than the other. Any line works due to infinite precision, but circles help people grasp it better.
ohaiya · 0 points · Posted at 09:44:46 on February 14, 2016 · (Permalink)
Alternatively, think of the sequence of whole numbers: 1, 2, 3, 4, ...
Now double each number in that sequence to produce the subset that is even numbers 2, 4, 6, 8, ...
Since the first sequence is infinite, so is the second, but it's only half the set of numbers as the first set
[deleted] · -2 points · Posted at 02:40:02 on February 14, 2016 · (Permalink)*
There are an infinite number of numbers between 1 and 2.
And it can be shown, there are twice as many numbers between 1 and 3 as there are between 1 and 2.
By induction, there are infinitely many times as many numbers between 1 and infinity as the infinite number of numbers between 1 and 2.
EDIT - Nevermind, these are all the same uncountable infinity.
envatted_love · 2 points · Posted at 05:27:47 on February 14, 2016 · (Permalink)
Not so! That's what's so cool about this stuff. The set of rational numbers between 1 and 2 is exactly the same size as the set of rational numbers between 1 and 3; in fact, each of these is exactly the same size as the set of all rational numbers! (The same goes if we substitute "real numbers" for "rational numbers" throughout.)
By analogy, the set of positive whole numbers isn't any bigger than the set of positive even whole numbers.
One way to understand this latter example is to imagine a function y = 2x, where x is populated by positive whole numbers. That means y must be populated by only positive even numbers. If the set of even whole numbers were smaller, then this function would have gaps--in other words, if the set of x values were bigger than the set of y values, then there would be a whole number that was missing a double! The graph y = 2x would have holes in it.
So our intuitions about infinity often turn out to be misleading upon closer inspection.
A key concept here is that of countably infinite sets. A set is countably infinite if it is the same size as the set of whole numbers (and thus, in theory, its every member can be paired with a specific whole number and thus counted). All countably infinite sets are the same size. Some countably infinite sets include:
Natural numbers
Integers
Positive integers
Positive even integers
Positive even integers that are also divisible by 7
Rational numbers
An example of a set that is bigger than any of these is the set of real numbers. The coolest proof of this, in my opinion, is Cantor's diagonal argument.
oarsman458 · -1 points · Posted at 02:50:55 on February 14, 2016 · (Permalink)
I explained it to my little cousins as: there are an infinite amount of negative numbers (-infinity to -1), and an infinite amount of numbers in the positive direction (1 to infinity), both are logically the same. But there's also an infinite amount of numbers between negative infinity and infinity, which would logically he greater than both of those other infinities.
fortenforge · 3 points · Posted at 04:14:44 on February 14, 2016 · (Permalink)
No. The sizes of those two infinite sets are considered to be the same by mathematicians.
oarsman458 · 2 points · Posted at 13:00:15 on February 14, 2016 · (Permalink)
Oh, then it's a good thing my little cousins aren't mathematicians.
spacepepperoni · -1 points · Posted at 06:38:20 on February 14, 2016 · (Permalink)
Or think of all the whole numbers and then think of just the even numbers. Both sets are infinite but one has half the numbers in the other.
mhblm · 1 points · Posted at 00:47:12 on February 15, 2016 · (Permalink)*
Actually, they have the same number of numbers. Half of infinity is still infinity. I would get into it but vsauce explains it better than I ever could:
https://youtu.be/s86-Z-CbaHA?t=363
Edit: Someone just posted a much better video demonstrating Hilbert's Infinite Hotel https://youtu.be/Uj3_KqkI9Zo
Spicy_Pak · -2 points · Posted at 04:47:35 on February 14, 2016 · (Permalink)
The way I understand it is this (excuse me because I'm only a college student taking higher level math courses) infinity is more of a concept of endless than it is an actual number. Because of this, infinity and infinity plus one represent different concepts of endlessness. It is clear which one is larger(the plus one).
envatted_love · 1 points · Posted at 05:06:39 on February 14, 2016 · (Permalink)
Actually, adding 1 to an infinite set does not make it larger. A cool way to think about this is with Hilbert's Hotel.
Spicy_Pak · 0 points · Posted at 05:43:17 on February 14, 2016 · (Permalink)
adding one to infinity doesn't make it larger in itself, it makes it larger than infinity. So A=infinity and B=infinity+1 so B is larger than A. This is used in things like finding the convergence of a limit where 1/(r+1) as r goes to infinity is smaller than 1/r and 1/r converges to zero so 1/(r+1) must also converge to zero.
envatted_love · 1 points · Posted at 07:42:51 on February 14, 2016 · (Permalink)
I'm not exactly sure what you mean here. The limit of 1/(r + 1) and the limit if 1/r are both zero as r approaches infinity.
It does not, and "larger than infinity" does not really make sense because there is more than one infinite set. What does make sense is to specify which infinite set you're referring to (e.g., the set of natural numbers); then we can discuss whether adding a finite quantity to it will make it bigger (it will not, as Hilbert's Hotel demonstrates).
In fact, even adding another infinite set to the set of natural numbers won't (necessarily) make the resulting set larger. For example, combining the set of the natural numbers and the set of all rational numbers will not result in a set larger than the natural numbers. The rational numbers are countably infinite, just like the naturals are.
[deleted] · 33 points · Posted at 00:07:53 on February 14, 2016 · (Permalink)
Correct. I had a theoretical statistics professor that explained this really well. Essentially, there is a countable infinity, and an incountable infinity. Coutable is the infinity thay we all typically think of when we hear the word "infinity." I start counting at 1, eventually get to a million, then a billion, trillion, quadrillion, etc. Uncountable infinity is, for instance, the number of numbers between 4 and 5. It's impossible to count how many there are, because it's impossible to find the "starting number" in the first place. I could start at 4.01, but 4.0001 is smaller, with 4.0000001 being smaller than that.
PM_ME_UR_OBSIDIAN · 8 points · Posted at 00:42:49 on February 14, 2016 · (Permalink)
It's actually crazier than that.
There's an operation called the "power set", which takes some collection A to the set of all of its subsets P(A). So P({1, 2, 3}) = {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {1, 2, 3}}.
Intuitively, the power set of a set will always be bigger than the set itself. By Cantor's Theorem, this holds even for the power sets of infinite sets.
Take the natural numbers. They're infinite, but "less infinite" than the real numbers. In fact, there are as many real numbers as there are subsets of the natural numbers! So the power set of the naturals is as large as the set of reals.
But what if you take the power set of the real numbers? You get something that's even bigger than uncountable.
[deleted] · 7 points · Posted at 01:28:19 on February 14, 2016 · (Permalink)
but wait, there's more
thmsoe · 4 points · Posted at 01:42:15 on February 14, 2016 · (Permalink)
Your explanation is almost true, but your last sentence also applies to the rational numbers between 4 and 5, which are countable. The classical argument to illustrate why the real numbers aren't countable is Cantor diagonalisation, which requires a bit of mathematical knowledge.
[deleted] · 1 points · Posted at 02:14:34 on February 14, 2016 · (Permalink)
Yes...the number of rational numbers between 4 and 5 is countably infinite. The number of numbers between 4 and 5 is on uncountably infinite. Cantor's diagonalization has to do with the fact that infinite sets don't necessarily coincide with the infinite set of natural numbers. That's where the expression of "uncountable sets" came from in the first place. This is where cardinal numbers come into place to help with more complex set theory.
almightySapling · 2 points · Posted at 06:46:22 on February 14, 2016 · (Permalink)
I think what he was trying to say was that your argument for why this is uncountable doesn't really add up, since the same trick should apply to the rationals, but those are countable.
Also, you should be more careful with how you toss around "numbers" as though the reals are the end-all be-all number system.
For instance, in the surreals, there are so many numbers between 4 and 5 that you can't describe them with any infinite cardinal, because they form a proper class.
Cremasterau · 1 points · Posted at 01:30:41 on February 14, 2016 · (Permalink)
But you can graph them and when you do so you appear to be left with -1/12th (see yellow shaded area).
meh100 · 1 points · Posted at 01:40:02 on February 14, 2016 · (Permalink)
4, 4.1, 4.01, 4.2, 4.001, 4.02, 002, 4.3, 4.0001, 4.0002, 4.03, 4.003, 4.003, 4.4...
The starting place is 4 (4.0) and the way you count is not by going strictly smaller, but by being creative.
It's not the decimals that are uncountable, it's irrational numbers.
[deleted] · 1 points · Posted at 02:17:47 on February 14, 2016 · (Permalink)
In the case of complex statistics, it is always assumed that numerical intervals are exclusive. Aka, (4,5) and not [4,5].
meh100 · 0 points · Posted at 14:59:27 on February 14, 2016 · (Permalink)
What?
LopsidedLolly · 26 points · Posted at 02:10:11 on February 14, 2016 · (Permalink)
Thanks John Green
[deleted] · 282 points · Posted at 20:34:48 on February 13, 2016 · (Permalink)
I once heard a physicist say he hated "infinity" because he felt it was a lazy mathematical concept that was a fancy way of saying "I don't know what goes here, so I'll just say 'infinity'"
AcellOfllSpades · 602 points · Posted at 21:36:54 on February 13, 2016 · (Permalink)*
That's not how it works at all. Infinity has a precise definition. A set S is infinite if and only if you can choose one of its proper subsets and then make a bijection between S and the chosen subset.
A proper subset is just a collection of things that are all members of a set, but not the entire set. For instance, some proper subsets of {1,2,3,4,5} are {2,4,5} ; {1,2} ; {4} ; and {}.
Some examples of things that aren't proper subsets of {1,2,3,4,5} are {2,4,9} and {1,2,3,4,5}. (The last one is a subset, but not a proper subset.)
A bijection is a rule that pairs up things from one set to things from another. For instance, a bijection between {A,B,C} and {1,2,3} could be
Nothing is repeated or left out on either side, so we have a bijection.
Now let's try it out with the natural numbers: {0,1,2,3,4,5,6...}. What subset could we pick? There are several good choices, but I'm going to demonstrate with the even numbers. Here's my bijection:
(You could also write this as f(n)=2n.)
All natural numbers appear on the left side and all even numbers appear on the right. Nothing repeats on either side. This means we have a bijection between naturals and evens, so the natural numbers are infinite.
(This also shows that there are the same number of natural numbers as there are even numbers!)
There are various types of infinite numbers - cardinals, ordinals, surreals, hyperreals... all of them are precisely defined and used in different contexts.
FUZxxl · 18 points · Posted at 23:05:28 on February 13, 2016 · (Permalink)
Finiteness is usually defined as “not admitting a bijection into a proper subset of itself” because that definition is equal and does not rely on the definitions of set size, real numbers and an ordering relation that allows you to order cardianls
magus145 · 18 points · Posted at 00:29:59 on February 14, 2016 · (Permalink)
That's the definition of Dedekind finite. The standard set theory definition of an infinite set is "does not have a bijection with a finite cardinal", i.e., it is not the same size as a natural number.
The two definitions are only equivalent using the Axiom of Choice, so you don't want to take Dedekind finite as your definition of an infinite set unless you're sure you're working over a set theory where they're equivalent.
zomenox · 4 points · Posted at 01:06:50 on February 14, 2016 · (Permalink)
As I can't accept well ordered real numbers, fuck the axiom of choice.
almightySapling · 1 points · Posted at 06:56:19 on February 14, 2016 · (Permalink)
I hate Choice too. But my question for you, how many real numbers do you think there are?
zomenox · 1 points · Posted at 10:37:11 on February 14, 2016 · (Permalink)
? Uncountable. That's really what bothers me. Well ordering is getting dangerously close to a mapping to the natural numbers.
almightySapling · 5 points · Posted at 11:50:50 on February 14, 2016 · (Permalink)
Right, but which uncountable? You've heard of the cardinal numbers, I'm sure? You would think it would make sense to talk about the "size" of the reals, right?
Without choice, we have no way to compare the "sizes" of arbitrary sets. We know we can't inject R into N (so under the usual definition, |N|<|R|, but we have no idea what functions may or may not exist between R and any higher cardinality, meaning |R| might not even be one of the usual cardinal numbers. Without Choice, some sets don't even have sizes in any usual sense of the word.
whiteandnerdy1729 · 1 points · Posted at 09:37:01 on February 14, 2016 · (Permalink)
As I must accept that the cartesian product of any collection of nonempty sets is nonempty, fuck not having the axiom of choice.
almightySapling · 3 points · Posted at 06:50:58 on February 14, 2016 · (Permalink)
But you don't need full choice. The equivalence is strictly weaker than Countable Choice.
magus145 · 1 points · Posted at 16:55:51 on February 14, 2016 · (Permalink)
"Only" might have been too strong a word. I meant that they're not equivalent over ZF.
AcellOfllSpades · 2 points · Posted at 23:46:44 on February 13, 2016 · (Permalink)
My mistake - fixed it!
rck_mtn_climber · 20 points · Posted at 01:06:57 on February 14, 2016 · (Permalink)
Wow, never did I think my discrete math class would come in handy for understanding the comments section of a reddit post.
StillsidePilot · 11 points · Posted at 01:42:11 on February 14, 2016 · (Permalink)
It will never come in handy.
jacybear · 7 points · Posted at 01:46:00 on February 14, 2016 · (Permalink)
Amen.
MiyamotoKnows · 9 points · Posted at 03:47:46 on February 14, 2016 · (Permalink)
Why did you have to hide that you were going to math class?
tellisk · 5 points · Posted at 03:58:21 on February 14, 2016 · (Permalink)
Not "discreet".
MiyamotoKnows · 8 points · Posted at 04:13:15 on February 14, 2016 · (Permalink)
A bad joke. :)
tellisk · 1 points · Posted at 15:47:34 on February 14, 2016 · (Permalink)
I always appreciate a bad joke. I just wasn't sure. =)
MiyamotoKnows · 1 points · Posted at 16:19:39 on February 14, 2016 · (Permalink)
Reddit is a hard medium to show sarcasm in. I probably should have italicized what I wrote. ;)
FUZxxl · 7 points · Posted at 23:48:31 on February 13, 2016 · (Permalink)
Not just “pairs up things” but “pairs up each thing from one set with one thing from the other set using each thing exactly once,” but maybe “pairs up things” is precise enough for the layman.
AcellOfllSpades · 1 points · Posted at 23:56:17 on February 13, 2016 · (Permalink)
Yeah, I explained the "uses each thing only once" after the table for ℕ vs 2ℕ. I figured that it would clutter up the definition too much if I explained it in-definition - I already had to explain proper subsets, and too much explanation would lose people. When people think of pairing things up in real life, most assume that you don't repeat anything. Hopefully that's good enough to get the point across.
(Even though the condition of not repeating anything is necessary, it may be seen as pedantic by "laypeople".)
FUZxxl · 1 points · Posted at 23:57:38 on February 13, 2016 · (Permalink)
maybe say “Nothing is repeated or omitted on either side” instead of just “Nothing is repeated on either side.” That should be sufficient.
AcellOfllSpades · 1 points · Posted at 00:00:28 on February 14, 2016 · (Permalink)
Oh, I see what you mean. I was referring to after the table for ℕ→2ℕ. Thanks for the suggestion! I put "left out" instead of "omitted" to keep the wording simple.
FUZxxl · 1 points · Posted at 00:14:27 on February 14, 2016 · (Permalink)
The new wording looks good to me.
unMasqed · 4 points · Posted at 02:01:13 on February 14, 2016 · (Permalink)
...please excuse my raging math boner.
ZizZazZuz · 2 points · Posted at 03:23:25 on February 14, 2016 · (Permalink)
Sometimes, I really do love reddit.
almightySapling · 1 points · Posted at 06:51:46 on February 14, 2016 · (Permalink)
PEMRMB? I'm not familiar with this order of operations.
unMasqed · 1 points · Posted at 13:31:30 on February 14, 2016 · (Permalink)
PEMRMB: Parentheses, Exponents, Multiplication, Reduction, Magnification, ...Bees?
Mr_s3rius · 2 points · Posted at 02:51:09 on February 14, 2016 · (Permalink)
So, my maths knowledge fits nicely into a shotglass but isn't that the definition of countable infinite sets? For uncountable infinite sets there is no such bijection but they're still infinite sets.
I think I learned that infinite sets are all sets that are not finite (and finite being defined as whatever. Cardinality or what have you).
AcellOfllSpades · 3 points · Posted at 02:54:17 on February 14, 2016 · (Permalink)
Uncountably infinite sets do have a bijection.
You wouldn't be able to make a chart like that, but it doesn't matter - all you need is for there to be a rule. So if you were looking at the real numbers from 0 to 1, you could do something like f(x) = x/2. If you were looking at all real numbers, you could do this:
if x is positive, f(x)=x+1
otherwise, f(x)=x
This is fairly easily reversible, and ℝ\[0,1) is a subset of ℝ.
Mr_s3rius · 2 points · Posted at 03:20:11 on February 14, 2016 · (Permalink)
Thanks, got it. Must've remembered it wrong. (It's a very small shot glass.)
DXvegas · 1 points · Posted at 02:04:39 on February 14, 2016 · (Permalink)
This is a really neat explanation. I know how infinity was defined in reference to limits of functions/sequences, but not set sizes. I'm curious, what would a bijection of S and a proper subset of S look like if S is infinite but not countably infinite?
AcellOfllSpades · 3 points · Posted at 02:13:22 on February 14, 2016 · (Permalink)*
You wouldn't be able to make a chart like that, but it doesn't matter - all you need is for there to be a rule. So if you were looking at the real numbers from 0 to 1, you could do something like f(x) = x/2. If you were looking at all real numbers, you could do this:
if x is positive, f(x)=x+1
otherwise, f(x)=x
This is fairly easily reversible, and ℝ\[0,1) is a subset of ℝ.
Kombat_Wombat · 1 points · Posted at 03:52:04 on February 14, 2016 · (Permalink)
Your function f(n)=2n is not onto because all of the odds in the codomain are not mapped to. Therefore it is not a bijection.
That is, unless the codomain listed as the evens. Is that the case?
AcellOfllSpades · 2 points · Posted at 03:53:11 on February 14, 2016 · (Permalink)
Yep - the codomain is the (nonnegative) even numbers.
Kombat_Wombat · 1 points · Posted at 05:01:28 on February 14, 2016 · (Permalink)
I've always wondered why we can do this because it feels like cheating. Why not take any function and just say that the codomain is the range of the function and then call it onto?
I suppose I could try to answer my own question. The set of evens we can easily generate, and some functions would be more difficult to generate the range. I suppose I've seen the notation 3N and 4N for multiples of those numbers. for a function f(n)= 2n2 +3 could we just define the codomain to be 2N2 +3 (or probably just 2N2 )?
AcellOfllSpades · 2 points · Posted at 05:03:37 on February 14, 2016 · (Permalink)
You can do that. Generally we have specific sets we want to look at, not just the ones that happen to be the range of a function.
(And it would have to be 2N2 + 3; 67 would be in it.)
the12thmusketeer · 1 points · Posted at 05:02:05 on February 14, 2016 · (Permalink)
THANK YOU, for including 0 in the set of natural numbers!
itisike · 1 points · Posted at 12:20:47 on February 14, 2016 · (Permalink)
Yeah, but some mathematicians don't believe in infinity. See https://en.wikipedia.org/wiki/Finitism
AcellOfllSpades · 1 points · Posted at 16:46:33 on February 14, 2016 · (Permalink)
And they're cranks.
itisike · 1 points · Posted at 17:02:29 on February 14, 2016 · (Permalink)
Be careful of calling people with theorems named after them cranks.
AcellOfllSpades · 1 points · Posted at 18:00:45 on February 14, 2016 · (Permalink)
There's a difference between studying finitism and believing that it is the only valid viewpoint.
[deleted] · 1 points · Posted at 15:15:33 on February 14, 2016 · (Permalink)
Sorry if this is a dumb question – how come you can use 2 once on the natural side and once on the even side? Does that not count as repeating?
AcellOfllSpades · 2 points · Posted at 16:46:16 on February 14, 2016 · (Permalink)
Things just not need to repeat on their own sides. We're trying to perfectly pair up the natural numbers with the even numbers - before pairing up we start with two "copies" of all the evens.
[deleted] · 1 points · Posted at 17:24:11 on February 14, 2016 · (Permalink)
Okay, thanks! That makes a lot more sense.
coredumperror · 1 points · Posted at 03:34:16 on February 15, 2016 · (Permalink)
That's something I totally don't understand. How can there be anything other than half as many evens as naturals?
AcellOfllSpades · 2 points · Posted at 05:05:52 on February 15, 2016 · (Permalink)
Infinite sets are weird. The names of the objects shouldn't matter in determining how many of them there are, right? But if you rename the even numbers to "A, B, C..." (and start making up your own symbols after a while) then there's no way to tell that they were originally every other natural number. So you can't compare things by looking at what they are - after all, renaming things shouldn't change how many of them there are.
So how can we compare things? We pair them up! If you can match everything from one side to everything from another without repeating, then there are the same amount of things on both sides.
This lets us compare things without worrying about their structure or anything else. Again, structure shouldn't matter when we're just looking at how big something is - you could "squish" the even numbers to be paired up perfectly with the naturals, so they have the same size.
But there is a sense in which there are half as many evens as naturals. It's not size though. It's natural density. Natural density is a property of subsets of the natural numbers. You can measure it by picking bigger and bigger intervals and checking what fraction is part of the subset you're looking at.
Here's how we'd check the natural density of the evens:
First, we look at the interval {0}. 100% of those numbers are even.
Then we look at the interval {0 to 1}. 50% of those numbers are even.
Then we look at the interval {0 to 2}. 66.66...% of those numbers are even.
Then we look at the interval {0 to 3}. 50% of those numbers are even.
As we keep getting bigger, everything after a certain point gets closer and closer to 50%. The limit of the density in the interval {0,n} as n goes to infinity is 1/2. So the evens have a natural density of 1/2.
[deleted] · 0 points · Posted at 02:14:38 on February 14, 2016 · (Permalink)
k
Porfinlohice · 0 points · Posted at 02:46:34 on February 14, 2016 · (Permalink)
Well yeah but what if
175gr · 112 points · Posted at 22:08:51 on February 13, 2016 · (Permalink)
That's not really true mathematically. Infinity is a rigorous concept. Whenever you see it, it means something specific, no matter what it is.
Being a physicist, he might be referring to different ways physicists deal with infinity. There are ways to assign finite values to divergent series, and these often give results that match experiments - a famous one is the use of zeta regularization to replace "1+2+3+..." With "-1/12".
A_Waskawy_Wabit · 7 points · Posted at 00:33:17 on February 14, 2016 · (Permalink)
I love physicists and mathematicians fighting. Every time I learn one of these in physics or math the next day my prof will tell us he'll get mad if he ever sees it in his course since math is usually theoretically correct while physics is practically correct
[deleted] · 5 points · Posted at 02:07:24 on February 14, 2016 · (Permalink)
It's even more fun if you're a chemist, because then you get to laugh at both of them for even bothering in the first place. As we all know, the only real data is empirical data.
anti_pope · 6 points · Posted at 03:34:47 on February 14, 2016 · (Permalink)
And then you take intro quantum mechanics and watch the professor derive the periodic table.
[deleted] · 4 points · Posted at 03:52:36 on February 14, 2016 · (Permalink)
Or more likely hydrogen and then do helium halfway before concluding that the next row would take all year so let's not.
indigo121 · 0 points · Posted at 07:29:14 on February 14, 2016 · (Permalink)
Have fun playing with your one particle.
Cremasterau · -2 points · Posted at 01:36:24 on February 14, 2016 · (Permalink)*
But there seems to be a mathematical way of deriving -1/12th from infinite numbers if you include all of them including fractions and negative numbers.
The formula for summing sequential numbers is 1/2x(x+1) and if you plot this at Wolfram this is what you get).
If you calculate the small area under the x axis you get -1/12.
If you minus the area under the graph above the x axis on the left from the one on the right you get zero leaving the sum of all numbers through to infinity at -1/12!
Edit: Included picture directly
ThirdFloorGreg · 8 points · Posted at 23:11:45 on February 13, 2016 · (Permalink)
Did this conversation take place in the 1860s?
TrainsareFascinating · 2 points · Posted at 11:55:11 on February 14, 2016 · (Permalink)
Folks who reply with objections that infinities are precisely defined mathematically misunderstand the point being made.
In physics when infinities arise as a consequence of the mathematics being used many physicists believe this indicates the physical theory is incomplete or flawed, otherwise there would be no infinities present.
nerga · 2 points · Posted at 02:04:16 on February 14, 2016 · (Permalink)
Was this physicist a college freshman?
[deleted] · 2 points · Posted at 03:00:06 on February 14, 2016 · (Permalink)
University professor.
drunz · 2 points · Posted at 22:38:38 on February 13, 2016 · (Permalink)
"Ugh, what a cop out. They just use infinity as a Deux ex Machina. Worst theorem ever."- how I imagine this conversation going
Pegguins · 1 points · Posted at 01:30:34 on February 14, 2016 · (Permalink)
For physics yes, when your physics equations give you infinity you done goofed. The maths of infinities are very rigorous.
shaun252 · 0 points · Posted at 01:45:36 on February 14, 2016 · (Permalink)
The physics of infinities are fairly well understood too since like the 60s.
[deleted] · 1 points · Posted at 20:59:03 on February 13, 2016 · (Permalink)
That's how I feel when I think about infinity, it's like a definite idea but obscure at the same time :p
[deleted] · 2 points · Posted at 21:19:21 on February 13, 2016 · (Permalink)
I'm the same way when I think about the concept. I'm not a mathematician in any sense of the word but infinity is quite fascinating as a concept.
georgeo · 3 points · Posted at 23:33:51 on February 13, 2016 · (Permalink)
Georg Cantor, the mathematician who did a lot of pioneering work on the topic, went insane. It's easy to see why.
[deleted] · 2 points · Posted at 01:25:08 on February 14, 2016 · (Permalink)
Yeah I think anyone would have some issues staying sane when numerous colleagues tried over and over to prove that their life's work was bullshit and in the midst of all this their kid died.
InfintySquared · 3 points · Posted at 23:47:02 on February 13, 2016 · (Permalink)
Yes! When I was in the seventh grade, I read about this in "Asimov On Numbers." It blew my freakin' mind.
The concept that you can have something more infinite than infinity was so damn cool to me that I took it for my own pseudonym. Been using it for over twenty years!
[deleted] · 1 points · Posted at 02:16:31 on February 14, 2016 · (Permalink)
[deleted]
InfintySquared · 1 points · Posted at 04:30:06 on February 14, 2016 · (Permalink)
I know this. However, I chose this phrasing because it's more accessible to the layman, I didn't want the Hebrew connotations of Aleph One, and lim (x -> inf) f(x)=x2 doesn't work well as a username.
Plus ∞2 makes for a pretty cool-looking monogram. I had it embroidered on a ballcap.
Stamboolie · 3 points · Posted at 03:06:27 on February 14, 2016 · (Permalink)
I think the problem with this is the naming - when we say infinity we talk about the natural number infinity perhaps, but then sometimes different infinities without really defining our terms.
infinity like other numbers is a mapping, the number 2 for instance is a mapping onto reality and represents some physical thing, we say have 2 pints of lager, and we all know what that means. So when we are kids and hear infinity we naturally think of infinite pints of lager, as others have mentioned this is the countable infinity, because we map this onto a succession of pints of lager.
Now there are different sorts of infinity and mathematicians name them differently, because they represent different mappings onto different number systems and so have different qualitative properties. Kids intuitively know this when they argue about something being infinity true, uh uh it's infinity times infinity, and so on. Intuitively the first infinity maps to the number of integers, the other infinities get closer and closer to the reals, which (if my memory is correct and its been a while since i studied this) is about as many infinities as you can get.
Toogoodtotroll · 2 points · Posted at 22:59:19 on February 13, 2016 · (Permalink)
Mine's definitely larger
[deleted] · 2 points · Posted at 23:02:23 on February 13, 2016 · (Permalink)
( ͡° ͜ʖ ͡°)
ubergooner · 2 points · Posted at 23:06:30 on February 13, 2016 · (Permalink)
But...how...
new_painter · -2 points · Posted at 00:06:11 on February 14, 2016 · (Permalink)
It makes sense the second you think about it. You cannot count to the end of all numbers because there is no end, you just keep counting and counting. We know from this that there is an infinite amount of numbers because it never ends.
Imagine that you count up all the odd numbers, you still can never get to the end, because it just continues into infinity, so this number is also infinite.
However, you also know that even though both sets are infinite one set has twice as many items within it.
cannotget · 2 points · Posted at 00:24:15 on February 14, 2016 · (Permalink)
Not true. Both sets are countably infinite, meaning that you can list all of them in order (1, 2, 3, ...) vs (2×1-1, 2×2-1, 2×3-1, ...). Because you can map each whole number to an odd number bijectively using f(x)=2x-1, these two sets have the same cardinality - they're both countably infinite
SmartAlec105 · 2 points · Posted at 00:38:12 on February 14, 2016 · (Permalink)
Yep. If you add together an infinite number of things that are infinitely small, you can get a finite amount. That's how integrals work.
determinedforce · 2 points · Posted at 00:58:09 on February 14, 2016 · (Permalink)
So my wiener could be the smaller of the infinities? Awwww...
[deleted] · 2 points · Posted at 01:00:03 on February 14, 2016 · (Permalink)
[deleted]
JohnFrusciante70 · 2 points · Posted at 01:08:36 on February 14, 2016 · (Permalink)
that's why infinity divided by infinity != 1
It might equal 1, but most of the time it doesn't
Njallstormborn · 2 points · Posted at 01:29:32 on February 14, 2016 · (Permalink)
A friend of mine, who terrifyingly intelligent and loves really complex math, explained this to me once. Failing to grasp the concept in its entirety, I simply said "so its infinity+1" and she became very flustered.
IWugYouWugHeSheMeWug · 2 points · Posted at 01:55:48 on February 14, 2016 · (Permalink)
I remember in my Calc II classes, people couldn't wrap their heads around why infinity/infinity was undefined and not 1 or some other number. After the prof explained how some infinities are bigger than the others, it blew my fucking mind. I basically spend the entire day thinking about it and trying to wrap my head about it, but I still don't think I entirely get it. Like I understand the explanations on a logically level, I just can't seem to "get" it.
retief1 · 2 points · Posted at 05:01:06 on February 14, 2016 · (Permalink)
There are as many whole numbers (0, 1, 2, 3 ...) as there are integers (..., -2, -1, 0, 1, 2, ...), but there are more real numbers between 0 and 1 than there are integers. The proof of that is even more fun.
the_lost_banana · 2 points · Posted at 05:08:50 on February 14, 2016 · (Permalink)
This statement reminded me of one of the ideas in "The End of Eternity" by Isaac Asimov
ShaneDAWS0N · 2 points · Posted at 05:38:05 on February 14, 2016 · (Permalink)
Let's get your upvotes to infinity!
salgat · 2 points · Posted at 06:55:59 on February 14, 2016 · (Permalink)
It's more accurate to say there are different ways to approach infinity, some being faster than others.
BiggerJ · 2 points · Posted at 07:17:10 on February 14, 2016 · (Permalink)*
Imagine counting up from zero to any number ever by whole numbers. As long as your target is part of the set you're counting through, then given enough time, you'll eventually reach it. The set is countably infinite.
Now imagine counting up from zero to any number ever by decimals. You'd start 'zero, zero point zero zero zero zero zero zero...' ad infinitum. You couldn't even start. The set is uncountably infinite.
Lareine · 2 points · Posted at 07:46:16 on February 14, 2016 · (Permalink)
Yes, but that goddamn quote in Fault in Our Stars gets it wrong. Get it together John Green.
[deleted] · 1 points · Posted at 00:50:21 on February 14, 2016 · (Permalink)
Infinity + 1
DishwasherTwig · 1 points · Posted at 01:53:06 on February 14, 2016 · (Permalink)
Infinity is as much a number as the color purple is. People don't always get that. It's a concept, not a specific number, all infinity means is that something is uncountable.
tweeblethescientist · 1 points · Posted at 01:54:37 on February 14, 2016 · (Permalink)
The easiest way to imagine it is you have a string of infinite length. Next to it is a much thicker string of infinite length. They're both infinite but one is bigger. I think.
hlposts · 1 points · Posted at 02:13:01 on February 14, 2016 · (Permalink)
Whatever, Bev.
Gerbster88 · 1 points · Posted at 02:18:51 on February 14, 2016 · (Permalink)
If someone hasn't mentioned it already, check out The Mystery of the Aleph. Interesting mix of historical novel and math investigation. The story of Gregor Cantor investigating this idea, his madness, and his persecution by the church for investigating infinity at a time when the idea was reserved for theology.
BabyLeopardsonEbay · 1 points · Posted at 02:24:42 on February 14, 2016 · (Permalink)
And yet they go on FOREVER. So weighing one vrs another type is merely just a concept. In a way it's a paradox.
yliu1021 · 1 points · Posted at 02:27:50 on February 14, 2016 · (Permalink)
Furthermore, contrary to popular-ish belief, there actually aren't more numbers between 0 to 1 lets say and 0 to 2. As long as you can make a direct mapping between items from one set to the other, then the two sets have an infinite but equal number of elements.
ShoggothEyes · 1 points · Posted at 02:40:49 on February 14, 2016 · (Permalink)
Depending how you define "larger" anyways. If "larger" = "more elements", then no.
mspe1960 · 1 points · Posted at 02:42:31 on February 14, 2016 · (Permalink)
I have heard it described as "more dense" than others. And that makes sense to me.
Paultimate79 · 1 points · Posted at 02:58:19 on February 14, 2016 · (Permalink)
There actually isn't.
Simply put you could repeat "12" infinite times or "123" infinite times. "123" would be "bigger" but that doenst apply to infinity long constructs. They are all the same length; forever.
msstark · 1 points · Posted at 03:00:34 on February 14, 2016 · (Permalink)
I read that in a John Green book and I had to put the book down awhile and think about it. It was probably the most time anyone probably spent thinking while reading a John Green book.
Sakinho · 1 points · Posted at 03:11:23 on February 14, 2016 · (Permalink)
Not only are there infinities larger than others, but there is an infinitude of infinities. These can be understood with set theory, where infinities are described as infinite sets whose sizes can be compared. In particular, from an infinite set, it's always possible to create a strictly larger infinite set by creating a set of all subsets of the starting infinite set. Therefore, set theory can generate and handle an infinite hierarchy of infinite sets.
Now, here's the crazy part. If there is an infinitude of infinite sets, how large is this infinitude? Turns out that even though you can make sets for very, very large infinities, the infinitude of infinite sets describes such a vast concept that it's too large to even form a set.
cayneloop · 1 points · Posted at 03:17:14 on February 14, 2016 · (Permalink)
i`m gonna hijack this comment cause it relates to the most astounding and simple math calculation in this thread:
1+2+3+4+5+...=1/12
explained here: https://www.youtube.com/watch?v=w-I6XTVZXww
CheezyMcWang · 1 points · Posted at 03:48:18 on February 14, 2016 · (Permalink)
I explain this as:
Infinity is made up of an infinite number of smaller infinities.
TwoColdOne · 1 points · Posted at 03:52:16 on February 14, 2016 · (Permalink)
1 is exactly equidistant from Infinity, as 1,000,000 is.
Ephemerality314 · 1 points · Posted at 03:54:21 on February 14, 2016 · (Permalink)
Yup. And in fact there are an infinite number of infinities, thus there is no largest infinity.
DimeTree · 1 points · Posted at 03:58:04 on February 14, 2016 · (Permalink)
Different types? Isn't infinity just the basic concept used to convey that numbers never end?
MVP_Redditor · 1 points · Posted at 04:13:49 on February 14, 2016 · (Permalink)
And that the infinity between 1 and 2 is larger than the infinity of all natural numbers.
[deleted] · 1 points · Posted at 04:22:47 on February 14, 2016 · (Permalink)
I'm a college undergrad. I got an A in calculus. I thought I had a grasp on math, now I am very very confused and sad.
[deleted] · 1 points · Posted at 04:25:31 on February 14, 2016 · (Permalink)
Me too, currently in discrete math. I'd recommend snagging a discrete math book or looking online, if you like math I think you'd find set theory/number theory interesting (if you haven't been exposed to this stuff before)
[deleted] · 1 points · Posted at 04:24:41 on February 14, 2016 · (Permalink)
to those confused, imagine a bunch of holes that are an infinite amount of miles deep as these different kinds of infinity. the larger infinities are holes with wider diameter than other holes.
creedofwheat · 1 points · Posted at 05:01:59 on February 14, 2016 · (Permalink)
Fault In Our Stars mentioned this.
_Psyki · 1 points · Posted at 05:15:54 on February 14, 2016 · (Permalink)
An excellent video on the topic, for those interested: https://www.youtube.com/watch?v=elvOZm0d4H0
bluesox · 1 points · Posted at 05:41:46 on February 14, 2016 · (Permalink)
Well, duh. Everybody learns about infinity plus one by the time they're seven years old.
stickfiguredrawings · 1 points · Posted at 09:35:13 on February 14, 2016 · (Permalink)
https://www.goodreads.com/quotes/487705-there-are-infinite-numbers-between-0-and-1-there-s-1
timndime · 1 points · Posted at 09:38:46 on February 14, 2016 · (Permalink)
some infinities are more equal than others
FadeInto · 1 points · Posted at 10:03:39 on February 14, 2016 · (Permalink)
Correct me if I am thinking about this wrong but I always use a thought experiment for this one. Imagine a grid with a one square line. The line continues infinitely. Now picture a line that is 2 squares thick. The one square line could be subtracted from the 2 square line and we would be left with a one square line, even though both are infinite. Thus one infinity is larger than the other.
myorangebook · 1203 points · Posted at 22:25:06 on February 13, 2016 · (Permalink)
Stopped 2+ years of lurking to make this comment. The Riemann Rearrangment theorem is pretty cool and explains a lot of the unintiutive things that happen when dealing with infinite sums. https://en.wikipedia.org/wiki/Riemann_series_theorem
waiting_for_rain · 21 points · Posted at 01:42:39 on February 14, 2016 · (Permalink)
I'm salty because my Calc 2 text said it was "Out of the Scope" of the class. Our professor explained it later.
Caststarman · 14 points · Posted at 05:52:15 on February 14, 2016 · (Permalink)
Wait a second that's calc 1 stuff tho
waiting_for_rain · 5 points · Posted at 07:22:19 on February 14, 2016 · (Permalink)
Our class finished derivatives and integrals was a self contained calc 2. Eased out the typically hard stuff like trig integration
[deleted] · 6 points · Posted at 07:56:19 on February 14, 2016 · (Permalink)
Trig integration isn't hard though. Where did you go to school?
rightbeforeimpact · 8 points · Posted at 08:37:44 on February 14, 2016 · (Permalink)
It can be sometimes. Doing the basic sin and cos are easy, but I learned in an Analog and Digital Communications class (AM/FM transmission stuff) that it can get very hairy when you're dealing with a complicated signal that is then encoded within another trig function.
[deleted] · 3 points · Posted at 14:56:50 on February 14, 2016 · (Permalink)
Yea real waves are hard but trig sub isn't so hard that it's worth skipping as a whole.
qwrty42 · 3 points · Posted at 08:31:07 on February 14, 2016 · (Permalink)
Depends on the school. My college didn't even get to antiderivatives until calc 2
QuietCurious · 63 points · Posted at 02:03:49 on February 14, 2016 · (Permalink)
I gave you an upvote only because you came out of hibernation. Everybody should come out and play once in a while.
physiology9 · 10 points · Posted at 04:59:59 on February 14, 2016 · (Permalink)
Very cool!
Now go back to your room.
mobius_stripe · 6 points · Posted at 03:08:01 on February 14, 2016 · (Permalink)
Fuck I remember I almost came in my pants when I saw the proof of this in my first real analysis course.
mafftastic · 3 points · Posted at 03:53:56 on February 14, 2016 · (Permalink)
Every time I explain this to my students, I'm pretty sure I see their heads explode.
LifeBehindHandlebars · 2 points · Posted at 06:21:47 on February 14, 2016 · (Permalink)
Now that you're not a lurker, let me ask you....why did you choose the username you did?
zacktheking · 2 points · Posted at 07:34:14 on February 14, 2016 · (Permalink)
I was flipping through my old analysis notebook and found this. I ha written TRIPPY and circled it in the margins at the time.
chevymonza · 1 points · Posted at 14:35:20 on February 14, 2016 · (Permalink)
I saw a giant "E" with an infinity on its head, skateboarding on top of n= something, and noped outta there fast.
[deleted] · 2 points · Posted at 08:35:11 on February 14, 2016 · (Permalink)
Was gonna answer this. For anyone still scratching their head at it, it makes a lot more sense when you consider that an "infinite sum", formally, is actually a limit of a sequence of partial sums. Students usually think of series as just being infinitely many terms added together, but this is a misconception.
Tharn11 · 4 points · Posted at 01:39:27 on February 14, 2016 · (Permalink)
Had to prove this as a homework assignment last year. That succckkkkeeedd
T-Rex96 · 1 points · Posted at 23:41:50 on March 11, 2016 · (Permalink)
Me too! Also I'm actually a physics student, so I still don't see how these proofs are important for me
404random · 5 points · Posted at 04:11:55 on February 14, 2016 · (Permalink)
I thought this would have summation of 1+2+3...=-1/12. Ah, the wonders of Riemann Zeta and complex analysis.
Low_discrepancy · 1 points · Posted at 09:51:52 on February 14, 2016 · (Permalink)
Do we also say now that -0.5-1.5-2.5-3.5....= -2sqrt(pi)?
nike0518 · 1 points · Posted at 05:08:26 on February 14, 2016 · (Permalink)
I felt so badass when I learned this for cal 2.
buckeyebearcat · 1 points · Posted at 05:14:44 on February 14, 2016 · (Permalink)
Before you learn of integral you are taught to find area under curve with Rieman sum. Basically infinite number of rectangles. So crazy
Serraptr · 1 points · Posted at 05:15:02 on February 14, 2016 · (Permalink)
Was it worth it
Skrub-Wrecker · 1 points · Posted at 09:56:04 on February 14, 2016 · (Permalink)
Redditor for 10 hours huh...
asifcool83 · 1 points · Posted at 10:03:12 on February 14, 2016 · (Permalink)
Really? Cmon? Really? First comment and gold!!! Fuck meeeee
BornInTheRSA · 1 points · Posted at 13:26:56 on February 14, 2016 · (Permalink)
This is of course the basis for integration.
NewbornMuse · 1 points · Posted at 14:07:31 on February 14, 2016 · (Permalink)
Whaaaaaaaaaat
that's crazy
deeschannayell · 1 points · Posted at 14:40:12 on February 14, 2016 · (Permalink)
Never seen this before.
Thanks, dude!
Falcoteer · 1 points · Posted at 16:16:33 on February 14, 2016 · (Permalink)
My favorite is still {1+2+3+4+...}=-1/12
Spiralofourdiv · 1 points · Posted at 17:07:34 on February 16, 2016 · (Permalink)
I agree it's unintuitive, but this never blew me away because conditional convergence is such a fine restriction.
STEALTHHUNTER88 · 1 points · Posted at 08:07:10 on May 18, 2016 · (Permalink)
"Although in standard presentation the alternating harmonic series converges to ln(2) ..."
Wait isn't ln(2) used in half-life calculations?
The_Farting_Duck · 1 points · Posted at 03:49:25 on February 14, 2016 · (Permalink)
That hurt to read.
[deleted] · 0 points · Posted at 03:47:50 on February 14, 2016 · (Permalink)
[deleted]
ilovelsdsowhat · 1 points · Posted at 05:11:40 on February 14, 2016 · (Permalink)
Obviously they made an account so they could comment. You can lurk without an account.
Edit: is account even the right word? It sounds weird to me.
Shipthenickels · 0 points · Posted at 07:14:07 on February 14, 2016 · (Permalink)
Go back to lurking
Edit : jk keep posting and have an upvote :)
ExtraCheesyPie · -3 points · Posted at 03:35:37 on February 14, 2016 · (Permalink)
How do people manage to lurk for 2 years? Is commenting really that unappealing?
Kandarr · 0 points · Posted at 04:34:55 on February 14, 2016 · (Permalink)
ExtraCheesyPie · 1 points · Posted at 05:23:48 on February 14, 2016 · (Permalink)
I get that, but that means he didn't have an account for two years right? Like why the fuck not, it lets you make comments, upvote stuff you like, make shitposts, whatever.
Also I'm not sure what the age of the account has to do with the length of the lurk.
ElectroBoof · 1 points · Posted at 06:39:22 on February 14, 2016 · (Permalink)
/u/kandarr thinks lurking means having an account but not posting for some reason
But yeah I agree with you. I lurked on reddit for a few months before finally making an account circa one year ago
Damn I'm never going back
usthcd · 3441 points · Posted at 19:41:33 on February 13, 2016 · (Permalink)
If you put 23 people in a room, there's over 50% chance that at least two of them have the same birthday.
WildxYak · 2773 points · Posted at 21:20:09 on February 13, 2016 · (Permalink)
/u/TYLERvsBEER had the best ELI5 description of this IMO
TYLERvsBEER · 1801 points · Posted at 22:50:48 on February 13, 2016 · (Permalink)
Thanks for the shout out!
lefendary · 59 points · Posted at 23:10:52 on February 13, 2016 · (Permalink)
Who won?
InterestingAroma · 51 points · Posted at 01:08:06 on February 14, 2016 · (Permalink)
You decide!
[deleted] · 30 points · Posted at 04:04:31 on February 14, 2016 · (Permalink)
EPIC RAP BATTLES OF HISTORY BLAARRGHARRA
[deleted] · 1 points · Posted at 02:17:13 on February 14, 2016 · (Permalink)
[deleted]
steventhewreaker · 5 points · Posted at 02:21:16 on February 14, 2016 · (Permalink)
eeeeeeeeeeeeeeEEEEEEEEEEpcrapbtlesofhstoreeeeee
TYLERvsBEER · 13 points · Posted at 03:39:04 on February 14, 2016 · (Permalink)
Not catholic but I always give up beer and wine for Lent so i lose a few easy pounds. Next 40 days is TYLERvsVODKA.
Tyler11223344 · 3 points · Posted at 08:55:42 on February 14, 2016 · (Permalink)
As a fellow Tyler, I shall carry the torch for the next 40 days
lefendary · 1 points · Posted at 15:50:56 on February 14, 2016 · (Permalink)
That's the wrong way bro Traditionally monks brew extra strong Beer during lent and eat less Source i'm German and live in a very catholic region There are a lot of feasts now with really good Beer 😃
timeslider · 2 points · Posted at 04:55:26 on February 14, 2016 · (Permalink)
Who's next?
lefendary · 1 points · Posted at 15:46:07 on February 14, 2016 · (Permalink)
You decide!!
g18suppressed · 2 points · Posted at 12:29:30 on February 14, 2016 · (Permalink)
Who's next?
MuxBoy · 5 points · Posted at 01:29:28 on February 14, 2016 · (Permalink)
Happy birthday!
Tarantulasagna · 4 points · Posted at 02:19:43 on February 14, 2016 · (Permalink)
I like the username, my name is also Beer
kogasapls · 3 points · Posted at 06:52:08 on February 14, 2016 · (Permalink)
Succinct and intuitive explanation, and correct to boot. Too many people cite the "253 possible pairs" argument without really understanding the problem. Your post will come in handy in the future whenever this problem comes up, so thanks.
skullturf · 1 points · Posted at 16:27:44 on February 14, 2016 · (Permalink)
How do you figure? Understanding that it's primarily about the number of pairs of people, not the number of people, is an enormous part of understanding the problem.
kogasapls · 1 points · Posted at 17:39:48 on February 14, 2016 · (Permalink)
1 - 365! / (365n (365 - n)!)
Adding each new person reduces their probability of having a unique birthday, rather than there being a constant chance evaluated repeatedly.
um00actually · 1 points · Posted at 14:31:09 on February 14, 2016 · (Permalink)
Quesiton!
But that's NOT a lot. Not compared to alllllll the possible pairs you get from 365 days. So how does that work?
skullturf · 2 points · Posted at 16:29:54 on February 14, 2016 · (Permalink)
It's not about the possible pairs of days. It's just about the 365 possible days.
For instance, maybe person #8 and person #17 happen to share the single birthday of October 30th.
um00actually · 1 points · Posted at 01:36:38 on February 18, 2016 · (Permalink)
23 people gives 253 pairs, a 50% chance. But 253 is much more than 50% of the 365 possible days. So how does that work?
skullturf · 1 points · Posted at 02:20:06 on February 18, 2016 · (Permalink)
253 isn't much more than 50% of 365. In terms of orders of magnitude, it's slightly bigger than 50% of 365.
Unfortunately, I don't know whether I can give you a short answer. The shortest answer is just "If you do the math in detail, you end up with 23 people which means 253 pairs."
I can give you some links for further reading, but I don't know what your math background is, so I don't know what level of detail is appropriate for you.
Everything you might need to know can be figured out by reading the links, but depending on your math background, it might take some time.
http://betterexplained.com/articles/understanding-the-birthday-paradox/
https://en.wikipedia.org/wiki/Birthday_problem
um00actually · 1 points · Posted at 02:28:31 on February 18, 2016 · (Permalink)
But it is. 22 people gives 231 possible pairs, which is still more than 50% of 365. Why not say you have over a 50% chance of finding a matching pair with 22 people? Why not say 21? Whatever number of people it takes to get 183 possible pairs should be the 50% number. (I don't know what that is, but it's much less than 23.)
skullturf · 1 points · Posted at 02:41:25 on February 18, 2016 · (Permalink)
Because it's not true.
You might guess that it would be, but it's not.
I know I might sound snarky. I know I might sound like I'm not explaining it. But the fact is, explaining it takes time. You have to work through some details.
I gave you some links that explain some of the details, but you might just have to spend some time on it.
What is your math background, if you don't mind me asking? One of the problems with conversations among strangers on the internet is that you don't know what the other person knows.
um00actually · 1 points · Posted at 02:57:01 on February 18, 2016 · (Permalink)
Engineering degree. I get the math.
You're contradicting yourself. You start out saying, essentially, "253 pairs gives a 50% chance because 253 is 50% of 365." But it's not, 183 is. So what's 253 50% of? What's the significance of 253?
skullturf · 1 points · Posted at 03:17:41 on February 18, 2016 · (Permalink)
No, you don't.
Did you read the links I provided in detail?
All I said is that 253 is close to 50% of 365, which provides a rough explanation of why about 253 pairs is enough.
The significance is that it just happens to work out that way.
You're asking for a quick intuitive explanation, but sometimes there isn't a quick intuitive explanation. You just have to work through the steps.
Probability of two people having different birthdays:
364/365
Probability of three people having different birthdays:
(364/365) * (363/365)
Probability of four people having different birthdays:
(364/365) * (363/365) * (362/365)
Continue in this way. It turns out, after you crunch the numbers, that with 22 people, the probability of all different birthdays is more than 50%, but with 23 people, the probability of all different birthdays is less than 50%.
That's just the way it happens to work out. If you really want to understand this, then work through the details yourself. Don't glibly ask for a simple explanation when there might not be one. Have the patience to work through the specific details, which can be found in the links I provided.
TYLERvsBEER · 1 points · Posted at 19:09:43 on February 14, 2016 · (Permalink)
I think you're over complicating it.
Think about it this way: Anytime a person meets another person there's a 1/365 chance that they share the same birthday. In my example this occurance, or "birthday check", is happening hundreds of times.
um00actually · 0 points · Posted at 01:38:32 on February 18, 2016 · (Permalink)
You're just explaining the scenario multiple times, you're not explaining how it works or answering my question.
The number of "checks" you get from 23 people is NOT anywhere near 50% of the number of "checks" you get from 365 people.
jayquincy · 1 points · Posted at 20:05:36 on February 18, 2016 · (Permalink)
Hey, how would you calculate this mathematically? Thanks
TYLERvsBEER · 1 points · Posted at 20:26:00 on February 18, 2016 · (Permalink)
I'm actually just a dumb sales guy who tries to simplify things to customers all of the time. This was my crack at it. There are some math guys who I believe explained the way to calculate this. Sorry!
jayquincy · 1 points · Posted at 13:25:27 on February 19, 2016 · (Permalink)
That's okay, I'll see if I can find the right equation on my own.
Zombi_Sagan · 14 points · Posted at 23:01:36 on February 13, 2016 · (Permalink)
That helped tremendously. Thank you.
pensfan92 · 26 points · Posted at 23:54:33 on February 13, 2016 · (Permalink)
Still don't buy this. 23 random numbers out of a possible 365 numbers. What am I missing?
Barkonian · 31 points · Posted at 01:05:51 on February 14, 2016 · (Permalink)
One point to remember is that you're not looking for two people who where born on a specific day i.e June the 7th. You're looking for two people who share a birthday, which could be any of the 365 days.
MajorDishes · 28 points · Posted at 01:31:01 on February 14, 2016 · (Permalink)
... that's my birthday.
SealTheLion · 7 points · Posted at 06:13:40 on February 14, 2016 · (Permalink)
Mine too. My heart skipped a beat when I read it.
DammitDan · 3 points · Posted at 14:24:52 on February 14, 2016 · (Permalink)
Wow! What are the odds?
SealTheLion · 2 points · Posted at 18:11:26 on February 14, 2016 · (Permalink)
About 1/365 lol. ;)
Kubby · 1 points · Posted at 08:18:49 on February 15, 2016 · (Permalink)
June 7th for the win.
Hara-Kiri · 2 points · Posted at 11:13:50 on February 14, 2016 · (Permalink)
WE'RE NOT LOOKING FOR YOU.
[deleted] · -1 points · Posted at 01:31:22 on February 14, 2016 · (Permalink)
[deleted]
Barkonian · 14 points · Posted at 01:35:49 on February 14, 2016 · (Permalink)
But it doesn't matter which day. Most people would think of it (incorrectly) like this: Guy #1 is born on June 7th, so now I have to find someone else born on June 7th in the rest of the 22 people. But there is 22 other days that you need to look at.
[deleted] · 0 points · Posted at 06:02:39 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 4 points · Posted at 06:07:25 on February 14, 2016 · (Permalink)
Yes. Now lets say Guy #1 can't find anyone with a June 7th birthday.
THAT'S NOT THE END OF IT!
He checked 22 other people and nobody had June 7th.
NOW, Guy #2 needs to check. His birthday is January 1st. He checks 21 other people with the January 1st birthday.
Now there have been 22 checks (guy 1 checking everyone for June 7th) + 21 checks (guy 2 checking everyone for January 1st) = 43 checks. Continue this down the road and you'll have
22 June 7th checks + 21 January 1st checks + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 253 checks. 253 possibilities for a match.
UndeadBread · 5 points · Posted at 02:47:06 on February 14, 2016 · (Permalink)
He means it's not a predetermined day.
WildxYak · 63 points · Posted at 00:07:18 on February 14, 2016 · (Permalink)
I'm no mathematician by any means, this just happens to be one I've spent time trying to get my head around.
/u/Frtipachi explained it well too with a more visual example that might help.
imthemostmodest · 15 points · Posted at 01:52:08 on February 14, 2016 · (Permalink)
Wow, that one made it click for me. Thanks!
Frtipachi · 6 points · Posted at 05:15:41 on February 14, 2016 · (Permalink)
;D
doogie88 · 1 points · Posted at 06:24:04 on February 14, 2016 · (Permalink)
Still don't get it. Why is it using 60 people. If we're using 23 people at around 20 people you're going to have the board about 1/16 colored. So confused.
WooperSlim · 4 points · Posted at 07:30:25 on February 14, 2016 · (Permalink)
It's because you have to add up all the probabilities as you go. 60 is an easier number to visualize.
So yeah, the 23rd person has a 94% chance of missing, but when you combine that with chances that each of the 23 of the others also missed, it comes to about 50%.
It's like if you have a spinner with only 1% chance of winning, but you have 70 spins, you have a much better chance of winning.
WildxYak · 3 points · Posted at 10:21:12 on February 14, 2016 · (Permalink)
At 60 people it becomes a ~99% chance. That's what the discussion was about when the original answer was posted.
The theory and method can still be applied for 23 people and getting the 50% chance.
nekoningen · 0 points · Posted at 05:13:02 on February 14, 2016 · (Permalink)
Except in the real world with birthdays the chances are a little higher than the math shows, because human birthdays tend to be clustered due to events (~9 months after valentines, christmas, snow-ins, large economic booms, disasters, etc).
BilllisCool · 16 points · Posted at 02:46:32 on February 14, 2016 · (Permalink)
I couldn't wrap my mind around it either, so I wrote a program that randomly generates a number from 1-365 23 times and checks if any numbers match. I had it loop 1000 times. Every time I ran the program, a match was found 50% of the time. I still don't understand it, but it definitely is true.
Broswagonist · 20 points · Posted at 03:14:44 on February 14, 2016 · (Permalink)
That's exactly why it works. You're not generating a number from 1-365 and looking for, say, 77. You generating 23 numbers.
Say you generate one number, eg. 5. The second number has a 1/365 chance of being 5. But it's not, maybe it's 143. Now the third number has a 2/365 chance of matching, since it could match either 5 or 143. And so on. By the time you get to the last number, you have a 22/365 chance of matching the previous numbers.
doogie88 · 1 points · Posted at 06:27:03 on February 14, 2016 · (Permalink)
But that's only 1/16 of a chance?
HhmmmmNo · 6 points · Posted at 06:29:59 on February 14, 2016 · (Permalink)*
Because you've got to add all the other chances up.
But that's not usually how the math goes. You have to work the chance of no match.
doogie88 · 2 points · Posted at 06:39:58 on February 14, 2016 · (Permalink)
I think(hope) I got it now after reading all these explanations. Correct me if I'm wrong. Say there is 23 of us spinning a wheel 1-365. Say all 23 of us spun the wheel and all landed on different numbers. That would be 23/365 of the board selected, or approx 1/16. So the next guy is going to have a 1/16 shot of landing on the same numbers as one of us. Not great odds, but all 23 people have those same odds. So if 23 people people spin the wheel with 1/16 of it taken, after 23 spins, someone is more than likely going to win that 1/16 odds. Yes? No?
HhmmmmNo · 2 points · Posted at 07:13:34 on February 14, 2016 · (Permalink)*
OK, think of it this way. In a room of 23 people there are 253 different pairs. That's (23 x 22)/2. The chance of any pair having the same birthday is 1/365, thus the chance of them not having the same birthday is 364/365 or 99.726%. But that chance needs to be multiplied by itself for each pair. That means the chance of no match is (364/365)253 or 49.95%. What's the chance of having a match? The reverse, 50.05%.
The people who spin the wheel don't have the same odds. The odds go up steadily each time and you need to combine them. The math I did above is a simple way to do that.
[deleted] · 0 points · Posted at 05:57:54 on February 14, 2016 · (Permalink)*
I don't get it because there's 23 people, and 365 days. Therefore there should be roughly a 23/365 chance that there's a match. That would mean that it should only match around 1/16 of the time.
All these helpful people and i still don't get it.
SealTheLion · 3 points · Posted at 06:23:40 on February 14, 2016 · (Permalink)
Yes, but only for the first guy. The first guy has a 22/365 chance, not including himself. But then the next guy has a 21/365 chance, and the next guy a 20/365 chance, then 19/365, 18/365, 17/365, etc. Keep going through all 23 people, dropping one number each time. That adds up.
Volpethrope · 2 points · Posted at 06:29:08 on February 14, 2016 · (Permalink)
You're trying to get the same number twice with 23 attempts. The second number has a 1/365 chance to be the same as the first number, obviously, but let's say it isn't. Now the third number has a 2/365 chance, because there are already two different numbers it can match to. The fourth one has 3/365 possible matches, and so on up to the twenty-third number having 22/365 possible matches. You add all these chances together and it comes out to a bit over 50% total for at least two of them to have been the same number.
Don't think of it as trying to find a match to a specific number of your choosing. With 23 people, there are over 250 possible pairings. All you need is one of those 250+ pairings to produce a match.
[deleted] · 0 points · Posted at 07:17:13 on February 14, 2016 · (Permalink)
I still don't get it. There should (logically) be 23 different numbers, with around a 1/16 chance of match.
My brain fails to understand anything else. Thanks for trying though.
Volpethrope · 2 points · Posted at 07:28:57 on February 14, 2016 · (Permalink)*
It's just adding up the chances for each number to match one of the previously-generated numbers. It's just (1/365)+(2/365)+(3/365)+...+(20/365)+(21/365)+(22/365). That adds up to a bit more than a 50% probability.
Your 23/365 is a single chance for a number to match one of 23 other numbers. Not the combined chances for any two of those 23 numbers to match each other.
doogie88 · -1 points · Posted at 06:26:47 on February 14, 2016 · (Permalink)
I'm on the same boat as you!
Plastonick · 4 points · Posted at 14:18:50 on February 14, 2016 · (Permalink)
I looked at a few replies to you but none seemed to really ELI5.
Take 23 darts, a poor darts player, and a large calendar.
The poor darts player is just good enough to hit the calendar every time but it randomly hits a date on the calendar, he hits each date with the exact same chance, whether or not he's already hit it.
Now he throws the first dart, since there are no darts already on the board he will definitely NOT hit a date that already has a dart on it. (Probability 1 = 365/365)
He throws the second dart, there is a 364/365 chance of not hitting a date with a dart already in it, since he has thrown one dart in one date.
He throws the third dart, there is a 363/365 chance of not hitting a date with a dart in it, since he has thrown two and hit two dates.
he throws the fourth, 362/365 chance of not hitting a date with a dart already in it, since he has thrown three already and hit three different dates.
so on, so forth, until he throws the 23rd dart into a different date with probability 343/365.
So the chance that we manage to throw 23 darts into all different dates is (365 * 364 * 363 * ... * 343) / (365 ^ 23), which WolframAlpha tells me is approximately 0.49. Hence the chance that we do NOT manage to throw 23 darts into all different dates is 1-0.49, or about 0.51.
kevms · 11 points · Posted at 02:17:55 on February 14, 2016 · (Permalink)
Here's my explanation:
Let's say there are 23 people standing in a line, all facing the same way. #1 checks with #2-23 to see if they have matching birthdays, then #2 checks with #3-23, and so on, all the way to #22 checking with #23. That's 253 checks. Keep this number in mind.
Now, let's say we DON'T want any of the birthdays to match. What are the chances? For any of the aforementioned checks, the chances that the birthdays DON'T match is 365/366, around 99.7%. Since we don't want ANY of the checks to get a match, the chances are (365/366)253. That's 50%.
Since there's a 50% chance that there would be NO matches, there's also a 50% chance that there's at least a match somewhere.
kogasapls · 3 points · Posted at 06:59:22 on February 14, 2016 · (Permalink)
This explanation isn't actually correct although it gives a very similar answer to the correct one. Assuming 366 days, the first person can have a birthday on any one of 366 days, leaving 365/366 for the next person to have a different birthday. But if this check is failed, the second person only has 365 days available, leaving 364/366 for the third. This continues until the nth person can have a birthday on any one of (366 - n) days.
P(n) = 1 - (366 * 365 * ... * [366 - n]) / 366n
P(23) = ~0.506
kevms · 1 points · Posted at 07:57:34 on February 14, 2016 · (Permalink)
Oh yeah, you're right. Forgot to account for that.
SealTheLion · 2 points · Posted at 06:12:15 on February 14, 2016 · (Permalink)*
Each person has 22 chances of having a matching birthday. That means 23 different people have 22 potential chances to have a birthday match in the room. Think about it like that and it's easier to conceptualize.
Edit: In reality, only one person actually has 22 chances, considering that once he goes through all 22, then he's now out of the picture as a match for the other 22 people. But it still makes it easier to conceptualize. 22/365, 21/365, 20/365, etc. It's likely that you'll eventually get a match.
[deleted] · 1 points · Posted at 01:30:21 on February 14, 2016 · (Permalink)
[deleted]
SealTheLion · 2 points · Posted at 06:25:35 on February 14, 2016 · (Permalink)
Each person has 22 chances of having a matching birthday. That means 23 different people have 22 potential chances to have a birthday match in the room. Think about it like that and it's easier to conceptualize.
In reality, only one person actually has 22 chances, considering that once he goes through all 22, then he's now out of the picture as a match for the other 22 people. But it still makes it easier to conceptualize. 22/365 chance for the next guy, then 21/365, 20/365, etc. It's likely that you'll eventually get a match because it adds up. There are a ton of chances.
OneWordExplanation · 1 points · Posted at 02:49:46 on February 14, 2016 · (Permalink)
Elimination.
doogie88 · 1 points · Posted at 06:21:38 on February 14, 2016 · (Permalink)
Same, that explanation was great, but still doesn't fully make sense. Like you said, if you take 23 random numbers from 1-365 how can there be a 50% chance out of 365 numbers, two people are going to land on the same number. :(
kogasapls · 2 points · Posted at 07:14:11 on February 14, 2016 · (Permalink)
1) You pick a number 1-365. You're the first to pick one, so you know that nobody else has picked it: probability 100%.
2) Person 2 picks a number 1-365. They have a whole 364 other numbers to choose, or the 1 number that's already picked. Probability of them picking a unique number: 364/365.
3) Person 3 picks a number 1-365. They have 363 unique numbers to choose, or the 2 numbers that have already been picked. Probability of them picking a unique number: 363/365.
However, that number (363/365) is the probability of that third person picking a unique number provided the first two people have already picked two different unique numbers. In order to find the probability of the first, second, and third people all picking different numbers, we multiply the probabilities for each event:
1 * 364/365 * 363/365.
or (365 * 364 * 363) / (365 * 365 * 365) = ~99.18%
That can be generalized to n people: P(n) = (365 * 364 * ... * [365 - n]) / (365n ). This number P(n) is the probability of n people all picking different numbers (randomly) out of 365 total numbers to pick from. The probability of some two people picking the same numbers is the opposite of this number: if it is NOT true that everyone picks unique numbers, then it IS true that some two people picked the same number.
So the probability of two people picking the same number out of 365 possible choices is 1 - (365 * 364 * ... * [365 - n]) / (365n ). It just so happens that at n=23 (where you have 23 people), that number exceeds 0.5, meaning the probability passes 50%. At 70 people, that number passes 99.9%.
DammitDan · 1 points · Posted at 14:30:40 on February 14, 2016 · (Permalink)
The odds of person 6 having the same birthday as person 14 is 1 in 365. But we're not talking about matching a specific person to another specific person. We're talking about any of the people in the room having the same birthday as any of the other people in the room.
JuntaEx · 32 points · Posted at 00:23:15 on February 14, 2016 · (Permalink)
Well, ok, in a room with 70 people, but the first post says in a room with 23 people... the same principle still applies? The chances are as high as in a room with 70 people?
WildxYak · 60 points · Posted at 00:38:58 on February 14, 2016 · (Permalink)*
Sorry about that, the example was a direct copy and paste. The principle is exactly the same for trying to find two people with the same birthday.
The 23 person example is the ~50% chance, the 70 people is for ~99.9% chance.
You can see a tables here (1) (2) with the probabilities. Probability of an unshared birthday is also listed first because when the actual math is done you're actually working out the chance of people not having the same birthday, the way it's spoken about (50% chance of having..) makes it sound more impressive (50% chance no one will have...)
ExcessivelyAverage · 8 points · Posted at 01:46:25 on February 14, 2016 · (Permalink)
No, the chances increase the more people you have in the room, he was just using 70 as an arbitrary number for the example. However, with 23 people you'd have roughly 250 unique birthday comparisons using the same methodology.
jepZack · 3 points · Posted at 02:20:07 on February 14, 2016 · (Permalink)
The chances will be higher with 70 people, as you will have had more 'checks'.
TheGunner79 · 4 points · Posted at 00:00:09 on February 14, 2016 · (Permalink)
August 2nd anyone?
Plastonick · 3 points · Posted at 14:24:40 on February 14, 2016 · (Permalink)
I realise this was a joke, but it's important to note that it's not a 50% chance that someone has YOUR birthday, but that two strangers will have each other's birthdays, which is unlikely to be you.
[deleted] · 6 points · Posted at 04:27:52 on February 14, 2016 · (Permalink)
[deleted]
Damn_Croissant · 5 points · Posted at 04:34:58 on February 14, 2016 · (Permalink)
Person 3: Nope. Next
A_Booger_In_The_Hand · 3 points · Posted at 04:56:23 on February 14, 2016 · (Permalink)
Person 4... Nope
rightbeforeimpact · 5 points · Posted at 08:16:49 on February 14, 2016 · (Permalink)
Person 5: no
TouchEmAllJoe · 4 points · Posted at 09:46:32 on February 14, 2016 · (Permalink)
Person 6: nope
nezamestnany · 1 points · Posted at 11:48:45 on February 14, 2016 · (Permalink)
Person 7: nope
exus · 2 points · Posted at 12:26:09 on February 14, 2016 · (Permalink)
Person 8: close but no cigar.
totally_not_a_zombie · 1 points · Posted at 13:09:41 on February 14, 2016 · (Permalink)
Person 9: Nu-uh
Micronex · 1 points · Posted at 13:50:53 on February 14, 2016 · (Permalink)
Person 10: Nope.
SwanJumper · 1 points · Posted at 15:13:34 on February 14, 2016 · (Permalink)
Person 11: nope
knnack · 1 points · Posted at 06:58:02 on June 26, 2016 · (Permalink)
Person 12: Not even close.
NerdyKirdahy · 1 points · Posted at 02:17:47 on February 14, 2016 · (Permalink)
The solution for this is related to the handshake problem. We do that at the start of each year in my 5th grade class.
A_Booger_In_The_Hand · 1 points · Posted at 04:56:47 on February 14, 2016 · (Permalink)
Handshake problem?
NerdyKirdahy · 1 points · Posted at 07:44:02 on February 14, 2016 · (Permalink)
Every individual in the room shakes hands with every other individual in the room. How many handshakes are there? We solve for the number of students and teachers in the room, and then find an algebraic solution that works for any number of people.
ScrewAttackThis · 1 points · Posted at 08:37:46 on February 14, 2016 · (Permalink)
You teach your 5th grade class something I learned in a college level discrete math class.
NerdyKirdahy · 1 points · Posted at 08:40:24 on February 14, 2016 · (Permalink)
Sweet! They enjoy challenges. Some of them find the algebraic solution within a few minutes. Kids are capable of a lot more than they're given credit for.
hidden_secret · 1 points · Posted at 02:27:51 on February 14, 2016 · (Permalink)
I don't find this one that much intuitive personally (one would assume that many of the "checks" are very similar and still don't understand).
I prefer to simply to picture "filling a room with people", and starting at 10 people already in the room. At this point it's more or less choosing a number between one and 30 and there's one in there that if you pick, you have the same birthday as someone else. But you're not alone, there are still 13 people who have to choose. They're going to fill about half of the 30 numbers, so there's about half a chance.
metju · 1 points · Posted at 03:08:25 on February 14, 2016 · (Permalink)
Even with all the explanations in seemed like bullshit to me, so naturally I engage smartass mode and write some code to prove it in practice... but fuck me, you're right.
http://codepen.io/anon/pen/KVJbKm
[deleted] · 1 points · Posted at 03:33:44 on February 14, 2016 · (Permalink)
Is there a more efficient way to do it?
josefjohann · 1 points · Posted at 03:37:39 on February 14, 2016 · (Permalink)
Thanks! I tried explaining it to my stepdad who believes in bigfoot and aliens on the moon. He confidently told me this was impossible. Maybe this explanation will help.
YeaTired · 1 points · Posted at 04:07:08 on February 14, 2016 · (Permalink)
How many checks total with those 70 people?
The_Celtic_Chemist · 1 points · Posted at 04:13:17 on February 14, 2016 · (Permalink)*
Please someone help me get this. If 1 person was born with a 1/365 probability of being born on any day, and they don't share a birthday with 23 people, then everyone else's birthday could land on 364 out of 365 days of the year. So now the remaining 22 people have a 1/364 probability of sharing the same birthday, because we have only deduced what day they weren't born. If we do this for all but the last 2 people, the probability that they'll share a birthday is 1/344. How have we deduced more than 342 extra dates (since you claim the odds are greater than 1/2)?
thejameskyle · 1 points · Posted at 04:35:24 on February 14, 2016 · (Permalink)
I'm jealous of what #1 did
DemeaningSarcasm · 1 points · Posted at 04:55:55 on February 14, 2016 · (Permalink)
My brain hurts. Monte Carlo, please save me.
WildxYak · 1 points · Posted at 10:26:25 on February 14, 2016 · (Permalink)
Monte Carlo you say! You may enjoy the 'Gamblers Fallacy!'
DemeaningSarcasm · 1 points · Posted at 18:54:44 on February 14, 2016 · (Permalink)
Huh. This is somewhat of an odd coincidence.
I was talking about running a Monte Carlo simulation on this. Turns out that there's also a Monte Carlo casino.
magicspeedo · 1 points · Posted at 04:57:08 on February 14, 2016 · (Permalink)
Can some one explain this to me further? If the probability is based on the number of checks, does it matter that the method for checking is horribly iinefficient? Its a bubble sort algorithm.
[deleted] · 1 points · Posted at 06:35:23 on February 14, 2016 · (Permalink)
I almost freaked my wife (an event planner) out when I was helping her with a networking event and I told her that the event would give people 2 seconds to talk if she wanted everyone to meet each other.
I had forgotten that more than two people can shake hands at the same time.
keboh · 1 points · Posted at 07:13:46 on February 14, 2016 · (Permalink)
Heh, number 1 did 69
omniron · 1 points · Posted at 07:29:12 on February 14, 2016 · (Permalink)
This is the best explanation I've seen for this. Makes it really easy to derive the algebraic proof too. Can't believe after take college level math classes I haven't seen such a concise explanation.
Also I just realized you can frame the question as "how many people need to be on a room for at least 1 to share a birthday" and "how many people have to be in a room for you to share a birthday with them". 2 similar worded questions with very different answers.
[deleted] · 1 points · Posted at 08:20:15 on February 14, 2016 · (Permalink)
This is one of those things like the game show with the 3 doors and the car and the goats and the host asking you if you want to change your mind.
It relies on the concept that you can apply the probabilities from a smaller pool of unknowns where definite "no" results have been eliminated to the original pool of results. Which seems fucking ridiculous to me. Plus it suggests that the theoretical probability of a match increases with the number of checks you do, which isn't fucking true either.
GAH. MATHS IS SO ANNOYING WHEN EVERYONE SAYS IT MAKES SENSE AND YOU JUST DON'T SEE IT.
JosephND · 1 points · Posted at 08:40:26 on February 14, 2016 · (Permalink)
I'm not a math but 70 people is higher than 23 people
[deleted] · 1 points · Posted at 13:27:21 on February 14, 2016 · (Permalink)
This person only picked the number 70 to write "number 1 did 69, and that's only the first one!" in an ELI5. He made trolling the moderators into a sport. Good job mister TYLERvsBEER.
blindsight · 1 points · Posted at 13:44:29 on February 14, 2016 · (Permalink)*
The math behind that explanation is incorrect; you're double counting handshakes.
The intuition for why that answer is incorrect is quite simple:
Suppose there are 28 people in the room. Then the number of handshakes is 27+26+...+2+1 = 378.
This implies that we've checked more than all possible days in the year, and thus there must be at least one collision.
This is clearly not true (by the pigeon hole property), but as an obvious counter example, they may have all been born on consecutive days in January.
So handshakes must not solve the problem.
Edit: the reason the handshakes method didn't work is because you're changing the conditional probability at each step, but incorrectly assuming it remains constant. If you don't share a birthday with anyone in line, then it's slightly more likely that someone in line shares a birthday with someone else.
For example, if everyone in line uses Steam, and you don't, then all of their birthdays are January 1. So you think you've checked 27 days, but you only checked 1. The next person also only checks 1. And by the end, the only collision checked is if your birthday is January 1st or not.
random314 · 1 points · Posted at 14:51:44 on February 14, 2016 · (Permalink)
Tldr... Two people having the same birthday != two people having the same birthday on particular date of your choosing.
thevoiceless · 1 points · Posted at 18:28:35 on February 14, 2016 · (Permalink)
Well now I feel stupid, because this eli5 version makes zero sense to me. Why 70 people? Why do the total number of asks matter? Where does 23 come in to things?
WildxYak · 1 points · Posted at 18:42:34 on February 14, 2016 · (Permalink)
The particular example uses 70 people to get to a 99.9% chance, 23 people is where it is a 50% chance. The theory and process is the same just a different number of people to get a higher chance.
The total number of asks is so that everyone asks everyone at the end and it's not just one person asking everyone. If that was the case #1 would ask 22 other people but those other 22 people wouldn't ask each other so you'd miss all those potential matches.
Satrinix · 1 points · Posted at 22:37:04 on February 14, 2016 · (Permalink)
Why don't they each just write it down on a card and stand in a circle? Then everyone could check at once.
[deleted] · 0 points · Posted at 22:48:15 on February 13, 2016 · (Permalink)
[deleted]
robson- · 1 points · Posted at 23:13:44 on February 13, 2016 · (Permalink)
No, it's 2,415.
Vekom · 0 points · Posted at 01:17:43 on February 14, 2016 · (Permalink)
Not sure, but I think there are way less comparisons, because the problem is transitive. When #1 and #2 dont match, and #2 and #3 dont match, you wouldnt have to check between #1 and #3.
Adarain · 3 points · Posted at 02:05:34 on February 14, 2016 · (Permalink)
Scenario A: People 1 and 3 share birthday, person 2 is different.
We compare 1 and 2 and find they have different birthdays. We compare 2 and 3 and find they have different birthdays.
Scenario B: All three have different birthdays.
We compare 1 and 2 and find they have different birthdays. We compare 2 and 3 and find they have different birthdays. (same as before)
Only if person 2 shares their birthday with one of the others do we not have to check the relation between person 1 and 3, but if both checks result in a "different" then we need to do the third check.
Vekom · 2 points · Posted at 03:34:23 on February 14, 2016 · (Permalink)
Ahh yes thank you, right.
musicmast · 0 points · Posted at 01:29:12 on February 14, 2016 · (Permalink)
Where did the number 23 come from?
sweetworld · 1 points · Posted at 02:15:12 on February 14, 2016 · (Permalink)
It's the first number that has a probability >50%.
WildxYak · 1 points · Posted at 10:31:29 on February 14, 2016 · (Permalink)
And the reason this example talks about 70 people is because that is when you get to ~99.9% chance (which is what the original reply was written for)
cereal310 · 0 points · Posted at 02:09:33 on February 14, 2016 · (Permalink)
Your line is full of douche bags who could have told everyone that the last two people in line share a birthday.
MrDoggle · 0 points · Posted at 04:23:14 on February 14, 2016 · (Permalink)
This is interesting. I can't figure out how it relates to the 'put 23 people in a room' fact? ELI5 please?
WildxYak · 2 points · Posted at 10:15:51 on February 14, 2016 · (Permalink)
The theory and method is the same for 70 people as it is for 23.
The reason the example (I've directly copy and pasted and not adjusted) is talking about 70 people is because that 70 people will give a 99.9% chance of a same birthday and that's what that discussion was about.
LqdDragon · 0 points · Posted at 05:26:08 on February 14, 2016 · (Permalink)
Back in havo (european(dutch to be more specific)) high school(?) age 12 to 16 I needed this explanation so bad in my life now that I read it years later I hope I can recall this trick or e able to go to my liked reddit comments and finding this particular one to explain it to whomever needs it, this concept was explained terrible by our math teacher i remember like 20% of the class getting it and the other 80% just giving up on it(myself being part of that. we used self written TI83 calculator programs to just calculate those answers for us by manualy imnputting the vallues).
IAmScare · 293 points · Posted at 19:47:37 on February 13, 2016 · (Permalink)
I've heard this one before, but it still confuses me.
(and yes, I have read the explanation and I understand the math behind it. It is just one of those mind bending questions)
ThereOnceWasAMan · 653 points · Posted at 20:13:11 on February 13, 2016 · (Permalink)
The most intuitive explanation for it is that with 23 people, there are over 250 PAIRS of people. With 250 pairs, you would expect there to be at least one pair with a matching birthday.
(This isn't quite rigorous, because the pairs aren't independent, but it provides a pretty good intuition for the answer).
DrNick2012 · 449 points · Posted at 21:06:57 on February 13, 2016 · (Permalink)
I think some people get confused as to what is being said. If you walk into a room of 23 people it is likely 2 will have the same birthday but it is unlikely any will have the same birthday as the person asking
delthebear · 331 points · Posted at 21:14:30 on February 13, 2016 · (Permalink)
actually this important distinction is how this finally made sense to me in my probability theory class back in school: one specific person asking if anyone has the same birthday as them is a different probability function than asking if any two individuals in the room have the same birthday
Felix_Tholomyes · 71 points · Posted at 21:55:22 on February 13, 2016 · (Permalink)
Yeah it's frustrating with combinatorics how painstakingly careful you have to be with problem formulations.
DashingLeech · 7 points · Posted at 03:08:19 on February 14, 2016 · (Permalink)
It's so unintuitive that even many scientists get it wrong. One of the most common intuition errors we make in this area is inverting the probabilities. The common one in both the above links is the difference between, "Given you have the disease, what are the odds of getting a positive text result?" and "Given you have a positive test result, what are the odds you have the disease?"
A highly accurate test result in the first question can still be a very low accuracy in the second question.
JanEric1 · 1 points · Posted at 15:34:35 on February 14, 2016 · (Permalink)
easy example here. your test ALWAYS says you have the disease. so when you have the disease it will always tell you that correctly, but just because it says you have it doesnt mean you actually have it.
[deleted] · 1 points · Posted at 04:18:01 on February 14, 2016 · (Permalink)
My frustration with combinatorics is how fast the numbers get very large. I have some nCr formulas that excel just totally shits the bed on.
Splinter1010 · 2 points · Posted at 08:45:17 on February 14, 2016 · (Permalink)
For anybody who still doesn't get it, even though the two sound similar, they're totally different. 23 people in a room and trying to find any two of them having the same birthday is 250 potential matches, each of which has 365 potential birthdates. That's a 250/365 chance, or approximately 68%. 1 person in a room with 22 other people looking for somebody with the same birthday is only 22 potential matches, each of which has 365 potential birth dates. That's only a 22/365 chance, or approximately 6%.
kbtrpm · 1 points · Posted at 14:23:36 on February 14, 2016 · (Permalink)
no, not 250/365, but 250/365.242199!
juschillinn · 2 points · Posted at 22:38:20 on February 13, 2016 · (Permalink)
No, I get this distinction and it still baffles me.
NemoDaTurd · 3 points · Posted at 23:18:34 on February 13, 2016 · (Permalink)
Me too. If I have 23 bowls with 365 numbers in each, and I draw one number from each, there can't possibly be 50% chance for me to draw two identical numbers.
featherfooted · 4 points · Posted at 02:26:31 on February 14, 2016 · (Permalink)
Shall we play a game?
I'll assume the reader is familiar with any reasonable programming language but I'll be using R, which is great for math problems like these.
and now some test runs:
The data supports the hypothesis that with 23 bowls there is a greater than 50% chance of having a duplicate.
[deleted] · 6 points · Posted at 23:35:05 on February 13, 2016 · (Permalink)
I did pretty much exactly that:
Basically, as you draw each number, there's more numbers for it to match with. The last number matching with something alone has a 22/365 chance. The one before that has a 22/365... sum that up, and you get over 50%
skullturf · 2 points · Posted at 17:07:14 on February 14, 2016 · (Permalink)
Sure there can.
You're underestimating how many chances for a match there are.
Doe the number from bowl #1 match the number from one of the other bowls? Maybe, maybe not... but the probability of that happening is not 1 in 365. It's more like 22 in 365, which is about 1 in 16.6.
(Actually, if you want to get technical, it's not exactly 22 in 365 -- you don't just add, because there is the small probability of an overlap, but that probability is small, and 22 in 365 is in the right ballpark.)
Okay, so 1 in 16.6 means it probably won't happen. But that was just bowl #1!
If the number from bowl #1 doesn't match the number from any of the remaining bowls, we move on to bowl #2. Maybe the number from that bowl matches bowl #3, or maybe it matches bowl #4, and so on. Bowl #2 could match any of the remaining bowls, and it has 21 chances to do so, so the probability of bowl #2 matching one of the later bowls is about 21 in 365, which is about 1 in 17.4.
So, to summarize:
Probability of bowl #1 matching one of the later bowls: about 22 in 365, or about 1 in 16.6
Probability of bowl #2 matching one of the later bowls: about 21 in 365, or about 1 in 17.4
Probability of bowl #3 matching one of the later bowls: about 20 in 365, or about 1 in 18.3
Probability of bowl #4 matching one of the later bowls: about 19 in 365, or about 1 in 19.2
And this continues for all the bowls. Yes, it usually won't be bowl #1 that matches one of the later bowls. That only happens about once in every 17 times. But of course, bowl #2 also has a chance to match one of the later bowls, and bowl #3 has a chance to match one of the later bowls, and bowl #4 has a chance to match one of the later bowls, and each of those chances is better than 1 in 20. (Not 1 in 365, by the way.) When you start adding up all these chances, you get a number that's not very small.
kogasapls · 1 points · Posted at 06:28:54 on February 14, 2016 · (Permalink)
Do it! (Or simulate it.)
Dd_8630 · 1 points · Posted at 01:10:48 on February 14, 2016 · (Permalink)
Actually, there's a greater than 50% chance of that happening.
a_soy_milkshake · 1 points · Posted at 23:39:53 on February 13, 2016 · (Permalink)
There's a difference in you alone asking :
and:
You alone asking is a single case. Consider instead if every person in the room asked that question. That's many more cases and the probability that any two will share a birthday is much higher.
juschillinn · 3 points · Posted at 00:03:03 on February 14, 2016 · (Permalink)
I get that distinction, it still baffles me.
Ubervelt · 3 points · Posted at 01:41:31 on February 14, 2016 · (Permalink)
/u/dontkickducks explanation helped me understand;
Compare no.1 with 2-70. That's 69 possibilities. Now compare no.2 with 3-70. That's another 68 possible matches. Now no. 3 with the remaining 67. And so on and so on. (By only comparing three people to everyone in the room you'd allready have 204 possible matches)
juschillinn · 1 points · Posted at 01:42:20 on February 14, 2016 · (Permalink)
thats at 70, the first example was like 23
kogasapls · 2 points · Posted at 06:42:13 on February 14, 2016 · (Permalink)*
The probability of a person having any given birthday is obviously 100%, 365/365. Add a second person. The probability of them having any birthday EXCEPT the first person's is 364/365. The probability of those two independent events coinciding is their product: 365/365 * 364/365. Continue on until you have 23 people: 365/365 * 364/365 * 363/365 * ... * 342/365, or otherwise: (365 * 364 *363 * ... * 342) / (365n).
Consequently, the probability of n people all having different birthdays is [365 * 364 * 363 * ... * (365 - n)] / (365)n.
In other words, that's [365! / (365 - n)!] / 365n
or P = 365! / [(365 - n)! * 365n ]. That's the probability for n people having different birthdays. The probability that two of n people share a birthday is 1 - P. Toss that into Wolfram Alpha and evaluate it at different points and you'll see that 1 - P > 0.5 at n=23.
Dd_8630 · 1 points · Posted at 01:11:48 on February 14, 2016 · (Permalink)
Which part of it baffles you?
juschillinn · 1 points · Posted at 01:41:23 on February 14, 2016 · (Permalink)
this other guy phrased it nicely:
a_soy_milkshake · 2 points · Posted at 02:45:19 on February 14, 2016 · (Permalink)*
The guy's reply to that is pretty helpful. Imagine you have all 23 bowls and you go down and one by one you pull out one of the numbers.
After you draw a number from the second bowl it is very unlikely that you will draw the same number as you drew from the first bowl.
Now you draw a number from the third bowl. Well that number can match with either the second or the first. Now you draw one from the fourth bowl. There's a chance that it will match with either the third, the second or the first. The pattern will continue, with each successive draw increasing the number of numbers with which the next draw can match.
As you move down the line of bowls, the number of possible matches increases because there are more numbers with which it can match. By the time you get to the 23rd bowl, there's a 50% chance that the draw from that bowl will match any of the previous 22 numbers you've already drawn. Does that help at all?
Dd_8630 · 1 points · Posted at 02:25:48 on February 14, 2016 · (Permalink)
But that still doesn't explain what part baffles you.
'It can't possibly' - why can't it possibly?
If you have 4 points, you can draw 6 straight lines between them. 5 points have 10 lines. 6 dots have 15 lines. 22 points have 231 lines. 23 points have 253 lines.
If you have 23 people in a room, there are 253 possible pairs. There's a 1-in-365 chance any one pair of people will share a birthday.
So 253, each with a 1/365 chance of being a success, means we expect at least 1 to be a success (253 x 1/365 = 0.693).
Does that help? If not, which part trips you up?
kogasapls · 1 points · Posted at 06:48:46 on February 14, 2016 · (Permalink)
FYI, your logic is flawed despite that it leads you to a more-or-less correct answer. The birthday problem can be considered a series of independent events yielding the formula:
1 - (365 * 364 * ... * [365 - n]) / (365n )
or
1 - 365! / [(365 - n)! * 365n ], which is greater than 0.5 at n=23, having a value of ~0.507297, not ~0.693 as your process led you to believe.
[deleted] · 0 points · Posted at 23:17:24 on February 13, 2016 · (Permalink)
This exact distinction is what confuses me about Monty hall
caried · 1 points · Posted at 01:36:18 on February 14, 2016 · (Permalink)
That made it make sense for me. Thanks
db0255 · 1 points · Posted at 05:31:23 on February 15, 2016 · (Permalink)
I like this explanation.
DrNick2012 · 1 points · Posted at 06:25:56 on February 15, 2016 · (Permalink)
Enough for gold? Thanks man
db0255 · 1 points · Posted at 06:35:00 on February 15, 2016 · (Permalink)
Simple, and just the facts.
How long do you get gold for anyway?
DrNick2012 · 1 points · Posted at 06:48:09 on February 15, 2016 · (Permalink)
I think I actually learned the explanation from the real hustle, and gold lasts 30 days but I have little idea what it does apart from know someone spent money for me
Firehed · 0 points · Posted at 01:22:30 on February 14, 2016 · (Permalink)
This messed with me for a while, because when my freshman math teacher explained the problem, I was one of the two students in the room that shared a birthday. It's really easy to go from "do two people share a birthday" to "does anyone share my birthday", where the latter works exactly as you'd expect.
Mathwards · -1 points · Posted at 00:51:59 on February 14, 2016 · (Permalink)
Same thing can be applied to lottery odds.
The odds of YOU winning the jackpot twice in a row is like 1:4,000,000,000,000 whereas the odds of ANYONE winning it twice in a row is closer to 1:30.
AcornHarvester · 4 points · Posted at 03:36:47 on February 14, 2016 · (Permalink)
You have 250 pairs, but not 250 birthdays. With 23 people you have 23 birthdays out of 365 days in a year. Am I missing something?
stratys3 · 2 points · Posted at 04:32:29 on February 14, 2016 · (Permalink)
Each pair is a possible match. You have 253 possible matches, and 365 possible dates.
The fact that there are only 23 birthdays is irrelevant, because you are attempting to match birthdays 253 times.
ThereOnceWasAMan · 1 points · Posted at 04:03:08 on February 14, 2016 · (Permalink)
I'll repeat what I wrote elsewhere:
Here's a simpler example. Say the year only had 10 days. If you gathered 5 people in a room, then, you might expect there to be a 50% chance of there being a shared birthday. There isn't -- it's actually 84%.
But you don't have to take my word for it. This link will generate 10 rows of random integers, with each integer somewhere between 1 and 10 inclusive. Each row has 5 integers. Count up how many rows contain a duplicate number (for example, a row that contains
contains a duplicate) and then divide your answer by 10. You will probably get a number pretty close to 0.8.
TeamMagmaGrunt · 8 points · Posted at 22:26:10 on February 13, 2016 · (Permalink)
This is probably the clearest explanation I've seen of the problem on this site. Thank you!
drunz · 4 points · Posted at 22:36:33 on February 13, 2016 · (Permalink)
that is actually the best simple explanation I have heard of this
Shadecraze · 2 points · Posted at 01:29:11 on February 14, 2016 · (Permalink)
thank you goddamn
VERNEJR333 · 2 points · Posted at 01:49:05 on February 14, 2016 · (Permalink)
It all makes sense now
ClintonCanCount · 2 points · Posted at 03:44:22 on February 14, 2016 · (Permalink)
One of the things that is helpful in this problem is that a degeneracy of pairs is a victory;
that is, if person A has a different birthday from persons B and C, but they don't use up two possible different birthdates, then that is because B and C have the same birthday which is a victory.
RiverRoll · 2 points · Posted at 05:40:38 on February 14, 2016 · (Permalink)*
I understand why there are more chances than it seems but I don't get what this kind if example means, with 28 people there's over 366 pairs, so what? They can still have 28 different birthdays.
ThereOnceWasAMan · 1 points · Posted at 08:54:16 on February 14, 2016 · (Permalink)
Which is why it isn't rigorous, as I said. The real reason is because each new person you consider has to be compared against the bevy of other people that have already been looked at. But in terms of intuition, it's easy to see why your probability of an overlap would grow very fast as you add more people (up to a point) by looking at how many pairs there are.
StillsidePilot · 2 points · Posted at 01:38:05 on February 14, 2016 · (Permalink)
There's actually 253 pairs unless I'm missing something?
ThereOnceWasAMan · 5 points · Posted at 02:11:34 on February 14, 2016 · (Permalink)
Yes, you are right. Like I said, over 250 pairs :)
stratys3 · 1 points · Posted at 04:28:46 on February 14, 2016 · (Permalink)
Finally an ELI5 that's only 2 sentences.
zoidbergWOOPWOOP · 1 points · Posted at 13:41:43 on February 14, 2016 · (Permalink)
The only thing I don't understand about this still is where the actual percentage comes from. What's the calculation for determining 50%?
ThereOnceWasAMan · 1 points · Posted at 16:31:22 on February 14, 2016 · (Permalink)
This is the actual calculation.
The wikipedia article on the problem explains it more in depth.
db0255 · 1 points · Posted at 05:38:22 on February 15, 2016 · (Permalink)
So put in to mathematical terms.
In a room full of 23 people, you'd have (22+21....+2+1) unique "birthday checks." That amounts to 253 chances someone could have the same birthday. If the odds of a person being born on a single day is held to be 1/365 (not true technically), then the odds two people have the same birthday are 253/365, ~69%. If you had 20 people, the odds are ~52%.
Is this correct? Also, while doing this I stumbled upon an easy way to calculate the sum of integers from 1 to any number. Apparently the formula for "triangular numbers" is n(n+1)/2. So if you had 53 people in the room, there would be 52*53/2 birthday checks.
Edit: This is wrong. Oh well, I had fun mathing.
kogasapls · 1 points · Posted at 06:26:34 on February 14, 2016 · (Permalink)
It provides a "pretty good intuition" in that it leads you to the right answer without providing actual understanding. It doesn't actually explain the correct answer properly.
ThereOnceWasAMan · 2 points · Posted at 08:57:50 on February 14, 2016 · (Permalink)
Except it does provide actual understanding. It just doesn't explain all the details. At a basic level, the issue is that as you consider more people, you have to match them against all the other people that have already been looked at. That is basically equivalent to pairing up every possible pair of people and seeing if a pair exists which has matching birthdays. No, that process won't give you the correct probabilities, but it is absolutely the right general way to think about it.
kogasapls · 1 points · Posted at 09:09:23 on February 14, 2016 · (Permalink)
Yes, at a basic level, it becomes more likely that two people share a birthday as the group becomes larger.
That's hardly counter-intuitive (or helpful).
But implying that you can calculate a 1/365 chance for 253 trials and arrive at the correct probability is just mi sleading.
ThereOnceWasAMan · 3 points · Posted at 09:11:04 on February 14, 2016 · (Permalink)
I don't know what to tell you. I clearly said in my original post that this provides intuition, and is not rigorous. There's nothing misleading there.
[deleted] · 0 points · Posted at 09:13:46 on February 14, 2016 · (Permalink)*
[deleted]
skullturf · 2 points · Posted at 17:23:00 on February 14, 2016 · (Permalink)
It's not a coincidence that it gives an answer close to the correct one. I could explain why, but the explanation requires a bit of math, and I'm not sure what your math background is.
But here's the basic idea.
Suppose I have a 20-sided die. One of the sides is red, and the other 19 are not. I roll the die several times, and I want to know the probability of getting red at least once.
Say I roll the die twice.
Exact probability of getting red at least once: 1 - (probability of no reds) = 1 - (19/20)(19/20).
Approximate probability of getting red at least once: 1/20 + 1/20.
It's not a coincidence that the approximation is close to the reality. The reason is as follows: (19/20)(19/20) is the same as
(1 - 1/20)(1 - 1/20)
= 1 - 1/20 - 1/20 + 1/400
and 1/400 is much smaller than 1/20, so this is in fact very close to
1 - 1/20 - 1/20
which, when subtracted from 1, gives 1/20 + 1/20.
Similar reasoning applies if you roll the die 3 or 4 or 5 times, although the algebra gets messier.
You are correct that the explanation from /u/ThereOnceWasAMan was not 100% rigorous, but it's not an accident that it provides a reasonable approximation.
ThereOnceWasAMan · 2 points · Posted at 18:05:28 on February 14, 2016 · (Permalink)
I was in the process of typing up a similar response. You beat me to it!
kogasapls · 1 points · Posted at 17:37:05 on February 14, 2016 · (Permalink)*
I know why the answer is similar, but I still don't think using the description of 253 pairs gives an adequate understanding of the problem. Yes, a reasonable approximation, in that 3.14 is a reasonable approximation for pi. But understanding why the true probability is slightly different allows for a more complete understanding of the problem in the same way that knowing that pi is transcendental affects the way we consider finitely-long approximations of pi.
skullturf · 2 points · Posted at 17:52:48 on February 14, 2016 · (Permalink)
Saying "There are 253 pairs" is an excellent way to start the explanation if somebody is completely befuddled by the whole thing and just says "But 23 is so much smaller than 365!"
Sure, I agree with that. But approximations also have their place. There are a great many situations where using 3.14 for pi gives good practical results because we don't care about more than two or three significant digits.
Similarly, with the birthday problem, as a start to the conversation, it might be appropriate to begin with some very rough approximations that informally suggest why we might expect the true probability to be closer to 253/365 than to 23/365 (in a rough overall order-of-magnitude sense).
kogasapls · 2 points · Posted at 18:09:01 on February 14, 2016 · (Permalink)
This is true. I wrote most of those replies around 4 AM, so I realize I was being pretty unfair. It's not useless intuition or tangentially related, it is a close approximation and a good starting point. The main reason I find issue with the approach is that it tends to lead to people evaluating (253/365) and getting a completely wrong answer. I always think working with concepts yields a stronger intuitive grasp for laymen than with numbers, so I favor the step-by-step approach of finding each person's chances, generalizing this, and then finding the total probability in general terms. Not only is this (slightly) more accurate but also I think easier to grasp. Of course if it isn't sticking, the binomial coefficient is a different angle.
Really, the tiny inaccuracy just bothers me when an algebraic proof of the problem is arguably simpler. But don't let me stop you from explaining it how you like. There's no reason you or most people should care, it's beyond trivial here.
[deleted] · 0 points · Posted at 01:42:31 on February 14, 2016 · (Permalink)*
[deleted]
ThereOnceWasAMan · 1 points · Posted at 02:32:23 on February 14, 2016 · (Permalink)
It isn't. Here's a simpler example. Say the year only had 10 days. If you gathered 5 people in a room, then, you might expect there to be a 50% chance of there being a shared birthday. There isn't -- it's actually 84%.
But you don't have to take my word for it. This link will generate 10 rows of random integers, with each integer somewhere between 1 and 10 inclusive. Each row has 5 integers. Count up how many rows contain a duplicate number (for example, a row that contains
contains a duplicate) and then divide your answer by 10. You will probably get a number pretty close to 0.8.
ramsncardsfan7 · 1 points · Posted at 02:45:50 on February 14, 2016 · (Permalink)
If the year had ten days how many people would it take for there to be a 50% chance?
ThereOnceWasAMan · 1 points · Posted at 03:14:13 on February 14, 2016 · (Permalink)
~3
[deleted] · 0 points · Posted at 02:51:32 on February 14, 2016 · (Permalink)
[deleted]
sizzlelikeasnail · 2 points · Posted at 03:19:20 on February 14, 2016 · (Permalink)
Oh and try it yourself
sizzlelikeasnail · 1 points · Posted at 03:08:20 on February 14, 2016 · (Permalink)
You're overcomplicated things. Walking into a room with 22 people and comparing yourself with 1 person is wrong. There's 250 possible combination of pairings in that room of 23. Each of the 250 possible pairs has a small chance of sharing a birthday. Those chances add up.
Edit: or if you're really interested, search up football squads. Statistically, over half will have 2 people sharing a birtbday
ThereOnceWasAMan · 1 points · Posted at 03:12:53 on February 14, 2016 · (Permalink)
I mean, that's easy enough. Here is a link with 40 rows, 23 numbers per row, numbers selected from 1-365 inclusive. Approximately 20 of the rows should contain a duplicate number. Knock yourself out.
ramsncardsfan7 · 1 points · Posted at 03:22:39 on February 14, 2016 · (Permalink)
Is there a way to sort these?
ThereOnceWasAMan · 1 points · Posted at 04:05:20 on February 14, 2016 · (Permalink)
Not that I know of. Your options are a) write a program to do this yourself (if you know any programming at all, this should be pretty easy -- you just need a random number generator), b) using the link I gave you and do it manually, c) use math.
Any of those methods will generate the same result.
stratys3 · 1 points · Posted at 04:33:17 on February 14, 2016 · (Permalink)
Are you saying there aren't 253 pairs of people?
baconlover24 · 0 points · Posted at 02:00:18 on February 14, 2016 · (Permalink)*
Hidden.
ThereOnceWasAMan · 2 points · Posted at 04:27:40 on February 14, 2016 · (Permalink)
You can do that experiment, sort of. I'll copy something I wrote elsewhere about this:
Here's a simpler example. Say the year only had 10 days. If you gathered 5 people in a room, then, you might expect there to be a 50% chance of there being a shared birthday. There isn't -- it's actually 84%.
But you don't have to take my word for it. This link will generate 10 rows of random integers, with each integer somewhere between 1 and 10 inclusive. Each row has 5 integers. Count up how many rows contain a duplicate number (for example, a row that contains
contains a duplicate) and then divide your answer by 10. You will probably get a number pretty close to 0.8.
kevms · 5 points · Posted at 02:08:54 on February 14, 2016 · (Permalink)
Let's say there are 23 people standing in a line, all facing the same way. #1 checks with #2-23 to see if they have matching birthdays, then #2 checks with #3-23, and so on, all the way to #22 checking with #23. That's 253 checks. Keep this number in mind.
Now, let's say we DON'T want any of the birthdays to match. What are the chances? For any of the aforementioned checks, the chances that the birthdays DON'T match is 365/366, around 99.7%. Since we don't want ANY of the checks to get a match, the chances are (365/366)253. That's 50%.
Since there's a 50% chance that there would be NO matches, there's also a 50% chance that there's at least a match somewhere.
regdayrF · 7 points · Posted at 21:29:47 on February 13, 2016 · (Permalink)*
Simple explanation, you just go through all the 23 people.
You go through the first one. He can't possibly have the same birthday as any other person, because you have checked noone yet.
You go through the second one. He either can have the same birthday as the second one, or could have birthday on another day.
You go through the third one. It would be fitting, if he had the same birthday as the first or the second one, but he still could have on another day.
You already see a certain trend here. Each time, you check the next person, this next person has a higher chance to have birthday on the same day, as the person, who was checked before him.
If you check the twentythird one, you already have 22 fitting possibilities to strike your event.
All the persons being checked later have quite a large number of birthdays, which could be on the same day as their own. This having quite a large chance to to have the same birthday as another person in the room. As it doesn't matter to you, if the second or twentythird one has birthday on the same day as another person, you kinda "add" the chances for all the 23 people on top of each other.
Why did I put "adding" them on top of each other in quotation marks ?
Well, in theory, the second one could have the same birthday as the first one, which is extremely unlikely. Then you don't even care about any other birthday anymore. Third one could have birthday, as the second or first one, then you don't care about any other birthday anymore, etc. pp.
gnorty · -2 points · Posted at 22:48:55 on February 13, 2016 · (Permalink)
lmao. You spelt "ridiculously overlong and boring" wrong.
See /u/ThereOnceWasAMan explained it - that's what simplicity looks like.
regdayrF · 1 points · Posted at 09:07:13 on February 14, 2016 · (Permalink)
I might have been terrible in expressing my thoughts into words, but some people actually liked this explanation.
In the linked explanation, they do the "checking" the other way around, but it has the same result as my explanation.
gnorty · 1 points · Posted at 17:37:19 on February 14, 2016 · (Permalink)
yea, my reply didn't come out as jokey as intended. Sorry.
ebbomega · -2 points · Posted at 23:33:09 on February 13, 2016 · (Permalink)
Hahahahahahahahah. You must not know math very well.
PortugueseBreakfast_ · 2 points · Posted at 22:38:44 on February 13, 2016 · (Permalink)
I found this fact during the World Cup '14. Have a look at teams on Wikipedia (about 22 people per team?) and more often than not, there are people who share birthdays.
malkin71 · 2 points · Posted at 07:38:25 on February 14, 2016 · (Permalink)
The big thing is that two people sharing any birthday is very different to two people sharing a PARTICULAR birthday.
NoNameSeven · 1 points · Posted at 21:43:38 on February 13, 2016 · (Permalink)
The best way is just to try it. Kind of didn't believe it at first, but then I realised that in our class of 24 people, two girls have the same birthday!
[deleted] · 1 points · Posted at 04:05:06 on February 14, 2016 · (Permalink)
Just go to Red Robin on your birthday. Or any day for that matter.
The staff sings happy birthday all day
trspanache · 1 points · Posted at 07:29:10 on February 14, 2016 · (Permalink)
What confuses me is if all 23 people highlighted their birthday on a calendar there are still only 23 or less days highlighted of 366.
procrastinating_atm · 1 points · Posted at 11:13:13 on February 14, 2016 · (Permalink)
Maybe you're just too self-centered to get it!
Wet_Walrus · 0 points · Posted at 21:54:11 on February 13, 2016 · (Permalink)
This might help
http://youtu.be/0TjRjqVNAYE
jordan13rl · 0 points · Posted at 22:34:52 on February 13, 2016 · (Permalink)
Basically you have to think as though your not the one comparing to everyone but as everyone is comparing to each other.
[deleted] · 0 points · Posted at 01:32:34 on February 14, 2016 · (Permalink)*
[deleted]
kevms · 2 points · Posted at 02:14:08 on February 14, 2016 · (Permalink)
This problem becomes much easier to understand if there were a million doors instead of 3. Let's say you choose door #421,639. No way you picked the right door, right? Now the host takes away 999,998 doors that don't have the prize, leaving the door you picked and door #392,402. Do you switch to door #392,402? Definitely.
mayonnaise_man · 0 points · Posted at 05:21:31 on February 14, 2016 · (Permalink)
I refuse to believe it.
Scrappy_Larue · -2 points · Posted at 23:16:54 on February 13, 2016 · (Permalink)
Part of the explanation is that the odds of being born on any particular day are not 1/365. Births cluster on certain days. Some dates are very popular, while others have very few births.
atrd · 3 points · Posted at 00:50:51 on February 14, 2016 · (Permalink)
The same result holds if you assume that birthdays are randomly distributed.
UlyssesSKrunk · 1 points · Posted at 07:39:44 on February 14, 2016 · (Permalink)
No. That's not part of the explanation at all. Not even a little.
[deleted] · -3 points · Posted at 03:00:58 on February 14, 2016 · (Permalink)
[deleted]
xtxylophone · 4 points · Posted at 05:00:16 on February 14, 2016 · (Permalink)
Maths doesn't care what you think
kogasapls · 3 points · Posted at 07:23:29 on February 14, 2016 · (Permalink)*
It is supported by both theoretical models and experimental data. Try it yourself at home. Instead of 365 days, try picking a number 1-16 using a random number generator online. Theoretically, you should get two matching numbers ~50% of the time if you pick the numbers in sets of 5. Pick half a dozen or so sets of 5 numbers and you should start to see this. Keep going and you'll get closer and closer to 50%.
edit: Funnily enough, I just tried it myself (using Wolfram Alpha's RNG from 1-16) exactly 6 times and got exactly 3 matches, 3 non-matches. But it would be reasonable to expect a less close ratio at only 6 trials.
5 15 6 9 16 NO
6 13 16 4 6 YES
16 13 7 10 3 NO
16 2 8 11 15 NO
1 15 2 13 15 YES
15 5 4 12 12 YES
UlyssesSKrunk · 2 points · Posted at 07:39:10 on February 14, 2016 · (Permalink)
Yeah, and gravity is fake too.
[deleted] · -2 points · Posted at 07:40:32 on February 14, 2016 · (Permalink)
[deleted]
UlyssesSKrunk · 3 points · Posted at 07:42:23 on February 14, 2016 · (Permalink)
wat
The fuck is wrong with you? You need to lighten up. All I did was say something almost but not quite as dumb as what you said, no need to get all worked up.
DarkDraconarius · 12 points · Posted at 21:58:07 on February 13, 2016 · (Permalink)
Ah, Discrete Math, one of the most interesting classes I've taken.
Redditzork · 9 points · Posted at 02:04:24 on February 14, 2016 · (Permalink)
Does this mean, if i ask 23 people to pick a number between 1 and 365 (1 for each date obviously) i have a 50% chance of 2 people picking the same number? (keeping out psychological stuff)
Smurfy7777 · 7 points · Posted at 02:43:20 on February 14, 2016 · (Permalink)
For some reason this seems way more improbable, but yeah. Theoretically it would be the same probability.
In practice the psychological stuff will throw it off, and the chances of a duplicate number would be slightly higher.
23Enigma · 1 points · Posted at 04:50:16 on February 14, 2016 · (Permalink)
I'll always pick 23
steadyasthepenisdrum · 3 points · Posted at 01:37:55 on February 14, 2016 · (Permalink)
And it's also very likely they'll be September babies... Christmas is apparently a fun time for a lot of people, and September a very expensive time.
[deleted] · 5 points · Posted at 02:21:48 on February 14, 2016 · (Permalink)
Here's an explanation I wrote up. It isn't extremely complicated, but it does use probability and so there's no way to make it super simple either. I explained all the steps so it's a bit lengthy and goes off at times to explain how things were done:
The odds of someone in a room of 23 having the same birthday as you is pretty low. But any two people is much different.
You have 23 people in a room. You start with the first person and go around to the other 22 people and compare birthdays. That’s 22 pairs. Then you move onto the next person and compare his/her birthday to everyone else. That's 21 more pairs since you’ve already paired the first and second person. You keep doing this, and it continues down to the last two people that make 1 pair.
So the number of pairs looks like: 22 + 21 + 20 + 19… + 1 = 253 pairs.
The shortcut to calculating this is 23 x 22 / 2 x 1 = 253 pairs.
The first person can be any of the 23 people, and the second person can be any of the remaining 22. If I multiply them together, I know how many pairs I can make. However, this includes every “arrangement” of the pairs. So for example, this is counting the pair “Person 1 & Person 5,” but also the pair of “Person 5 & Person 1.” Since these pairs are the same, we need to divide by the number of possible arrangements of each pair to cancel them out. There are 2 ways of arranging a pair, so we divide by 2.
You can also see this works by adding (22+1) + (21 + 2) + (20 + 3)… etc. Each pair adds up to 23. You will eventually get to 12 + 11, which is the 11th pair. So it’s 23 x 11, or 23 x (22 / 2)
At this point, it should be easier to understand how there might be a 50% chance with only 23 people, because 23 people make a lot of pairs. Now let’s calculate the probability.
I want to show the math I’ll be using with coin flips, because it’s much easier to see that it works. If I asked what are the chances of getting at least 1 heads in two coin flips, how would you do that? You need to calculate the odds of getting only tails. This is simple, there’s a 50% chance of getting tails on each flip, so you multiply: .5 x .5 = .25 or 25% chance of getting two tails, or only tails. Then simply take the inverse to find the odds of getting at least one heads. It’s 75%.
Here are the possibilities laid out: HH, HT, TH, TT. It’s obvious that there’s a 25% chance of getting two tails, and 75% of getting at least one heads.
If we flip 3 times it works the same: .5 x .5 x .5 = .125 or 1/8 chance of getting 3 tails, or only tails. So it’s a 7/8 chance of getting at least one heads. If we flip 253 times, it would be .5 x .5 x .5… and so on 253 times, or .5253.
The birthday problem will use the exact same concept since we are only concerned with one matching pair. We know there are 253 pairs, so what are the chances of getting at least one matching pair? Unlike the coin flip though, there’s a 364/365 chance (ignoring leap year) that any single pair do not match (just like the 50% chance of getting tails). So all we do is multiply to find the odds of not getting any matching birthdays, and then take the inverse to find the odds of at least one matching birthday. Again, there are 253 pairs, so it’s (364/365)253 = .4995 or 49.95%. Take the inverse to get 50.05%. It’s slightly off since it’s not accounting for leap year.
Damokles · 1 points · Posted at 10:33:18 on February 14, 2016 · (Permalink)
This is emphatically incorrect. As opposed to the individual coin flipping, the birthday pairs are not independent. (Eg.with your method, the probability that three people have the same birthday is the probability that each pair has the same birthday (1/365), so you get (1/365)3, but in reality the probability is (1/365)2.
The correct probability for the original birthday problem with 23 people is 49.3% (see wikipedia or wolfram mathworld).
[deleted] · 2 points · Posted at 20:59:42 on February 14, 2016 · (Permalink)
Oops, you're right. It should definitely be (365/365) x (364/365) x (363/365) and so on 23 times out.
Funny that the wrong method worked out as a pretty close approximation though.
Kalima · 2 points · Posted at 02:03:41 on February 14, 2016 · (Permalink)
If there are 46 people does that increase to over 100%?
DingyWarehouse · 6 points · Posted at 03:25:31 on February 14, 2016 · (Permalink)
No. For 46 people, there are 1035 pairings. For each pairing the probability that their birthdays dont match is 364/365.
Calculate for 1035 pairings, the chance that nobodys birthdays match is (364/365)1035 = 0.058.
So the probability that there will be at least a match is 1-0.058 , which is 0.942
EpicGoats · 5 points · Posted at 20:44:08 on February 13, 2016 · (Permalink)
Some friends and I tried it last night, and we found 2 people had t g e same birthdah, it was cool
regdayrF · 3 points · Posted at 20:50:53 on February 13, 2016 · (Permalink)*
For anyone wondering about the math behind it:
Assumption: Each day of the year is as likely to be a birtday as another day. Every birthday of the people in the room are independent to each other.
AC = No person has birthday on the same day
A = At least 2 persons have birthday on the same day
P(A) = 1 - P(AC ) = 1-(365!/(342! * 36523 ))
Small reminder: 365!/342! = 365 * 364 * ... * 343
( This is the amount of possibilities, that are out there for 23 different birthdays, now you just have to divide it by 36523, which is the amount of possibilities for the experiment. )
It follows the same principle as the possibility for one specific number on a dice to appear. P(B) = 1/6 --> P(BC ) = 1 - P(B) = 5/6. B being the event for one specific number to appear. BC being the event for this specific number not to appear. You have 6 numbers in total, and each number represents one possibilities. In this case 6 ~ 36523 and 5 ~ 365!/342!
chief_dirtypants · 2 points · Posted at 23:09:08 on February 13, 2016 · (Permalink)
If you put 365 people in a room, what are the chances that two of them WON'T have the same birthday?
DingyWarehouse · 2 points · Posted at 03:19:20 on February 14, 2016 · (Permalink)
The chance that 2 randomly selected people wont have the same birthday? Thats just 364/365
Smurfy7777 · 1 points · Posted at 02:36:01 on February 14, 2016 · (Permalink)
Someone else please check my logic. This feels right but probability is weird.
The chance that none of them will have the same birthday as another is 1.4 * 10-147 .
Basically, for each person that enters the room, what are the chances that their birthday matches none of the others that are already in the room. The expression below is what I used to solve it.
(365/365) * (364/365) * (363/365) * .... * (2/365) * (1/365) = 365!/(365365 )
mnewman19 · 0 points · Posted at 04:59:50 on February 14, 2016 · (Permalink)
You have to take leap years into account
No idea how the probability would work, but you would have to.
fiftypoints · 1 points · Posted at 03:44:49 on February 14, 2016 · (Permalink)
I think you're pushing lottery odds at that point.
[deleted] · 1 points · Posted at 04:23:23 on February 14, 2016 · (Permalink)
0% which is kinda BS but that's math.
themasterofallthngs · 2 points · Posted at 05:17:28 on February 14, 2016 · (Permalink)
Math is really not BS. As in, people spent hundreds of years making sure they were not doing BS.
[deleted] · -1 points · Posted at 06:08:41 on February 14, 2016 · (Permalink)
it's not as final as people think it is.
themasterofallthngs · 2 points · Posted at 06:45:24 on February 14, 2016 · (Permalink)*
Actually, it is basically the only field of knowlodge that you can actually say something is final. I highly doubt you have studied even past Calculus to truly understand why that is true.
edit: correction
[deleted] · -1 points · Posted at 06:56:38 on February 14, 2016 · (Permalink)
i have an engineering degree but w/e
themasterofallthngs · 2 points · Posted at 07:01:53 on February 14, 2016 · (Permalink)
Engineering degree != math degree
One thing any real mathematician knows is that what they study is true. There is no doubt about it. They don't make meaningless assumptions. They do not speculate. They work with logic. It might take them hundreds or thousands of years to actually answer a problem as it has happened multiple times, but they do what they do in order to get something final. Once something is proven and verified by other mathematicians, there is no doubt that it is not a complete, absolute and final result.
[deleted] · -1 points · Posted at 07:57:22 on February 14, 2016 · (Permalink)
math is based on axioms. axioms are theorems. theorems are not final. i mean heck even 1+1=2 is a theory.
themasterofallthngs · 2 points · Posted at 08:02:42 on February 14, 2016 · (Permalink)
It is a theory, but that doesn't mean the results obtained by it are any less true or final.
I have already argued with people who thought the same way you do (some even invalidating centuries of mathematical research) and it just ends up with me having wasted a lot of time and not having accomplished anything, so I think I'm just gonna go to bed now instead of walking around in circles with you (which is almost always how this ends).
[deleted] · 0 points · Posted at 08:10:58 on February 14, 2016 · (Permalink)
true. i was actually contemplating on not answering back either. theory's are always prone to be disproven and respectable mathematical theory have been disproven before. Even if you think something's right, it's only correct within our frame of reference.
eternally-curious · 1 points · Posted at 07:43:54 on February 14, 2016 · (Permalink)
What? No! You're saying that if there are 365 people in a room, then 2 of them must have the same birthday? Mathematically, that's not true.
CorvusSplendens · 1 points · Posted at 06:29:56 on February 14, 2016 · (Permalink)
Decimal point followed by 79 zeroes then a 7.
survivethe5 · 1 points · Posted at 22:21:19 on February 13, 2016 · (Permalink)
In one my classes with 23+ students, my friend and I have the same birthday. Small world!
superfreak784 · 1 points · Posted at 23:33:32 on February 13, 2016 · (Permalink)
I've seen this proved in a class. The first person the teacher asked had the same birthday as me.
BeaverCleaver69 · 1 points · Posted at 01:06:59 on February 14, 2016 · (Permalink)
I like this one because last year, when I first read this, the average class size at my school was was 20-25 people. So I thought to myself "who in my classes have the same birthdays?" That's when I remembered that one of my classes had a pair of twins, and another class had two of my friends, who I know shared a birthday. So basically, ~50% of my classes, averaging out to 23 people each, had two people that shared a birthday.
[deleted] · 1 points · Posted at 01:24:16 on February 14, 2016 · (Permalink)
There are 24 people in my college class and me and a friend have the same birthday
thePurpleAvenger · 1 points · Posted at 02:16:54 on February 14, 2016 · (Permalink)
The best way to prove this is to compute the probability P that no two people in that room have the same birthday. Then 1-P gives you the answer. It makes a lot more sense to me that way.
[deleted] · 1 points · Posted at 02:23:57 on February 14, 2016 · (Permalink)
And if only two of them are twins it becomes a 100% chance!
DoctorSingh · 1 points · Posted at 02:43:34 on February 14, 2016 · (Permalink)
Has there been any real life application to this? Meaning has there been an experiment where this was proven?
LeTrakster · 1 points · Posted at 02:48:13 on February 14, 2016 · (Permalink)
I love this one! I was at a dinner party with 6 professors and their S.O.s (with me being a student) and I wanted to impress them with this statistical "trick" if you will. I explained the idea to them and we went around the table and no one had the same birthday, until the very last person . Then everyone freaked out and I was a hero for 5 minutes.
therealme23 · 1 points · Posted at 02:59:43 on February 14, 2016 · (Permalink)
Mind. Fuck.
mildlybreezy · 1 points · Posted at 03:01:01 on February 14, 2016 · (Permalink)
My homeroom in high school had 3 other people with the same birthday as me.
dotcomaphobe · 1 points · Posted at 03:51:03 on February 14, 2016 · (Permalink)
I learned this from Perplex City. Great stuff.
bkkrazy1234 · 1 points · Posted at 04:08:03 on February 14, 2016 · (Permalink)
Do we share the same math professor? Mine literally talked about this a couple weeks ago.
bluglesniff4 · 1 points · Posted at 04:19:28 on February 14, 2016 · (Permalink)
I was gonna argue with this because it makes no sense to me (I have a lot of math experience, however discrete math is apparently a different beast). I figured the easiest way to prove the theory right/wrong is just to test it by randomly assigning numbers out of 365 until I get a duplicate result. The 10 tests averaged out around 23 numbers until I got a duplicate, which proves the theory correct, long story short. It's crazy but I can't argue with something I'm looking at.
Citizen51 · 1 points · Posted at 04:34:55 on February 14, 2016 · (Permalink)
And when you reach 70 people you have a 99.9% chance two people share a birthday
23Enigma · 1 points · Posted at 04:48:30 on February 14, 2016 · (Permalink)
23 is everywhere!
[deleted] · 1 points · Posted at 04:56:39 on February 14, 2016 · (Permalink)
I teach college composition, with classes that cap out at 24. I pull this trick on my students every semester. More than half the time I blow their minds with my prediction that two people in the room have the same birthday.
They often assume I have access to their records, which includes their birthdays, but I don't. Also, who has time to look up all your students' birthdays for a quick gag?
sopranokelleyhollis · 1 points · Posted at 05:52:34 on February 14, 2016 · (Permalink)
Had a professor in college who would have us all, on the first day of class, stand in a circle in birthday order to prove this. Sure enough we had some pairs.
[deleted] · 1 points · Posted at 06:00:08 on February 14, 2016 · (Permalink)
In theory. But in practice, think about this. You go to school for almost your whole childhood about from 5-18 years old. I don't know about you, but throughout all my school days not once in all of my classes did 2 people have the same birthday. There were upwards of 23 kids in those classes, and almost every year there was plenty of people joining and leaving those classes.
Maybe I am just extremely unlucky.
Scuderia · 1 points · Posted at 06:26:13 on February 14, 2016 · (Permalink)
Assuming that birthdays are equally distributed across a given year.
massivecomplexity · 1 points · Posted at 06:51:40 on February 14, 2016 · (Permalink)
We did this in my pre-calc class in high school for funsies. There was ony about 20 of us, the teacher went through the math and showed it was about under 50% that we shared a birthday with someone. So naturally we decided to test it. She asked every person, one by one, their birthday. We got to the last row of people, and our chances were looking grim. She asked the second last person, and she says (insert birthday month day here). I shit you not, the last person turns and says the same date. Everyone in the class went nuts, and by nuts I mean a few loud "woah"s and "what"s.
RDandersen · 1 points · Posted at 08:11:09 on February 14, 2016 · (Permalink)
Our math teacher taught us this with a practical example. Schooling in my country has static classes for 80% of subjects and classes at the school were 20-25 students, with 18 classes total. According to the school records 7 of those classes had two students with the same birthday.
It's was quite unbelievable until he explained the maths behind.
zuriel45 · 1 points · Posted at 10:28:48 on February 14, 2016 · (Permalink)
Also there is a 100% chance that if 367 people are in a room at least two of them share a birthday.
Meistermett · 1 points · Posted at 10:31:02 on February 14, 2016 · (Permalink)
Oh, I remeber this. Back in school I bet against my math teacher that we'll never find 2 with the same birthday out of 50 random people, so we ran through the school asking people for their birthdays, later on I won but I remember that their were a row of 15 or 16 people that had birthday in april one after another
arenlr · 1 points · Posted at 11:07:26 on February 14, 2016 · (Permalink)
I still don't get it even after reading all the explanations
Let's say I have 23 jars, each filled with a ball labeled 1 to 365.
If I pick one ball at random from each jar, I would expect in most of the cases not to end up with 2 matching balls
regular_author · 1 points · Posted at 11:08:41 on February 14, 2016 · (Permalink)
Why then, in classes of ~30 where the teacher keeps track of the kids birthdays, do I remember so rarely two kids having the same one?
Semlohwerd · 1 points · Posted at 12:33:57 on February 14, 2016 · (Permalink)
This is unsettling because I've never met someone with the same birthday as me.
kbtrpm · 1 points · Posted at 14:22:10 on February 14, 2016 · (Permalink)
I have always wondered about this: the probabilistic computation is easy, but I think it's wrong: nobody ever takes into account the existence of leap years. Not that it affects the 50% conclusion, but the computed probability is not exact.
Burnt_Couch · 1 points · Posted at 14:29:51 on February 14, 2016 · (Permalink)
Interestingly enough this got brought up in my Physics lecture at college at the start of the semester.
The professor decided to spend a few minutes proving it, we had more than 23 people in the room (maybe 40-50?) so the odds were quite good (more than 50%).
So he started by having everybody with a birthday in January raise their hand, 4-5 people did. The first girl he asked what her birthday was said something like January 13th and a kid a few rows away said "uhhh, did you say January 13th? That's my birthday."
So while the odds were about 50% that two people would share the same birthday in the class, the chances of it happening with the first few people are low.
LifeArrow · 1 points · Posted at 16:19:50 on February 14, 2016 · (Permalink)
This is so simple it baffles me how someone could not get it.
JamesEarlDavyJones · 1 points · Posted at 18:00:36 on February 14, 2016 · (Permalink)
It'a called the Birthday Paradox.
It's like someone took the Pigeonhole Principle from combinatorics, and decided to try to prove it with bubble sorting from sorting/group ordering theory; and to their surprise, it more or less worked. So they left the special case they'd discovered and skipped off into the sunset for others to explain.
hypervelocityvomit · 1 points · Posted at 11:06:26 on February 15, 2016 · (Permalink)*
Also, there are about as many 4-digit numbers with a repeated digit as there are without.
If we have 4 digits a,b,c,d, there are 9 choices for b (the tenth digit would be a) , 8 for c (the other two would be a or b), and 7 for d. Of 1000 4-digit numbers starting with the same a, only 9*8*7 = 504 do not repeat a digit.
EDIT: Markup fix. 9\8*7, dammit)
ShameBoy · 1 points · Posted at 15:01:18 on February 15, 2016 · (Permalink)
I've been thinking about this for over a day and I still dont get it. You're telling me that if I had a random number generator spit out 23 numbers ranging from 1-365 that there's over a 50% chance that two will match? That seems absurd.
pornomatique · 1 points · Posted at 00:53:52 on February 14, 2016 · (Permalink)
This is actually an incredibly easy question in combinatorial probability
ghroat · 0 points · Posted at 02:14:34 on February 14, 2016 · (Permalink)
i've never met anyone with my birthday
xtxylophone · 3 points · Posted at 05:02:47 on February 14, 2016 · (Permalink)
It's a 50% chance for any pair, not a 50% chance with just you
ghroat · 1 points · Posted at 14:20:34 on February 14, 2016 · (Permalink)
Oh yeah
skullturf · 0 points · Posted at 17:41:56 on February 14, 2016 · (Permalink)
That's not true.
You've met hundreds or even thousands of people. You only know the birthdays of a few of them.
[deleted] · 0 points · Posted at 23:55:10 on February 13, 2016 · (Permalink)
It's actually just shy of 50% sauce and a pretty decent explanation too
Ganjisseur · 0 points · Posted at 06:16:14 on February 14, 2016 · (Permalink)
So you're telling me that randomly waking to an adoption center, picking an adorable tuxedo cat, and then finding out it has the same birthday as me isn't so special after all? :(
LucifersBarrister · -31 points · Posted at 20:03:13 on February 13, 2016 · (Permalink)
False: Put 366 people in a room, each with a different birthday and there is 0% chance any of them have the same birthday.
Felix_Tholomyes · 13 points · Posted at 20:10:42 on February 13, 2016 · (Permalink)
That doesn't invalidate his claim. You change the question if you specify their birthdays.
LucifersBarrister · -35 points · Posted at 20:13:20 on February 13, 2016 · (Permalink)
Yes it does. Take 23 people with different birthdays and there is a 0% chance that they have the same birthday.
Felix_Tholomyes · 11 points · Posted at 20:19:10 on February 13, 2016 · (Permalink)
Again, that's not an equivalent problem. However I saw your comment on 0.999999…=1 so I realize now that you are trolling. If anyone else wants me to explain why he's wrong I can do that but I won't spend more time on trolls.
LucifersBarrister · -19 points · Posted at 20:24:18 on February 13, 2016 · (Permalink)
Disagree=troll? How open-minded of you.
/s
MakhnoYouDidnt · 7 points · Posted at 20:50:19 on February 13, 2016 · (Permalink)
It's not something you can disagree on, you just blatantly don't get statistics.
mccune68 · 3 points · Posted at 00:17:51 on February 14, 2016 · (Permalink)
Judging by his comments in this submission, more like Math in general.
angelsandbuttermans · 2 points · Posted at 21:02:40 on February 13, 2016 · (Permalink)
You added another condition; in his the 23 people have random birthdays, while in yours you have taken the time to make sure each person doesn't have the same birthday ahead of time. His is random, yours is definite.
regdayrF · 1 points · Posted at 20:45:44 on February 13, 2016 · (Permalink)
Well, you are right to a certain degree. In mathematics you always have to make some assumptions. In this case, you would have to say something along the lines of:
Each day of the year is as likely to be a birtday as another day. Every birthday of the people in the room are independent to each other.
Then you can calculate the chance for each person to have birthday on another date ( AC ),
A = At least 2 persons have birthday on the same day
P(A) = 1 - P(AC) = 1-(365!/(36523 *342!))
[deleted] · 2 points · Posted at 20:53:13 on February 13, 2016 · (Permalink)
After reading the whole thread it's gotten to the point where I now know that every comment below the score threshold on this thread is most likely going to be a comment made by you.
lolcavstrash · -1 points · Posted at 01:56:48 on February 14, 2016 · (Permalink)
Youre a retard
Digital_Kahn · 795 points · Posted at 19:31:46 on February 13, 2016 · (Permalink)
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a roulette, a curve generated by a curve rolling on another curve.
25 years later, I still trace that out if I see something rolling.
(If I see it rollin', I'm tracin')
Hitlerdinger · 270 points · Posted at 23:30:30 on February 13, 2016 · (Permalink)
somebody explain this because i dont want to spend 5 minutes analyzing this comment
TomasTTEngin · 451 points · Posted at 00:07:30 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Cycloid
neat little gif herein
Wootsaur · 56 points · Posted at 04:24:11 on February 14, 2016 · (Permalink)
http://imgur.com/fOujilx
Gif here for the lazy and res users
baconatorX · 5 points · Posted at 05:42:36 on February 14, 2016 · (Permalink)
Mobile usr thnx u
ElectroBoof · 5 points · Posted at 06:24:25 on February 14, 2016 · (Permalink)
What? I clicked the wikipedia link on my phone and within two seconds the gif was loaded and also the biggest thing on the screen
Kent_o0 · 3 points · Posted at 07:41:44 on February 14, 2016 · (Permalink)
He might be using data though and would like to conserve it as best as he can
ElectroBoof · 5 points · Posted at 07:46:43 on February 14, 2016 · (Permalink)
Browsing reddit and is willing to load a gif
But won't open a wikipedia page?
ihavetenfingers · 4 points · Posted at 10:44:50 on February 14, 2016 · (Permalink)
Still extra data if were being nitpicky.
Norgenigga · 17 points · Posted at 01:13:52 on February 14, 2016 · (Permalink)
That is pretty satisfying, would be even better if it was a perfect loop.
[deleted] · 7 points · Posted at 02:27:22 on February 14, 2016 · (Permalink)
Hahaha. I had a crazy math professor who loved the software Mathematica. He taught it for half of a class and many of the exercises were writing math code to produce the gifs seen on wikipedia. In particular, it was this one.
intensely_human · 2 points · Posted at 03:15:34 on February 14, 2016 · (Permalink)
I love how nonchalant that rolling disc seems.
007T · 2 points · Posted at 03:37:21 on February 14, 2016 · (Permalink)
Practical application: https://www.youtube.com/watch?v=LgbWu8zJubo
kaibee · 1 points · Posted at 08:44:41 on February 14, 2016 · (Permalink)
""practical""
V1russ · 1 points · Posted at 17:49:59 on February 14, 2016 · (Permalink)
How else are we going to make square tricycles when then circles take over the world?
mrvoxen · 2 points · Posted at 07:13:20 on February 14, 2016 · (Permalink)
That gif made so much more sense than the explanation
der_luke · 2 points · Posted at 09:50:26 on February 14, 2016 · (Permalink)
Now the amazing part is really the length of this arc. It's not something with pi, or square roots or so...
It's 8
KobeReincarnate · 1 points · Posted at 03:36:17 on February 14, 2016 · (Permalink)
Wow, that's extremely similar to the absolute value of cos (x).
Moter8 · 1 points · Posted at 07:46:37 on February 14, 2016 · (Permalink)
We have to draw the middle part with just a straight edge and a compass in technical drawing class. Also some similar ones.
cattdaddy · 1 points · Posted at 17:54:17 on February 17, 2016 · (Permalink)
Also! If the diameter of that circle is 1, the space between the two vertices is exactly pi!
uReallyShouldTrustMe · 143 points · Posted at 23:49:30 on February 13, 2016 · (Permalink)
It is a play on the song "ridin dirty" by chamillionaire.
TheOldHen · 10 points · Posted at 00:47:07 on February 14, 2016 · (Permalink)
Ah, the old reddit math-a-roo
Pduffs · 1 points · Posted at 05:20:53 on February 14, 2016 · (Permalink)
Hold my protractor! I'm going in!
Hitlerdinger · 3 points · Posted at 23:49:55 on February 13, 2016 · (Permalink)
the other part
uReallyShouldTrustMe · 1 points · Posted at 12:27:16 on February 14, 2016 · (Permalink)
Oh, here
siamthailand · 1 points · Posted at 03:23:01 on February 14, 2016 · (Permalink)
This is the real LPT.
ShadowedNexus · 1 points · Posted at 06:50:02 on February 14, 2016 · (Permalink)
I have you labelled as "Future Deep Sea Masturbater". So my real question is, have you done so yet?
uReallyShouldTrustMe · 2 points · Posted at 06:59:25 on February 14, 2016 · (Permalink)
Not yet, patience my friend, it's winter!
thatCamelCaseTho · 3 points · Posted at 23:45:00 on February 13, 2016 · (Permalink)
Follow the end of a spoke on a tire. Within the wheel it moves circularly, but on the flat plane it moves linearly. The two combine to make a nice swirl.
NahSoR · 2 points · Posted at 02:16:04 on February 14, 2016 · (Permalink)
A true lazer
nskll · 1 points · Posted at 09:40:54 on February 14, 2016 · (Permalink)
Tadashi to the rescue ! https://www.youtube.com/watch?v=JuuYFt8bahE
abedneg0 · 15 points · Posted at 02:44:57 on February 14, 2016 · (Permalink)
The coolest thing about the cycloid is that it is the solution to the following problem. You have a marble at the top of a tower. You want to build a marble run that will get the marble from the top of the tower to the ground some distance away as quickly as possible. What is the shape of that marble run? The answer -- a cycloid.
hexane360 · 6 points · Posted at 04:58:47 on February 14, 2016 · (Permalink)
And it's also the tautochrome, meaning that no matter where on the ramp you put the ball, it'll finish in the same amount of time.
JustReadingThisStuff · 3 points · Posted at 10:47:00 on February 14, 2016 · (Permalink)
came here to say this. Aditional fun fact: german pilots in WWII were trained to take this paths while descendin during dogfights giving them a huge advantage.
PoisonMind · 1 points · Posted at 03:02:55 on February 14, 2016 · (Permalink)
Also known as the brachistochrone problem.
Atario · 1 points · Posted at 11:15:03 on February 14, 2016 · (Permalink)
I thought this was a catenary? Or am I thinking of a different criterion? (Max speed at the ground or some such instead of min time elapsed?)
Phoenix_667 · 4 points · Posted at 02:20:17 on February 14, 2016 · (Permalink)
that's the cycoid
that's the circle
the fuck? wasn't the curve rolling on a straight line?
[deleted] · 7 points · Posted at 03:26:27 on February 14, 2016 · (Permalink)
[deleted]
Phoenix_667 · 5 points · Posted at 06:19:59 on February 14, 2016 · (Permalink)
Really? My geometry teacher would make a very strict distinction between straight and curved lines
EDIT: I'm not claiming you are wrong, I've been misled by school way too many times. My biology teacher once said South Africa did not exist.
[deleted] · 1 points · Posted at 06:50:53 on February 14, 2016 · (Permalink)
[deleted]
Phoenix_667 · 1 points · Posted at 07:08:03 on February 14, 2016 · (Permalink)
Now that I think about it, it might be a semantic issue (I grew in latin america)
dmacle · 3 points · Posted at 23:59:11 on February 13, 2016 · (Permalink)
A spirograph is a good application of this principle.
https://en.m.wikipedia.org/wiki/Spirograph
hexane360 · 1 points · Posted at 04:56:14 on February 14, 2016 · (Permalink)
Yep. Those are normally hypotrochoids though
KillingVectr · 2 points · Posted at 04:03:34 on February 14, 2016 · (Permalink)
A very important property of the cycloid is that it is the solution to the Tautochrone Problem: find a curve that the amount of time it takes something to fall to the bottom is independent of the height where it starts. This lead Huygens to realize that a cycloid pendulum should give a more accurate clock than a traditional fixed length pendulum.
For a traditional pendulum, the period of the swing depends slightly on the amplitude of the swing; it is only an approximation of small amplitude that gives period independent of the amplitude. The cycloid pendulum precisely has the period independent of the amplitude of the swing. However, real world effects such as friction make it not practical.
OleksiyGuy · 2 points · Posted at 04:17:06 on February 14, 2016 · (Permalink)
https://www.youtube.com/watch?v=JuuYFt8bahE
Here is a cool use of the cycloid to explain a neat little toy a researcher is using.
foyf · 2 points · Posted at 04:17:32 on February 14, 2016 · (Permalink)
The really interesting thing about the cycloid curve is that it is the fastest path a rolling object can take down a curve. In other words, a derby car dropped from a cycloid curve will finish before it would on ANY other curve.
hellochase · 2 points · Posted at 19:50:39 on February 15, 2016 · (Permalink)
(Tryna catch me ridin' nerdy)
workethicsFTW · 1 points · Posted at 03:06:46 on February 14, 2016 · (Permalink)
Wouldn't it trace a circle?
intensely_human · 1 points · Posted at 03:14:09 on February 14, 2016 · (Permalink)
Hop hop hop
motorolaradio · 1 points · Posted at 03:21:20 on February 14, 2016 · (Permalink)
Slip, don't forget skid
foyf · 1 points · Posted at 04:17:29 on February 14, 2016 · (Permalink)
The really interesting thing about the cycloid curve is that it is the fastest path a rolling object can take down a curve. In other words, a derby car dropped from a cycloid curve will finish before it would on ANY other curve.
ImS0hungry · 1 points · Posted at 04:31:52 on February 14, 2016 · (Permalink)
even more cool is that the cycloid from a circle with a radius of 1 has a length of pi.
Weekend833 · 1 points · Posted at 05:11:19 on February 14, 2016 · (Permalink)
Time to go play with the spirograph I bought my kid for Christmas.
Polish__Sausage · 1 points · Posted at 05:46:18 on February 14, 2016 · (Permalink)
A hyperbolic paraboloid is a three dimensional shape that when traced onto the three planes in 3D space, yields two parabolas and a hyperbola. It is modeled by the equation "z = (y2 / a2) - (x2 / b2)". Its shape can be visualized easier with Pringles.
Morall_tach · 1 points · Posted at 05:48:18 on February 14, 2016 · (Permalink)
Related weird thought: If the wheel in question is not slipping, that means the point on the wheel's edge directly contacting the surface is not moving.
No matter how fast the vehicle is moving, there is a point (or a line, technically) on the wheel at any given time whose velocity, relative to the ground, is zero. That blows my mind.
bigfondue · 1 points · Posted at 07:24:29 on February 14, 2016 · (Permalink)
So like a spirograph?
Ucantalas · 1 points · Posted at 08:03:40 on February 14, 2016 · (Permalink)
So like... the mathematical end of a Spirograph?
rightbeforeimpact · 1 points · Posted at 08:03:53 on February 14, 2016 · (Permalink)
FULL BRIDGE RECTIFIER https://www.youtube.com/watch?v=sI5Ftm1-jik
_FranklY · 1 points · Posted at 08:11:52 on February 14, 2016 · (Permalink)
And if you do the same thing around a circle, you get a cardioid!
Jdrawer · 1 points · Posted at 08:34:01 on February 14, 2016 · (Permalink)
Would this video contain one? https://youtu.be/JuuYFt8bahE
PotatoesAreUs · 1 points · Posted at 10:38:35 on February 14, 2016 · (Permalink)
I always thought it would make a sine curve.
Parcec · 1 points · Posted at 11:09:14 on February 14, 2016 · (Permalink)
Perhaps the coolest application of cycloids: https://en.wikipedia.org/wiki/Skyhook_(structure)
JooJoona · 1 points · Posted at 11:29:22 on February 14, 2016 · (Permalink)
Found the Numberphile subscriber.
Eepopfunny · 1 points · Posted at 13:25:13 on February 14, 2016 · (Permalink)
The numberphile channel on YouTube did a video on this just this week.
EonesDespero · 1 points · Posted at 15:04:22 on February 14, 2016 · (Permalink)*
A cycloid is also the shape of a toboggan which would gives you the fastest travel between two points x and y, in the presence of a gravity field.
That and the hanging chain in the presence of a gravity field are two classical examples of the utilization of the variational principle.
tolkienlover · 1 points · Posted at 22:59:54 on February 14, 2016 · (Permalink)
Another cool thing about these is that it takes the same amount of time to get to the bottom from any point along the curve (if it is inverted in an upside down u shape and a mass is subject to gravity). This makes it ideal for timing things like seconds in a clock, because even if the weight loses momentum along the curve over time and doesn't reach as high (due to air resistance, general friction) it will continue to beat out at the same time interval!
Feynman1998 · 0 points · Posted at 00:24:42 on February 14, 2016 · (Permalink)
Interestingly if u wanted a slide that would bring u down from A to B (and they aren't on the same axis), a cycloid slide will have the shortest slide time.
JamesIgnatius27 · 2200 points · Posted at 19:33:54 on February 13, 2016 · (Permalink)
22/7 is closer to the actual value of pi than 3.14 is.
grogipher · 602 points · Posted at 22:38:58 on February 13, 2016 · (Permalink)
That's why in the UK, we celebrate Pi Day on the 22nd of July.
Omg-can-you-not · 264 points · Posted at 02:54:21 on February 14, 2016 · (Permalink)
I didn't know this. I just kinda assumed it would be on the 3rd of...
oh.
snicklefritz73 · 104 points · Posted at 04:13:02 on February 14, 2016 · (Permalink)
31st of April?
palordrolap · 157 points · Posted at 07:52:24 on February 14, 2016 · (Permalink)
Contact me on the 31st of April and I'll give you Reddit Gold.
snicklefritz73 · 11 points · Posted at 07:57:10 on February 14, 2016 · (Permalink)
Breaking my heart....
Nerfi · 3 points · Posted at 13:55:35 on February 14, 2016 · (Permalink)
I found your use of that line in this context far more emotionally moving than Natalie Portman's attempt to display a similar emotion in the film "Revenge of the Sith."
Packin_Penguin · 9 points · Posted at 13:40:10 on February 14, 2016 · (Permalink)*
Remind me! 76 days.
April 31st would be 76 days away if it existed. Intent of contract is to be respected if the author of the contract makes a minor error based on well known facts to be intentionally misleading.
Source
NotUrMomsMom · 4 points · Posted at 14:19:49 on February 14, 2016 · (Permalink)
RemindMe! April 31, 2016
AlphaApache · 1 points · Posted at 16:41:41 on February 14, 2016 · (Permalink)
RemindMe! April 30, 2016
ImAStupidFace · 1 points · Posted at 06:23:54 on February 15, 2016 · (Permalink)
RemindMe! April 31 2016
[deleted] · 1 points · Posted at 22:55:47 on April 30, 2016 · (Permalink)
[deleted]
palordrolap · 1 points · Posted at 23:34:54 on April 30, 2016 · (Permalink)
Aww man, you must have missed it! Today's the 1st of May. Sorry about that, chap.
[deleted] · 1 points · Posted at 00:08:21 on May 1, 2016 · (Permalink)
[deleted]
palordrolap · 1 points · Posted at 00:23:16 on May 1, 2016 · (Permalink)
Then you're contacting me on the 30th! Naughty. No gold for you.
nunobelmar13 · 1 points · Posted at 01:35:29 on May 1, 2016 · (Permalink)
I feel like I still deserve the Gold merely based on effort, no?
palordrolap · 1 points · Posted at 01:40:29 on May 1, 2016 · (Permalink)
Eeh. Not a lot of effort goes into a RemindMe and a comment. You win this.
flyqer · 6 points · Posted at 07:49:00 on February 14, 2016 · (Permalink)
Dodecember
palordrolap · 3 points · Posted at 07:52:46 on February 14, 2016 · (Permalink)
Lousy Duodecember weather.
[deleted] · 1 points · Posted at 14:16:07 on February 14, 2016 · (Permalink)
Next February?
JakkuScavenger · 0 points · Posted at 14:45:23 on February 14, 2016 · (Permalink)
Did you mean Match 14th? Oh, right.
Gehalgod · 59 points · Posted at 02:12:51 on February 14, 2016 · (Permalink)
Oh fuck you.
bacontimbit · 23 points · Posted at 04:57:56 on February 14, 2016 · (Permalink)
Remember they don't have 4/20 with that date format.
QCMBRman · -1 points · Posted at 17:51:01 on February 14, 2016 · (Permalink)
Losers
GoodShitLollypop · 8 points · Posted at 02:30:28 on February 14, 2016 · (Permalink)
Not the third day of next February?
[deleted] · 4 points · Posted at 06:06:57 on February 14, 2016 · (Permalink)
Is this true??
EscapeTrajectory · 3 points · Posted at 06:53:55 on February 14, 2016 · (Permalink)
That day has sadly been given a different meaning in Scandinavia :(
thtrf · 4 points · Posted at 12:32:00 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/2011_Norway_attacks for those wondering
fite_me_fgt · 1 points · Posted at 17:36:44 on February 19, 2016 · (Permalink)
How the fuck has it been five years
aDerpyPenguin · 2 points · Posted at 03:36:26 on February 14, 2016 · (Permalink)
I don't get it.
Smilotron · 12 points · Posted at 03:56:44 on February 14, 2016 · (Permalink)
In the UK dates are written in a different order. In the US there is no 22/7
Balind · 1 points · Posted at 03:06:16 on February 14, 2016 · (Permalink)
Oh that's clever.
pyroSeven · 1 points · Posted at 07:54:24 on February 14, 2016 · (Permalink)
Nerds!
Curran919 · 1 points · Posted at 08:38:45 on February 14, 2016 · (Permalink)
That would be so much better than having it compete with steak and a bj day...
thtrf · 1 points · Posted at 12:32:48 on February 14, 2016 · (Permalink)
So is Einstein birthday on 22 july as well in UK?
PM_ME_YOUR_ANYTHlNG · 1 points · Posted at 13:37:21 on February 14, 2016 · (Permalink)
But while you guys are just stuck at 22/7, we get to wait for the magical moment of March 14th, at 1:59:26535...
steppe5 · 1 points · Posted at 14:41:48 on February 14, 2016 · (Permalink)
Why not April 31st?
bagelmakers · 1 points · Posted at 20:18:39 on February 14, 2016 · (Permalink)
At our school we have 3 pi days so that every semester can celebrate. April 14th is pi day, November 10th because it is the 314th day of the year where we serve pie, and 7/22 (July 22nd) where we celebrate approximately pi day and serve cake.
quesman1 · 1 points · Posted at 06:49:15 on February 15, 2016 · (Permalink)
WOAH THAT'S MY BIRTHDAY!!!
Thanks! On the other hand, I can't believe I never thought of that!
SongstressInDistress · 1 points · Posted at 00:07:53 on March 13, 2016 · (Permalink)
Isn't it March 14th, tomorrow (I'm in Asia)?
grogipher · 1 points · Posted at 10:39:59 on March 13, 2016 · (Permalink)
14/3 doesn't make Pi. 22/7 does.
SongstressInDistress · 1 points · Posted at 10:44:30 on March 13, 2016 · (Permalink)
Dude. 3.14.
grogipher · 1 points · Posted at 10:50:02 on March 13, 2016 · (Permalink)
Dude. That's not how we right the date!
That's why my comment was prefaced "That's why in the UK..."
SongstressInDistress · 1 points · Posted at 17:16:39 on March 14, 2016 · (Permalink)
Ooooh I didn't know that!
Happy pi day!
herovision · -1 points · Posted at 05:08:37 on February 14, 2016 · (Permalink)
Unfortunately in America, July the 22nd is written as 7/22, so this might go over a few heads.
finallynamenottaken · -4 points · Posted at 04:36:38 on February 14, 2016 · (Permalink)
Wouldn't that be 22 * (of) 7?
PresidentSwartzneger · 2 points · Posted at 05:58:21 on February 14, 2016 · (Permalink)
No
MrFurrypants · 1013 points · Posted at 19:50:19 on February 13, 2016 · (Permalink)
355/113 is even closer
aparker314159 · 2688 points · Posted at 21:27:55 on February 13, 2016 · (Permalink)*
31415926535897932384/10000000000000000000 is even closer.
eviltreesareevil · 93 points · Posted at 00:24:55 on February 14, 2016 · (Permalink)*
31415926535897966666666666666666666666/10000000000000000000000000000000000000 is closer still!
LogicalEmotion7 · 117 points · Posted at 00:59:23 on February 14, 2016 · (Permalink)
I don't know, ln(-1)/i is closer.
qwertygasm · 79 points · Posted at 01:42:39 on February 14, 2016 · (Permalink)
Pi/1 is the same distance.
LogicalEmotion7 · 23 points · Posted at 01:49:47 on February 14, 2016 · (Permalink)
Does P=(π/i)?
NoGardE · 23 points · Posted at 03:01:14 on February 14, 2016 · (Permalink)
No P = m x v.
9392263 · 24 points · Posted at 03:07:56 on February 14, 2016 · (Permalink)
No it doesn't, P=nRT/V, and p=m*v not m x v
NoGardE · 16 points · Posted at 04:04:31 on February 14, 2016 · (Permalink)
Fuuuuuuuuuck mass isn't a vector.
InfanticideAquifer · 6 points · Posted at 06:26:21 on February 14, 2016 · (Permalink)
p = γ*m*v, actually.
9392263 · 2 points · Posted at 06:37:23 on February 14, 2016 · (Permalink)
Okok in the nonrelativistic limit ok :P
ColonialDagger · 1 points · Posted at 03:18:59 on February 14, 2016 · (Permalink)
I think that π is just a tiny bit closer.
dark_sniper · 1 points · Posted at 03:50:04 on February 14, 2016 · (Permalink)
Pi is closer to the value of Pi than 3.14
Signumus · 1 points · Posted at 19:43:36 on February 14, 2016 · (Permalink)
No PxT=MxV
1wjl1 · 12 points · Posted at 01:18:45 on February 14, 2016 · (Permalink)
Loving the Euler reference
GangreneMeltedPeins · 1 points · Posted at 03:34:52 on February 14, 2016 · (Permalink)
High level meta
hypervelocityvomit · 1 points · Posted at 11:11:06 on February 15, 2016 · (Permalink)
4 arctan(1)
xmindallas · 1 points · Posted at 06:16:00 on February 14, 2016 · (Permalink)
C / d is closer than that.
[deleted] · 2 points · Posted at 01:41:07 on February 14, 2016 · (Permalink)
Why all the sixes? I would have gone with something cooler next. Maybe a 3.
hypervelocityvomit · 1 points · Posted at 11:10:43 on February 15, 2016 · (Permalink)
"Best pie in town. Call 314159265...3"
jonathanroxalot · 2 points · Posted at 06:43:53 on February 14, 2016 · (Permalink)
Are you guys telling me that there is some sequence of rational numbers that converges to a number that's not rational?!
Leminems · 1 points · Posted at 06:50:36 on February 14, 2016 · (Permalink)
No
fnybny · 1 points · Posted at 07:26:21 on February 14, 2016 · (Permalink)
Real numbers are only equivalence classes of cauchy sequences of rational numbers
techlos · 1 points · Posted at 09:32:24 on February 14, 2016 · (Permalink)*
eviltreesareevil · 5 points · Posted at 09:42:51 on February 14, 2016 · (Permalink)
no man, you have a zero earlier in that number
hypervelocityvomit · 1 points · Posted at 11:12:34 on February 15, 2016 · (Permalink)
Should have ctrl-F'ed that stuff and highlight all 0's. Pucking pheasant. smh
dengseng · 1 points · Posted at 11:11:28 on February 14, 2016 · (Permalink)
3.141592653589793238
every time I see a pi reference I'd remember a few more numbers
once-and-again · 28 points · Posted at 02:22:08 on February 14, 2016 · (Permalink)
312689/99532 is three times closer than that, yet scarcely half as long.
[deleted] · 23 points · Posted at 04:51:14 on February 14, 2016 · (Permalink)
I like watching the mathematics undergrads competing in this thread.
GodlessPerson · 4 points · Posted at 13:16:27 on February 14, 2016 · (Permalink)
π is closer.
once-and-again · 1 points · Posted at 04:41:44 on February 16, 2016 · (Permalink)
I should be ashamed, since I graduated years ago. But I'm not. :D
[deleted] · 4 points · Posted at 15:01:08 on February 14, 2016 · (Permalink)
Ahh the old continued fractions I'm guessing. Best rational approximations anywhere this side of the denominator.
LuckyNumberHat · 9 points · Posted at 03:43:30 on February 14, 2016 · (Permalink)
That's not reduced. They are both divisible by 5.
TheRealZoidberg · 6 points · Posted at 02:03:06 on February 14, 2016 · (Permalink)
And even closer if it was 31415926536/10000000000, since the next number after the last five is an eight, so you round up!
Mnyyy · 3 points · Posted at 04:32:20 on February 14, 2016 · (Permalink)
Crazy how nature do that
operez1990 · 3 points · Posted at 04:00:12 on February 14, 2016 · (Permalink)
314159265358979323846/10000000000000000000 is closer
Epicjay · 1 points · Posted at 01:18:33 on February 14, 2016 · (Permalink)
Well, you're not wrong.
Always_smooth · 1 points · Posted at 04:42:44 on February 14, 2016 · (Permalink)
pi/1 is even closer.
erythro · 1 points · Posted at 11:45:10 on February 14, 2016 · (Permalink)
355/113 is really good though. I checked a few irrational numbers and no other fractional approximation is as good per digit.
Cocolumbo · 1 points · Posted at 13:20:01 on February 14, 2016 · (Permalink)
why didnt you reduce that fraction like you have been taught in school?
jesus christ.... the young generation....
JakkuScavenger · 1 points · Posted at 14:45:50 on February 14, 2016 · (Permalink)
Just writing pi is closest!
[deleted] · 0 points · Posted at 04:50:15 on February 14, 2016 · (Permalink)
yeah but that's not a convergent of the fraction expansion.
355over113 · 2157 points · Posted at 00:26:18 on February 14, 2016 · (Permalink)
You called?
superpower4 · 131 points · Posted at 03:13:48 on February 14, 2016 · (Permalink)
8 months not bad not bad at all.
[deleted] · 18 points · Posted at 03:38:57 on February 14, 2016 · (Permalink)
[deleted]
355over113 · 81 points · Posted at 04:42:35 on February 14, 2016 · (Permalink)
I made my account knowing that it represented a fraction close to Pi but wasn't as common as 22/7. It was pure coincidence that I came across this post.
reddit__scrub · 28 points · Posted at 06:37:38 on February 14, 2016 · (Permalink)
You don't have a bot running the subreddits notifying you of posts containing "355/113"?? Shit if I had a cool username I'd totally do that
IamRule34 · 41 points · Posted at 06:45:13 on February 14, 2016 · (Permalink)
That's why you're a scrub
reddit__scrub · 37 points · Posted at 06:55:16 on February 14, 2016 · (Permalink)
I was destined for ungreatness
habeeb51 · 3 points · Posted at 12:35:28 on February 14, 2016 · (Permalink)
How in the hell..?
-Hegemon- · 2 points · Posted at 14:52:41 on February 14, 2016 · (Permalink)
Right???
gudgeonpin · 12 points · Posted at 02:39:47 on February 14, 2016 · (Permalink)
Yes. Hungry, but not sure what for. Any suggestions?
WithoutTheQuotes · 3 points · Posted at 10:25:49 on February 14, 2016 · (Permalink)
Stir-fry
yParticle · 2 points · Posted at 08:44:44 on February 14, 2016 · (Permalink)
cake
MooseEngr · 3 points · Posted at 20:49:25 on February 14, 2016 · (Permalink)
That's a dirty lie, you asshole!!!
[deleted] · 9 points · Posted at 05:58:31 on February 14, 2016 · (Permalink)
/r/beetlejuicing
Juicysteak117 · 7 points · Posted at 05:26:34 on February 14, 2016 · (Permalink)
Looks like he checks out.
reddit__scrub · 7 points · Posted at 06:36:41 on February 14, 2016 · (Permalink)
Holy shit, you weren't just created
Somebodys · 5 points · Posted at 05:09:32 on February 14, 2016 · (Permalink)
You need more fake internet points.
[deleted] · 6 points · Posted at 06:17:21 on February 14, 2016 · (Permalink)
Seriously what the fuck?
stevestevetwosteves · 5 points · Posted at 06:36:50 on February 14, 2016 · (Permalink)
Ok what the hell
[deleted] · 9 points · Posted at 05:22:49 on February 14, 2016 · (Permalink)
R/retiredusernames
lifeof314159 · 3 points · Posted at 08:32:55 on February 14, 2016 · (Permalink)
greets with secret handshake
rezen__ · 3 points · Posted at 06:38:57 on February 14, 2016 · (Permalink)
You're either on Reddit way too much or you're a magician. How did you find this comment? A scraper?
355over113 · 3 points · Posted at 14:46:23 on February 14, 2016 · (Permalink)
-WPD- · 2 points · Posted at 06:49:50 on February 14, 2016 · (Permalink)
Well I'll be damned, Milü
DoublePlusTall · 2 points · Posted at 07:17:00 on February 14, 2016 · (Permalink)
Now he's even closer!!
IlanRegal · 2 points · Posted at 07:38:30 on February 14, 2016 · (Permalink)
Whoa
[deleted] · 2 points · Posted at 08:30:28 on February 14, 2016 · (Permalink)
Hello there.
MrShlash · 2 points · Posted at 10:34:02 on February 14, 2016 · (Permalink)
Impressive
dotmax · 2 points · Posted at 10:42:31 on February 14, 2016 · (Permalink)
Oh, at first I thought you meant this:
http://imgur.com/fzH6bMO
nufcneilo · 2 points · Posted at 12:12:53 on February 14, 2016 · (Permalink)
How did you know to appear?!
J_tt · 2 points · Posted at 12:37:15 on February 14, 2016 · (Permalink)
Username checks out.
GrassGriller · 2 points · Posted at 14:49:01 on February 14, 2016 · (Permalink)
Cool.
Zobtzler · 2 points · Posted at 15:53:47 on February 14, 2016 · (Permalink)
/r/retiredusername
little_kid_lover69 · 2 points · Posted at 17:00:39 on February 14, 2016 · (Permalink)
Ooooohhh shit!
[deleted] · 2 points · Posted at 06:06:01 on February 14, 2016 · (Permalink)
Wait. WTF?? Has this fraction come up so often that you created an alert when it's mentioned? Or was this complete coincidence?
This is by far my favorite Reddit moment.
germanyjr112 · 3 points · Posted at 10:58:54 on February 14, 2016 · (Permalink)
"I made my account knowing that it represented a fraction close to Pi but wasn't as common as 22/7. It was pure coincidence that I came across this post." - from an earlier comment
New_World_Era · 203 points · Posted at 20:38:47 on February 13, 2016 · (Permalink)
Ohhh I need to remember this one
CookieTheSlayer · 220 points · Posted at 21:08:49 on February 13, 2016 · (Permalink)
It's not that hard to actually learn a bunch of digits of pi. I remember 3.1415926535 and everything beyond that is something I don't need
nottherealslash · 664 points · Posted at 21:28:26 on February 13, 2016 · (Permalink)*
If I remember correctly, you only need about 20 digits of pi to calculate the diameter of the observable Universe to a precision within the diameter of a single hydrogen atom
EDIT: added "observable Universe"
EDIT 2: as others have pointed out, it's actually 39. Still not all that many in the grand scheme of things
TheRandomnatrix · 915 points · Posted at 21:59:51 on February 13, 2016 · (Permalink)
Yeah, but you need at least 10 more to be interesting at parties
Cohomotopian · 518 points · Posted at 22:38:41 on February 13, 2016 · (Permalink)
"interesting"
EmpireOfTheTsun · 405 points · Posted at 23:17:52 on February 13, 2016 · (Permalink)
"parties"
RedditsLittleSecret · 29 points · Posted at 00:12:03 on February 14, 2016 · (Permalink)
"at"
AlmightyB · 24 points · Posted at 01:47:37 on February 14, 2016 · (Permalink)
""""
[deleted] · 2 points · Posted at 02:08:15 on February 14, 2016 · (Permalink)
[deleted] · 1 points · Posted at 09:23:40 on February 14, 2016 · (Permalink)
How. Did. You. Do..... That?
Edit: Nevermmind
[deleted] · 1 points · Posted at 09:23:55 on February 14, 2016 · (Permalink)
[deleted] · 1 points · Posted at 12:56:28 on February 14, 2016 · (Permalink)
[deleted]
Kaijem · 1 points · Posted at 12:57:38 on February 14, 2016 · (Permalink)
DillyBaby · 1 points · Posted at 05:08:02 on February 14, 2016 · (Permalink)
"To be"
SquidManHero · 1 points · Posted at 06:54:13 on February 14, 2016 · (Permalink)
"Be"
DragoonDM · 2 points · Posted at 00:33:11 on February 14, 2016 · (Permalink)
Much like the guy who brings his acoustic guitar.
DingyWarehouse · 1 points · Posted at 03:45:11 on February 14, 2016 · (Permalink)
"Hey guys wanna hear a song I wrote"
Swito · 2 points · Posted at 04:35:05 on February 14, 2016 · (Permalink)
Any "skill" that only one individual present at the party knows can be an interesting party trick.
Delivery is the important part here.
Flight714 · 1 points · Posted at 01:13:20 on February 14, 2016 · (Permalink)
"at parties"
HeWhoKnox · 1 points · Posted at 01:43:40 on February 14, 2016 · (Permalink)
"at"
ectish · 1 points · Posted at 04:26:39 on February 15, 2016 · (Permalink)
Because you'll never be invited back and won't get to repeat the sequence?
zacree · 11 points · Posted at 02:50:34 on February 14, 2016 · (Permalink)
My first week at college, there was a meeting with every guy on my floor.
Not even thirty minutes in, they're reciting digits of pi in unison as some sort of contest. They're a couple dozen digits in (more than twenty guys), eyes wide with delight and shaking their fists like they're roman gods watching slaves fight for glory.
ONE. FOUR. ONE. FIVE. NINE...
I have never been further out of my depth. I was really uncomfortable and really wanted to leave but I didn't wanted to be branded as "that guy who left while we were all so happy".
They really were happy, and in a way I was happy for them. Because these were the math nerds from all of our highschools and they were finally meeting other people who they identified with on that level. You could see it in their faces that they were dreading coming to college and having to try to fit in or suffer the consequences and that in this moment it was instantly relieved. They fit in perfectly and nobody in that room was pretending.
Except for me. I was terrified that at some point they were going to notice that I wasn't chanting digits and they were going to ask me to prove some theory that didn't exist and pants me when I stood up and tried.
But then I went and got super high later with some graphic design chick and I forgot all about that until now, about a decade later.
SoldierofNod · 6 points · Posted at 03:24:44 on February 14, 2016 · (Permalink)
That reminds me of a story a friend of mine told me about.
His middle school had this "Recite pi for pie!" competition. The idea being, whoever could recite the most digits would earn a pie. He wanted the pie, so he got to work and memorized 200 digits.
The thing is, he didn't know how many digits other people had memorized.
The second place competitor had memorized pi to 10 digits.
The pie sucked.
Avatar_Of_Brodin · 2 points · Posted at 03:32:44 on February 14, 2016 · (Permalink)
"Yes, I know a number."
Yahoo, pi to four places.
"How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics."
Boom. Pi to 15 places.
And Mike Keith did it to 740 digits as follows.
hypervelocityvomit · 1 points · Posted at 11:19:44 on February 15, 2016 · (Permalink)
Thats / Awesome
Mikeismyike · 1 points · Posted at 01:57:10 on February 14, 2016 · (Permalink)
I know 200, how "interesting" am I?
whatsausername90 · 1 points · Posted at 04:10:47 on February 14, 2016 · (Permalink)
Or you can just memorize the first 6 digits, and makes the rest up off the top of your head. Since nobody else will know if you're wrong.
QuaggaSwagger · 1 points · Posted at 05:47:14 on February 14, 2016 · (Permalink)
What if you know say...150?
Are you cool? :-D
nyrol · 1 points · Posted at 06:20:32 on February 14, 2016 · (Permalink)
Off the top of my head. 3.14159265358979323846264338327950288419
Thanks to this song it's easier to remember by singing it.
imstupidplzhelp · 1 points · Posted at 18:42:05 on February 15, 2016 · (Permalink)
I've found it easier to break it down into chunks of 5 digits after the decimal. I remember it like this:
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
MrxAvicenna · 3 points · Posted at 21:58:58 on February 13, 2016 · (Permalink)
I think it was 32 or 35, but regardless it kinda makes memorizing a significant number of digits of Pi useless
nottherealslash · 3 points · Posted at 22:26:20 on February 13, 2016 · (Permalink)
Yeah, I forget the exact number, the point was more to demonstrate just how little of it we actually need to discern things to a remarkable degree of accuracy. The trillion-decimal place version or whatever they've got it up to these days is useless beyond demonstrating computing power
bobby8375 · 2 points · Posted at 02:18:24 on February 14, 2016 · (Permalink)
Useless? Preposterous! We need a million digits of pi, precisely so we can roll it out on an airport strip: https://youtu.be/0r3cEKZiLmg
nottherealslash · 1 points · Posted at 13:21:23 on February 14, 2016 · (Permalink)
Wow
Habtra · 7 points · Posted at 21:49:39 on February 13, 2016 · (Permalink)
Observable universe.
nottherealslash · 6 points · Posted at 21:52:14 on February 13, 2016 · (Permalink)
That was implicit to my statement but yes, the observable Universe to be more precise
chilly-wonka · 7 points · Posted at 21:57:23 on February 13, 2016 · (Permalink)
I'm not saying you're wrong but that sounds impossible
ClareDeLoon · 11 points · Posted at 23:05:32 on February 13, 2016 · (Permalink)
20 digits is a precision of 1020, which is 10 million trillion. So you're precise to a ten-million-trillionth of the universe which is presumably smaller than the size of an atom.
isrly_eder · 2 points · Posted at 00:36:18 on February 14, 2016 · (Permalink)
a quick google tells me that there's approximately "1078 to 1082 " atoms in the universe, so there seems to be a mismatch there. can someone explain
PM_ME_CUTE_PUPPYS · 9 points · Posted at 00:43:20 on February 14, 2016 · (Permalink)
It only matters how many atoms there are I'm a diameter of the universe, not total.
isrly_eder · 5 points · Posted at 00:47:21 on February 14, 2016 · (Permalink)
Oh yeah, I'm an idiot
da_chicken · 4 points · Posted at 05:11:02 on February 14, 2016 · (Permalink)
Well, it's 37 digits, but it's still correct.
Take a ring of atoms that's also the size of the observable universe. Now, a ring of atoms isn't a perfect circle, but let's treat it as such and calculate the circumference. How well do we need to know pi to get the circumference to be accurate within the level of detail a ring of atoms gives us?
An atom is about 1.0 × 10-10 m in size. That means that if we assume atoms behave like marbles (they don't but let's pretend) that the distance from the center of an atom to the center of the next atom in our ring is 1.0 × 10-10 m.
The observable universe is 93 billion light years in diameter, or 8.8 × 1026 m. Let's say we actually have an exact value for it.
The circumference of a circle is pi × diameter.
If you have 37 digits of pi, that reaches past the 10-10 place. So, by the rules for significant figures, if you know pi to 37 places then the error in your circumference calculation caused by the fact that your circle is constructed using physical object and not abstract geometry is greater than the error caused by not knowing the value of pi well enough.
The funny part is if you say, "Well, what if we have it wrong? What if the observable universe is actually 930 billion light years across?" Well, in that case... you need 38 digits. Orders of magnitude are powerful.
chilly-wonka · 1 points · Posted at 05:35:04 on February 14, 2016 · (Permalink)
That was a really great explanation, thank you
nottherealslash · 1 points · Posted at 22:25:09 on February 13, 2016 · (Permalink)
To calculate the diameter of the observable Universe?
chilly-wonka · 0 points · Posted at 22:28:50 on February 13, 2016 · (Permalink)
you didn't say observable, you just said "the diameter of the Universe"
nottherealslash · 5 points · Posted at 22:31:41 on February 13, 2016 · (Permalink)
The observable was implicit in my statement, but since you're the second person to call me out on this I'll amend the original comment
slapdashbr · 2 points · Posted at 01:58:35 on February 14, 2016 · (Permalink)
I'll just round it to 3
nottherealslash · 1 points · Posted at 13:22:33 on February 14, 2016 · (Permalink)
Top jej
Bara_Chat · 2 points · Posted at 04:42:10 on February 14, 2016 · (Permalink)
Wait. I watched a Numberphile video at one point and the guy said 39 digits if I remember correctly. It doesn't matter much either way, 39 is still a lot lower than most people would expect, including me before watching that vid.
Edit : Found it!
nottherealslash · 2 points · Posted at 13:20:38 on February 14, 2016 · (Permalink)
Yeah, I didn't think I was bang on the money. It was more to demonstrate that you don't need all that much at all, as you said
Gh3rkinman · 2 points · Posted at 08:41:45 on February 14, 2016 · (Permalink)
this is my favorite fact here. It was so interesting I googled the exact number of digits you'd need. It's 39.
tombue · 2 points · Posted at 09:05:16 on February 14, 2016 · (Permalink)
39 digits.
SnicketKnight · 2 points · Posted at 15:00:52 on February 14, 2016 · (Permalink)
Michael here...
VoilaVoilaWashington · 2 points · Posted at 18:11:33 on February 14, 2016 · (Permalink)
24 is enough to shoot a bullet at a dime at the edge of the observable universe.
bevelled_margin · 1 points · Posted at 22:22:06 on February 13, 2016 · (Permalink)
Sir, I bear a rhyme excelling
In mystic force and magic spelling
Celestial sprites elucidate
All my own striving can't relate.
nottherealslash · 1 points · Posted at 22:23:54 on February 13, 2016 · (Permalink)
Beautiful
Antithesys · 1 points · Posted at 02:01:11 on February 14, 2016 · (Permalink)
I'd say it's easier to memorize the damn numbers.
TheRealZoidberg · 1 points · Posted at 02:11:13 on February 14, 2016 · (Permalink)
I thought it was 38... But anyways, how am I supposed to then calculate the circumference of the universe? I mean, I know pi up to about 40 digits (3.141592653589793238462643383279502884197169), but I don't know the observable universe's radius. I guess you could derive it from the speed of light (299792.458 km/s) and the universe's age, but then again, we don't really know what that is. It's about 13.72 billion years, with an uncertainty of, like, a few hundred million years, so that's quite a big thing to say that one could calculate the circumference of the earth with a deviation of a few femtometers, when one of the factors is still only so vaguely known...
nottherealslash · 1 points · Posted at 13:22:16 on February 14, 2016 · (Permalink)
You'd need a better person than me to show you how to do it, my studies aren't focussed on astrophysics
pureboy · 1 points · Posted at 10:04:48 on February 14, 2016 · (Permalink)
Can you show me how to calculate?
nottherealslash · 1 points · Posted at 13:19:37 on February 14, 2016 · (Permalink)
I, unfortunately, cannot. At least not without going away and doing some research on how to. My studies aren't focussed on astrophysics
Kevz417 · 3 points · Posted at 22:07:37 on February 13, 2016 · (Permalink)
Should be 3.1415926536 because an 8 follows.
CookieTheSlayer · 2 points · Posted at 22:46:50 on February 13, 2016 · (Permalink)
Eh, close 'nuff
KCB24 · 2 points · Posted at 09:34:07 on February 14, 2016 · (Permalink)
http://imgur.com/gallery/Dpio4lu
New_World_Era · 1 points · Posted at 21:59:15 on February 13, 2016 · (Permalink)
I know, I just like learning different estimates
babytimekade1 · 1 points · Posted at 01:07:43 on February 14, 2016 · (Permalink)
they made us memorize pi to 50 decimal places in junior high. I can still get to like 45.
CookieTheSlayer · 1 points · Posted at 01:26:10 on February 14, 2016 · (Permalink)
Some of my friends know it to like 300 places. Its scary :(
glorioussideboob · 1 points · Posted at 15:14:28 on February 14, 2016 · (Permalink)
I know 150 and I can't even remember a phone number, it's weird. Suprisingly easy if you try.
Delicious_Nipples · 1 points · Posted at 01:52:53 on February 14, 2016 · (Permalink)
I believe i have, 3.14159265358979626 i may be wrong with some of the later numbers.
Kevinvac · 1 points · Posted at 02:24:01 on February 14, 2016 · (Permalink)
I'm at 3.1415926535897932384626, one day I'll add more. I just slowly tack on more throughout the years
MattieShoes · 1 points · Posted at 02:25:23 on February 14, 2016 · (Permalink)
Or just learn an infinite series...
4/1 - 4/3 + 4/5 - 4/7 + 4/9 ... converges on pi, though it's slow. :-)
phx-au · 1 points · Posted at 03:20:26 on February 14, 2016 · (Permalink)
Engineer here. I just use 3, because it's within 5%.
HakushiBestShaman · 1 points · Posted at 03:27:09 on February 14, 2016 · (Permalink)
I always remember 38.
I was aiming for 100 and got bored.
3.14159265358979323846264338327950288419
zeetotheex · 1 points · Posted at 03:41:53 on February 14, 2016 · (Permalink)
It's easy to remember the first couple thanks to 3rd Rock From The Sun. John Lithgow did a football cheer: sine sine cosine sine 3 point 14159!
cool299 · 1 points · Posted at 03:50:53 on February 14, 2016 · (Permalink)
Actually, you should round that last digit to a 6 since it goes 3.141592653589...etc.
ForgotDeoderant · 1 points · Posted at 04:05:14 on February 14, 2016 · (Permalink)
When I was in middle school, I was in a contest with the rest of my class to memorize pi. The kid who memorized the most got to like 270 digits or something. I was second at 84.
And I thought I had too much time on my hands! pfft
Trezzie · 1 points · Posted at 05:10:42 on February 14, 2016 · (Permalink)
3.141592653589793238462....
WASPandNOTsorry · 1 points · Posted at 05:12:25 on February 14, 2016 · (Permalink)
It's pointless.
CookieTheSlayer · 1 points · Posted at 05:13:53 on February 14, 2016 · (Permalink)
Well yeah, most circles are
bookworm2692 · 1 points · Posted at 06:26:49 on February 14, 2016 · (Permalink)
Those are the exact digits I memorised!
purple_paper · 1 points · Posted at 06:46:56 on February 14, 2016 · (Permalink)
3.1415926536 (if you're gonna just quit there and you round properly)
Spraginator89 · 1 points · Posted at 07:05:40 on February 14, 2016 · (Permalink)
If you're going to end it there..... it should be 3.1415926536
Fancy_Pantsu · 1 points · Posted at 08:05:30 on February 14, 2016 · (Permalink)
I know up to 3.1415926535897932384626 only because we had an extra credit question on a math test once that we got to know about ahead of time. If we could memorize pi to at least 20 decimal places we got an extra 5 points. I memorized one extra number just because it was easier for me to remember 626 than 62.
KryptoniteDong · 1 points · Posted at 08:30:11 on February 14, 2016 · (Permalink)
This could be someone's phone number in Cali .. how cool would that be!
Eloquent44 · 1 points · Posted at 08:55:32 on February 14, 2016 · (Permalink)
3.14159265358979
[deleted] · 1 points · Posted at 11:16:14 on February 14, 2016 · (Permalink)
http://youtu.be/5NgjkwQ-7lY
[deleted] · 1 points · Posted at 13:10:07 on February 14, 2016 · (Permalink)
Better round that up correctly to 3.1415926536 now!
HungryChemist · 1 points · Posted at 13:46:20 on February 15, 2016 · (Permalink)
One better than a standard calculator display. I got to 3.1415926535897932384. My brain then tells me it's '6264' but I don't trust it.
1100101000 · 1 points · Posted at 01:36:01 on February 14, 2016 · (Permalink)
Rational approximations to Pi are pointless, just learn the digits, you have to remember the same amount either way.
New_World_Era · 1 points · Posted at 01:55:11 on February 14, 2016 · (Permalink)
I know, I just like learning some of the approximations.
Matmobile · 1 points · Posted at 05:16:51 on February 14, 2016 · (Permalink)
New_World_Era will remember that.
jumpedupjesusmose · 1 points · Posted at 05:17:13 on February 14, 2016 · (Permalink)*
11 3\3 55
websnarf · 2 points · Posted at 04:40:41 on February 15, 2016 · (Permalink)
(2143/22)1/4 is even closer.
GLOOTS_OF_PEACE · 1 points · Posted at 14:59:57 on February 14, 2016 · (Permalink)
355/113 is only accurate to this many digits: 3.14159, which is exactly the same number of characters as 355/113. Might as well just remember 3.14159
[deleted] · 1 points · Posted at 00:33:14 on February 23, 2016 · (Permalink)
Simplify that and it equals 22/7
MrFurrypants · 1 points · Posted at 00:50:26 on February 23, 2016 · (Permalink)
It doesn't simplify cleanly. A couple of thousandths remain.
BeaverCleaver69 · 6 points · Posted at 01:20:17 on February 14, 2016 · (Permalink)
According to what I learned from this thread, 22/7 is 3 and 1/7, meaning it is 3.142857
3.142857 - 3.14159 < 3.14159 - 3.14
This checks out
JamesIgnatius27 · 2 points · Posted at 01:21:04 on February 14, 2016 · (Permalink)
:D
Govanator · 5 points · Posted at 01:21:05 on February 14, 2016 · (Permalink)
As a physicist, I just assume that pi≈3
thestickystickman · 15 points · Posted at 20:04:57 on February 13, 2016 · (Permalink)
Yes, so is any number within +/- 0.00159 (3 s.f.) of pi.
TheSnoz · 3 points · Posted at 00:16:10 on February 14, 2016 · (Permalink)
'Pi is exactly 3!'
Andrei_Vlasov · 2 points · Posted at 02:53:57 on February 14, 2016 · (Permalink)
Wtf pi is 6?
[deleted] · 1 points · Posted at 14:03:48 on February 17, 2016 · (Permalink)
Close enough in physics.
dj0 · 3 points · Posted at 02:10:32 on February 14, 2016 · (Permalink)
Cubed root of 31 is even closer
GunPoison · 3 points · Posted at 09:21:25 on February 14, 2016 · (Permalink)
I have a horrible story about 22/7.
At a company bonding day we were doing trivia. One of the questions is what the first 5 decimal places of Pi are. Maths nerd here, I was born knowing that. Immediately I start writing the answer for our team.
EXCEPT the big fat bald CEO who happens to be on my team stops me, and condescendingly corrects me that no actually Pi is 22/7. And he happens to have his cutting-edge Nokia brick phone (this was a while ago) that had a calculator function.
I try to explain that 22/7 is just an approximation you give to school children but he smugly divides 22 by 7 (beep beep bup boop) and writes down his answer while a circle of sycophants at the table nod and compliment him. I try not to vomit with rage. It is still one of the most horrible moments of my life.
rumborak · 2 points · Posted at 04:28:25 on February 14, 2016 · (Permalink)
Sadly, I once wasted half an hour on a coworker who was convinced that 22/7 is Pi.
naughty_ottsel · 2 points · Posted at 16:29:41 on February 14, 2016 · (Permalink)
This is why I class 22nd July as British Pi Day.
JV19 · 1 points · Posted at 06:10:05 on February 14, 2016 · (Permalink)
Is that really a cool fact though? I don't think anyone goes around thinking that 3.14 is some exact value or anything.
bunker_man · 1 points · Posted at 06:52:52 on February 14, 2016 · (Permalink)
...That's not that cool. It stands to reason that some fractions involving small numbers are more accurate than two decimal places to a thing.
Guitarswithlegs · 1 points · Posted at 09:20:39 on February 14, 2016 · (Permalink)
In the 1800's, congress unanimously passed a bill that set pi at a value of approximately 9.
TeaTimeWithKarl · 1 points · Posted at 10:09:25 on February 14, 2016 · (Permalink)
I don't know why this is blowing my mind so much
[deleted] · 1 points · Posted at 11:13:16 on February 14, 2016 · (Permalink)
That's why 22nd July should be pi day!
someonethatiusedtobe · 1 points · Posted at 14:01:36 on February 14, 2016 · (Permalink)
How come?
syntax1993 · 1 points · Posted at 20:02:31 on February 18, 2016 · (Permalink)
As Immortal Technique once said in one of his songs: 'Using numerology, to count the people I sent to Heaven Produces more digits than 22 divided by 7'
I thought it was kind of clever.
Anyways, we used 22/7 back in school instead of Pi.
dank_memeologist_420 · -5 points · Posted at 21:32:21 on February 13, 2016 · (Permalink)
and my link karma is even closer
Hitlerdinger · 9 points · Posted at 23:25:21 on February 13, 2016 · (Permalink)
314 is way off
IkonikK · 0 points · Posted at 04:49:53 on February 14, 2016 · (Permalink)
What about 5/7?
[deleted] · 0 points · Posted at 16:21:27 on February 15, 2016 · (Permalink)
That's because that is the value of pi... The number of radians in a circle is 3 and one seventh or 22/7
[deleted] · -2 points · Posted at 07:56:03 on February 14, 2016 · (Permalink)
I think you mean that 22/7 is the actual value of pi, whereas 3.14 is an approximation.
[deleted] · 2 points · Posted at 14:01:51 on February 14, 2016 · (Permalink)
I hope you're trolling
[deleted] · 1 points · Posted at 23:05:26 on February 14, 2016 · (Permalink)
My bad. Let's just say I was trolling.
OZONE_TempuS · 1849 points · Posted at 19:19:42 on February 13, 2016 · (Permalink)*
epi*i + 1 = 0, it relates some of the most important mathematical constants into one equation.
edit: Since there seems to be a lot of confusion or wonder as to why this is so neat, read the explanation of its mathematical beauty.
DuckBillHatypus · 758 points · Posted at 20:09:48 on February 13, 2016 · (Permalink)
Gotta love Euler. Apparently there was a spate of cars being destroyed and fire-bombed in the early 2000s by a bunch of eco-terrorists, who spraypainted stuff like "Gas-Guzzler" on them, you know usual eco-terrorist stuff.
However, completely out of place, one the the patches of graffiti contained Euler's Identity (epi*i + 1 = 0), which the police where able to use to trace back to a student at a local university; when they questioned him, apparently he said that he considered the identity so important that he had to let people know about it, and considered the attention his attacks were getting the perfect opportunity
PropaneLover · 666 points · Posted at 23:35:18 on February 13, 2016 · (Permalink)
Another fun fact: Euler was so remarkably prodigious that they decided to stop calling theorems and equations after him due to the vast number already in existence; the theorems are now named after the second person to discover them after him
vambot5 · 23 points · Posted at 04:39:04 on February 14, 2016 · (Permalink)
If I recall correctly from undergrad, many of Euler's theorems had very vague proofs. He would posit the result, do a few calculations, and wave his hands, basically leaving the rest as an exercise for the student. He was, to my knowledge, always right, but he did not lay out full and complete proofs for all of his findings. Learning this, one of my classmates lamented "So you're saying that Euler was just a hand-waving hack?!" in class.
canarycream · 19 points · Posted at 07:26:49 on February 14, 2016 · (Permalink)
Alright, Euler was a time traveler who went back to claim credit for discovering a shit ton of theories of mathematics to spite his rival in his own time. Calling it now.
Thinks_Too_Logically · 12 points · Posted at 09:26:15 on February 14, 2016 · (Permalink)
He went blind and could recite the Aeneid verse by verse from memory. The dude was incredible and what he saw as obvious isn't nearly the same to us.
hercaptamerica · 6 points · Posted at 21:50:34 on February 14, 2016 · (Permalink)
I believe I read that he approximated e-pi/2 to the 150th digit in his head when solving for ii
Tyg13 · 17 points · Posted at 05:30:09 on February 14, 2016 · (Permalink)
I think he saw the mathematics working at levels he couldn't fully explain, but at the same time knew to be true. It took people later to come along and lay down the in-betweens of why his arguments work.
Phapples · 18 points · Posted at 12:17:15 on February 14, 2016 · (Permalink)
That's how it works with most people though, everyone who has studied mathematics has had a situation where they know something is true but they have no idea how to prove it - you can feel in your gut this incredible certainty that it's true but you can't articulate why.
limited-papertrail · 1 points · Posted at 08:53:20 on February 18, 2016 · (Permalink)
I think this happens to everyone deep into their field. Genetics, Evo, even Psych.
Crazy_Asian_Man · 3 points · Posted at 13:51:39 on February 14, 2016 · (Permalink)
So what you're saying is that Euler is every undergrad math lecturer who didn't want to finish solving the example problems.
[deleted] · 115 points · Posted at 00:39:52 on February 14, 2016 · (Permalink)
"I asked you to prove Euler's theorem XLI, that was VLI"
UserAndAJunkie · 138 points · Posted at 02:23:47 on February 14, 2016 · (Permalink)
You must be one of those people whom they called it Super Bowl 50 for.
toodrunktofuck · 25 points · Posted at 03:24:20 on February 14, 2016 · (Permalink)
IIIIIIIIII = 10
doihavemakeanewword · 7 points · Posted at 03:41:22 on February 14, 2016 · (Permalink)
Even though this is the only time for another 50 years where they could only use one digit.
PM_girl_peeing_pics · 2 points · Posted at 04:02:33 on February 14, 2016 · (Permalink)
That one digit is probably one they don't want to use though. "L"? In sports L means loss...
Aristo-Cat · 1 points · Posted at 04:51:23 on February 14, 2016 · (Permalink)
Superbowl take this L
RocketPapaya413 · 1 points · Posted at 17:16:42 on February 14, 2016 · (Permalink)
For whom* as long as we're being picky
UserAndAJunkie · 2 points · Posted at 18:18:54 on February 14, 2016 · (Permalink)
Yup, saw it after I hit send; I thought I'd leave it for someone to call me out on.
CHUCK_NORRIS_AMA · 9 points · Posted at 03:28:10 on February 14, 2016 · (Permalink)
FTFY
myusernameranoutofsp · 9 points · Posted at 04:16:16 on February 14, 2016 · (Permalink)
I had a math professor that joked that Euler was so influential that Edmonton named their hockey team after him.
_Z_A_C_ · 6 points · Posted at 01:56:54 on February 14, 2016 · (Permalink)
This is one of the more interesting things I've read here. Pretty amazing guy. I didn't know.
hchan1 · 4 points · Posted at 02:24:31 on February 14, 2016 · (Permalink)
Man, I bet I could get some of those named after me. Just need to dig through his old notes; gotta be some that haven't been claimed yet, right?
zedderled · 4 points · Posted at 03:27:19 on February 14, 2016 · (Permalink)
Got any examples?
PropaneLover · 12 points · Posted at 05:04:46 on February 14, 2016 · (Permalink)
Sorry, I don't but:
https://en.wikipedia.org/wiki/List_of_things_named_after_Leonhard_Euler
skyman724 · 8 points · Posted at 09:48:05 on February 14, 2016 · (Permalink)
More like Euler: Fokken Genius!
chevymonza · 2 points · Posted at 14:44:46 on February 14, 2016 · (Permalink)
But the link says that other people came before him that probably paved the way......you'd think they'd name it after them.
OZONE_TempuS · 1 points · Posted at 02:35:46 on February 14, 2016 · (Permalink)
One of my math professors named his cat after Euler...
Ponderay · 1 points · Posted at 05:12:27 on February 14, 2016 · (Permalink)
For the record this a joke not something which actually happens.
DownGoesGoodman · 1 points · Posted at 05:44:33 on February 14, 2016 · (Permalink)
Similar thing happened with Isaac Newton in physics.
jax_the_champ · 1 points · Posted at 05:51:52 on February 14, 2016 · (Permalink)
If he discovered it should be easy to rediscover right?
[deleted] · 1 points · Posted at 19:47:22 on February 20, 2016 · (Permalink)
remember a guy in r/math laughing at the fact that "euler theorem" was on a list of things you had to know for a test. Like, which one ?
abecedarius · 24 points · Posted at 21:54:13 on February 13, 2016 · (Permalink)
Was he going to Caltech? Years ago I read about a case just like that, except for no mention of Euler's identity. Maybe it was in some part of the story I skipped over.
FILE_ID_DIZ · 5 points · Posted at 03:17:22 on February 14, 2016 · (Permalink)*
Yes, that's the guy:
http://articles.latimes.com/2004/nov/20/local/me-guzzler20
https://en.wikipedia.org/wiki/William_Cottrell
edit; found the indictment:
http://brianoconnor.typepad.com/animal_crackers/files/CottrellIndictment.pdf
https://www.google.com/maps?q=1125+Central+Avenue,+Duarte
StrangeRover · 6 points · Posted at 03:12:34 on February 14, 2016 · (Permalink)
I'm trying to figure out how you could take any mention of Euler's identity out of that story and still have it be the same story.
abecedarius · 1 points · Posted at 06:31:18 on February 14, 2016 · (Permalink)
I know! Maybe they hid it in the third page?
CaptainCheif · 6 points · Posted at 01:49:00 on February 14, 2016 · (Permalink)
Gotta love Euler
Mutha fucka wrote beautiful formulas why wouldn't you love him.
meodd8 · 6 points · Posted at 03:56:57 on February 14, 2016 · (Permalink)
Euler is the reason I drink
spinozasrobot · 5 points · Posted at 02:10:51 on February 14, 2016 · (Permalink)
True fact: his name is pronounced "oy-ler"
FILE_ID_DIZ · 3 points · Posted at 03:31:40 on February 14, 2016 · (Permalink)
Learning this gave me a feeling of oy-phoria!
Juicysteak117 · 4 points · Posted at 05:28:12 on February 14, 2016 · (Permalink)
How the hell did they trace that to the student?
DraconisRex · 4 points · Posted at 10:48:59 on February 14, 2016 · (Permalink)
I find in ironic that he was protesting poor fuel economy while immortalizing a dude's name that's pronounced "Oiler"...
jeaguilar · 3 points · Posted at 03:45:29 on February 14, 2016 · (Permalink)
Can you answer a related question? Is Euler pronounced Youler or Oiler?
boathouse2112 · 5 points · Posted at 04:47:54 on February 14, 2016 · (Permalink)
Oiler
DuckBillHatypus · 1 points · Posted at 22:25:30 on February 14, 2016 · (Permalink)
It should be Oiler, but I say it Youler
diabolical-sun · 3 points · Posted at 05:58:48 on February 14, 2016 · (Permalink)
I would love to take a "History of Math" class. Things like logarithms, natural logs, and e are just buttons on a calculator for me (and so many other people). But I feel like delving into the where, how, why of their creations would really help put there practical uses in perspective.
Super_Link · 2 points · Posted at 02:45:49 on February 14, 2016 · (Permalink)
Wow that kid sounds like a pompous douche bag
2_old_2B_clever · 2 points · Posted at 03:32:27 on February 14, 2016 · (Permalink)
It worked, that's the only reason I know that equation.
[deleted] · 2 points · Posted at 13:04:28 on February 14, 2016 · (Permalink)
According to this Euler was one sharp dude! (The video is really worth a watch, even if you aren't very interested in math.)
Ripred019 · 2 points · Posted at 13:46:53 on February 14, 2016 · (Permalink)
How the hell did police accomplish this? Is this town so small that there was only a handful of people that could know Euler's identity? Was there only one student at the local college that was passing his math classes?
eulerup · 2 points · Posted at 14:40:00 on February 14, 2016 · (Permalink)
Wooo, a group of people who fully appreciate my username.
chevymonza · 2 points · Posted at 14:43:53 on February 14, 2016 · (Permalink)
This tidbit is what compelled me to click on the link above it.
What is it used for, though? It's considered beautiful simply due to all the constants being packed into one equation?
xERR404x · 59 points · Posted at 00:27:54 on February 14, 2016 · (Permalink)
Interestingly enough, all this is really saying is that cos(pi)=-1 and sin(pi)=0. Euler's formula states that ei*x=cos(x)+isin(x), and Euler's identity is just that formula solved for 0 in terms of pi. Still cool, though.
su5 · 6 points · Posted at 04:16:45 on February 14, 2016 · (Permalink)
And shows that sin and cosine and eix and e-ix aren't linearly indepe
arbyq5000 · 17 points · Posted at 07:29:18 on February 14, 2016 · (Permalink)
RIP /u/su5
InfieldTriple · 2 points · Posted at 03:19:19 on February 14, 2016 · (Permalink)
Seeing why the formula is true is much more interesting imo
thehellbean · 3 points · Posted at 03:27:30 on February 14, 2016 · (Permalink)
In the "exponential imaginary growth is rotation" way, or the "Taylor series matches up on both sides" way?
popejubal · 1 points · Posted at 03:35:23 on February 14, 2016 · (Permalink)
Both. And also the fact that you can stuff addition, multiplication and exponents (i.e. everything that you cover in elementary and middle school) into one equation that only uses the four basic "unit" values for each operation. That is pretty sexy.
InfieldTriple · 1 points · Posted at 19:10:59 on February 14, 2016 · (Permalink)
No the solution to a differential equation way. It's a DE that should only have a unique solution but ei*x and cos(X)+isin(X) both satisfy the equation.
jofwu · 6 points · Posted at 01:58:01 on February 14, 2016 · (Permalink)
Yeah... People always throw this one out, but when I realized why it's true I stopped being impressed. Euler's identity is a cool equation. But that's all that's going on here. It's not as magical as it looks. The e and i pretty much just drop out of the equation.
[deleted] · 14 points · Posted at 04:17:07 on February 14, 2016 · (Permalink)
It's not amazing because it's supposedly some big coincidence, it's amazing because it shows that all these numbers are connected, and no matter the number system you use they can be connected in a similar way. You have 5 of the most important numbers in any system. The natural exponent, pi, the imaginary identity, the additive identity, and the multiplicative identify. The connection of them all suggests just how integral they are to mathematics.
articfire77 · 20 points · Posted at 04:03:04 on February 14, 2016 · (Permalink)
What makes it so beautiful is that you're taking an irrational number and raising it to another irrational multiplied with an imaginary number and it equals a rational number.
That's crazy.
Just because Euler's formula describes this relation doesn't make the fact that the equation is true any less amazing. At least in my opinion.
whacko_jacko · 3 points · Posted at 06:20:53 on February 14, 2016 · (Permalink)
The short-version takeaway from Euler's formula is that complex arithmetic has a whole hell of a lot to do with circles. In that context, the appearance of pi is not surprising. It's the geometry and calculus of complex numbers which give beauty to the formulas.
The appearance of e may seem surprising, but its importance can be realized without mention of complex analysis.
jofwu · 1 points · Posted at 12:43:40 on February 14, 2016 · (Permalink)
That's a good point!
CruddyQuestions · 3 points · Posted at 04:38:25 on February 14, 2016 · (Permalink)
Everybody else brings up some points, but I'd like to tell you that the equation is used extensively to figure out the energy levels of particles "in a box"; a widely taught subject in most physical chemistry classes. This equation in particular helps understand electrons transition from one energy level to the next and how to calculate them.
jofwu · 2 points · Posted at 12:42:56 on February 14, 2016 · (Permalink)
Like I said, the equation is really cool. But the e/pi/i trick just isn't as magical as it appears, to me.
Help_Me_Im_Diene · 2 points · Posted at 07:11:24 on February 14, 2016 · (Permalink)
My favorite application of this is that you can use this to show that ii is a real number equal to e-pi/2
MathPolice · 1 points · Posted at 16:32:49 on February 14, 2016 · (Permalink)
Well, technically ii has infinitely many possible values. But the interesting thing is that all of them are real numbers.
(Because the complex logarithm is multi-valued. Your answer just chose one branch.)
DonGateley · 1 points · Posted at 07:12:38 on February 14, 2016 · (Permalink)
Define sin and cos algebraically (without geometry) and without using e.
Nine_Gates · 12 points · Posted at 01:46:39 on February 14, 2016 · (Permalink)
I like the general one more. eix = cosx + isinx. It beautifully links complex numbers and trigonometry together.
Timothy_Claypole · 16 points · Posted at 23:44:10 on February 13, 2016 · (Permalink)
This is my favourite. It involves taking a real transcendental number, raising it to the power of a complex trascendental number and getting an integer.
NewbornMuse · 7 points · Posted at 00:55:19 on February 14, 2016 · (Permalink)
And your weird transcendental numbers showed up in completely different contexts "before" (in your mathematical career). Deal with geometry and circles and all that? Use pi. Derivatives, differential equations, and so on? e is what you want. Nowhere do you use both, until you get to complex math/analysis and you pretty much have to use them both.
[deleted] · 4 points · Posted at 02:11:09 on February 14, 2016 · (Permalink)
That's not entirely true. e and pi can show up at the same time if you're working with trigonometric differentials.
NewbornMuse · 1 points · Posted at 02:15:22 on February 14, 2016 · (Permalink)
Example?
[deleted] · 1 points · Posted at 03:55:11 on February 14, 2016 · (Permalink)
esin(x+pi/2)
NewbornMuse · 1 points · Posted at 04:03:19 on February 14, 2016 · (Permalink)
Yeah, you just made a function that uses both. Do they ever natively (whatever that means) occur together in real (as in non-complex) problems?
meodd8 · 1 points · Posted at 04:00:07 on February 14, 2016 · (Permalink)
Laplace and Fourier transforms would like a word with you.
NewbornMuse · 1 points · Posted at 04:01:59 on February 14, 2016 · (Permalink)
Especially Laplace sensibly gets introduced after complex numbers (the Laplace transform is a complex-valued function, after all), and even Fourier makes a lot more sense in the complex world.
meodd8 · 1 points · Posted at 15:06:55 on February 14, 2016 · (Permalink)
Ah, didn't see your last sentence. My bad.
SelfAwardingTrophy · 1 points · Posted at 02:15:58 on February 14, 2016 · (Permalink)
it can also be used to show that ii is real.
PlasmicDynamite · 27 points · Posted at 19:39:36 on February 13, 2016 · (Permalink)
I didn't realize how important 1 was.
Felix_Tholomyes · 118 points · Posted at 20:21:09 on February 13, 2016 · (Permalink)
1 is the multiplicative identity, 0 is the additive identity
hobbescalvin · 1 points · Posted at 02:07:38 on February 14, 2016 · (Permalink)
What are those?
DemiPixel · 8 points · Posted at 02:22:14 on February 14, 2016 · (Permalink)
X*1 = X
42*1 = 42
X+0 = X
23+0 = 23
Felix_Tholomyes · 3 points · Posted at 02:42:26 on February 14, 2016 · (Permalink)
1 is the multiplicative identity meaning if you multiply some number x by 1 you get the same number x
0 is the additive identity meaning if you add 0 to some number x you get the same number x
aMAYESingNATHAN · 2 points · Posted at 02:42:40 on February 14, 2016 · (Permalink)
An identity operation is one where when you perform it, the result is the same thing you performed the operation on, i.e. multiplying a number by 1 does nothing, and adding 0 does nothing.
This seems pretty unimportant, but it's very useful when manipulating equations, because if you multiply something by (x+1)/(x+1), it might help solve your problem, and you're not changing the equation because it's just multiplying by 1. The same is true for 0, because you can add (x+1)-(x+1) to something and all you're doing is adding 0.
PoisonousPlatypus · 27 points · Posted at 22:14:26 on February 13, 2016 · (Permalink)
It's called wau for a reason.
koproller · -16 points · Posted at 19:57:47 on February 13, 2016 · (Permalink)
Without 1, no 2.
It's the basis of all math. That's why they (unsuccessfully) tried to prove 1+1=2 for so long.
shayler4 · 7 points · Posted at 20:13:04 on February 13, 2016 · (Permalink)
Are you serious?
No one can show 1+1=2?
KingCaspianX · 5 points · Posted at 20:23:53 on February 13, 2016 · (Permalink)
Someone did, but the proof is terribly complex.
It goes for 160 pages
OZONE_TempuS · 10 points · Posted at 20:32:04 on February 13, 2016 · (Permalink)
That's kind of misleading because what they did in their proof rigorously goes over axiomatic foundations for mathematics, this proof is a better job of showing the complexity of the problem without being too out there.
1100101000 · 2 points · Posted at 01:38:28 on February 14, 2016 · (Permalink)
You can easily prove 1+1=2. Deriving arithmetic over the natural numbers using Lambda Calculus or a similar logic isn't remotely difficult for a mathematician.
patiofurnature · 1 points · Posted at 20:24:34 on February 13, 2016 · (Permalink)
No, it still hasn't been solved...
...by anyone wearing mittens.
ConnerennoC · 0 points · Posted at 20:42:06 on February 13, 2016 · (Permalink)
What is the argument that people make for 1 + 1 cannot = 2
[deleted] · 5 points · Posted at 21:54:22 on February 13, 2016 · (Permalink)
[deleted]
Il_Gigante_Buono · 3 points · Posted at 23:11:54 on February 13, 2016 · (Permalink)
Not true at all. This is a misunderstanding of Godel and principia Mathematica.
1100101000 · 1 points · Posted at 01:40:33 on February 14, 2016 · (Permalink)
No it isn't. Under Russell and Whitehead's chosen axioms it took them 160 pages before they had built up enough framework to decide to include the proof of 1+1=2. That is a specific case and they did not set out to prove that specifically, near any mathematician can derive Peano addition on the naturals in a few pages.
[deleted] · 16 points · Posted at 21:14:27 on February 13, 2016 · (Permalink)
Owarimonogatari anyone?
Urgullibl · 3 points · Posted at 22:24:55 on February 13, 2016 · (Permalink)
Lisez Euler, lisez Euler, c'est notre maître à tous !
iluvkfc · 3 points · Posted at 00:27:48 on February 14, 2016 · (Permalink)
Another one I like related to Euler's identity: ii = e-π/2
overconvergent · 3 points · Posted at 02:59:16 on February 14, 2016 · (Permalink)
iI has infinitely many values, only one of which is e-π/2.
iluvkfc · 1 points · Posted at 07:01:41 on February 14, 2016 · (Permalink)
True. I wanted to put emphasis on the fact that imaginaryimaginary = real, found it interesting the first time I encountered it.
1100101000 · 3 points · Posted at 01:42:41 on February 14, 2016 · (Permalink)
ALL of them? Really? Arguably the most important, but still.
[deleted] · 6 points · Posted at 22:36:59 on February 13, 2016 · (Permalink)
Yup. I asked my math teacher what his favorite math equation was and he said this.
Coequalizer · 2 points · Posted at 03:25:47 on February 14, 2016 · (Permalink)
There's way more important mathematical constants than you realize.
apple-sauce · 3 points · Posted at 21:33:38 on February 13, 2016 · (Permalink)
What is i
OZONE_TempuS · 12 points · Posted at 21:35:23 on February 13, 2016 · (Permalink)
Square root of -1.
Felix_Tholomyes · 9 points · Posted at 21:49:19 on February 13, 2016 · (Permalink)
Technically it's defined by i2 = -1
boathouse2112 · 2 points · Posted at 04:51:28 on February 14, 2016 · (Permalink)
Is there a difference?
Dodobirdlord · 4 points · Posted at 05:44:12 on February 14, 2016 · (Permalink)
Yes. -1 has two square roots, i and -i.
boathouse2112 · 2 points · Posted at 05:52:46 on February 14, 2016 · (Permalink)
Isn't (-i)2 equal to -1, too?
Dodobirdlord · 3 points · Posted at 05:56:22 on February 14, 2016 · (Permalink)
Yes, that's true. That's what it means for -i to be a square root of -1.
boathouse2112 · 2 points · Posted at 07:12:06 on February 14, 2016 · (Permalink)
so, if i is defined as x2 = -1, and i squared and -i squared both equal -1, and sqrt(-1) is equal to i and -i, what's the difference between the two definitions?
Dude13371337 · 2 points · Posted at 11:17:05 on February 14, 2016 · (Permalink)
With i2 = -1, you get 2 choices of i, each opposite to the other. You can choose either one, they correspond to a counterclockwise turn or a clockwise turn.
boathouse2112 · 2 points · Posted at 18:12:37 on February 14, 2016 · (Permalink)
And with sqrt -1 you get both?
Dude13371337 · 3 points · Posted at 01:49:53 on February 15, 2016 · (Permalink)
Using radical notation for numbers besides those in ℝ+ is problematic, since a radical implies principle root and there is no such consistent thing outside ℝ+. You could use sqrt if you're sure to define it explicitly as both of the roots, tho doing that creates ambiguity (you now have extra solutions with a "+/-"). So the standard way of doing things is to just use i as defined by one of the roots of -1 and then specifying a radical as i*sqrt(b) rather than sqrt(-b).
apple-sauce · 2 points · Posted at 21:38:39 on February 13, 2016 · (Permalink)
Ah I see, thanks :)
RadiantSun · 4 points · Posted at 21:38:56 on February 13, 2016 · (Permalink)
Baby don't hurt me
NewbornMuse · 2 points · Posted at 00:58:48 on February 14, 2016 · (Permalink)
You can define a new "thing" called the imaginary unit, i, and i2 = -1. If you let your numbers have both real and imaginary components (4 + 3i would be such a number), and you define plus and minus and times and division sensibly, it turns out that the system doesn't break: You can still add and multiply and divide, and all the more advanced operations also transfer: You can square numbers, you can take their sine and cosine, and so on. There are even a few things that work better than before.
apple-sauce · 1 points · Posted at 21:19:25 on February 14, 2016 · (Permalink)
thanks!
LittleDinghy · 1 points · Posted at 00:49:02 on February 14, 2016 · (Permalink)
As an electrical engineering student, I really like Euler's identity. It's very helpful for describing signals. If you have mastered Euler's identity and a Fourier transform, dealing with electrical signals becomes much easier.
ToxDoc · 1 points · Posted at 01:31:25 on February 14, 2016 · (Permalink)
For my college departmental graduation (which included math, chemistry and physics), one of the math professors, who was tasked with "the speech" talked about the beauty of this equation for over 30 minutes before one of the chemistry professors stopped him. It was a memorable experience.
gnash117 · 1 points · Posted at 01:32:30 on February 14, 2016 · (Permalink)
I was going to post the same thing. This fact still fascinates me. I found out about it years ago. Even picked up the book Euler's magic formula to learn more. Sadly I just don't have time to read the book.
aahdin · 1 points · Posted at 01:49:20 on February 14, 2016 · (Permalink)
Hey I posted the same thing a while after you. This thread got me curious and I started googling around for an intuitive explanation of what is actually going on with ei*x. I've gone over the proofs in diffeq but it still felt like black magic to me.
I found
https://www.youtube.com/watch?v=F_0yfvm0UoU
and
https://www.youtube.com/watch?v=1rVHLZm5Aho
If you've got ~12 minutes, these are some really amazing explanations.
unMasqed · 1 points · Posted at 02:02:53 on February 14, 2016 · (Permalink)
One of the most gorgeous equations there is. It's a pretty fun (and easy) proof base as well. Can show why ii is a real number with this.
blazedancer1997 · 1 points · Posted at 02:14:18 on February 14, 2016 · (Permalink)
We derived this in class last semester as the final thing for the series unit and this straight up blew my mind.
PJDubsen · 1 points · Posted at 02:14:41 on February 14, 2016 · (Permalink)
WHAT
PJDubsen · 1 points · Posted at 02:14:54 on February 14, 2016 · (Permalink)
WHAT
Lelanderthal · 1 points · Posted at 02:18:40 on February 14, 2016 · (Permalink)
I got so hype in class when I learned this. Looking around like "why don't you people think this is awesome!?"
Nettius2 · 1 points · Posted at 02:22:40 on February 14, 2016 · (Permalink)
When this was originally demonstrated, Euler assumed that certain math that he knew worked for real numbers also worked for complex numbers. (It needs the complex number versions of some Calculus I.)
He played with the Taylor series expansions of sine and cosine and this just kinda happened. So beautiful that it had to be true.
thefreeman419 · 1 points · Posted at 02:44:32 on February 14, 2016 · (Permalink)
I can't believe I had to go so far down to this. That formula is beautiful
HiddenKrypt · 1 points · Posted at 02:45:19 on February 14, 2016 · (Permalink)
Ahh, but ei*tau = 1 is even better
ar0cketman · 1 points · Posted at 02:45:37 on February 14, 2016 · (Permalink)
This really needs to be the top post.
LeTrakster · 1 points · Posted at 02:51:13 on February 14, 2016 · (Permalink)
I love this equation so much I got a tattoo of it (my one and only tattoo btw)
[deleted] · 1 points · Posted at 02:57:35 on February 14, 2016 · (Permalink)
This means that epi*1 = -1 right?
luckierbridgeandrail · 1 points · Posted at 03:29:10 on February 14, 2016 · (Permalink)
In other words, when you've gone half way around a circle, you're opposite where you started.
popejubal · 1 points · Posted at 03:31:13 on February 14, 2016 · (Permalink)
Came here to post this. I love this equation.
Yegie · 1 points · Posted at 03:31:29 on February 14, 2016 · (Permalink)
Ohhh, I had an assignment just a couple weeks ago to prove this. It really is cool.
WagwanKenobi · 1 points · Posted at 03:46:01 on February 14, 2016 · (Permalink)
Some people consider this an indication that the universe was designed, like a kind of universe easter egg left by the designers.
DisRuptive1 · 1 points · Posted at 03:53:19 on February 14, 2016 · (Permalink)
I prefer epi*i = -1 since that equation makes more sense when you graph the equation.
ClintonCanCount · 1 points · Posted at 03:53:20 on February 14, 2016 · (Permalink)
It relates 5 important mathematical constants in one equation.
There are significantly more important constants than that.
peekay427 · 1 points · Posted at 04:09:57 on February 14, 2016 · (Permalink)
This is by far my favorite math fact.
7-SE7EN-7 · 1 points · Posted at 04:27:52 on February 14, 2016 · (Permalink)
I do like this one a lot, I like that it makes no sense to me
vambot5 · 1 points · Posted at 04:34:18 on February 14, 2016 · (Permalink)
I had assumed that Euler's identity would be at the top. Maybe the topic is too arcane/intimidating for the average redditor to appreciate. A bit of trivia about rational numbers is easy to wrap your head around. An identity involving the base of the natural logarithms, complex numbers, exponential functions, and the irrational number pi is admittedly more involved. I think one could explain why it is so cool without having to explain the underlying mathematics, but it is hard to avoid the "I don't already understand this, so I will downvote" tendency.
canoe123 · 1 points · Posted at 04:38:05 on February 14, 2016 · (Permalink)
Now, move the 1:
ei*pi = -1
And take the square root of each side:
ei*pi/2 = i
Raise each side to the power of i:
ei2 pi/2 = ii
Replace i2 with -1:
ii = e-pi/2 or ~.207
philalether · 1 points · Posted at 04:54:44 on February 14, 2016 · (Permalink)
I prefer the form:
ei*tau = 1, where tau = 2*pi, or the ratio of a circle's circumference to its radius.
It's even more beautiful! Instead of describing going half-way around the unit circle in the complex plane, it describes going one complete turn around.
disignore · 1 points · Posted at 05:11:18 on February 14, 2016 · (Permalink)
Indeed a beauty. I remember learning this in high school and just like that everything made sence.
making-flippy-floppy · 1 points · Posted at 06:06:12 on February 14, 2016 · (Permalink)
I would put it stronger than that, it relates the five most important mathematical constants into an extraordinarily simple (although non-obvious) equation.
OZONE_TempuS · 1 points · Posted at 06:10:32 on February 14, 2016 · (Permalink)
I got a bunch of comments that kept telling me how I don't know how many constants there are or The most important? Really?, so I just changed it to that.
arakys · 1 points · Posted at 06:09:30 on February 14, 2016 · (Permalink)
This is the post that I was looking for, thank you!
oldmythologies · 1 points · Posted at 07:08:32 on February 14, 2016 · (Permalink)
I clicked on that link, saw the sheer number of Greek letters and then immediately closed it.
NotSelfReferential · 1 points · Posted at 07:40:13 on February 14, 2016 · (Permalink)
Yep, this is mindblowing
MusiclsMyAeroplane · 1 points · Posted at 07:46:22 on February 14, 2016 · (Permalink)
Oh my. euler's identity is integral to electrical engineering. I know that identity (and its uses) like my own dick.
You can use Euler's identity to show quite a few trigonometric identities without even looking at a triangle. I stopped trying to remember those identities when i figured out they could be quickly and easily derived from this equation. Not to mention the applicability to elecromagnetic waves and theory, and field theory in general. Who knew an exponential would make waves and shit? it's awesome
is a got dam life saver
SippantheSwede · 1 points · Posted at 08:09:12 on February 14, 2016 · (Permalink)
Was this the equation that launch'd a thousand ships,
and burnt the topless towers of Ilium?
fire1299 · 1 points · Posted at 08:13:37 on February 14, 2016 · (Permalink)
Using tau it would be etau*i =1.
atomly · 1 points · Posted at 08:42:02 on February 14, 2016 · (Permalink)
Came to post the same. This blew my young mind and forced me to learn enough math to actually understand it...
VacuouslyUntrue · 1 points · Posted at 08:58:41 on February 14, 2016 · (Permalink)*
As a BSc in mathematics, I find the frequency that this comes up annoying. That is Euler's Identity
It is a fact that ( * ) et*(pii) = cos(t(pi))+isin(t(pi)).
Set t = 1 and you get ( ** ) epi*i = cos(pi) = -1.
(*) is the more interesting and general statement, but it's also so ubiquitous and pragmatic that it is rendered boring by overexposure.
Euler's identity is just a specific case of this otherwise mundane fact about complex circles. There is much radder and novel mathematics stuff around.
CaptainRuhrpott · 1 points · Posted at 10:42:02 on February 14, 2016 · (Permalink)
This is the video where I first heard about it.
Atario · 1 points · Posted at 11:27:11 on February 14, 2016 · (Permalink)
Also the most important mathematical operations (addition, multiplication, exponentiation)
HolyGarbage · 1 points · Posted at 11:48:41 on February 14, 2016 · (Permalink)
etau*i = 1 is even more beautiful imo as it actually behaves like a identity. When taking the product of two complex numbers you multiply their absolute value and adding their angles. Adding tau wraps around making a full revolution. Hence the angle remains unchanged: An identity.
Cicote · 1 points · Posted at 12:20:37 on February 14, 2016 · (Permalink)
etau*i = 1, even smoother gotta love tau
0theus · 1 points · Posted at 12:43:28 on February 14, 2016 · (Permalink)
Was looking for this one. Thanks for posting
magdasmash · 1 points · Posted at 13:17:01 on February 14, 2016 · (Permalink)
https://xkcd.com/179/
jaredjeya · 1 points · Posted at 13:22:06 on February 14, 2016 · (Permalink)
Euler's identity has always annoyed me though.
It ought to be written eiπ = -1, in my opinion. The 0 in there is completely superfluous - it's just moving all the terms to one side.
Or write e2iπ = 1, since 2π is arguably more fundamental than π in the context of angles.
Or, just write the whole thing: eiθ = cosθ + isinθ, showing how exponential and trigonometric functions are fundamentally related - a far more important and interesting result that encapsulates Euler's identity by setting θ = π.
skesisfunk · 1 points · Posted at 13:29:51 on February 14, 2016 · (Permalink)
One of the cooler thing about this is that it can be shown in a direct manner through taylor expansions. Substitute 'ix' for 'x' in the taylor series for ex and it just falls out.
Triquetra4715 · 1 points · Posted at 21:08:39 on February 14, 2016 · (Permalink)
Is this an amazing coincidence, or is there a clearer reason?
Crixomix · 1 points · Posted at 17:05:10 on February 18, 2016 · (Permalink)
Prolly gonna get lost. But here's the BEST explanation I have ever seen (the first time I actually UNDERSTOOD why it works) https://www.youtube.com/watch?v=Yi3bT-82O5s
OZONE_TempuS · 1 points · Posted at 22:09:34 on February 18, 2016 · (Permalink)
I use Euler's identity almost every day, so I already knew it but that was a very well done explanation. Thanks for showing me that!
[deleted] · -1 points · Posted at 20:12:12 on February 13, 2016 · (Permalink)
[deleted]
DrMonkeyLove · 3 points · Posted at 20:39:05 on February 13, 2016 · (Permalink)
One reason it's important is because it's a special case of Euler's formula: ei*x = cox(x) + i*sin(x)
Which happens to be super useful.
OZONE_TempuS · 2 points · Posted at 20:29:14 on February 13, 2016 · (Permalink)
Zero is one of the constants and all of these numbers are hugely important in so many advancements. All of mathematics is based off of the concepts of 1 and 0 so those go without saying, a lot of electrical engineering deals with i, compound interest is based off of e and π has so many applications that I'm not even going to name them.
So I'm not sure what you're getting at, Euler's identity is just an equation that takes some of the most important mathematical concepts and relates them. Read the Wikipedia section on its Mathematical beauty.
[deleted] · 1 points · Posted at 20:40:50 on February 13, 2016 · (Permalink)*
[deleted]
OZONE_TempuS · 1 points · Posted at 20:45:34 on February 13, 2016 · (Permalink)
What are you talking about...
HauckPark · 1 points · Posted at 20:57:18 on February 13, 2016 · (Permalink)
Thanks for the explanation, it was really interesting. I appreciate the time you took to share!
Randomdude2846 · 3489 points · Posted at 19:10:11 on February 13, 2016 · (Permalink)
The creators of Futurama actually had to create a new mathematical formula to solve the brain swapping issue they had. It's called The Futurama Theorem
dougie0341 · 1905 points · Posted at 19:36:01 on February 13, 2016 · (Permalink)
The theorem proves that, regardless of how many mind switches between two bodies have been made, they can still all be restored to their original bodies using only two extra people, provided these two people have not had any mind switches prior (assuming two people cannot switch minds back with each other after their original switch).
ynnekf76 · 507 points · Posted at 22:10:44 on February 13, 2016 · (Permalink)
How do prove something that's never been done
the_schnudi_plan · 1091 points · Posted at 22:47:25 on February 13, 2016 · (Permalink)
In this case that it is brain switches doesn't matter. It could be a variety of tip where you can't tag someone who tagged you. Basically how many extra nodes are needed in a map with only one directional edges
dixego · 601 points · Posted at 23:53:48 on February 13, 2016 · (Permalink)
So you're saying graph theory has applications? Holy shit.
...
...
...
/s in case it wasn't obvious.
[deleted] · 43 points · Posted at 02:07:04 on February 14, 2016 · (Permalink)
As a serious reply to this, graph theory is pretty fucking awesome. It can be used for some pretty creative solutions to problems you might run into.
I suppose my most recent example of this is actually one I used for leisure in a game I've been playing lately, FFXIII-2. In this game are several puzzles, of which one type is based on a clock. There is an arbitrary number of nodes surrounding a center point in a circle (think of a clock), each one with a number associated with it and displayed inside of the node. You may choose any node as your starting point. The number for any particular node represents how many nodes away from the current node you may travel for your next selection (e.g. if you choose a node with a 2, you may choose the next node that is either 2 nodes clockwise from your current position or 2 nodes counter-clockwise). The object of the puzzle is to go from node to node until you've traveled each one. This can be represented as a directed graph, and you can make logical deductions to decide the ordering of certain nodes (e.g. if a node has an in-degree of 0, then it MUST be the starting node; if it has an out-degree of 0, then it MUST be the ending node; otherwise, if a node has an in-degree of 1, then it probably has to be preceded by the node pointing to it (though it's possible that the node under consideration is actually a starting point)). The graph can then be continually reduced to a smaller and smaller subset of nodes representing these orderings (e.g. you might start with A, B, C, D, E, F and then end up with AB, CDE, F) allowing you to reasonably decide an appropriate solution by checking the remaining possibilities. It can be a time-consuming process, sure, but when you have to choose between random selection (likely to fail, and the nodes may change) or brute-forcing your solution (much more time-consuming than the graphing method), it definitely proves to be the preferred alternative!
featherfooted · 33 points · Posted at 02:11:59 on February 14, 2016 · (Permalink)
My personal "graph theory aha" was in Dragon Age: Inquisition. There's a series of puzzles (literally dozens of them) where you have to do a traveling salesmen between a series of nodes, with pre-defined edges to use. The game is that you can only use each edge once, but you can pick which node to start with. (i.e. Konigsburg Bridges Problem, but for DA players: astrariums).
Since we can assume that there is at least one solution, then WLOG we can start at the node with the lowest (or tied-for-lowest) odd degree and solve the problem. I think the first 2 were hard until I recognized it and then the entire rest of the game I breezed through them.
[deleted] · 9 points · Posted at 02:34:17 on February 14, 2016 · (Permalink)
Ha! That's fantastic! It's always incredibly satisfying when you can see these mathematical elements and exploit them appropriately.
mxzf · 8 points · Posted at 04:02:37 on February 14, 2016 · (Permalink)
I've also used graph theory for Ticket to Ride, the board game. I input all of the nodes and links into a graph and then calculated the most efficient route to complete each ticket in the game. I was able to determine which connections I should prioritize claiming for myself due to the large number of routes which travel through that linkage in an optimal path.
Of course, the strategy on any given game is much more dependent on which tickets you actually get and which colors you draw, but knowing which links are used very frequently can be useful for overall strategy.
[deleted] · 3 points · Posted at 04:51:55 on February 14, 2016 · (Permalink)
I've never actually heard of that game and had to perform a quick search to figure out what it was so I could understand your strategy, but that's an interesting way of producing average-case decisions for the game!
mxzf · 4 points · Posted at 05:04:43 on February 14, 2016 · (Permalink)
Yep, that's basically what I was doing. It's impossible to 'solve' the game ahead of time, since you get random routes which may or may not use the most common links, but it does give you an idea of which links are more likely to be needed by other players (and therefore ones you should secure early if you need them yourself) and which ones are much less likely to be in demand. It was definitely more of a "this seems fun" thing than an actual important project, but it was still fun to do and semi useful.
[deleted] · 2 points · Posted at 05:25:59 on February 14, 2016 · (Permalink)
Oh, certainly. Most of my problem-solving exercises are done for leisure. It's just fun discovering solutions to new problems or discovering new solutions to old problems you've encountered before.
spenrose22 · 2 points · Posted at 05:01:22 on February 14, 2016 · (Permalink)
so can you post those results?
[deleted] · 6 points · Posted at 05:13:47 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 2 points · Posted at 05:17:49 on February 14, 2016 · (Permalink)
If you're serious, that sounds like a fascinating read!
[deleted] · 3 points · Posted at 05:36:01 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 05:52:32 on February 14, 2016 · (Permalink)
Oh, definitely. I'm finishing off my last year of a CS major myself, so I've learned all too well the importance of graph theory in networks. For some reason I failed to associate the concept with neural networks, however, and the thought of such an application is interesting.
I'd very much like to be kept up to date on the results, as even though many of the low-level concepts would go far over my head, the high-level details would be of great interest.
[deleted] · 2 points · Posted at 06:28:18 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 0 points · Posted at 07:50:10 on February 14, 2016 · (Permalink)
It appears that my university does indeed allow access. Thanks for the recommended reading! It's quite dense, so it's a bit much to read this late at night, but I will definitely be looking at this. Thank you (:
casino_r0yale · 2 points · Posted at 08:10:37 on February 14, 2016 · (Permalink)
This still sounds like it might be NP-hard, regardless of your small optimizations
[deleted] · 0 points · Posted at 08:47:22 on February 14, 2016 · (Permalink)
I don't believe I've ever encountered a puzzle with more than 13 nodes, so the time complexity of this kind of problem isn't of major interest. For an arbitrary number of nodes approaching larger numbers, however, this would certainly be cumbersome. I believe we would still be bounded by n*2n-1 possible paths to check (n possible starting nodes, and each node can only point to a maximum of two other nodes), though of course I'm open to being corrected if I'm mistaken. I imagine the amortized complexity will also be much lower than this bound as well, as many paths will have one or both branches of a node in the path pointing toward already-visited nodes (thus ending a path prematurely).
I'm not really the person to ask, though, as I can only speculate (:
casino_r0yale · 2 points · Posted at 16:42:22 on February 14, 2016 · (Permalink)
Ah yes, if we fix the number of nodes then it's all constant time anyway :) but it was still a very intriguing problem
Young_Neil_Postman · 1 points · Posted at 07:47:31 on February 14, 2016 · (Permalink)
Lol he was being sarcastic! whoooosh
[deleted] · 1 points · Posted at 07:54:49 on February 14, 2016 · (Permalink)
I'm very much aware that he was being sarcastic. I was just expanding upon the point by providing an example scenario that many reddit users are likely to encounter (i.e. a videogame). Graph theory is an enjoyable subject, so I wanted to point out a practical application in a non-professional setting.
ranthria · 8 points · Posted at 01:29:07 on February 14, 2016 · (Permalink)
It has a graph theory interpretation, but the theory reads more like abstract algebra.
icespout · 2 points · Posted at 20:33:47 on February 14, 2016 · (Permalink)
As a serious reply to an obviously sarcastic remark: Applied graph theory, especially directed graphs, has/have some good engineering applications:
Circuit Design
Designing Control Systems in the State Space.
Edit: I forgot how to English.
little_seed · 1 points · Posted at 02:10:04 on February 14, 2016 · (Permalink)
wait why is that /s, isn't that an application?
dixego · 3 points · Posted at 02:11:50 on February 14, 2016 · (Permalink)
The /s is to note that I know graph theory has multiple very useful applications (I'm currently studying Computer Science). I didn't want people to think I was serious about saying graph theory was useless.
glorioussideboob · 2 points · Posted at 15:04:06 on February 14, 2016 · (Permalink)
Then why make the joke if it isn't like a 'thing' that graph theory is useless?
Genlsis · 1 points · Posted at 02:18:24 on February 14, 2016 · (Permalink)
Yep! Cartoon based proofs! A whole range of cartoons too! I can't think of any other than Futurama, but I'm sure there are lots more!
JamesEarlDavyJones · 1 points · Posted at 17:55:50 on February 14, 2016 · (Permalink)
As soon as I saw this, I wanted to say "found the first-year grad student"
kblaney · 3 points · Posted at 01:52:18 on February 14, 2016 · (Permalink)
Having never read the actual paper only seen the episode, I thought it was a group theory problem (specifically the problem of the existence of representations of inverses in a subgroup of permutation groups). I didn't know it was actually a graph theory paper.
the_schnudi_plan · 2 points · Posted at 11:10:17 on February 14, 2016 · (Permalink)
I haven't read it either but it is the sort of proof that I could use in graph theory, whether they proved it with it doesn't matter as much for applications
suluamus · 2 points · Posted at 04:16:18 on February 14, 2016 · (Permalink)
So I guess you're Welsh then?
the_schnudi_plan · 1 points · Posted at 11:10:34 on February 14, 2016 · (Permalink)
Aussie actually
Snatch_Pastry · 116 points · Posted at 23:11:57 on February 13, 2016 · (Permalink)
That's why they call it a mathematical proof. It's not that the actually experiment is feasible to perform, it's that the hypothetical experiment can be stated in terms that are mathematically rigorous.
MasteringTheFlames · 9 points · Posted at 00:25:49 on February 14, 2016 · (Permalink)
This theorem is easily applied to the real world. Instead of switching brains, imagine x number of people each have a pencil. After any number of random swaps in which no two people swap with each other twice, all pencils can be returned to their owners if just two more people (and pencils) are added
boathouse2112 · 1 points · Posted at 04:37:45 on February 14, 2016 · (Permalink)
And that's why word problems are silly :P
Paid_Corporate_Shill · 12 points · Posted at 23:29:03 on February 13, 2016 · (Permalink)
The same way know the Pythagorean theorem works for every right triangle even though there are an infinite number of possible right triangles.
Named_after_color · 18 points · Posted at 22:48:20 on February 13, 2016 · (Permalink)
Math.
xxyphaxx · 2 points · Posted at 23:04:28 on February 13, 2016 · (Permalink)
Sure, that's your answer for everything, Joe.
virginal_sacrifice · 3 points · Posted at 02:49:38 on February 14, 2016 · (Permalink)
His name is Hugh.
LordUncleBob · 0 points · Posted at 04:22:50 on February 14, 2016 · (Permalink)
No, he's named "after color"
[deleted] · 1 points · Posted at 10:20:24 on February 14, 2016 · (Permalink)
Or philosophy
PurpleDotExe · 4 points · Posted at 23:17:45 on February 13, 2016 · (Permalink)
Something as simple as "two people can't switch minds with each other more than once" is purely rudimentary logic. Just because it hasn't actually been done doesn't mean that it can't be proven.
Bashar_Al_Dat_Assad · 2 points · Posted at 03:48:12 on February 14, 2016 · (Permalink)
Radical empiricism strikes again
bluglesniff4 · 4 points · Posted at 03:41:58 on February 14, 2016 · (Permalink)
So when your elementary school teacher asked you, "if Sally gives you 5 apples and you already have 3, how many apples do you have?", was your response, "how can I solve that, no one named Sally has ever given me 5 apples before?"
crystalistwo · 2 points · Posted at 04:43:17 on February 14, 2016 · (Permalink)
I just kick and scream that I don't believe in apples. Then I run for Congress.
DefinitelyNotLucifer · 2 points · Posted at 23:40:17 on February 13, 2016 · (Permalink)
Ask a theoretical physicist.
[deleted] · 2 points · Posted at 04:48:16 on February 14, 2016 · (Permalink)
[deleted]
ynnekf76 · 1 points · Posted at 05:17:44 on February 14, 2016 · (Permalink)
Good to see that with one sentence I can make you throw a infantile fit. Good for you lol
[deleted] · -1 points · Posted at 05:23:54 on February 14, 2016 · (Permalink)
[deleted]
ynnekf76 · 2 points · Posted at 06:49:49 on February 14, 2016 · (Permalink)
Yep that's what people are talking about when they say the NFL has a concussion problem: that people watching it are getting brain damage
[deleted] · 0 points · Posted at 07:02:12 on February 14, 2016 · (Permalink)
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[deleted] · 0 points · Posted at 08:41:57 on February 14, 2016 · (Permalink)
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[deleted] · 1 points · Posted at 13:48:29 on February 14, 2016 · (Permalink)
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[deleted] · 0 points · Posted at 21:27:19 on February 14, 2016 · (Permalink)
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[deleted] · 1 points · Posted at 21:34:24 on February 14, 2016 · (Permalink)
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[deleted] · 0 points · Posted at 22:00:14 on February 14, 2016 · (Permalink)
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[deleted] · 1 points · Posted at 22:08:24 on February 14, 2016 · (Permalink)
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[deleted] · 0 points · Posted at 22:21:43 on February 14, 2016 · (Permalink)
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[deleted] · 1 points · Posted at 22:27:35 on February 14, 2016 · (Permalink)
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[deleted] · 1 points · Posted at 22:46:18 on February 14, 2016 · (Permalink)
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boldra · 1 points · Posted at 07:22:23 on February 14, 2016 · (Permalink)
You never prove anything by "doing it". You might have just been lucky.
mojomofo1 · 1 points · Posted at 10:27:59 on February 14, 2016 · (Permalink)
It's just a no brainer
Sutarmekeg · 1 points · Posted at 13:30:02 on February 14, 2016 · (Permalink)
You account for all possibilities.
logos__ · 1 points · Posted at 19:24:03 on February 14, 2016 · (Permalink)
Because the whole point of math is that it abstracts away from the concrete so that it can discover general truths.
i_hope_i_remember · 1 points · Posted at 01:54:49 on February 14, 2016 · (Permalink)
Here's an ongoing working example
erremermberderrnit · 11 points · Posted at 22:56:43 on February 13, 2016 · (Permalink)
Wait, why are the two helpers even necessary? Can't you just take the group of people with switched minds, switch one mind into the correct body, remove the corrected person from the equation, and repeat until everyone is corrected? I must be missing something.
Schnutzel · 40 points · Posted at 23:08:31 on February 13, 2016 · (Permalink)
There was another limitation: if two people had their mind swapped, they can't have their mind swapped with each other again.
ss4444gogeta · 3 points · Posted at 22:19:49 on February 13, 2016 · (Permalink)
Sounds like Captain Ginyu.
ArthurTheAstronaut · 3 points · Posted at 03:00:06 on February 14, 2016 · (Permalink)
555 upvotes for following the link and copy/pasting? I need to step up my reddit game.
Arancaytar · 3 points · Posted at 09:29:41 on February 14, 2016 · (Permalink)
Wow, was this inspired by the Stargate SG-1 episode?
NeverStopWondering · 3 points · Posted at 11:23:53 on February 14, 2016 · (Permalink)
This is used almost verbatim (complete with the body-switching) in an early episode of Stargate SG1.
Greghole · 1 points · Posted at 02:07:58 on February 14, 2016 · (Permalink)
And they say higher mathematics has no real world applications.
SockSmuggler · 1 points · Posted at 05:28:58 on February 14, 2016 · (Permalink)
Read this in the professor's voice...
And then the parentheses hit.
playaspec · 1 points · Posted at 05:47:26 on February 14, 2016 · (Permalink)
You should really give credit where credit is due.
sherlip · 1 points · Posted at 07:01:38 on February 14, 2016 · (Permalink)
What I don't get is why you can't just switch them back the same way you switched them the first time?
atillathepun1 · 0 points · Posted at 00:54:04 on February 14, 2016 · (Permalink)
...this is literally just the third paragraph down on the page.
won_vee_won_skrub · 2 points · Posted at 02:11:27 on February 14, 2016 · (Permalink)
Prevents people from having to leave Reddit.
OZONE_TempuS · 645 points · Posted at 20:08:50 on February 13, 2016 · (Permalink)
Ken Keeler (the writer of the episode and the theorem) has a PhD in mathematics. There a lot of little math Easter eggs hidden in the Simpsons and Futurama.
cvkxhz · 253 points · Posted at 05:18:27 on February 14, 2016 · (Permalink)
Bender: "Hey, brobot, what's your serial number?"
Flexo: "3370381"
Bender: "No way! Mine's 2716057!"
(Both laugh)
Fry: "heheheheh...I don't get it?"
Bender (annoyed): "We're both expressible as the sum of two cubes!"
Radiatron · 27 points · Posted at 23:13:06 on February 13, 2016 · (Permalink)
Book of it isn't there?
osrevad · 37 points · Posted at 01:25:16 on February 14, 2016 · (Permalink)
It's called The Simpson's and Their Mathematical Secrets.
freudianchips · 4 points · Posted at 08:44:42 on February 14, 2016 · (Permalink)
Which is a great book that I would recommend to anyone- I read it and it made me a lot more excited about math (a couple years of college math had sucked the life out of me).
hayberry · 12 points · Posted at 22:26:25 on February 13, 2016 · (Permalink)
I love finding those! First one I ever noticed was P = NP in the background somewhere. Think it was a book.
OZONE_TempuS · 18 points · Posted at 22:27:13 on February 13, 2016 · (Permalink)*
There's also some instances where they have "solutions" to Fermats Last Theorem.
EltaninAntenna · 5 points · Posted at 10:18:46 on February 14, 2016 · (Permalink)
To be fair, the solution that 'just barely doesn't fit in a margin' hasn't been found yet.
ishkariot · 4 points · Posted at 13:51:11 on February 14, 2016 · (Permalink)
I thought it was commonly assumed he probably made some calculation mistake as we do have solved it but we have no "simple, elegant solution" unless you overlook certain things. I'll have to google it.
EltaninAntenna · 1 points · Posted at 14:15:55 on February 14, 2016 · (Permalink)
I guess that's the thing, we'll never know, at least until we find it. Maybe the "simple, elegant solution" is still out there...
ishkariot · 1 points · Posted at 14:47:33 on February 14, 2016 · (Permalink)
I tend to doubt it. Mathematics isn't alchemy or some sort of arcane art and Fermat's last theorem is something many mathematicians have obsessed over. I find it hard to believe that so many people looking for short and simple answers have found all of the erroneous ones but not an equally short but correct one
hypervelocityvomit · 1 points · Posted at 11:27:11 on February 15, 2016 · (Permalink)
Something like xxxxxxxx212 + yyyyyyyy112 = zzzzzzzz212 .
I looked at it for one second, somebody asked, "Is that Fermat equation real?" and I was like, "The hell? How dazed are you? That's Even + Odd = Even for you."
30 seconds pass, he goes, "Oh."
In his defense, he was way more drunk at that time.
PalestraRattus · 9 points · Posted at 05:47:17 on February 14, 2016 · (Permalink)
Closet Fry and Amy hide in early on while dating. P NP are the books on the bottom shelf.
In the episode where Bender is pulled into the can opener and tours with Beck. When they pan out to a map of the US Oregon has be renamed Xoregon.
hayberry · 2 points · Posted at 06:01:23 on February 14, 2016 · (Permalink)
Not sure I understand the xoregon one! Does it have to do with XOR SAT?
bwisey · 4 points · Posted at 13:31:10 on February 14, 2016 · (Permalink)
It's a portmanteau of XOR and Oregon suggesting there is an exclusive Oregon in the future.
hayberry · 1 points · Posted at 19:36:44 on February 14, 2016 · (Permalink)
I'm aware of what XOR is, I just thought that it had something to do with P = NP from the orders of the post.
PalestraRattus · 2 points · Posted at 15:49:34 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Exclusive_or
hayberry · 1 points · Posted at 19:35:51 on February 14, 2016 · (Permalink)
I know what XOR is. I thought it had something to do with P = NP in context, hence why I asked about XOR SAT. Changing and OR to XOR doesn't really seem that clever if that's all there is to it...
dizzi800 · 5 points · Posted at 03:36:57 on February 14, 2016 · (Permalink)
My favourite is a2 + b2 > c2 which is true on a sphere
little_seed · 5 points · Posted at 02:16:41 on February 14, 2016 · (Permalink)
that use of italics makes me uncomfortable for some reason
DarshDarshDARSH · 7 points · Posted at 03:28:48 on February 14, 2016 · (Permalink)
Also, from the Simpsons I learned "Pi is exactly three!". Prof. Frink said that.
TitusTorrentia · 2 points · Posted at 01:08:12 on February 14, 2016 · (Permalink)*
And yet, in the episode where Bender uses the Banach-Tarski printer, the professor says the series modeling Bender's replication is divergent (and therefore he would use up all the matter on earth or something), but the nominator cancels with the exact same expression in the denominator, and thus the remaining series would actually converge.Edit: As /u/wadss said below, it still diverges, I brain-farted and switched terms. Though, still, why would the Professor not show the series in simplest form?But most likely anyone who hasn't taken Differential Calculus, or at the very least Pre-Calculus, wouldn't notice because they probably don't know enough about series.Here is a blog post where someone does the math to say that the formular the Professor comes up with is actually just plain wrong for the situation. But, despite my math degree, I can't say anything on its validity.
It is possible whoever did other episodes was either not very well-versed or did it on purpose to make the Professor look not-so-smart. There are other instances in the show and movies where either stuff is completely wrong, makes no sense, or what is on the board has nothing to do with what they are talking about. Edit: There are different instances of things not really making sense, such as in The Beast with a Billion Backs, The Professor and Wernstrom claim to prove a certain conjecture, but the writing on the board has nothing to do with the conjecture.
Still a great show, I love re-watching it (the movies not so much), there is always something new I notice.
wadss · 1 points · Posted at 01:50:35 on February 14, 2016 · (Permalink)
the series 1/n diverges, 1/n2 converges
TitusTorrentia · 1 points · Posted at 01:52:44 on February 14, 2016 · (Permalink)
Whoops! I cancelled out the wrong terms when I looked at it, swore that the numerator was (n+1). Thanks.
slutvomit · 1 points · Posted at 09:30:48 on February 14, 2016 · (Permalink)
That bloke would be absolutely fantastic to hang out with. He'd have such a wide variety of talent to show and experiences to talk about.
GaiusAurus · 265 points · Posted at 22:35:01 on February 13, 2016 · (Permalink)
Stargate did this before futurama, but they didn't go through the trouble of building a proof (SG-1: Holiday)
implonator_ · 81 points · Posted at 00:42:29 on February 14, 2016 · (Permalink)
Indeed
rubbery_yoke · 17 points · Posted at 02:26:41 on February 14, 2016 · (Permalink)
Thanks for that, Teal'c
tealc_comma_the · 15 points · Posted at 06:24:34 on February 14, 2016 · (Permalink)
You're welcome Daniel Jackson.
samsg1 · 13 points · Posted at 02:54:47 on February 14, 2016 · (Permalink)
It did not go well General Hammond.
Ya think!?
FoxtrotBeta6 · 13 points · Posted at 02:10:39 on February 14, 2016 · (Permalink)
You will NOT shave my head.
ManualNarwhal · 8 points · Posted at 02:06:34 on February 14, 2016 · (Permalink)
Not to mention it's been a standard brain teaser and puzzle in games.
Daggertrout · 4 points · Posted at 05:19:14 on February 14, 2016 · (Permalink)
It was also half as many people.
winklevos · 4 points · Posted at 07:02:00 on February 14, 2016 · (Permalink)
Came here to say this... Sigh
that-writer-kid · 1 points · Posted at 15:55:26 on February 14, 2016 · (Permalink)
Yeah, Futurama got the credit because they showed their work.
Literally.
[deleted] · -9 points · Posted at 23:30:14 on February 13, 2016 · (Permalink)
So they didn't do it.
[deleted] · 11 points · Posted at 02:02:25 on February 14, 2016 · (Permalink)
It means they did it, but they never formally proved that this would actually work. They just showed that it worked for the particular numbers that they were interested in and assumed it was a general rule. Futurama proved that it actually does work as a general rule.
TheOboeMan · 9 points · Posted at 02:53:07 on February 14, 2016 · (Permalink)
They didn't assume it worked generally. The characters in Stargate are typically interested in the easiest solutions to their current life-threatening puzzle, and don't care about generalities.
How_do_I_potato · 5 points · Posted at 05:08:31 on February 14, 2016 · (Permalink)
Hey, that isn't fair to say about the entire team. Daniel clearly wasn't very interested in avoiding death.
GaiusAurus · 17 points · Posted at 23:33:28 on February 13, 2016 · (Permalink)
I'm talking about the plot of the episode and the mathematical concept
bisensual · -8 points · Posted at 00:24:33 on February 14, 2016 · (Permalink)
So you're saying they did not?
Pegthaniel · 8 points · Posted at 01:29:06 on February 14, 2016 · (Permalink)
Well, they did. They came up with the same algorithm (the "mathematical formula") which is the part OP was talking about.
playaspec · -4 points · Posted at 05:50:11 on February 14, 2016 · (Permalink)
You mean the one you just said they didn't up above?
Pegthaniel · 4 points · Posted at 05:51:53 on February 14, 2016 · (Permalink)
They didn't build the proof out for people to see, but the actual solution was stated... 2 different things, they were only talking about the solution.
imbogey · 2 points · Posted at 06:08:41 on February 14, 2016 · (Permalink)
I must be missing something.. In sg the extra bodies are already switched bodies so shoudn't this be a different case?
Pegthaniel · 0 points · Posted at 06:29:03 on February 14, 2016 · (Permalink)
I'm fairly sure it's just a sub case of the Futurama theorem. You have an even number of "circles" to deal with so you need no "fresh" helpers.
playaspec · -7 points · Posted at 05:48:54 on February 14, 2016 · (Permalink)
Then they didn't do it. The point here is that a mathematical proof was made, which you just admitted they didn't do.
imp3r10 · -1 points · Posted at 14:09:20 on February 14, 2016 · (Permalink)
So, they didn't do this?
geweldigzinloos · 5 points · Posted at 00:32:18 on February 14, 2016 · (Permalink)
Poor washbucket :((
MuttinChops · 5 points · Posted at 02:02:16 on February 14, 2016 · (Permalink)
I actually paused that episode towards the beginning when the professor was trying to figure it out. Spent like half an hour scribbling like a mad man trying to figure it out.
Sw0rDz · 2 points · Posted at 07:56:49 on February 14, 2016 · (Permalink)
That was because Futurama had a writer with a PH.D in applied math. The other writers were engineers/physics grads. If you watch that episode carefully. The proof for the theorem is on the green chalkboard.
wardsac · 1 points · Posted at 01:23:13 on February 14, 2016 · (Permalink)
Razzle-Dazzle Globetrotter Math....
Curdflappers · 1 points · Posted at 03:41:44 on February 14, 2016 · (Permalink)
There's a Mathologer video on it for a great visualization.
ChickenBrad · 1 points · Posted at 04:21:51 on February 14, 2016 · (Permalink)
for the love of god I need to see this part of the episode.
Boslof · 1 points · Posted at 05:02:39 on February 14, 2016 · (Permalink)
My linear algebra professor had a theorem named after her in the show. Image of it.
lurk_n_throw · 1 points · Posted at 08:28:12 on February 14, 2016 · (Permalink)
I feel like this is another implementation of tower of hanoi.
Triquetra4715 · 1 points · Posted at 20:03:47 on February 14, 2016 · (Permalink)
The show so smart it forgot to be funny.
[deleted] · 0 points · Posted at 09:49:33 on February 14, 2016 · (Permalink)
[deleted]
Randomdude2846 · 1 points · Posted at 12:37:15 on February 14, 2016 · (Permalink)
Because 1) This is a mathematical fact. 2)I found this cool
wspaniel · 86 points · Posted at 23:52:50 on February 13, 2016 · (Permalink)
1 + 1/2 + 1/3 + 1/4 + ... diverges. That's standard. But throw out all numbers with a 9 in the denominator, and the series converges.
It gets stranger. You can remove any string of numbers and it still works. For example, you could remove all numbers containing 164812458737002 in the denominator, and that series converges.
It gets even stranger. The series of numbers containing 164812458737002 diverges.
[deleted] · 9 points · Posted at 12:41:09 on February 14, 2016 · (Permalink)
[deleted]
wspaniel · 3 points · Posted at 19:18:49 on February 14, 2016 · (Permalink)
Whoa. Proof?
hypervelocityvomit · 4 points · Posted at 11:50:20 on February 15, 2016 · (Permalink)
Prove that a larger series still converges:
1/11+e + 1/21+e + 1/31+e + 1/41+e + 1/51+e + 1/61+e + 1/71+e + 1/81+e + ...
< 1/11+e + 1/21+e + 1/21+e + 1/41+e + 1/41+e + 1/41+e + 1/41+e + 1/81+e + ...
(If there's a number that's not a power of two in the denominator, I'll decrease it until it is. This will increase some parts of the sum, but never decrease any.)
During my next trick, I'll group terms with equal denominators and then cancel the powers of two:
1/11+e + 1/21+e + 1/21+e + 1/41+e + 1/41+e + 1/41+e + 1/41+e + 1/81+e + ...
= 1/11+e + 2/21+e + 4/41+e + 8/81+e + ...
= 1/1e + 1/2e + 1/4e + 1/8e + ...
Finally, introduce u = 1/2e .
1/1e + 1/2e + 1/4e + 1/8e + ...
= 1 + u + u2 + u3 + ...
And that's a geometric series, which is known to converge. I hope that helps.
thebigbadben · 1 points · Posted at 12:57:34 on February 16, 2016 · (Permalink)
Integral test, for one
samlee405 · 4 points · Posted at 06:47:43 on February 14, 2016 · (Permalink)
That's actually fascinating. Is there a formal proof of that somewhere?
wspaniel · 12 points · Posted at 08:44:36 on February 14, 2016 · (Permalink)
I remember seeing it here a long time ago. IIRC correctly, the intuition is that almost all elements of the series contain a 9 (once you get to really large denominators), so you basically stop adding stuff at the end. (And I think you can start grouping things together formally and show that each of the elements is smaller than a geometric series that converges.)
The same is true for any string of numbers---once the denominator gets large, basically all of them contain any given string. But since any of them contain the string, they are basically like the harmonic series and diverge.
hypervelocityvomit · 2 points · Posted at 11:56:37 on February 15, 2016 · (Permalink)
Basically, 9 of the first 10 numbers do not contain the number 9, 92 of the first 100, and 9n of the first 10n numbers, and a lower percentage after that.
Effectively, the culling of the 9-numbers makes the sequence geometric, and this proof applies from then on.
almightySapling · -2 points · Posted at 14:02:45 on February 14, 2016 · (Permalink)*
Certainly not "almost all" elements contain a 9. In fact, exactly 1/9 of the terms contain a 9. For any n-digit string, exactly 1/(10n-1) of the terms contain that string.But the idea isn't that you are throwing out all the terms, it's that you are throwing out enough terms, since our series "almost" converges.
Edit: I was really high when I wrote this and I overlooked a lot of terms. The density of digits with a 9 is 1, not 1/9, which changes things pretty severely.
truckiewow · 5 points · Posted at 14:49:48 on February 14, 2016 · (Permalink)
That doesn't seem right. It seems to be more than 1/(10n -1).
Take the one digit numbers (0-9). There is one number that contains a 9, and that is the number 9. So that is 1/10 or 1/9 (depending on whether you start counting at 0 [correct] or 1 [heathens]).
For two digit numbers, it is the same for each group of 10 through the 80s (9, 19, 29, 39, 49, 59, 69, 79, 89) = 9 numbers, plus all the 90s (90-99=10 numbers). So there are (9+10)/100 = 19/100 two digit numbers that contain a 9.
For three digit numbers, this repeats for the first 900 numbers (19 in 0-99, 19 in 100-199, ... , 19 in 800-899), plus all the 900s. So there are (9*19 + 100)/1000 = (171 + 100)/1000 = 271/1000.
Similarly, there are 3439/10,000 four digit numbers and 40951/100,000 five digit numbers that contain a 9.
Am I missing something?
AMvariety · 1 points · Posted at 15:46:25 on February 14, 2016 · (Permalink)
What almightysappling has calculated is probability that given a series of terms that are non zero the probability that a term will contain a given sequence is 1/(10n -1), where n is the length of the term. But the question was asking what is the probability the a series of length n contains a nine, as n tends to infinity.
almightySapling · 1 points · Posted at 22:17:38 on February 14, 2016 · (Permalink)
No, you are totally, completely right. I way overlooked some things.
I'll have to finish waking up to get down to it and see what it really evaluates to.
PMBOOBSORMATHPUZZLES · 4 points · Posted at 18:07:16 on February 14, 2016 · (Permalink)
Most integers do have a digit that's 9. Most integers have a digit that's 3 also. Numberphile has a video: https://www.youtube.com/watch?v=UfEiJJGv4CE
So yes, if you take the harmonic series and throw away all the terms with a 9 in the denominator, you are throwing away almost all (in the technical sense) of the terms.
Crixomix · 3 points · Posted at 17:08:51 on February 18, 2016 · (Permalink)
Well if you throw out all numbers with a 9 in the denominator, since we are talking about an INFINITE series, eventually, the probability that a term has a 9 in the denominator is ~100%. As it's like 609 numbers long, or 4000 numbers long, or 15 billion numbers long. So you're basically removing almost every single term, as the terms have longer and longer strings of numbers.
Thus why you can remove any numbers like the ones you listed. Eventually, the probability of the term containing THAT is still ~100%
Thopterthallid · 1368 points · Posted at 01:14:51 on February 14, 2016 · (Permalink)
1000000000000066600000000000001
Ciriacus · 300 points · Posted at 04:25:09 on February 14, 2016 · (Permalink)
You're right, that sounds metal as fuck dude.
[deleted] · 22 points · Posted at 05:23:15 on February 14, 2016 · (Permalink)
[deleted]
googolplexbyte · 3 points · Posted at 18:46:11 on February 14, 2016 · (Permalink)
Math Rock slash Heavy Metal?
Fishbone_V · 1 points · Posted at 01:13:50 on February 15, 2016 · (Permalink)*
Well there is already Belphegor.
Maybe they could do a collaboration with Blotted Science.
Commander_Prime · 21 points · Posted at 06:51:34 on February 14, 2016 · (Permalink)
Belphegor's Prime = Optimus Prime's musically inclined cousin?
KnightArts · 4 points · Posted at 08:11:14 on February 14, 2016 · (Permalink)
or optimus prime's dick
dude_pirate_roberts · 6 points · Posted at 08:06:49 on February 14, 2016 · (Permalink)
By Belphegor's Hammer!
mgosiris · 2 points · Posted at 14:19:57 on February 14, 2016 · (Permalink)
Dude.
Sharkn91 · 2 points · Posted at 16:09:35 on March 1, 2016 · (Permalink)
What kind of car does Belphegor Prime turn into?
Wheres_The_Pepsi · 17 points · Posted at 07:29:51 on February 14, 2016 · (Permalink)
If only numbers could have umlauts over them
sonyka · 9 points · Posted at 10:44:03 on February 14, 2016 · (Permalink)
Technically, those are known as "rök döts."
Fun fact!
Ucantalas · 12 points · Posted at 08:15:44 on February 14, 2016 · (Permalink)
I like this one because I failed Grade 9 math but still understand why this is interesting.
federgolo · 7 points · Posted at 05:10:54 on February 14, 2016 · (Permalink)
There's an "Elementary" episode where some mathematicians are killed over this shit.
Laxiken · 7 points · Posted at 08:14:09 on February 14, 2016 · (Permalink)
I literally thought you just made this number up out of your head. Went to look up and realized it was real
MadnessMethod · 5 points · Posted at 05:24:07 on February 14, 2016 · (Permalink)
Fucking brutal
ashcroftt · 6 points · Posted at 08:23:02 on February 14, 2016 · (Permalink)
FTFY
hypervelocityvomit · 1 points · Posted at 11:36:25 on February 15, 2016 · (Permalink)
[deleted] · 3 points · Posted at 07:03:14 on February 14, 2016 · (Permalink)
[deleted]
SatanakanataS · 19 points · Posted at 07:12:36 on February 14, 2016 · (Permalink)
It has an odd number of zeros on either side of the 666.
Thopterthallid · 4 points · Posted at 07:18:39 on February 14, 2016 · (Permalink)
1000000000000066600000000000001
It's read backwards, and forwards exactly the same.
1, thirteen zeroes, three sixes, thirteen zeroes, 1.
Anakinss · 3 points · Posted at 09:20:41 on February 14, 2016 · (Permalink)
It's a palindrome because it's a number determined to be. It's like saying "The letter L, then thirteen o, then three m, then thirteen o, then a L... Oh my god, it's a palindrome!"
The neatest thing is that it's a prime number.
Ausderdose · 5 points · Posted at 09:37:41 on February 14, 2016 · (Permalink)
That sounds metal as fuck if you play it as tabs.
Caraes_Naur · 3 points · Posted at 05:40:35 on February 14, 2016 · (Permalink)
666 is a mistranslation of the "number of the beast", which is actually 616.
confusedThespian · 8 points · Posted at 06:59:25 on February 14, 2016 · (Permalink)
Stan Lee is the Antichrist confirmed.
[deleted] · 5 points · Posted at 07:09:08 on February 14, 2016 · (Permalink)
If you'd said Alan Moore I might've believed you.
mgosiris · 1 points · Posted at 14:20:48 on February 14, 2016 · (Permalink)
Hello there true believers!
nappingrabbit · 1 points · Posted at 08:35:27 on February 14, 2016 · (Permalink)
That true? How you know?
skimitar · 5 points · Posted at 08:48:33 on February 14, 2016 · (Permalink)*
[deleted]
hypervelocityvomit · 1 points · Posted at 11:39:43 on February 15, 2016 · (Permalink)
666 in Roman numbers is DCLXVI, i.e. one of each, except M (which was uncommon back then). It was what they wrote for a fairly large but unknown number, like we sometimes use 123.
OTOH, their algebra was easy. X was 10 all the time. scnr
LostMyPasswordNewAcc · 1 points · Posted at 10:43:14 on February 14, 2016 · (Permalink)
Belphegor's Prime? Damn.
FourBox · 1 points · Posted at 14:02:55 on February 14, 2016 · (Permalink)
I can headbang to that \m/
ThompsonBoy · 1 points · Posted at 14:54:40 on February 14, 2016 · (Permalink)
It's actually throwing the devil horns too.
alex4point0 · 1 points · Posted at 02:34:53 on February 15, 2016 · (Permalink)
Belphegor
necessity is the mother of invention but Belphegor provides the seed
Reddichu9001 · 1 points · Posted at 15:46:28 on February 20, 2016 · (Permalink)
Also: It has 31 digits, which is 13 backwards.
[deleted] · -1 points · Posted at 06:13:19 on February 14, 2016 · (Permalink)
Read this number and OP's mom came knocking on my door...
nerd_needing_a_quest · 1759 points · Posted at 20:11:25 on February 13, 2016 · (Permalink)
1 million secs is roughly 11.5 days. 1 billion seconds is a little under 32 years.
[deleted] · 728 points · Posted at 20:56:10 on February 13, 2016 · (Permalink)*
[deleted]
ThirdFloorGreg · 168 points · Posted at 23:08:57 on February 13, 2016 · (Permalink)
And 1 foot per nanosecond is within 2% of the speed of light. That's closer than the approximation the Apollo missions used for the square root of 2.
[deleted] · 13 points · Posted at 04:34:22 on February 14, 2016 · (Permalink)
I guess I have no conception of how long a nanosecond is, but that really surprised me
Alphaetus_Prime · 17 points · Posted at 05:24:26 on February 14, 2016 · (Permalink)
A nanosecond is a single-digit number of CPU clock cycles.
playaspec · 22 points · Posted at 05:44:25 on February 14, 2016 · (Permalink)
FTFY.
KarmicFedex · 7 points · Posted at 06:41:39 on February 14, 2016 · (Permalink)*
1 GHz = 1000 MHz 1 MHz = 1000 KHz 1 KHz = 1000 Hz
1/1000/1000/1000 seconds?
As in 0.000,000,001?
1-billionth of a second ?
Edit: correction from /u/madeuser
MadeUser · 10 points · Posted at 06:55:08 on February 14, 2016 · (Permalink)
One ten billionth. When counting to the right of the decimal, you start with tenths instead of, uhm, singles(?).
KarmicFedex · 3 points · Posted at 07:22:30 on February 14, 2016 · (Permalink)
Thank you, I fixed it.
deeperest · 2 points · Posted at 12:32:53 on February 14, 2016 · (Permalink)
Singleths.
574N13Y · 1 points · Posted at 14:34:34 on February 14, 2016 · (Permalink)
unit
ameya2693 · 3 points · Posted at 13:43:30 on February 14, 2016 · (Permalink)
So what you are really saying is that Americans should move over to foot per nanosecond metric system...
[deleted] · 2 points · Posted at 04:54:27 on February 14, 2016 · (Permalink)
But who uses those, most physicists prefer sitting down.
Ltbsd · 1 points · Posted at 14:22:33 on February 14, 2016 · (Permalink)
Yup, a "light-foot", as my grandma taught me.
CIearMind · 416 points · Posted at 22:09:41 on February 13, 2016 · (Permalink)
355/113 :)
[deleted] · 986 points · Posted at 00:08:20 on February 14, 2016 · (Permalink)
3meta.14me
FettShotFirst · 11 points · Posted at 06:52:26 on February 14, 2016 · (Permalink)
/r/im3.14andthisisdeep
hypervelocityvomit · 3 points · Posted at 11:31:10 on February 15, 2016 · (Permalink)
/r/im3.14andthisisgoodenoughforme
fagalopian · 13 points · Posted at 00:50:51 on February 14, 2016 · (Permalink)
QT355/113 😉
Simmienz · 4 points · Posted at 05:58:46 on February 14, 2016 · (Permalink)
22meta/ 7me
criticallyAnalytical · 4 points · Posted at 02:45:06 on February 14, 2016 · (Permalink)
22meta7me
raaneholmg · 3 points · Posted at 13:53:36 on February 14, 2016 · (Permalink)
/u/355over113 ?
355over113 · 3 points · Posted at 14:41:26 on February 14, 2016 · (Permalink)
Ahem,
"You called?"
hypervelocityvomit · 1 points · Posted at 11:31:34 on February 15, 2016 · (Permalink)
356/113 with rice
nordicminy · -4 points · Posted at 00:25:06 on February 14, 2016 · (Permalink)
Meta AF.
ELwain66 · 4 points · Posted at 00:20:58 on February 14, 2016 · (Permalink)
Wait, actually?
angrymachinist · 5 points · Posted at 16:20:24 on February 14, 2016 · (Permalink)
Pi? Yes, I'll have seconds
nss68 · 2 points · Posted at 09:27:56 on February 14, 2016 · (Permalink)
wouldn't pi seconds just be 3.14etc.etc.etc seconds? like less than 4 seconds?
d47 · 3 points · Posted at 10:08:48 on February 14, 2016 · (Permalink)
Yes, a nano century.
nss68 · 3 points · Posted at 17:23:54 on February 14, 2016 · (Permalink)
oh doi.
thanks.
AngusPepperer · 1 points · Posted at 08:23:48 on February 14, 2016 · (Permalink)
3.14 seconds?
2LateImDead · 1 points · Posted at 23:49:48 on February 14, 2016 · (Permalink)
I get that pi is infinite, but only after the decimal. So pi seconds is .14blahblahblah more than 3 seconds, isn't it?
hypervelocityvomit · 1 points · Posted at 11:41:06 on February 15, 2016 · (Permalink)
Upvoted to +666. (Search for Belphegor's Prime.)
[deleted] · 1 points · Posted at 02:21:32 on February 14, 2016 · (Permalink)
how is it close to a nanocentury? Isn't pi seconds just 3.1415.... seconds?
smurphatron · 11 points · Posted at 03:27:15 on February 14, 2016 · (Permalink)
Yes, and a nanocentury is a billionth of a century. Which is close to 3.1415 seconds.
yes_oui_si_ja · 0 points · Posted at 23:45:35 on February 13, 2016 · (Permalink)
And one year is incredibly close to Pi * 107 seconds. This blows my mind.
[deleted] · 9 points · Posted at 00:16:57 on February 14, 2016 · (Permalink)
That's pretty much exactly the same thing as what they said.
yes_oui_si_ja · 2 points · Posted at 06:22:47 on February 14, 2016 · (Permalink)
Haha, yes. Now I see it! Of course!
AtomicSquid · -1 points · Posted at 02:05:06 on February 14, 2016 · (Permalink)
And a year is about pi*107 seconds
Floyddit · -2 points · Posted at 02:59:46 on February 14, 2016 · (Permalink)
Which is only natural since the earth's orbit is awful goddamn close to a circle.
smurphatron · 2 points · Posted at 03:26:46 on February 14, 2016 · (Permalink)
It has nothing to do with that. It wouldn't be true on Mars, for example.
hypervelocityvomit · 1 points · Posted at 11:34:30 on February 15, 2016 · (Permalink)
BecauseMars orbit is way more elliptic.Coincidence. The orbit of Venus is almost perfectly circular, and it doesn't hold there.
[deleted] · -14 points · Posted at 23:34:07 on February 13, 2016 · (Permalink)
3.14 seconds is not a century. Try rewording.
[deleted] · 4 points · Posted at 00:17:09 on February 14, 2016 · (Permalink)
rocket222 · 26 points · Posted at 21:03:13 on February 13, 2016 · (Permalink)
And a trillion is a little under 32000 years
[deleted] · 30 points · Posted at 01:29:49 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 2 points · Posted at 12:39:10 on February 14, 2016 · (Permalink)
this makes it worse:
www.usdebtclock.org
MichaelJayDog · 4 points · Posted at 04:23:11 on February 14, 2016 · (Permalink)
Outkast will never finish apologizing to Ms. Jackson
NoiceOne · 2 points · Posted at 04:32:56 on February 14, 2016 · (Permalink)
I am for reaaal
handym12 · 7 points · Posted at 23:42:38 on February 13, 2016 · (Permalink)
No Such Thing As A Fish?
monkiebars · 1 points · Posted at 00:03:58 on February 15, 2016 · (Permalink)
The squid sperm story was so messed up.
jamesno26 · 12 points · Posted at 21:17:38 on February 13, 2016 · (Permalink)
It makes sense when you think about it, because 1 billion is basically 1,000 million
Duuhh_LightSwitch · 27 points · Posted at 21:49:36 on February 13, 2016 · (Permalink)
It's not that this doesn't make sense. It's that thinking about it this way really illustrates the difference in size between a million and a billion
iforgotmy-password · -3 points · Posted at 22:11:58 on February 13, 2016 · (Permalink)
It's about 1000 times bigger. Shocker.
Seal3824 · 15 points · Posted at 22:36:41 on February 13, 2016 · (Permalink)
Yes, but when most people just heard the words "1000 times bigger" they can't really fully grasp the size of it. You can have a rough idea, but usually people need to see the difference to actually comprehend the size difference.
comradeda · -1 points · Posted at 03:45:35 on February 14, 2016 · (Permalink)
It's 999 million bigger.
[deleted] · 0 points · Posted at 12:47:22 on February 14, 2016 · (Permalink)
More like people can't grasp the scale of time so well.
I'm pretty sure anyone is able to grasp the size of 1m and 1km.
TheTrevLife · 0 points · Posted at 09:04:11 on February 14, 2016 · (Permalink)
Yes. It's 1,000x larger.
[deleted] · 0 points · Posted at 12:51:47 on February 14, 2016 · (Permalink)
Yeah we can. It's the same as the difference between 1m and 1km.
1 million micrometers is the 1m. 1 billion micrometers is 1km.
Or let's try it another way. 1 week is well, 1 week. 1 thousand weeks is over 19 years.
Not so exciting is it now?
TheJerinator · 3 points · Posted at 02:44:50 on February 14, 2016 · (Permalink)
Well I mean... It is...
A billion minus a million is still pretty much a billion
killmetonight · 2 points · Posted at 04:51:01 on February 14, 2016 · (Permalink)
why did you write secs the first time, and seconds the second time?
nerd_needing_a_quest · 1 points · Posted at 05:31:35 on February 14, 2016 · (Permalink)
I didn't realize that XD. Guess I was just lazy the first time but not the second?
VoilaVoilaWashington · 1 points · Posted at 18:13:04 on February 14, 2016 · (Permalink)
He had a lot more time with a billion seconds.
[deleted] · 1 points · Posted at 22:50:33 on February 13, 2016 · (Permalink)
it has been almost one quadrillion hours since the big bang.
[deleted] · 1 points · Posted at 01:34:26 on February 14, 2016 · (Permalink)
What I wouldn't give for a million secs...
DDJSBguy · 1 points · Posted at 02:14:01 on February 14, 2016 · (Permalink)
All this secs and I'm still single for valentines day ;-:
wolffangz11 · 1 points · Posted at 02:30:51 on February 14, 2016 · (Permalink)
I want 1 million secs
IAMA_dragon-AMA · 1 points · Posted at 02:33:03 on February 14, 2016 · (Permalink)
That's a lot of secs.
johnmatthewwilder · 1 points · Posted at 03:34:57 on February 14, 2016 · (Permalink)
Neato! I just read a short story by Andy Weir, where 1 billion seconds fact was brought up.
K3R3G3 · 1 points · Posted at 03:40:23 on February 14, 2016 · (Permalink)
This one never impressed me because I just see "11,500 days is approximately 32 years" which is very believable.
I_too_amawoman · 1 points · Posted at 04:27:44 on February 14, 2016 · (Permalink)
Do you know what a trillion would be??
nerd_needing_a_quest · 2 points · Posted at 05:30:58 on February 14, 2016 · (Permalink)
A little under 31,710 years.
I_too_amawoman · 1 points · Posted at 14:30:17 on February 14, 2016 · (Permalink)
WOW thanks!
CrabbyBlueberry · 1 points · Posted at 05:00:14 on February 14, 2016 · (Permalink)
As a consequence, just a little over 64 years after 1970, computers using 32-bit timestamps will roll back to 1901.
mokojin · 1 points · Posted at 06:17:31 on February 14, 2016 · (Permalink)
107 seconds are pretty exactly one year.
YourLittleBuddy · 1 points · Posted at 06:52:30 on February 14, 2016 · (Permalink)
Wow, that really puts into perspective the difference between those numbers.
Clipsterman · 1 points · Posted at 07:40:30 on February 14, 2016 · (Permalink)
Someone just listened to No such thing as a fish :)
togame27 · 1 points · Posted at 07:44:34 on February 14, 2016 · (Permalink)
Oh don't stop there! One trillion is about 30,000 years or all of human history!
romulusnr · 1 points · Posted at 09:42:37 on February 14, 2016 · (Permalink)
If you've ever dealt with Unix timestamps, you probably knew this.
ItsSansom · 1 points · Posted at 10:18:14 on February 14, 2016 · (Permalink)
All you're doing is multiplying by a thousand. It sounds crazy when you first read it, but then you realise it's pretty logical
NAN001 · 1 points · Posted at 11:59:09 on February 14, 2016 · (Permalink)
1000*11.5 days are 32 years. Nothing crazy here.
reddituser08016 · 1 points · Posted at 12:47:05 on February 14, 2016 · (Permalink)
I will remember this next time the lottery reaches a billion dollars.
QCMBRman · 1 points · Posted at 17:52:07 on February 14, 2016 · (Permalink)
Ooh look at you having a million sex.
KevansMcGurgen · 1 points · Posted at 10:46:44 on February 18, 2016 · (Permalink)
Is that surprising? That 11.5*1000 is 11,500?
santaliqueur · 0 points · Posted at 01:37:26 on February 14, 2016 · (Permalink)
1 million seconds is 11 days. 1 billion is the number of times I've read this statistic on Reddit.
mantisbenji · 0 points · Posted at 01:57:43 on February 14, 2016 · (Permalink)
I don't get why people get so impressed over this. I mean, a billion is a thousand times one million, so 11500 days, which is quite clearly some 30 or so years. Maybe the amazement is product of the words being similar.
arzthaus · 0 points · Posted at 04:36:01 on February 14, 2016 · (Permalink)
1 million secs is a million more than all the mathematicians here have had.
[deleted] · 357 points · Posted at 22:19:35 on February 13, 2016 · (Permalink)*
[deleted]
KSFT__ · 12 points · Posted at 03:02:58 on February 14, 2016 · (Permalink)
For people who can't/are too lazy to find the SMBC comic (because it's really hard to find particular ones for some reason), here's how it works:
Say you're multiplying
abyb. According to this trick, the tens place is(a-5)+(b-5), and the ones place is(5-(a-5))(5-(b-5)). This givesluckierbridgeandrail · 17 points · Posted at 03:37:56 on February 14, 2016 · (Permalink)
Seems to be the top result for https://www.google.com/search?q=SMBC+Polish+hand+magic and the second for https://www.google.com/search?q=Polish+hand+magic
… I'm afraid to check Bing for ‘Polish hand magic’ because the results probably involve a woman named Dominika doing something I don't want in my browser history.
[deleted] · -1 points · Posted at 18:26:08 on February 14, 2016 · (Permalink)*
[deleted]
bjb406 · 9 points · Posted at 06:04:41 on February 14, 2016 · (Permalink)
I had never heard of SMBC before. You bastard. How will I ever escape my computer screen now?
Ihavenofriendzzz · 9 points · Posted at 09:38:49 on February 14, 2016 · (Permalink)
This is so much harder than memorizing times tables.
[deleted] · 8 points · Posted at 09:42:43 on February 14, 2016 · (Permalink)*
[deleted]
Ihavenofriendzzz · 1 points · Posted at 18:51:11 on February 14, 2016 · (Permalink)
I know. I was kind of joking. It's a cool trick.
OPreco · 3 points · Posted at 07:11:35 on February 14, 2016 · (Permalink)
Along the same lines, you can use your hands to quickly calculate 9*x for 1<x<9.
Hold both hands in front of you. Imagine your fingers are numbered from 1-10 going left to right. I.e. If you are looking at the backs of your hands, your left pinkie is "1" and your right pinkie is "10".
Fold down the finger that corresponds to the multiple of 9 you are trying to calculate. Let's say 9*6, so your right thumb. The fingers to the left of this one represent the tens place(5), the fingers to the right represent the ones place (4). Together, they are your product 54.
If you haven't already memorized 18,27,36,45,54,63,72, and 81, now you don't have to. Notice the pattern in the numbers ;)
CasualRamenConsumer · 2 points · Posted at 15:52:31 on February 14, 2016 · (Permalink)
My sister taught me this when I was quite young. Helped me memorize these and it's a pretty neat trick.
Banditosaur · 2 points · Posted at 03:44:01 on February 14, 2016 · (Permalink)
Do you have the link to the SMBC comic?
phle · 3 points · Posted at 14:55:12 on February 14, 2016 · (Permalink)
Here you go:
the Saturday Morning Breakfast Cereal (SMBC) comic mentioned;
direct link to the image
(found by following one of the Google search links in /u/luckierbridgeandrail's comment;
no idea why no-one's not bothered direct-link to it, though)
theshinygreen · 1 points · Posted at 10:23:30 on February 14, 2016 · (Permalink)
A similar trick for the nine times table - say you wanted to do 4 * 9.
Put your 4th finger down. The number of fingers to the left of that finger is the number of 10s (3 times 10, count them) and the number of fingers on the right is the number of ones (6*1).
Add these together to get your number. It only works up to 10*9.
Irru · 1 points · Posted at 11:37:07 on February 14, 2016 · (Permalink)*
Wait, does this work for 6*6 too?
One finger on each hands gives a result in the 20s?
phle · 3 points · Posted at 14:50:08 on February 14, 2016 · (Permalink)
Ok, let's do this by just copy-paste-ing the instructions, but change the numbers to our task:
Represent each number with a hand
in our case: one will have one finger up; the other will have one finger up
This is your tens place
in our case: (1+1)* 10 = 20.
This is your ones place
in our case: 4 × 4 = 16
in our case: 20 + 16 = 36
(the Saturday Morning Breakfast Cereal (SMBC) comic mentioned;
direct link to the image)
Irru · 1 points · Posted at 15:37:32 on February 14, 2016 · (Permalink)
Ahahaha, yes of course.
chairitable · 1 points · Posted at 16:36:34 on February 14, 2016 · (Permalink)
That's why you have to show your work!
I've been doing math on khan Academy for fun and long-form divisions are kicking my ass...
marashadows · 1 points · Posted at 17:04:18 on February 19, 2016 · (Permalink)
Handy.
sederts · -4 points · Posted at 23:48:17 on February 13, 2016 · (Permalink)
this method gives 8 * 8 = (3+3) * 10 + 3 * 3 = 69
You sure this works?
[deleted] · 26 points · Posted at 00:15:00 on February 14, 2016 · (Permalink)
You've got 6 fingers on each hand. Are you from the South?
ducttape83 · 6 points · Posted at 06:22:47 on February 14, 2016 · (Permalink)
My name is Inigo Montoya, you killed my father. Prepare to die.
dude_pirate_roberts · 1 points · Posted at 07:57:49 on February 14, 2016 · (Permalink)
Well done! How many "six finger" opportunities are there?!
[deleted] · 6 points · Posted at 00:22:55 on February 14, 2016 · (Permalink)
8 x 8
Palm=5, Finger=1
So that's:
60 + 4 = 64
[deleted] · 4 points · Posted at 06:09:09 on February 14, 2016 · (Permalink)
Maybe I'm not getting this, 7x7 with this method isn't giving me 49? What am I doing wrong?
Never mind, figured it out. Duhh.
bonadzz · 1 points · Posted at 20:28:50 on February 14, 2016 · (Permalink)
7 x 7
Palm=5, Finger=1
Left hand (2 fingers up, 3 down)
Right hand (2 fingers up, 3 down)
So that's:
(2 + 2) fingers up x 10 = 40
(3 x 3) fingers down = 9
40 + 9 = 49
[deleted] · -11 points · Posted at 00:10:42 on February 14, 2016 · (Permalink)
[deleted]
qwertygasm · 6 points · Posted at 01:54:01 on February 14, 2016 · (Permalink)
6
[deleted] · 6 points · Posted at 02:25:53 on February 14, 2016 · (Permalink)*
[deleted]
[deleted] · 2 points · Posted at 02:19:15 on February 14, 2016 · (Permalink)
You sure showed him!
CHUCK_NORRIS_AMA · 1 points · Posted at 03:32:25 on February 14, 2016 · (Permalink)*
Edit: this comment is meaningless without the parent
Dont_Ask_I_Wont_Tell · 0 points · Posted at 04:33:51 on February 14, 2016 · (Permalink)
😂😂
antijudo · 91 points · Posted at 21:09:49 on February 13, 2016 · (Permalink)
The hairy ball theorem says that there is always a point on earth where there is no wind.
Sodium1970 · 118 points · Posted at 01:29:16 on February 14, 2016 · (Permalink)
And that point is never Wellington, New Zealand.
cumuloedipus_complex · 2 points · Posted at 01:07:32 on February 15, 2016 · (Permalink)
Nor Chicago, Illinois.
lucidianforge · 1 points · Posted at 20:01:59 on February 18, 2016 · (Permalink)
Nor Cheyenne, Wyoming.
Vimda · 1 points · Posted at 08:17:18 on February 14, 2016 · (Permalink)
My parents used to say that when there was no wind there was an earthquake coming. Obviously not true in Wellington.
VacuouslyUntrue · 3 points · Posted at 09:34:24 on February 14, 2016 · (Permalink)
It is vacuously true if there is always wind.
Zappulon · 2 points · Posted at 14:33:30 on February 14, 2016 · (Permalink)
Christchurch on the other hand...
Mysticjosh · 2 points · Posted at 01:56:19 on February 15, 2016 · (Permalink)
I think the new zealands have pissed of the elementals. Wind in Wellington, Earthquakes in Christchurch, weird water in cape reinga, and lava from them volcanoes. I knew Maui shouldnt have taken all that fire
[deleted] · 3 points · Posted at 03:09:43 on February 14, 2016 · (Permalink)
I'm not sure the Hairy Ball theorem applies to an atmosphere -- couldn't the air travel up and down to produce wind as well? In fact, I'm pretty sure that's what would happen in the "no wind" places, since otherwise the air would just... build up infinitely, I think. I dunno.
Boukish · 1 points · Posted at 06:10:06 on February 14, 2016 · (Permalink)
But air moving up/down isn't "wind" in the conventional meaning of the term (perceptible current); yes it'd translate to an area of higher/lower pressure to be sure, but you'd stand there and wouldn't feel any wind.
[deleted] · 1 points · Posted at 19:54:30 on February 14, 2016 · (Permalink)
You can feel wind if it's traveling up and down. To prove this, lie down when it's gusty.
Admittedly, I don't know if the up-and-down winds would be strong enough to feel; I don't know enough about meteorology.
VacuouslyUntrue · 1 points · Posted at 09:35:30 on February 14, 2016 · (Permalink)
Yes the theorem is about the surface of a sphere, a 2d object. Our atmosphere is not the surface of a sphere, it is a 3d object. So wind can travel up and down as well as tangentially to the surface and so the theorem does not apply.
VacuouslyUntrue · 1 points · Posted at 09:33:05 on February 14, 2016 · (Permalink)
Eh, it says that there are is no, non vanishing, tangent vector field on a sphere. It's not clear to me that the space in which wind occurs is topologically equivalent to a sphere.
This would however be true for wind considered at a specific elevation, but not wind overall. This is because the theorem is about a 2 dimensional object, the surface of a (topological) sphere. But our atmosphere, is a 3 dimensional object.
IAMA_Printer_AMA · 0 points · Posted at 05:07:18 on February 14, 2016 · (Permalink)
You're leaving out the part where that space with now wind is the center of a cyclone.
StarFoxN64 · 191 points · Posted at 20:02:48 on February 13, 2016 · (Permalink)
A number divided by itself-repeated gives .x0x9 repeated, with x being the number of times the number after it appears based on how many digits the numerator is. Works for any whole number.
1/11 = .090909 43/4,343 = .009900990099 612/612,612= .000999000999
gansmaltz · 62 points · Posted at 00:40:57 on February 14, 2016 · (Permalink)*
So 1/1 = .999999...?
Edit: I already know, I just thought it was cool that this is another proof of that fact
karmapopsicle · 32 points · Posted at 03:36:22 on February 14, 2016 · (Permalink)
1 = 0.9...
So yes.
Nichdel · 16 points · Posted at 05:25:50 on February 14, 2016 · (Permalink)
Yes!
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999... or 1
This is called non-uniqueness.
Madmeerkat55 · 5 points · Posted at 11:09:54 on February 14, 2016 · (Permalink)
Can't tell if math or meta
robertmath · 4 points · Posted at 11:31:10 on February 14, 2016 · (Permalink)
or meth
Skullkid9 · 1 points · Posted at 17:16:04 on February 14, 2016 · (Permalink)
Yes
YetAnotherDumbGuy · 12 points · Posted at 01:41:03 on February 14, 2016 · (Permalink)
If you divide the both sides of the fraction by the numerator then you can see why this works:
hypervelocityvomit · 1 points · Posted at 11:59:33 on February 15, 2016 · (Permalink)
All digits 9 is insightful, too:
heap42 · 1 points · Posted at 23:57:54 on February 13, 2016 · (Permalink)
I am to lazy to verfiy/proof but does the same hold for all bases as in bas 8 would be .x0x7?
Fake_Name_6 · 1 points · Posted at 00:58:44 on February 14, 2016 · (Permalink)
Yes, it would be. I can't give you a strict proof of this, but it makes sense if you consider that a number repeated is 100.....01 times itself (number of zeros is 1 less than the number of digits in the original number)
[deleted] · 1 points · Posted at 06:14:56 on February 14, 2016 · (Permalink)
WITCHCRAFT.
djabor · 1 points · Posted at 12:46:50 on February 14, 2016 · (Permalink)
weirdness
CHiLLSpeaks · 31 points · Posted at 05:46:33 on February 14, 2016 · (Permalink)
If you only buy two different styles of socks (for example, white and black or short and long), you will always have at least two that match if you pull three socks out of your sock drawer without looking.
Changed my life.
blindsight · 9 points · Posted at 14:19:09 on February 14, 2016 · (Permalink)
That's the pigeon hole principle. In general, if you have n styles of socks, then you need to pull out n + 1 socks to be guaranteed a matching pair.
(The pigeon hole principle is essentially that if you try to put more pigeons into pigeon holes than you have holes, then at least one hole will have 2 pigeons.)
gozman · 1 points · Posted at 03:27:48 on February 17, 2016 · (Permalink)
What if I had 5 of each pair of socks, couldn't I pull put 3 individual socks that are the exact same?
blindsight · 2 points · Posted at 11:35:03 on February 17, 2016 · (Permalink)*
You could even have infinite of each type of socks, and the pigeon hole principle applies. If you have n varieties of socks, then you only need to pull out n+1 socks to be guaranteed at least one match.
The proof for why this is true is quite intuitive: imagine that this wasn't the case. This would mean that you have n+1 distinct socks. But that's impossible, since there are only n types of socks. Thus we have a contradiction, so you must have at least one matching pair.
Note that this doesn't say that you'll have exactly one match. You could have up to (n+1)/2 matches. Or you could have more than two of one kind of sock. But you are guaranteed to get at least one matching pair.
gozman · 1 points · Posted at 13:53:28 on February 17, 2016 · (Permalink)
Ahhh, sorry. I was really focussed on taking specifically three socks out at a time. I get it now, cheers
q3w3e3 · 1 points · Posted at 15:25:19 on February 23, 2016 · (Permalink)
Couldnt I pull out three of the same type in a row?
blindsight · 3 points · Posted at 15:52:12 on February 23, 2016 · (Permalink)
Which contains one match.
-MagicHands- · 8 points · Posted at 10:16:51 on February 14, 2016 · (Permalink)
Why don't you only buy one type of sock.. then you only ever have to grab 2 :)
CHiLLSpeaks · 4 points · Posted at 16:30:05 on February 14, 2016 · (Permalink)
Sometimes the color of your socks can bring together the outfit.
bob85m · 3 points · Posted at 02:51:41 on February 18, 2016 · (Permalink)
That's some solid math right there!
[deleted] · 3 points · Posted at 06:43:37 on February 14, 2016 · (Permalink)
Applied Ramsey theory. Sexy.
[deleted] · 304 points · Posted at 20:39:42 on February 13, 2016 · (Permalink)
The natural logarithm of a number equals the integral of 1/x from one to that number (if I recall correctly). I think it's weird that something as tricky as the logarithm comes from such a simple expression.
CaesarTheFirst1 · 74 points · Posted at 22:17:05 on February 13, 2016 · (Permalink)
This gives intuition: https://arcsecond.wordpress.com/2011/12/17/why-is-the-integral-of-1x-equal-to-the-natural-logarithm-of-x/
LabKitty · 92 points · Posted at 23:17:50 on February 13, 2016 · (Permalink)
It's wild that logarithms were around before calculus was invented.
Then, one day someone asks what the antiderivative of 1/x is. You can't use the power rule (because it would divide by zero) so we decide to make up a new function -- call it blerg(x).
You start checking out the properties of blerg(x) and you realize you rediscovered the log function!
Nine_Gates · 12 points · Posted at 01:57:26 on February 14, 2016 · (Permalink)
They probably figured that the derivative of log(x) was 1/x first.
CoronelNiel · 1 points · Posted at 02:41:19 on February 14, 2016 · (Permalink)
iirc limits help this out a lot but I might not be
NoGardE · 5 points · Posted at 03:04:03 on February 14, 2016 · (Permalink)
Iirc there's a decently easy* way to calculate it from the limit.
*For Euler or Gauss.
[deleted] · 2 points · Posted at 07:42:52 on February 14, 2016 · (Permalink)
There's also a dead easy way to calculate it for anyone.
Derivatives are isomorphisms. That is, their inverse transform is defined. Hence, if the derivative of 1/x exists, so does its integral.
Consider:
y = ex ; dy/dx = ex = y
Hence dy/dx = y
(1/y)dy = (1)dx
Integral of (1/y) = x
y = ex thus x = ln(y)
So the integral of (1/y) is ln(y).
NoGardE · 3 points · Posted at 08:21:02 on February 14, 2016 · (Permalink)
Could you mention that it's integral of (1/y)dx = x? Got a bit confused on that bit,made me think you were integrating on different variables on different sides.
[deleted] · 3 points · Posted at 08:48:16 on February 14, 2016 · (Permalink)
I was integrating both sides according to different variables. According to y on the left hand side, and x on the right hand side to be more precise.
See, if y = f(x) and dy/dx = f'(x), then:
dy = f'(x)dx
Integrating both sides with respect to y and x, we get:
y = f(x)
That's where the dx and dy come from when you integrate. Here, the integral of 1/y with respect to y is equal to the integral of 1 with respect to x, which is equal to x. Going back to y = ex , it becomes clear that ln(y) = x, hence the integral of (1/y) with respect to y is equal to ln(y).
NoGardE · 1 points · Posted at 09:08:47 on February 14, 2016 · (Permalink)
But you can't integrate dy on the left and dx on the right. Pulling away from the limit, that's multiplying by (y-y0) on the left, and by (x-x0) on the right.
I'm pretty sure both sides is integrated dx. Since y is a function of x, it's valid and correct math.
[deleted] · 1 points · Posted at 09:22:53 on February 14, 2016 · (Permalink)
Yes. Yes I can. No offence but I'm math major and I aced my Ordinary Differential Equations class, as well as Advanced Calculus I and II.
There's no pulling away from the limit whatsoever. Integrating y dy and f(x) dx is the exact same thing given you change your range of integration accordingly. Here, there's no range as we are dealing with general forms. We do not seek to find a scalar as an answer.
Here:
y = x
dy/dx = 1
dy = dx
y = x
I integrated with respect to y on the left side, and with respect to x on the right side.
qaisjp · 1 points · Posted at 10:46:16 on February 14, 2016 · (Permalink)
I do A2 further maths and now you have destroyed everything I've learnt in pure maths in the last two years
Good bye.
[deleted] · 1 points · Posted at 15:39:25 on February 14, 2016 · (Permalink)
Allow me to destroy it a little more just to show you that I am not trolling.
Exponential growth or decay is defined as:
dx/dt = kx
(1/x)dx = k dt
ln(x) = kt + u ; u is a constant
x = ekt+u = ekt eu = cekt ; c is a constant
x(t) = cekt is precisely the function for exponential growth and decay, with c = x(0). You can look it up on wikipedia.
To be fair, I shouldn't have renderend anything you've learn so far invalid. You just haven't learn about what I'm showing you yet.
qaisjp · 1 points · Posted at 16:09:47 on February 14, 2016 · (Permalink)
that's just differential equations?
maybe I made that comment too early in the morning, i understand your algebra now
[deleted] · 1 points · Posted at 16:28:34 on February 14, 2016 · (Permalink)
Yes, it's very basic differential equations, which can be used to find the antiderivative of 1/y
qaisjp · 1 points · Posted at 16:30:49 on February 14, 2016 · (Permalink)
gotta love auxiliary equations
and trial functions(!)
easy but a PITA
12345abcd3 · 1 points · Posted at 23:45:09 on February 14, 2016 · (Permalink)
I'd be curious if you could explain exactly how you get from
dy/dx=f(x)
To
dy=f(x)dx?
Obviously this is how you were taught to solve separable DEs and it works, but really this line is not particularly well defined.
Instead what you're actuality doing is integrating both sides of this line
dy/dx=f(x)
With respect to x. And the integral of dy/dx wrt x is the same as the integral of 1 wrt y.
[deleted] · 1 points · Posted at 05:00:32 on February 15, 2016 · (Permalink)
It's dy/dx = f'(x), not f(x)
y = f(x)
dy = f'(x) dx
And you cannot integrate dy/dx wrt x. You integrate some f(y) dy wrt y or some f(x) dx wrt x.
If you're wondering how dy/dx = f'(x) goes to dy = f'(x) dx... Then that's just by multiplying both sides by dx.
12345abcd3 · 1 points · Posted at 12:20:48 on February 15, 2016 · (Permalink)
But dy/dx is not a fraction, "multiplying by dx" is not a valid justification. You can certainly integrate dy/dx with respect to x, in fact I'm not sure how you could think that you could integrate the right hand side of an equation (f'(x)) with respect to x but not the letft hand side (dy/dx)? Both sides are the same...
I'm well aware of the method. "Multiply by dx" is not a justification, as when defining dy/dx we never define dy or dx separately. Of course you can think of dx as "a small change in x" but I think you would struggle to define it rigorously.
Have you taken any analysis?
[deleted] · 1 points · Posted at 18:49:28 on February 15, 2016 · (Permalink)*
First of all, we'll clarify right off the bat that yes, dy/dx is a fraction, and yes, I can multiply by dx.
http://imgur.com/a/oaQ42
First screenshot: implicit differentiation when f(x,y) = c. Label z = c, hence dz = 0. The partial derivative of z(x,y) is dz = F(x)dx + F(y)dy = 0. Dividing both sides by dx and isolating dy/dx gives the formula dy/dx = -F(x)/F(y).
Second screenshot: two integrals with respect to different variables being equal. The original equation was (1+x)dy - ydx = 0 which is the exact same thing as dy/dx = y/(1+x). Had this been dy/dx = 1/(1+x), then dy = 1/(1+x) dx and we'd have integrated with respect to different variable, hence why dy = f(x) dx is perfectly valid.
So all in all, I don't think you are well aware of the method. I don't think you've taken any ODE class either.
dx is perfectly well defined. Integrating with respect to different variables means you're doing the Riemman sum with h times delta(x) or h' times delta y, with h being the height under the curve. dx is the notation we give to delta(x) once we've put lim n-> infinity where n is the number of h times delta(x) aka number of intervals where we approximate the area under the curve. Doing this along the x axis or y axis yields the exact same result.
I am taking analysis right now, but I highly doubt you are. There's no way someone who is taking analysis would have no knowledge of advanced calculus. No knowledge of ODEs, that's fair enough.
So what are your academic credentials? I find it extremely odd that someone would argue that two integrals cannot be equal if they aren't integrated with respect to the same variable... Given he's knowledgeable math-wise.
Edit: let me give you a very basic example.
y = 3x ; 0<x<3 Hence x = y/3 ; 0<y<9
Then int[0~ 3] 3x dx = [0~ 9] y/3 dy =13.5
Which enlighten the fact that the Riemman sum, aka integral, taken along one axis or the other is the same.
If we do not care about intervals and do not seek to obtain a scalar as an answer, then:
int 3x dx = (3/2)x2 = (3/2)(y/3)2 = (1/6)y2
int (y/3) dy = (1/6)y2 = int 3x dx
Tada. So dy/dx = 3 ; dy = 3dx ; int dy = int 3dx ; y = 3x is 100% valid.
Edit #2: Here's a clear example of the procedure I was following for dy/dx = g(x). http://imgur.com/wtsSFtJ
They integrate dy, yielding y, and equate y = int g(x) dx. Clearly, they do not integrate dy/dx, as they multiply both sides by dx first.
Moreover, if T: Rn -> Rn+1 is defined by T(v) = int v dv, a linear transformation which inverse is defined, then:
int f(x) dx = T(f(x)) = T(y) = int y dy
T-1 (int f(x) dx) = T-1(T(f(x))) = f(x) = T-1(T(y) = y
so y = f(x) implies dy/dx = f'(x) ; dy = f'(x)dx ; T(1) = T(f'(x))
Hence int (1) dy = y = int f'(x) dx = f(x)
I'm pretty sure you thing int (dy/dx) dx is done with respect to x, but it isn't. the dx cancel out and it becomes dy, which is integrated with respect to y, yielding y.
12345abcd3 · 1 points · Posted at 22:41:52 on February 15, 2016 · (Permalink)
Maths credentials - about to finish my masters in maths. Yes I've taken a course in ODEs which is why I know this method.
I think you're misunderstanding me but that could be me not communicating well. I'm not saying this method doesn't work, I'm not saying its wrong, my original question was just hoping to lead to some discussion about why the method works.
To be clear our methods are the same, however where you would write
dy/dx=f'(x)
dy=f'(x)dx
Integrate both sides
y=f(x)+c
I would rewrite it equivalently (but slightly more rigorously) as
dy/dx=f'(x)
Integrate both sides wrt x
But the integral of dy/dx wrt x is equal to the integral of 1 wrt y. And so we have
y=f(x)
Maybe once you've done some analysis you might see what I'm getting at when I say that "multiply by dx" isn't exactly rigorous. In some cases treating dy/dx as a fraction might work, eg in the chain rule, but it doesn't always. If you want an example of when it doesn't work look up the total derivative.
Sorry if that sounded condescending, but I do think that after a bit more maths you will see that "multiply by dx" isn't exactly the most sound mathematical argument. Incidentally, I don't think I said or at least didn't mean to imply that two integrals integrated with respect to different variables cannot be equal. My point was that it is possible to integrate dy/dx with respect to x, which it certainly is.
[deleted] · 1 points · Posted at 22:59:30 on February 15, 2016 · (Permalink)
Well I thought you and I were doing the same thing in different ways, and you were just treating dy/dx as a function of x hence doing the exact same thing as int f'(x) dx but saying it doesn't equate to int y dy.
I do need more math training regarding Real Analysis, tho.
[deleted] · 1 points · Posted at 09:56:32 on February 14, 2016 · (Permalink)
No, it's very much possible, and it's a very common method in solving differential equations that you learn among the first things there. The integral is just a dumb operator, the dx or dy is an infinitesimal multiple that determines its value.
He just solved a simple, fully separable differential equation. Probably the simplest there is. It gets a lot more complicated when you add second derivatives and functions of x and y; this is about as simple as differential equations get, however. Source: the second applied math course I took in physics.
NoGardE · 1 points · Posted at 15:59:13 on February 14, 2016 · (Permalink)
Ahhhhhhhh, right. Looks like it's been too long since I did any continuous math.
I_EAT_GUSHERS · 2 points · Posted at 03:09:35 on February 14, 2016 · (Permalink)
They exist because they're the "inverse" of exponentiation.
Crazy_Asian_Man · 2 points · Posted at 13:59:43 on February 14, 2016 · (Permalink)
Hey! That's blerg(x)+C
hypervelocityvomit · 2 points · Posted at 12:01:20 on February 15, 2016 · (Permalink)
Ermahgerd blergarithms so sorry
[deleted] · 4 points · Posted at 04:55:27 on February 14, 2016 · (Permalink)
the logarithm isn't really that tricky though, it's just the inverse of exponentiation.
[deleted] · 1 points · Posted at 11:33:07 on February 14, 2016 · (Permalink)*
The logarithm is very tricky when you meet it the first time in school. It's a thing where you put in a number, and another number comes out and doesn't look at all like what you put in, and there's no readily understandable way (for a kid) to know how it got there.
EDIT: Particularly when the first thing you learned was the base 10 logarithm, which you just sort of understand if you tilt your head and squint, but then they dump the totally random natural logarithm on your head, and tell you to use that instead.
[deleted] · 3 points · Posted at 01:37:38 on February 14, 2016 · (Permalink)
If you take 1/x where x>=1 and rotate it in three dimensional space about the x-axis the resulting surface has infinite surface area but finite volume. That is to say you could fill it with a finite amount of paint, but you could never have enough paint to cover its exterior. This surface is known as the Gabriel's Horn or Torricelli's trumpet.
PM_girl_peeing_pics · 3 points · Posted at 04:09:26 on February 14, 2016 · (Permalink)
You mean, "something as tricky as the natural logarithm". Logarithms in general aren't tricky, they're simply one of the two inverse operations of exponentiation (the other is root/radicals). For any ab = c, log[base a] c = b.
Pegguins · 2 points · Posted at 01:35:53 on February 14, 2016 · (Permalink)
The logarithms just the start, you get to find all sorts of wonderful functions we define in terms of integrals, Bessel functions, error functions (my favourite), hyper geometric functions etc.
LiamsFriend · 4 points · Posted at 21:48:30 on February 13, 2016 · (Permalink)
thats cos the integral of 1/x is equal to the natural log of x. And the natural log of 1, is 0
sup3rdr01d · 74 points · Posted at 22:12:41 on February 13, 2016 · (Permalink)
Lol don't abbreviate "because" to "cos" in a mathematical thread...
Nettius2 · 1 points · Posted at 02:25:44 on February 14, 2016 · (Permalink)
You can actually define the natural log from this integral. But then you have to prove that it is the inverse function of the exponential function.
snkn179 · 1 points · Posted at 04:23:31 on February 14, 2016 · (Permalink)
If you know that the derivative of ex is the y-value (on the graph y=ex), you can see that the derivative of ln(x) is 1/x since the graph is flipped about the x=y line so the new tangent slope is 1/(previous slope) and the derivative is now determined by the x-axis instead of the y-axis. Difficult to explain in writing but this was something that helped me understand it.
iIsLegend · 1 points · Posted at 07:18:36 on February 14, 2016 · (Permalink)
Telling first year Calc students to find the indefinite integral of 1/x is hilarious.
Rodbourn · 1 points · Posted at 11:48:28 on February 14, 2016 · (Permalink)
That's why it's called the natural logarithm.
Tyndall_on_the_green · 1 points · Posted at 13:10:48 on February 14, 2016 · (Permalink)
Here is what gets me about it. Things are a bit tricky, so beware...
The natural log and ex are inverse functions, and 1/x is its own inverse. ex is a function that is its own derivative. Now, if I take the antiderivative of a function that is its own inverse (1/x) I get an answer (ln x). Take the inverse function of that answer to get a new function (ex). That final function is its own derivative. I find it difficult to express what is happening here, but it feels nifty in terms of the logic.
Phantom1thrd · 1341 points · Posted at 19:24:10 on February 13, 2016 · (Permalink)
0.9999999 (repeating) equals 1
regdayrF · 1081 points · Posted at 20:16:32 on February 13, 2016 · (Permalink)
The very short thought behind it:
1/3 + 1/3 + 1/3 = 1
1/3 + 1/3 + 1/3 = 0.33333... + 0.33333... + 0.33333... = 0.99999....
[deleted] · 2218 points · Posted at 21:01:20 on February 13, 2016 · (Permalink)*
[deleted]
happy_felix_day_34 · 519 points · Posted at 21:29:40 on February 13, 2016 · (Permalink)
This one used to piss me off. Then one day I saw this proof and I was converted.
ThirdFloorGreg · 86 points · Posted at 23:14:23 on February 13, 2016 · (Permalink)
This proof is not very rigorous. The same sort of logic can be used to prove that the sum of all natural numbers is -1/12.
happy_felix_day_34 · 10 points · Posted at 23:24:03 on February 13, 2016 · (Permalink)
Example?
sederts · 22 points · Posted at 23:44:18 on February 13, 2016 · (Permalink)
https://www.youtube.com/watch?v=w-I6XTVZXww
The result they derive is a bastardization of a true result.
ζ(-1) = -1/12,
and ζ(n) is defined as 1-n + 2-n +3-n +4-n ...
so -1/12 = ζ(-1) = 1+2+3+4....
but that definition only holds for n > 1.
In the youtube video they use some cool infinite sum tricks to show the same thing, 1+2+3+4... = -1/12, and its very understandable and worth watching.
happy_felix_day_34 · 22 points · Posted at 23:59:38 on February 13, 2016 · (Permalink)
That's pretty interesting but also very obviously incorrect math. If you subtract the sum of one infinite series from another, you have to take the whole sums subtracted from each other. You can't break it up into parts to make certain things cancel out.
So, yes, this is interesting, but it's just wrong. The sum of any infinite series with a rate greater than one is infinity. It can't be stated as a value.
Shaxys · 14 points · Posted at 00:59:00 on February 14, 2016 · (Permalink)
If I remember correctly, it can be done with somewhat correct mathematics, one of the guys in the video had a blog post about analytic continuation and whatnot.
I think the real deal is that zeta of 1 is equal to -1/12 but the sum of all natural numbers can only be said to equal -1/12 if we "force" it to converge (as in, it would be the only thing the sum could converge to, if it were to converge).
ccpuller · 4 points · Posted at 06:14:42 on February 14, 2016 · (Permalink)
Yeah but it doesn't converge.
Shaxys · 2 points · Posted at 14:04:11 on February 14, 2016 · (Permalink)
No, it doesn't.
barbadosslim · 7 points · Posted at 03:59:37 on February 14, 2016 · (Permalink)
This objection doesn't seem to apply to the x=.999... proof though.
ThirdFloorGreg · 1 points · Posted at 06:34:17 on February 24, 2016 · (Permalink)
Scooting everything over one decimal place is the same sort if error.
barbadosslim · 1 points · Posted at 03:07:16 on February 25, 2016 · (Permalink)
So 10*.999... = Sum (n=1 -> infinity) 10*9*10-n happens to be true, but c*Sum(n=1 -> infinity) y =/= Sum(n=1 -> infinity) c*y in general? I don't remember that at all damn
ThirdFloorGreg · 0 points · Posted at 03:09:51 on February 25, 2016 · (Permalink)
It is usually fine, but isn't strictly allowed. There are other, more complicated cases, where it will give you values for series that diverge.
barbadosslim · 1 points · Posted at 03:30:02 on February 25, 2016 · (Permalink)
Can you give an example?
ThirdFloorGreg · 0 points · Posted at 04:01:06 on February 25, 2016 · (Permalink)
Not really, haven't taken a math class in a long time.
barbadosslim · 1 points · Posted at 04:37:35 on February 25, 2016 · (Permalink)
Yeah I just re-enrolled myself I don't know shit about shit.
[deleted] · 0 points · Posted at 18:12:50 on February 14, 2016 · (Permalink)
It doesn't, and you don't need to prove it.
barbadosslim · 1 points · Posted at 22:47:56 on February 14, 2016 · (Permalink)
lol
[deleted] · 1 points · Posted at 00:05:08 on February 15, 2016 · (Permalink)
... It's literally just a definition.
.999... =1 cause we say it does. It's just another way to write the number. You have to use this fact to "prove" it.
barbadosslim · -1 points · Posted at 18:40:46 on February 15, 2016 · (Permalink)
No it isn't, it's defined as .9+.09+.009... Which is a sum equal to 1.
jorl17 · 5 points · Posted at 04:52:37 on February 14, 2016 · (Permalink)
It is correct maths within an appropriately defined system. It yields correct results within constrained contexts.
savagepotato · 8 points · Posted at 04:00:02 on February 14, 2016 · (Permalink)
You're really arguing with a bunch of professional mathematicians and physicists about a result that is actually important to physics. Just because it's counterintuitive doesn't mean that it's wrong. The same channel has released a bunch of videos about why -1/12 is actually a worthwhile and important idea and not just a trick of math or "very obviously incorrect". There isn't anything wrong with the math they show.
https://www.youtube.com/watch?v=0Oazb7IWzbA
https://www.youtube.com/watch?v=d6c6uIyieoo&feature=youtu.be
https://www.youtube.com/watch?v=E-d9mgo8FGk&feature=youtu.be
Obyeag · 15 points · Posted at 04:39:02 on February 14, 2016 · (Permalink)
It is wrong, at least in a general sense. The only reason why it is correct is due to analytical continuation or the assignments of sums to divergent series. The result 1+2+3+...=-1/12 relies on the assignment of 1/2 as the sum of 1-1+1-1+... which is actually a divergent series. The reason why people take fault with the numberphile video is because they don't explain analytical continuation, ramanajuan sums or anything, leading layman to incorrect conclusions.
[deleted] · 0 points · Posted at 07:03:31 on February 14, 2016 · (Permalink)
[deleted]
Kai_Daigoji · 1 points · Posted at 15:27:46 on February 14, 2016 · (Permalink)
No, it's called a Ramanujan sum, and it's only true in certain specialized contexts.
Xguy28 · 1 points · Posted at 05:15:48 on February 14, 2016 · (Permalink)
Why not? 1+2+3+4 =10 and 2+3+1+4 =10. The order you add sums does not matter.
Lehona · 2 points · Posted at 06:28:34 on February 14, 2016 · (Permalink)
That's not always true though. I'm on mobile, but the general idea is: You can only do that with a sum if it's absolutely convergent (ie if you can make every term positive and it still converges).
Xguy28 · 1 points · Posted at 06:51:47 on February 14, 2016 · (Permalink)
What about the sum of all real number - the sum of all real numbers. Surely that's zero right? I know that you can't subtract from a diverging series since infinity - any finite number is still infinity, but that doesn't make it wrong to subtract a number.
Anyway I think this is a good video explaining it in a bit more depth.
Lehona · 1 points · Posted at 05:15:21 on February 15, 2016 · (Permalink)
That's the point though. I will give an example using integers because it's easier: I can write the sum of all integers like this:
(-1 + 2) + (-2 + 3) + (-3 + 4) + (-4 + 5)... + 1. Every parenthesis evaluates to one and there are infinitely many terms, so the sum is infinite already!
You're only allowed to rearrange terms if it's absolutely converging.
Xguy28 · 1 points · Posted at 06:56:45 on February 15, 2016 · (Permalink)
OK, I'll buy that.
Lehona · 1 points · Posted at 20:10:38 on February 16, 2016 · (Permalink)
Also consider the following: While intuitively it should add up to zero (For every positive number there's a negative one with equivalent magnitude, right?), it's not actually a converging sum. I don't want to bother you with definitions (although I guess they'd be very helpful here?), but depending on where you start, the sum up to the nth term would be either 0, -n/2 or n/2 (approximately). So it's constantly changing between different values, never getting closer to one in particular but actually growing apart as n gets bigger. Thus it's very wrong to assign a particular value to the sum, because it's constantly changing.
There are reason why you'd assign -1/12 to the sum of all natural numbers, but it's in a very specific context.
[deleted] · -1 points · Posted at 03:49:54 on February 14, 2016 · (Permalink)
[deleted]
Archangel_117 · 3 points · Posted at 04:41:06 on February 14, 2016 · (Permalink)
But they aren't adding positive numbers forever, that's the point. The question is the SUM of ALL natural numbers, not the sum of all numbers up to a point, but the sum of every natural number, of which there are an infinite quantity. Because infinity is a concept rather than a number itself, it has properties that numbers don't have.
This theory doesn't argue that you won't get a forever increasing positive number as you forever add positive integers, it's stating what happens when you reach the end of forever (infinity), that if you literally sum ALL of them, you get -1/12.
happy_felix_day_34 · 0 points · Posted at 04:47:38 on February 14, 2016 · (Permalink)
Except that it is actually 1+2+3+4+5+....
Meaning that it is constantly adding a number one number value greater than the one before it. So it is actually adding forever increasing positive numbers.
How can the sum of all of these numbers be less than the smallest number in the series?
neos300 · 2 points · Posted at 06:12:27 on February 14, 2016 · (Permalink)
Short answer: infinity and the equal sign are more complicated than you think.
[deleted] · 6 points · Posted at 08:38:44 on February 14, 2016 · (Permalink)
The video does a pretty terrible job of explaining it. It starts with the assumption that the series (sum)(-1)n is equal to 1/2, but this is never justified. It would also be impossible to justify since it's untrue.
sederts · 1 points · Posted at 16:31:15 on February 14, 2016 · (Permalink)
I said it was a bastardization of a true result, and the video is understandable. Yes, Ramanujan summation does not allow setting the sum of the series "equal" to the value you derive, but what they did was still cool nonetheless.
[deleted] · 2 points · Posted at 17:21:35 on February 14, 2016 · (Permalink)
My reply was meant more for the average person who might click on that link and be horribly misled. Also, not to sound like a curmudgeon, but I really despise that video and the channel it comes from. It tries to pass off that result as a paradox but does so by starting with an assumption that isn't even true for sums of series in the traditional sense. Like, the only way that result could be "astounding" is if you're stuck thinking of series as sequences of partial sums (or informally as "infinite sums"), but it's actually not that interesting of a result if it just flows from the assumptions of Ramanujan or Cesaro sums. The video makes no such clarification, and so you have morons in the comments saying "math is flawed" and feebly trying to refute the video without adequate knowledge of the subject.
What I find most silly is that if viewers think 1+2+3+4... = -1/12 is some shocking result, why do they have no problem accepting 1-1+1-1+... = 1/2 which is also extremely counterintuitive? It would be like if I told my students that 1+1=0, and from that I could show that 2+2=0. But it's not false because they were expressed in mod 2 the whole time (which I casually don't tell them so that they're left thinking math is all lies).
Bobius · 3 points · Posted at 08:51:05 on February 14, 2016 · (Permalink)
Please stop spreading this kind of stuff. My students all think it's true in some form of useful way and it irritates me to no end.
ThirdFloorGreg · 1 points · Posted at 23:28:51 on February 13, 2016 · (Permalink)
Ugh, formatting on Reddit is a pain. Google Ramanujan summation and see if you can figure it out.
YCobb · 2 points · Posted at 08:52:46 on February 14, 2016 · (Permalink)
Just out of curiosity, what's wrong with its logic? It looks fine to me (as a programmer, not a mathematician) so I'm curious what the trick is.
ThirdFloorGreg · 2 points · Posted at 09:05:59 on February 14, 2016 · (Permalink)
Repeating decimals are basically shorthand for a series, in this case 9*10-n indexed from 0. You can't treat series like that, you can get all kinds of contradictory answers if you do.
please-disregard · 2 points · Posted at 14:30:01 on February 14, 2016 · (Permalink)
Well, that's true that you have to be careful with limits, but every step in the proof is actually valid for dealing with limits. The thing you really need to be careful with is rearranging the terms in a series. The one thing he needs to be careful with is assuming that the limit exists in the proof. But that's fairly simple to show. Since the sequence 0.99... is monotone, it follows from the fact that it's bounded above by 1 that the series converges. The proof above is valid for showing that the limit is exactly 1.
ThirdFloorGreg · 2 points · Posted at 16:29:12 on February 14, 2016 · (Permalink)
.999... is a number not a function. Talking about limits makes no sense.
dispatch134711 · 1 points · Posted at 21:52:45 on February 14, 2016 · (Permalink)
What is the limit of the sequence {0.9, 0.99, 0.999, ...} ?
you can show it's 1 with the geometric series.
ThirdFloorGreg · 1 points · Posted at 22:31:21 on February 14, 2016 · (Permalink)
That's a sequence, not a series. 0.999... Is a numerical representation of the limit of the series 910-n (indexed from 1). It doesn't have a limit, it *is a limit. And since the limit of that series is 1, 0.999... must equal 1.
Edit: I swear that your comment called it a series the first time I read it. I then proceeded to make essentially the same point. But 0.999... is still a number, not a series. Numbers don't have limits, they are limits.
dispatch134711 · 1 points · Posted at 22:40:27 on February 14, 2016 · (Permalink)
That was another guy calling it a series, which is a sum. You can consider it a sequence of partial sums 0.9, 0.9+ 0.09, 0.9 + 0.09 + 0.009, ... but yes.
ThirdFloorGreg · 1 points · Posted at 22:43:20 on February 14, 2016 · (Permalink)
That was me being sloppy. Repeating decimals can be thought of as a representation of a series, but they aren't really series.
[deleted] · 1 points · Posted at 16:26:07 on February 14, 2016 · (Permalink)
Yes, S(n) -> 1
But if the sum [k: 1 -> n] ~ 9x10-k = S(n)
Then (10-1) S(n) = 9 - 9x10-n
Hence 0.9999... Doesn't equal 1. I mean, its least upper bound is 1 so obviously S(n) isn't equal to 1. The proof above states that S(n) = lub[S(n)] which is laughable at best.
MyAssholeSmellsAwful · -4 points · Posted at 10:50:40 on February 14, 2016 · (Permalink)
Believe me, we can tell that you aren't one. You really don't have to say so out loud.
YCobb · 1 points · Posted at 17:03:09 on February 14, 2016 · (Permalink)
Thanks mate
Ness4114 · 1 points · Posted at 15:43:33 on February 14, 2016 · (Permalink)
Yes but chances are these proofs are back of the envelope type things for people without an extensive math background, and a truly rigorous proof would glaze their eyes right over.
Alphaetus_Prime · 0 points · Posted at 05:33:00 on February 14, 2016 · (Permalink)
Which it is, in a certain sense. You can't sum all natural numbers, but if you could, you'd get -1/12.
ThirdFloorGreg · 4 points · Posted at 05:39:27 on February 14, 2016 · (Permalink)
That is not how divergent series work.
Alphaetus_Prime · -1 points · Posted at 05:58:14 on February 14, 2016 · (Permalink)
It kind of is though.
[deleted] · 0 points · Posted at 06:59:53 on February 14, 2016 · (Permalink)
[deleted]
Thinks_Too_Logically · 2 points · Posted at 09:46:37 on February 14, 2016 · (Permalink)
The Ramanujan summation of the natural numbers is -1/12. The series is divergent.
The -1/12 result basically shows another way of thinking about divergent series and how you can manipulate them. It's important to distinguish between the actual sum of a series (which in the case of 1+2+3+... diverges) and when you're using a different language to describe divergent series.
"It's actually true" isn't true when you're talking about the classical definition of series and summations. It is true when you're talking about other ways to analyze series.
ThirdFloorGreg · 3 points · Posted at 09:03:33 on February 14, 2016 · (Permalink)
The fact that this technique is useful in certain narrowly defined circumstances does not mean it is true. The series diverges, it has no finite sum.
MyAssholeSmellsAwful · -2 points · Posted at 10:34:06 on February 14, 2016 · (Permalink)
You didn't have to tell us explicitly - we could see that for ourselves.
Sphecks · 1 points · Posted at 05:00:18 on February 14, 2016 · (Permalink)
If you wanted to put it into layman terms, you can try to explain it this way. You can define a number by saying that a number always has to exist between it and another number. For example, 0.98 is a number because there is a number 0.99 between 0.98 and 1.0. In integer form, 1 is a number because 2 is between 1 and 3. However, can anything be possibly between 0.99 and 1? No, so we know that these have to be the same number.
That's just the logician way of doing it, though it may be less convincing, depending on the people, than writing out the proof which /u/WILLYOUSTFU provided.
snowfaller · 1 points · Posted at 11:47:59 on February 14, 2016 · (Permalink)
Yeah, but I can still take a whole pie and convert it to thirds, then make a whole. Putting it into decimal or base notation screws it up because it's infinitely repeating. Not really too earth shattering now is it?
all4hurricanes · 1 points · Posted at 14:56:10 on February 14, 2016 · (Permalink)
I do not like any of the mathematical proofs but I found a conceptual one that I think is pretty convincing. .999... is a rational number because the digits repeat infinitely and there are no consecutive rational numbers (there is infinite rational and irrational numbers between to rational numbers) since there are no numbers between .99... and 1, .999 repeating must be one.
regdayrF · 177 points · Posted at 21:06:05 on February 13, 2016 · (Permalink)
It's not meant as proof, but I feel like it is the easiest way for some people to grasp it. Believing 0.33... + 0.33... = 0.66... is not difficult in my opinion as you just add every position onto the other. Luckily, you can view every position on it's own as no position affects the other in this scenario, so one just has to believe in 3 + 3 = 6.
Using infinity sums and positional notation is way better than, what I did, but lots of people don't understand it anymore at that point.
RichardRogers · 98 points · Posted at 22:58:33 on February 13, 2016 · (Permalink)
The problem isn't accepting 0.33... + 0.33... = 0.66..., the problem is that 1/3 = 0.33... is equivalent to the statement you're trying to prove.
Ph1llyCheeze13 · 8 points · Posted at 03:40:40 on February 14, 2016 · (Permalink)
I'm pretty sure simple long division will get you as far as 1/3 = .333...
RichardRogers · 1 points · Posted at 05:18:00 on February 14, 2016 · (Permalink)
Not rigorously, since long division is an algorithm which in this case doesn't terminate.
Ph1llyCheeze13 · 2 points · Posted at 13:53:37 on February 14, 2016 · (Permalink)
Ok
Shaxys · 13 points · Posted at 00:59:28 on February 14, 2016 · (Permalink)
But often more people accept that.
RichardRogers · 2 points · Posted at 02:27:47 on February 14, 2016 · (Permalink)
But it's a circular argument, which is a shitty way to educate people about math even if it does get them to agree with you.
KSFT__ · 6 points · Posted at 03:04:54 on February 14, 2016 · (Permalink)
No, it isn't a circular argument. It uses one statement to prove another. It isn't completely rigorous, but that isn't the same as being circular.
RichardRogers · 3 points · Posted at 04:57:38 on February 14, 2016 · (Permalink)
It is circular because the important part is not the choice of 1 but the question of whether certain fractions can be perfectly represented by a decimal with infinitely many terms. Appealing to 1/3 instead convinces people because it's what they've been taught and doesn't challenge their intuition, but it only answers the case of 1 and handwaves the underlying question.
It's like if someone asked why ei*pi + 1 = 0 and you answered "because ei*pi = -1". Removing yourself from the conclusion by one trivial operation doesn't mean your argument is no longer circular, since you're still assuming the entire conclusion in a slightly different formulation.
Thinks_Too_Logically · 4 points · Posted at 10:01:13 on February 14, 2016 · (Permalink)
The 1/3 argument relies on the other party already believing that 1/3 = .333... I disagree that it's like saying "ei*pi + 1 = 0, because ei*pi=-1"; it's like saying "ok, you agree that ex expands into the Taylor series centered at 0: x0/0! + x1/1! + x2/2! +..." and continuing to prove ei*pi + 1 = 0 from there.
Agreeing that the Taylor series centered at 0 for ex is xn/n! from n=0 to infinity is the same as agreeing that ei*pi = -1. That doesn't make the logic circular, that's how math works. You start from accepted truths and work towards a new truth using accepted transformations.
For people who aren't deep into mathematics, you start with what they're most familiar with. You don't start by proving 1+1=2, then showing that there are infinities of different sizes to derive the real numbers, and so on. You start from what they know. People know 1/3 = .333... They understand that 1/3 + 1/3 = 2/3 and that 2/3 = .666... And you can get them to agree that .999... = 1 from the starting point of 1/3 = .333...
KSFT__ · 2 points · Posted at 18:40:08 on February 14, 2016 · (Permalink)
Proving [;e^{i\pi}-1=0;] given [;e^{i\pi}=-1;] is very easy, but that doesn't mean there's anything wrong with the obvious proof. A circular argument is useless because one of its premises is also its conclusion. Proving [;0.999...=1;] given [;\frac{1}{3}=0.333...;] is easy too. If that proof convinces someone that [;0.999...=1;], then that person clearly accepts the premises of the proof. If it's valid (it is in this case, as it is not a circular argument) and it satisfies someone, it isn't a bad way to educate them. If they didn't accept that [;0.999...=1;] before the proof, and they do after, the "underlying question" was obviously answered by the proof. If it doesn't satisfy you, you can read a more rigorous proof, but this one is absolutely not circular, and that issue is separate from whether it's useful or requires premises that aren't obvious, which is subjective. I think it's pretty clear that it doesn't, for people who accept the conclusion after reading it.
spiritualboozehound · -3 points · Posted at 05:24:30 on February 14, 2016 · (Permalink)
If they do, they still truly won't understand the end result. This is the problem with education in America. We find some unrelated thing they were told to have bought before (because we all buy that 1/3 = .3333... but only because of dicking around with a calculator) and then use that badly-founded knowledge the be the base for more knowledge. It's why we're fucked. If we truly knew why 1/3 = .333... from the get-go this wouldn't have even been a question.
[deleted] · -2 points · Posted at 01:10:57 on February 14, 2016 · (Permalink)
[deleted]
DoughnutHole · 11 points · Posted at 02:04:59 on February 14, 2016 · (Permalink)*
We can, it's actually pretty simple, you just have to wrap your head around a number that repeats to infinity. Let's start with 0.333... instead of 1/3.
x = 0.333...
10x = 3.333...
10x = 3 + 0.333...
10x = 3 + x,
10x - x = 3,
9x = 3,
x = 3/9,
x = 1/3,
0.333... = 1/3 ⬛
Gufnork · -8 points · Posted at 09:28:58 on February 14, 2016 · (Permalink)
Apparently it's not that simple since you're doing it wrong.
x = 0.333...333
10x = 3.333....330
10x != 3 + 0.333...333 since 3.333...333 != 3.333...330.
You apparently can't wrap your head around a number that repeats to infinity since you don't realize that even though it has an infinite number, it still has an end. It has a start, an end and an infinite series of numbers in between.
Thinks_Too_Logically · 5 points · Posted at 10:06:21 on February 14, 2016 · (Permalink)
There are infinitely many natural numbers. What's the end of the natural numbers? There isn't. There is no maximum natural number (and before you say it, infinity isn't a number). There is no final digit in .333... just like there's no maximum natural number. 10 * 1/3 = 3.33...
You can't append a 0 in there because there is no place to append a 0. There simply isn't an end. It trails on forever. The number 1/3 represented in base 10 does not terminate.
Gufnork · -4 points · Posted at 11:37:53 on February 14, 2016 · (Permalink)
Even if there's nowhere to append a 3, 3.333.... repeating has one more 3 than 0.333... repeating. You added that 3 when you multiplied by 10 incorrectly. That 3 is what makes this math off. That 3 is after an infinite amount of 3's, so you'll never get to it, nevertheless it's there.
DoughnutHole · 3 points · Posted at 11:58:48 on February 14, 2016 · (Permalink)*
You didn't "add" any 3; you moved every 3 forward a decimal place. Seeing as behind every 3 there's another 3, you never reach any 0. You're not grasping that 0.333... indicates an infinite number of threes. There's no such thing as infinity plus one.
Thinks_Too_Logically · 1 points · Posted at 17:50:53 on February 14, 2016 · (Permalink)*
What you're saying is equivalent to saying that the set of integers (Z) is one element larger than the set of integers minus 0 (Z\{0}). However, you can make a bijection from the Z to Z\{0} and show that they're the same size. There is no "one more" integer in Z, there is no "one more" 3 in 3.333...
And unless you can grasp this concept, then you're not able to discuss this. I'm sorry, but you're not following the same definitions and axioms we are.
hermy_own · 3 points · Posted at 10:13:25 on February 14, 2016 · (Permalink)*
Wow. condescending and so so very wrong.
A decimal with infinitely many repeating 3s does not terminate. It is, by the very definition of infinity, endless. This is best represented as 0.333... but if you're feeling bold, you can also represent it as 0.333333333...
0.333...333 (or 0.333333...3333 if you're still feeling bold) terminates. It has an end. It does not repeat. It might be made up with 100 3s, a trillion 3s, or googolplex 3s. Exactly how many 3s? I dunno. It's a poorly defined number. Either way, there are still a countable number of 3s in that decimal. Not an infinite quantity, not a countably infinite quantity, *but a countable number of 3s.
BurningLed · 3 points · Posted at 02:05:23 on February 14, 2016 · (Permalink)
We can though -- we express it as 1/3. We can't express pi either, except as π.
If you really want a terminating sequence, then we can move to other bases. For example, .1 in base 3 is the same as 1/3 or .3333... in base 10.
Awkwardly, though, 1/2 is a neat .5 in base 10, but in base 3 it's .1111....
If natural-number bases aren't doing it, there's also beta expansions, but those are kind of crazy.
classicfighter · 23 points · Posted at 01:13:25 on February 14, 2016 · (Permalink)
My math teacher told me that there is no number between 1 and 0.9999... so they have to be equal, that really made sense to me.
Thinks_Too_Logically · 2 points · Posted at 10:09:34 on February 14, 2016 · (Permalink)
I don't like this argument personally. How do you prove that there's no real numbers between .999... and 1 without first proving that .999... = 1?
MyAssholeSmellsAwful · 4 points · Posted at 11:43:45 on February 14, 2016 · (Permalink)
Because - what would that number's decimal representation be?
Thinks_Too_Logically · 2 points · Posted at 17:32:18 on February 14, 2016 · (Permalink)
I don't know. If it's an irrational number, I don't know how to write it out.
Let A = .999..., B = 1, and C = (A + B) / 2. If A != B, then A < C < B and I've found the counterexample you're looking for. If A == B then A = C = B and there is no counterexample.
So right now I've found a number between A and B unless you can show me that A == B.
Let me state it more generally. If you have two real numbers, A and B. How do you show that there is no real number C such that A < C < B without showing that A == B? Mathematical proofs don't end on questions for the reader to answer. You can't just ask "what's the number between A and B?" and act like you've shown A and B are equal. You have to show that there's no number between A and B.
[deleted] · -4 points · Posted at 11:24:17 on February 14, 2016 · (Permalink)
[deleted]
themouseinator · 2 points · Posted at 17:45:34 on February 14, 2016 · (Permalink)
cough 0
-Reddit_Account- · 3 points · Posted at 23:06:05 on February 13, 2016 · (Permalink)
Reddit does addition
zRook · 1 points · Posted at 00:21:48 on February 14, 2016 · (Permalink)
To use a Numberphile explanation.
Infinite sums that behave well equal a whole number. If you add 1/3 + 1/3 + 1/3 it IS 1. Adding 1/2+1/4+1/8+1/16....=1
romulusnr · 1 points · Posted at 09:45:13 on February 14, 2016 · (Permalink)
I've always prefered the "limit as x->∞" reasoning.
Alkadron · -2 points · Posted at 01:30:39 on February 14, 2016 · (Permalink)
There are a lot of very interesting discussions to be had surrounding the idea of what, exactly IS meant as a proof, and what that means, and what it means to prove something.
Best I've come up with so far is "a proof is a convincing argument, as judged by a competent audience." Which turns out is super subjective. So. I'll believe that your comments were, in fact, meant as a proof of sorts.
kogasapls · 1 points · Posted at 07:47:06 on February 14, 2016 · (Permalink)
A lot of other people have answered that question after quite a lot more deliberation than is possible for one person to match.
Alkadron · 0 points · Posted at 18:53:37 on February 14, 2016 · (Permalink)
I'm well aware, I've read a lot of their work, which is why I mentioned there being a lot of very interesting discussions.
Having read a lot of their work, I can tell you: There's no real consensus on the matter. I'm not saying "Best I've come up with..." to imply i know better than they do, I'm saying "Best I've come up with... " to imply that there is no single, well-agreed-upon answer, but I know what my answer is.
reddit__scrub · 9 points · Posted at 06:52:12 on February 14, 2016 · (Permalink)
I'm no math guy, but I feel like something is wrong with the first step...
If x = 0.99 (for simplicity, lets just say 2 decimal places)
Then it's assumed that 10x = 9.99
But shouldn't it be 10x = 9.9?
I know infinity entails an infinite number of decimals in this place. But infinities are not equal, especially continuous numbers, correct? I feel like there's a loss of precision or something.
NC-Lurker · 1 points · Posted at 09:37:24 on February 14, 2016 · (Permalink)
Yes, that's exactly why you're not supposed to apply the standard rules of arithmetic on infinite (in this case, repeating) numbers. I've heard that being taught pretty early in many schools, but apparently adding or multiplying ".11111..." is common practice in America...
At any rate, you're right. The whole "proof" relies on doing an operation with an infinite number and assume the result is correct. Actual maths will deal with limits instead, but for all intents and purposes, .999 = 1.
tententai · 1 points · Posted at 09:38:43 on February 14, 2016 · (Permalink)
Yeah the same thing disturbed me. Basically in base 10 multiplying by 10 means shifting everything to the left and add a 0 on the right. But how do you add a 0 on the right of something infinitely long? Anytime infinite is involved in math, it's really hard to have stuff check out intuitively, you have to rely on abstract conventions that just work. edit: missing word
skullturf · 2 points · Posted at 18:03:13 on February 14, 2016 · (Permalink)
It doesn't have to.
What's 0.8675309 times 10?
It's 8.675309.
It's also correct to write it as 8.6753090, but you don't have to. You don't need to write that 0 at the end. You just simply shift each digit by one position.
tententai · 1 points · Posted at 18:22:02 on February 14, 2016 · (Permalink)
Yes you're right, for non integers the 0 on the right is meaningless. What bother me is how do you shift stuff on the left when that thing has infinite length? You basically add something by doing this, though in this case the somethign is infinitely small.
Lol I feel like a drunk guy talking philosophy in a pub, I should leave that to mathematicians.
skullturf · 1 points · Posted at 18:43:16 on February 14, 2016 · (Permalink)
Well, it's not a physical task, so it doesn't matter that it has infinite length.
You shift the digit in the second position to the first position. You shift the digit in the third position to the second position. And so on.
Each of the infinitely many digits is in a particular position, and you shift each digit one position.
Really, the answer to the question "How do you shift stuff?" is: You just do it! This is a theoretical exercise, not a physical task.
If I tell you what digit goes in each position, then I've told you how to shift.
Why do you think you add something? You're just moving things. You're not adding anything.
You move whatever's in position 100 to position 99. You move whatever's in position 101 to position 100. And so on. You are only moving things. You're not adding anything at the end. (In fact, there is no end.)
tententai · 1 points · Posted at 19:23:44 on February 14, 2016 · (Permalink)
In fact I was trying to build an intuition of it by imagining how numbers are encoded as bits in a computer. In binary multiplying by 2 means shifting bits to the left, in a computer's memory kind of physically (sometimes literally). So if you have an inifintely long number, shifting it feels like creating a loophole on the right of it, which would be worth an infinitely small value.
It's like saying that that 0.999... = 1 - 0.000...1, and that this last small number is actually infinitely small and can be ignored.
I agree with you that the whole physical analogy doesn't make sense, I was just trying to build intuition on something that can't be understodd by intuition.
skullturf · 1 points · Posted at 19:42:18 on February 14, 2016 · (Permalink)
It can be understood by intuition, but you just have to work on developing the intuition.
If you have an infinitely long decimal, then there is a first position, second position, third position, and so on, but there is no infinitieth position.
skullturf · 1 points · Posted at 18:01:43 on February 14, 2016 · (Permalink)
Yes, IF you start with x = 0.99 (which ends after two 9s), then 10x would be 9.9.
However, if you start with x = 0.999... where the 9s continue forever, then 10x is 9.99..., with the 9s continuing forever.
[deleted] · 8 points · Posted at 01:25:58 on February 14, 2016 · (Permalink)
My favorite is just asking people to subtract .999... From 1. Because then they get 0. They still don't believe me...
IckGlokmah · 6 points · Posted at 03:45:44 on February 14, 2016 · (Permalink)
Why wouldn't you get .000.......1?
TooMuchPants · 5 points · Posted at 04:41:10 on February 14, 2016 · (Permalink)
There would never be a 1 on the end because there's an infinite number of 0s.
Archangel_117 · 7 points · Posted at 04:37:16 on February 14, 2016 · (Permalink)
Because there are an infinite number of 9's, so you never get far enough in the 0's to write the 1.
IthiQQ · 2 points · Posted at 14:42:38 on February 14, 2016 · (Permalink)
The flaw in this line of thinking is the assumption that there is a final number of the sequence. There is no 1 at the end of the sequence because the end of the sequence does not exist.
tornato7 · 1 points · Posted at 05:15:37 on February 14, 2016 · (Permalink)
This should be a thing. 0 repeating 1 could be defined as the limit of 1/x as x goes to infinity...
then .0...1 x infinity = 1 just as .01 x 100 = 1
You can also say .0...2 x infinity = 2, which would come from 2/x and you don't lose information in those conversions.
This is probably stupid
kogasapls · 2 points · Posted at 07:52:02 on February 14, 2016 · (Permalink)
Although infinite and infinitesimal numbers are not usually defined using limits or rational numbers, there are information-preserving concepts of these ideas. For example, the hyperreal numbers include numbers larger and numbers smaller than any real number, and "normal" operations between them work. Surreal numbers are a little more difficult to construct, but can represent similar concepts.
In the real numbers, there is no .0...1 or "infinity." They aren't real numbers. The limit of 1/x as x goes to infinity is 0. But you can take many approaches to defining numbers outside the reals which lets you do what you're thinking of. In other words, your idea is not stupid.
skullturf · 1 points · Posted at 18:00:17 on February 14, 2016 · (Permalink)
But that's just the number 0.
Bree899 · 0 points · Posted at 12:08:40 on February 14, 2016 · (Permalink)
I agree. 1 - 0.9 = 0.1, so 1 - 0.99...99 should be 0.00...01. Close enough to 0 that you can almost ignore it, and you definitely won't ever reach the 1 at the end (due to infinite 0s), but that doesn't mean it isn't there. An infinitely small number. Not 0.
GangsterRaspberry · 2 points · Posted at 16:34:32 on February 14, 2016 · (Permalink)
Exactly! My explanation of this is essentially equivalent to yours, which is that (from number theory) two numbers are unequal if there exists a number in between them. Therefore, since there is no number greater than 0.999... that is less than 1, it must be that 0.999... = 1.
silmarilen · 2 points · Posted at 01:16:44 on February 14, 2016 · (Permalink)
I don't like that one either, i prefer the one that uses the infinite sum of 1/10n
akqjten · 2 points · Posted at 03:03:10 on February 14, 2016 · (Permalink)
1/9 = .111... 2/9 = .222... 3/9 = .333... 4/9 = .444... 5/9 = .555... 6/9 = .666... 7/9 = .777... 8/9 = .888... .999... = ???
callaghan87 · 2 points · Posted at 04:32:13 on February 14, 2016 · (Permalink)
Neither of these are mathematically rigorous though. For a real proof, we say .9999.... = .9 + .09 + .009 + .0009 +... = .9/(1-.1) = .9/.9 = 1. The formula I used is the formula for the sum of an infinite geometric series, a1/(1-r), a1= first term in the series, r= the common ratio, or the number that each term in the series is multiplied by to get the next term
psychoSheep · 2 points · Posted at 05:15:06 on February 14, 2016 · (Permalink)
The problem of "proving" that 0.999... = 0. ̅9̅ = 1 is that it's not a mathematical problem at all but rather a problem of notation. It just so happens that in our notation "0.999..." holds the same value as "1". The actual mathematical entity that these symbols represent is stupefying and incomprehensible in much the same way the concept of an infinite number of 9's after 0. is stupefying and incomprehensible.
Count_Long_Dong · 3 points · Posted at 22:15:21 on February 13, 2016 · (Permalink)
How would you work this backwards though?
You have x = 1
Then 9x = 9
9x - x = 9 - x
8x = 8
Which just shows again that x = 1
I guess the technique would have to be different backwards, but I don't know what it would be.
JackFlynt · 3 points · Posted at 23:02:23 on February 13, 2016 · (Permalink)
If you're working backwards the line would have to be
9x + x = 9 + x
That said, it's an issue because you're going from the normal form of 1 to the form you're trying to prove.
ClareDeLoon · 5 points · Posted at 22:59:04 on February 13, 2016 · (Permalink)
10x = 9 + x
0.99... satisfies this equation
The answer is unique
Therefore x = 0.99...
[deleted] · 0 points · Posted at 00:39:16 on February 14, 2016 · (Permalink)
[deleted]
injygo · 1 points · Posted at 18:00:11 on February 14, 2016 · (Permalink)
Yes, that's the point of the proof.
grumpkin100 · 1 points · Posted at 20:09:05 on February 14, 2016 · (Permalink)
I was replying to the guy who said that the answer is unique...
injygo · 1 points · Posted at 20:25:42 on February 14, 2016 · (Permalink)
The answer is unique. 0.999999.... is 1.
grumpkin100 · 1 points · Posted at 20:34:10 on February 14, 2016 · (Permalink)
Didn't sound like that's what he meant but maybe it was. I thought he was saying that x only equals 0.9... But obviously it's both
injygo · 1 points · Posted at 21:09:13 on February 14, 2016 · (Permalink)
There's just one solution to the equation and it's the number that's one more than zero, also known as "0.9999999999..." and "1". That's what the person you were replying to was trying to convey with the proof, that both "0.99999..." and "1" refer to the same number.
kogasapls · 2 points · Posted at 08:09:50 on February 14, 2016 · (Permalink)
x = 1 is correct. But x = .99... is also correct because 1 = .99...
The reason it's trickier to work backwards through is when we have 9x = 9 and solve for x, we think x = 1, but x = 1 = .99... Assuming this, the algebra works fine backwards.
ThePantsThief · 1 points · Posted at 07:14:56 on February 14, 2016 · (Permalink)
.9 times 10 is 9, not 9.9.
[deleted] · 0 points · Posted at 22:20:39 on February 13, 2016 · (Permalink)
[deleted]
kogasapls · 3 points · Posted at 07:58:21 on February 14, 2016 · (Permalink)*
10x - x = 9x
x(10 - 1) = 9x
x(9) = 9x
9x = 9x
Unless you're working with some very strange axioms of algebraic manipulation, 10x - x always equals 9x. And the proof appears less inconsistent if you consider that .999... actually does equal 1; although there might seem to be some contradiction when you get 9 = (9 * 0.999...), there is none. 9 = 9 * 1.
If you can get to 10x - x = 9.99... - x you see:
(since 10x - x = 9x) 9x = 9.99... - x
(since x = .99...) 9.99... - x = 9
9x = 9
x = 1
x = .99... = 1
[deleted] · -1 points · Posted at 12:21:36 on February 14, 2016 · (Permalink)
[deleted]
kogasapls · 3 points · Posted at 17:41:01 on February 14, 2016 · (Permalink)
It does... x= .99...
10x-x = 9.99... - .99... = 9
You can't use a calculator to work with infinitely long decimals. You won't get an exact answer.
[deleted] · 0 points · Posted at 18:14:30 on February 14, 2016 · (Permalink)
[deleted]
kogasapls · 2 points · Posted at 18:23:36 on February 14, 2016 · (Permalink)
.99... Is a real number. It is an alternative expression of the number 1.
[deleted] · 0 points · Posted at 18:52:25 on February 14, 2016 · (Permalink)
[deleted]
kogasapls · 2 points · Posted at 19:20:18 on February 14, 2016 · (Permalink)
Infinitely repeating numbers are not irrational. 0.33... is the ratio 1/3. 0.66... is 2/3. 0.99... is 3/3. In fact, every single infinitely repeating number is rational.
ScrewAttackThis · 2 points · Posted at 09:02:30 on February 14, 2016 · (Permalink)
Uh, it's not wrong. I'm not sure why you think (10x-x) != 9x.
[deleted] · 1 points · Posted at 01:39:57 on February 14, 2016 · (Permalink)
Why? I've always thought of it like that.
[deleted] · -4 points · Posted at 02:50:08 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 3 points · Posted at 02:53:43 on February 14, 2016 · (Permalink)
So you're saying that 9x does not equal 9.9... - .9... = 9? What is 10x-x then?
[deleted] · -3 points · Posted at 03:34:22 on February 14, 2016 · (Permalink)
[deleted]
bearsandwitches · 0 points · Posted at 04:11:21 on February 14, 2016 · (Permalink)
10x - x = 9 - x
10x - .9 = 9 - .9
10x = 9
x = .9
Count_Long_Dong · 1 points · Posted at 22:26:01 on February 13, 2016 · (Permalink)
You're right. I missed that.
kogasapls · 2 points · Posted at 08:05:19 on February 14, 2016 · (Permalink)
He's wrong, you didn't miss anything.
DisRuptive1 · 2 points · Posted at 03:57:16 on February 14, 2016 · (Permalink)
I'm still not convinced. My reasoning is that .999... should be treated like it was infinity and therefore can't be modified, otherwise you can do all sorts of crazy things with it.
My second reason is that if .999... = 1, then what number is closest to 1 while also being less than 1?
benful · 5 points · Posted at 05:47:10 on February 14, 2016 · (Permalink)
This is actually kind of a valid criticism of that argument. Infinite sums are a bit subtle - some of the techniques you can use with finite sums don't always work on infinite ones. In this particular case everything is fine, but proving that is harder than proving that 0.999... = 1.
There isn't one, just like there isn't a number that is closest to 1/3 while also being less than 1/3, or a number that is closest to pi while also being less than pi.
regdayrF · 0 points · Posted at 12:16:16 on February 14, 2016 · (Permalink)*
In this case, we're dealing with irrational numbers not rational numbers.
For rational numbers, no matter how small the difference is between numbers, you will always find infinite numbers in between both of them. Let's say, we chose the interval [0.99999999, 1]. In this interval, there are infinite numbers in between 0.99999999 and 1. This can be applied for any real number out there, thus, you will never find a number, that is closest to 1 while not being one. For any given real number a, you will find infinite numbers in between a and 1. No matter how "close" a was to 1, you will still find infinite numbers in between them.
0.333.... with an infinite amount of 3's is an irrational number and can be desplayed as 1/3. Then everything applies what I've typed above.
1/3 + 1/3 + 1/3 = 0.333... + 0.333... + 0.333... = 0.999...
In this case, you look into one specific position and add them on top of each other. This will hold true for every single position up until infinity.
0.3 + 0.3 + 0.3 = 0.9, 0.03 + 0.03 + 0.03 = 0.09 and so on.
1/3 + 1/3 + 1/3 = 3/3 = 1
injygo · 2 points · Posted at 18:03:19 on February 14, 2016 · (Permalink)
1/3 is a rational number though, even when you write it 0.33333...
regdayrF · 1 points · Posted at 18:06:42 on February 14, 2016 · (Permalink)
I got mixed up between rational and irrational numbers. Sorry !
Yep, 1/3 is a rational number, pi for exampe is an irrational number.
DisRuptive1 · 1 points · Posted at 02:22:38 on February 15, 2016 · (Permalink)
The part of your explanation I don't agree with is:
1/3 = .333...
I think that:
1/3 > .333...
though both numbers are very close to each other.
cormac596 · 2 points · Posted at 03:59:59 on February 14, 2016 · (Permalink)
Also,
.111...=1/9
.222...=2/9
.333...=3/9=1/3
.444...=4/9
.555...=5/9
.666...=6/9=2/3
.777...=7/9
.888...=8/9
.999...=9/9=3/3=1
[deleted] · 1 points · Posted at 02:33:23 on February 14, 2016 · (Permalink)
How did you go from 10x to 9x on the left side of the equation?
10x-x wouldn't be 9.0, would it? Would it not be 9.000...0001?
once-and-again · 3 points · Posted at 02:44:49 on February 14, 2016 · (Permalink)
No, because you never run out of nines.
[deleted] · 1 points · Posted at 03:38:17 on February 14, 2016 · (Permalink)
Well I know it never actually ends, but theoretically at the end wouldn't there still be a .00...01 left?
once-and-again · 2 points · Posted at 04:20:29 on February 14, 2016 · (Permalink)
If it never ends, then there can't be anything at the end.
Using the word "theoretically" doesn't change that.
[deleted] · 2 points · Posted at 04:44:24 on February 14, 2016 · (Permalink)
Fair enough, I suppose it's just hard for humans to grasp something not ending lol
ScrewAttackThis · 1 points · Posted at 09:08:08 on February 14, 2016 · (Permalink)
It's just basic algebra. They're subtracting an x from 10x, thus 9x. You can see it's true pretty easily if you just start plugging numbers in. You can take my word that it's true for any number.
[deleted] · 2 points · Posted at 17:46:27 on February 14, 2016 · (Permalink)
right. i was overcomplicating it lol
bro_cunt · 1 points · Posted at 02:53:49 on February 14, 2016 · (Permalink)
Why is 10x-x = 9?
nerraw92 · 1 points · Posted at 02:55:57 on February 14, 2016 · (Permalink)
x = .AAA...
10x = A.AAA...
10x - x = A.AAA... - .AAA...
9x = A
x = A/9
attimus080 · 1 points · Posted at 03:00:18 on February 14, 2016 · (Permalink)
This is incorrect, 10x would be 9, not 9.9. 9.9 would be 11x.
Asmor · 1 points · Posted at 03:00:31 on February 14, 2016 · (Permalink)
I still remember seeing this in... like... 3rd or 4th grade. I totally didn't understand what the teacher was trying to get across, and I thought she was just demonstrating a weird trick with math.
Personally, my favorite way of expressing the fact that 0.9... is the same as 1 is to ask someone what 1 - 0.9... is, or alternatively ask them what's a number between 1 and 0.9...
I_EAT_GUSHERS · 1 points · Posted at 03:03:07 on February 14, 2016 · (Permalink)
Using this same method, you can prove that 99999999999999...=-1 and ...9999999999999999999.99999999999999999...=0.
EastCoast2300 · 1 points · Posted at 03:15:17 on February 14, 2016 · (Permalink)
The first 2 lines don't make any sense: if X is .9, then 10X is not equal to 9.9
SquirrelicideScience · 1 points · Posted at 04:11:52 on February 14, 2016 · (Permalink)
To be fair, your second step
relies on the same principle that /u/regdayrF held to be true. Multiplication is a shorthand for adding together groups. So, saying 10*0.9... = 9.9... is just like saying 9.9... = 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... + 0.9... , which relies on the fact that one must believe that these infinite decimals can be added in such a way. And if that is true, then 0.3... + 0.3... = 0.6... is just as valid.
faaaks · 1 points · Posted at 04:22:22 on February 14, 2016 · (Permalink)
Personally, I've just asked people to name any number between .9... and 1.
sorif · 1 points · Posted at 04:29:56 on February 14, 2016 · (Permalink)
So, how does THIS work for a pickup line?
Natedawg187 · 1 points · Posted at 04:48:44 on February 14, 2016 · (Permalink)*
Even taking this a bit further, any repeating decimal can be represented as
(repeating digits)/(10#repeatingDigits - 1)
.999... = 9/9 = 1
.333... = 3/9 = 1/3
.8484... = 84/99
etc
The reason why is the same as your proof. You are multiplying by a power of 10 to move one sequence of the repeating digits to the left of the decimal point to get your multiple of x you can work with. Then subtract 1 from that power of 10 to eliminate what's to the right of the decimal, and you have a whole number multiple of x over the power of ten (less 1).
Edited: Tried to make my explanation as clear as possible.
galadedeus · 1 points · Posted at 04:57:07 on February 14, 2016 · (Permalink)
damn
alsdjkhf · 1 points · Posted at 05:43:06 on February 14, 2016 · (Permalink)
I just like to think that if something is infinitely small, then you'll never be able to measure it, so it technically doesn't exist.
Bosterito95 · 1 points · Posted at 05:44:38 on February 14, 2016 · (Permalink)
how did x = .9 become 10x = 9.9? shouldnt it be 10x = 9?
[deleted] · 1 points · Posted at 05:51:01 on February 14, 2016 · (Permalink)
0.9 is not same as 9, 9 =/= 1
[deleted] · 1 points · Posted at 05:55:08 on February 14, 2016 · (Permalink)
Can't X mean anything as long as it's the same on both sides, or is that the point?
invrt · 1 points · Posted at 06:12:01 on February 14, 2016 · (Permalink)
I simply prefer to put it this way: 1-0,99... = ??? 0,000000....????
Gnarok518 · 1 points · Posted at 06:28:57 on February 14, 2016 · (Permalink)
What are the implications of this? It seems kind of important.
Elgin_McQueen · 1 points · Posted at 06:36:04 on February 14, 2016 · (Permalink)
??? If x=0.9 then 10x=9.0
Roulette88888 · 1 points · Posted at 06:36:34 on February 14, 2016 · (Permalink)
...Wouldn't 10x equal 9?
[deleted] · 1 points · Posted at 08:48:20 on February 14, 2016 · (Permalink)*
It is 0.9 repeating (hence the ellipsis[...])
So
(he did one part wrong)
Roulette88888 · 1 points · Posted at 08:58:29 on February 14, 2016 · (Permalink)
Ohhh. Gotcha. :)
the_okay · 1 points · Posted at 06:47:17 on February 14, 2016 · (Permalink)
You said:
x = 0.999...
That means:
9(0.999...) ≠ 9
I don't see how your proof made it any easier than the former.
bunker_man · 1 points · Posted at 06:58:44 on February 14, 2016 · (Permalink)
Yeah. If someone thinks that the repeating decimal is an approximation rather than literal, why would they suddenly forget they think this when you add them.
Clyzm · 1 points · Posted at 07:07:13 on February 14, 2016 · (Permalink)*
I'm still not a fan of this one, really;
10x - x = 9.9 - x
10x - x = 9.9 - 0.9...
Is murky at best. You're trying to say you want to prove this to someone who doesn't believe 0.333... + 0.333... = 0.666..., but you multiply 0.999... by 10. Something more fool proof would be to prove by contradiction that if 1 != 0.99..., then that implies 0.999... must be > or <1, and the existence of a number >0.999... and <1 (or <0.999... and >1) by density of R.
ForeignTorque · 1 points · Posted at 07:08:06 on February 14, 2016 · (Permalink)
I have a problem with this. X=.9... Right so although this goes on forever when you multiply it by ten you dont add a 9 to the front you add a 0 to the end. So for example maybe its originally .9999999999 when you multiply that by 10 it becomes 9.999999999 NOT 9.9999999999 Redo all the steps assuming that and you end up with .9999999999=.9999999999
ThePantsThief · 1 points · Posted at 07:09:59 on February 14, 2016 · (Permalink)
Uh am I missing something?
10 • .9is9, not9.9…dopiumthefinest · 1 points · Posted at 07:27:12 on February 14, 2016 · (Permalink)
This isn't really accomplishing anything mathematically. You're first line says x = 0.9. Next line you say 10x=9.9. You do some algebra then say that based on that algebra x has two distinct values, when you really just declared two different values in the beginning. If x = 0.9 (first line) then 10 * x would equal 9, not 9.9.
I suppose it does help to see how it works. I like to think of it like a limit when your variable approaches infinity. You technically never touch the line, but you eventually converge on the line.
Grabthelifeyouwant · 1 points · Posted at 07:34:40 on February 14, 2016 · (Permalink)
The problem with all of these IMO is that they all rely on axiomatically selecting against the existence of infinitesimals. If you axiomatically choose for them to exist, none of your math is right.
The tricky bit is that by using 9.9... and 10 in the same formula with a layperson without explicitly stating your axiomatic choice, you have primed the layperson to think under the assumption that infinitesimals exist, in which case they are correct in assuming 10 and 9.9... are different numbers.
kogasapls · 1 points · Posted at 07:44:58 on February 14, 2016 · (Permalink)
You haven't really solved the problem you yourself posed, but your proof is the classic elegant one.
.33... + .33... = .66... is hardly different from your x = 0.99... -> 10x = 9.99...
2(.33...) = .66...
10(.99...) = 9.99...
Both are multiplication of infinitely long decimals.
Grazfather · 1 points · Posted at 07:54:29 on February 14, 2016 · (Permalink)
Yeah that's a good explanation, but I understood it best when I realized that the only reason this question is at all confusing is because we have decided to represent numbers in base 10. I would then explain how half in base 3 has the same problem.
0.111... + 0.111... = 1.
[deleted] · 1 points · Posted at 08:08:54 on February 14, 2016 · (Permalink)
At the stage:
How do you get from 10x - x to 9x in the next line? Surely it's 9.1...x = 9?
bassinastor · 1 points · Posted at 08:22:14 on February 14, 2016 · (Permalink)
My favorite way to think about it is to look at n/9.
1/9 = .111... 2/9 = .222... 3/9 = .333... ... 8/9 = .888...
Logically it would follow that 9/9 would be .999... but of course it's just 1.
overkill · 1 points · Posted at 08:56:28 on February 14, 2016 · (Permalink)
I used this to explain it to someone once. Their response was "when you multiply it by 10 the last digit of 0.99.... becomes 0. Proof". I said "which last digit of the infinite series is that then?"
kyle1qaz7ujm · 1 points · Posted at 09:02:36 on February 14, 2016 · (Permalink)
But 10x = 9.0 not 9.9
ScrewAttackThis · 1 points · Posted at 09:04:31 on February 14, 2016 · (Permalink)
If you're dealing with someone that "doesn't believe .333... + .333... = .666..." then there's no way you're going to get them to believe a process that takes a considerable amount of more steps and algebraic manipulation.
I really don't see how 1/3 + 1/3 + 1/3 = 1 isn't the simplest way to show the concept.
[deleted] · 1 points · Posted at 09:43:19 on February 14, 2016 · (Permalink)
Uh... This is technically the same thing as what regdayrf said... You are just hiding multiple additions of '0.999...' under one multiplication, and then subtracting, which is also, kinda, addition... So, basically, your method is just more complex than regdayrf's
romulusnr · 1 points · Posted at 09:44:42 on February 14, 2016 · (Permalink)
Why on earth wouldn't .3... + .3... = .6... ? Any less than .1... + .1... = .2...?
NeatAnecdoteBrother · 1 points · Posted at 09:50:20 on February 14, 2016 · (Permalink)
How does this make sense? Shouldn't it be 10x = 9?
Save4321 · 1 points · Posted at 10:20:28 on February 14, 2016 · (Permalink)
10x - x = 9.9... - x
Isn't this step invalid?
golfalien · 1 points · Posted at 10:57:36 on February 14, 2016 · (Permalink)
Am I lost? Doesn't 0.9 times 10 equal 9?
SushiAndWoW · 1 points · Posted at 12:08:19 on February 14, 2016 · (Permalink)*
This transition is crucial to the intuitive click. On closer observation, though, it's questionable for the same reason that .3... + .3... == .6... seems questionable. If a person does not trust one, I'm not convinced they should trust the other.
I like the pragmatic argument. For arbitrarily small ε, there is a number of digits N such that 1 - 0.9...9 (repeated N times) < ε.
zodiacR · 1 points · Posted at 12:11:49 on February 14, 2016 · (Permalink)
Hate you for that, how is it possible?
Bree899 · 1 points · Posted at 12:30:53 on February 14, 2016 · (Permalink)
Admittedly not knowing a whole lot about math, could I ask for a serious response to my current opinion?
I'd like to think this is wrong because multiplying 0.99...99 by 10 is not the same as adding it to 9 (which the above example relies on when it says 10x - x = 9).
Look at this:
x = 0.9
10x = 9 (and, incidentally, 10x - x = 8.1)
x + 9 = 9.9
so: x+9 > 10x
Let's add another 9 to that:
x = 0.99
10x = 9.9 (making 10x - x = 8.91)
x + 9 = 9.99
again: x+9 > 10x
This stays the same however many 9s you add to the value of x. So even when x contains an infinite number of 9s, you can't simply multiply by 10, then subtract 9 and expect to be left with a number that has the same value as x.
Instead, it would become as follows:
x = 0.99...99
10x = 9.99...99
10x - x = 8.99...991 (rather than exactly 9)
9x = 8.99...991
x = 0.99...99 (not 1)
If I'm right about this, it renders the whole argument invalid, doesn't it?
And that would allow me to go back to my comfortable life of believing 1/3 is not 0.33...33 and 1 is also not 0.99...99 (but rather there is a difference of an infinitely small number, 0.00...001).
TrainerDusk · 1 points · Posted at 12:35:54 on February 14, 2016 · (Permalink)
The problem with that proof is that 10 times 0.999... is 9.99...0
If you are going to treat a fraction as an infinite decimal, then it doesn't make sense to ignore the decimal way of handling numbers. If you multiply anything by 10, move all the digits to the left and stick a zero on the end.
incaseanyonecared · 1 points · Posted at 12:38:53 on February 14, 2016 · (Permalink)
Also, thinking about the principle that between any two real numbers there exists another real number, you can't put a real number between 0.999... and 1.
Showkeazy · 1 points · Posted at 12:55:37 on February 14, 2016 · (Permalink)
Wait a second, 10x doesn't equal 9.9. 0.9 X 10 = 9. So this explanation can't be right
garblegarble12342 · 1 points · Posted at 13:00:38 on February 14, 2016 · (Permalink)
Or you can use this, 0.999... is 1 - 0.00...1 right? Well since the one never comes, 0.00...1 is equal to zero, so that means that 0.999 = 1-0 which is 1.
DivideByZeroDefined · 1 points · Posted at 13:39:11 on February 14, 2016 · (Permalink)
A simpler thing to understand for people who don't like the witchery of algebra is to state the fact that for any two real numbers, there is an infinite number of numbers between them, then as what number is between 1 and .9999999.......
NomNomNomNation · 1 points · Posted at 13:40:22 on February 14, 2016 · (Permalink)
My maths teacher taught us this with a similar method.
x = 0.9...
10x = 9.9...
10x - x = 9x = 9
This means that x = 9/9
9/9 = 1
1985WasAnOkayYear · 1 points · Posted at 13:42:34 on February 14, 2016 · (Permalink)
Holy shit.
flaming_plutonium · 1 points · Posted at 14:37:03 on February 14, 2016 · (Permalink)
Well it's not quite right to say x is both .9… and 1 because they're actually the same value
[deleted] · 1 points · Posted at 14:52:16 on February 14, 2016 · (Permalink)
Why's that a problem for them? You just go along the pairs of digits summing them, and it's always going to be 3 + 3 = 6, so no one has a problem with it. It's intuitively very different from equating a recurring decimal with a whole number, which is the leap-to-far for laypersons.
chevymonza · 1 points · Posted at 15:01:40 on February 14, 2016 · (Permalink)
But.....but..............Gabriel's Trumpet!
I guess that just means absolute zero is impossible to get to, but then ........I mean............you can just round up to 1 I suppose due to the domino effect going back from the last 9........but if there's an infinite number of 9s............god dammit.
SlowlySailing · 1 points · Posted at 15:13:11 on February 14, 2016 · (Permalink)
Well, except that 10 * 0,9 is just 9.
[deleted] · 1 points · Posted at 16:15:47 on February 14, 2016 · (Permalink)
You're cheating tho.
If you define x as the sum of 9 10-k ; [k:1~n] , then multiply by 10 and subtract x, you still haven't eliminated 9 10-n, hence why "x" isn't equal to 1.
You're plugging n = infinity hence n = n-1 before you even start your calculations. So your proof is wrong. As someone said below, these kind of bogus "proofs" are very irritating.
KitAndKat · 1 points · Posted at 17:20:45 on February 14, 2016 · (Permalink)
I don't think there's a lot of difference between the two proofs. One relies on adding two infinite series (0.333... + 0.333...), and the other on subtracting two infinite series (9.999... - 0.999...).
IzSynergy · 10 points · Posted at 22:40:51 on February 13, 2016 · (Permalink)*
you also prove it like this:
1 - 0.999...= 0.000... or just 0
noggin-scratcher · 7 points · Posted at 23:26:39 on February 13, 2016 · (Permalink)
Somewhat equivalent to the above: "Any two numbers that are different have a third number that is between them. But there is no number that's more than 0.999... and less than 1, therefore they're equal"
Except phrasing it that way isn't generally very good at convincing people who don't already grasp the maths; they'll try to suggest "0.999...5" without intuitively getting the concept that the infinite chain of 9s doesn't have an end to put the 5 on the end of it.
h_saxon · 0 points · Posted at 23:23:35 on February 13, 2016 · (Permalink)
This is the simplest to me.
_____D34DP00L_____ · -4 points · Posted at 01:26:21 on February 14, 2016 · (Permalink)
You must point out that there is supposed to be a theoretical 1 at the 'end' of those infinite zeroes.
KSFT__ · 3 points · Posted at 03:12:43 on February 14, 2016 · (Permalink)*
The word "theoretical" is meaningless in math. Math doesn't deal with theories; it deals with theorems. There's an important difference there. In science, theories are ideas that seem probably true based on empirical measurements. In math, theorems are statements that have been proven based on axioms, definitions, and rules of deduction. In order to be sure that a statement is true, it's important to be precise about what you mean in math, which is why there's formal notation. You aren't precise enough with your claim, "there is supposed to be a theoretical 1 at the 'end' of those infinite zeroes", for me to explain why it's false (I think it's false, but I can't be sure because I don't know what it is).
DingyWarehouse · 3 points · Posted at 03:51:46 on February 14, 2016 · (Permalink)
There is no 1, since there are infinte zeroes. You cannot put the 1 at all.
IzSynergy · 2 points · Posted at 02:37:16 on February 14, 2016 · (Permalink)*
Saying there's a theoretical 1 at the end is like saying there is a theoretical number at the end of pi
Help_I_think_Im_Emo · 2 points · Posted at 01:30:11 on February 14, 2016 · (Permalink)
or you can use 3/11 + 8/11. 3/11 + 8/11= .27... + .72.... = 1 and .9.... That's how my teacher explained it.
UberTork · 2 points · Posted at 00:58:46 on February 14, 2016 · (Permalink)
1/9=.1111...
2/9=.2222...
8/9=.8888...
9/9=.9999....
checks out.
mypolarbear · 2 points · Posted at 01:29:26 on February 14, 2016 · (Permalink)
The way it was explained to me:
1/9 = .111111
2/9 = .222222
3/9 = .333333
4/9 = .444444
5/9 = .555555
6/9 = .666666
7/9 = .777777
8/9 = .888888
9/9 =
TheVermonster · 2 points · Posted at 16:53:01 on February 14, 2016 · (Permalink)
I love the visual of this method. You can teach this to someone that has very basic math understanding. Ask them what 9/9 is, if they know it =1 then you are good to go. Use a calculator to show that 1/9 = 0.11111.... then 2/9 = 0.222222.... Then ask them to continue writing 3/9, 4/9, 5/9, ect. Instinctively, 99% of the time they will write 9/9 = 0.999999....
It's fun to watch their brain explode.
AroundtheTownz · 1 points · Posted at 22:26:17 on February 13, 2016 · (Permalink)
can you explain why this isn't true in a ELI5 manner?
I only assume this isn't true..it think
practicing_vaxxer · 3 points · Posted at 23:35:58 on February 13, 2016 · (Permalink)*
This is the only explanation I understood:
If two numbers are not equal, there has to be a number between them, so if 0.9999.... <> 1, there would have to be a number higher than 0.9999.... that didn't equal 1, so 0.9999... couldn't be the next lowest number than 1. So it has to equal one.
Edited because my first version was more ambiguous than it could have been.
AroundtheTownz · 1 points · Posted at 23:37:13 on February 13, 2016 · (Permalink)
what's that number though
practicing_vaxxer · 5 points · Posted at 23:51:24 on February 13, 2016 · (Permalink)
There isn't any. 0.999... = 1.
I edited my answer; maybe it will make more sense now.
[deleted] · 3 points · Posted at 02:20:53 on February 14, 2016 · (Permalink)
0.999... = 1. There's something like a hundred different ways to prove that it's true. All of them are a bit awkward, and it never actually matters anyway unless you're planning on a PhD in mathematics.
almightySapling · 4 points · Posted at 07:11:48 on February 14, 2016 · (Permalink)
What? The non-rigorous "awkward" proofs should be accessible to any high school student (1/3 * 3 should be sufficient).
The actual rigorous proof is typically doable at the end of a 2 semester calculus course, once series are covered. That's like college freshman level.
A PhD student should have enough experience under their belt that they understand innately that two different representations may refer to the same thing.
Seroton1n · 1 points · Posted at 11:15:26 on February 14, 2016 · (Permalink)
I fully accepted it when I imagined a number line. There's 0 and 1, and 0.999... would be somewhere in between. 0.9 is really close to 1. 0.99 is even closer. 0.999 even closer than that. Now imagine the number 0.99999999... With every 9 you get closer and closer to one, but because this number is infinite you're becoming closer and closer with no end. And 'eventually' you're going to reach 1.
ThirdFloorGreg · 0 points · Posted at 23:16:08 on February 13, 2016 · (Permalink)
It is true, although this is a garbage proof.
cannonman360 · 1 points · Posted at 03:30:34 on February 14, 2016 · (Permalink)
That blew my mind! Bravo
voidqk · 1 points · Posted at 04:12:17 on February 14, 2016 · (Permalink)
People always use 1/3 when talking about this... I prefer saying 3/9 instead:
1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333...
...
8/9 = 0.8888...
9/9 = 0.9999...
SkylineGitiare · 1 points · Posted at 09:13:23 on February 14, 2016 · (Permalink)
I like to think of it as:
1 divided by 3 = 0.3333...
0.9999... divided by 3 = 0.3333...
regdayrF · 1 points · Posted at 09:20:24 on February 14, 2016 · (Permalink)
0.9999... divided by 3 = 0.3333... is pretty much the same as
0.3333... + 0.3333.... + 0.3333... = 0.9999.... as this is just another version of
3*0.3333.... = 0.9999.... , which would be
0.9999... /3 = 0.3333....
steeledmallard05 · -1 points · Posted at 06:38:44 on February 14, 2016 · (Permalink)
No, that's not true. 1/3 does not equal .3..., it's just the closest number we've got to it.
m50d · 50 points · Posted at 21:07:19 on February 13, 2016 · (Permalink)
That's not mathematics, just notation. People might get less confused if we worked with Dedekind cuts directly (though it would be cumbersome)
solidangle · 10 points · Posted at 00:12:29 on February 14, 2016 · (Permalink)
Why should we use Dedekind cuts when we can use Cauchy sequences?
somadIcanteven · 8 points · Posted at 02:57:47 on February 14, 2016 · (Permalink)
Your comment is much more helpful than mine was going to be.
"lol @ Dedekind cuts"
[deleted] · 1 points · Posted at 03:29:32 on February 14, 2016 · (Permalink)
I'm doing real analysis! I understand this!
thesleepingtyrant · 5 points · Posted at 01:39:04 on February 14, 2016 · (Permalink)
Certainly it is mathematics. It's a statement about one very boring geometric series. After all, how else are you defining decimal expansions?
[deleted] · -7 points · Posted at 22:10:52 on February 13, 2016 · (Permalink)
[deleted]
RichardRogers · 7 points · Posted at 22:59:40 on February 13, 2016 · (Permalink)
/r/iamverysmart is for people who say things that are wrong, not just for people who say things you don't understand.
jorellh · 4 points · Posted at 03:08:10 on February 14, 2016 · (Permalink)
easy proof. 0.9 repeating will always be closer to 1 than any number you can imagine.
either that or 1/9 = 0.1 repeating so 9*(1/9) or 9/9 or 1 = 0.9 repeating.
[deleted] · 3 points · Posted at 05:18:49 on February 14, 2016 · (Permalink)
The definitions here are complex for laypeople, but I tried to be as honest to them as I could without making this too long. Real numbers are (often) defined as Cauchy sequences of rational numbers. Cauchy sequences are more or less sequences which vary by less as they go on (for any variance, I can find a point in the sequence after which no two numbers in the sequence vary by more than that variance).
1 is just shorthand for the real number {1,1,1,1,1,....}. Now we define addition as an extension of how we define rational addition by adding the terms of the sequence (which are all rational numbers). so {1,1,1,1,...}+{1,1,1,1,...}={2,2,2,2,...}
We define a real number to be equal to 0(real) if it has 0(rational) as a limit point of it's sequence. so {1,1/2,1/4,1/8,...} = 0(real).
Then finally, we declare a=b if a-b=0.
.9999... is shorthand for {.9,.99,.999,.9999,...} and we see that 1-.999.... = {.1,.01,.001,.0001,...} which has zero as a limit and therefore they are equal.
It seems like we cheated because we defined these things in such a way that .99999...=1 so how could we be proving anything, but in mathematics we don't work with anything that we don't define ourselves. If we don't define the things we work with, then there can't BE any proof. The people who have trouble with .9...=1 aren't making a grievous error of logic, they simply haven't been given the definitions, indeed there are ways of defining .9... which are consistent with everything you've learned about numbers so far such that it does NOT equal 1, so try not to be a jerk when you are explaining.
CreepyStickGuy · 3 points · Posted at 05:44:04 on February 14, 2016 · (Permalink)
This is also the reason why parallel lines intersect at the point infinity in projected space.
MichaelOChE · 5 points · Posted at 20:13:50 on February 13, 2016 · (Permalink)
It can be written as 9 times sum (1<=n<infinity) 10-n with the latter factor being equal to 1/9. Thus, .999...=9 times .111...=9 times (1/9)=1.
And yes, I know writing that notation in Reddit is pretty much impossible.
TheSpoonyBard · -11 points · Posted at 22:28:00 on February 13, 2016 · (Permalink)
If you're working in such a space that the minute difference between .99999 repeating and 1 is important, then you can't assume that .111111 repeating is equal to 1/9.
While it is true that if you perform long division to find 1/9, you'll get .111111 repeating, it is important to keep in mind that because it repeats, the operation is never completed, and the fraction is never satisfied.
ThePantsParty · 9 points · Posted at 00:23:55 on February 14, 2016 · (Permalink)
There is no difference, minute or not.
ThirdFloorGreg · 8 points · Posted at 23:16:38 on February 13, 2016 · (Permalink)
That isn't how math works.
[deleted] · 2 points · Posted at 06:09:53 on February 14, 2016 · (Permalink)*
[deleted]
Phantom1thrd · -1 points · Posted at 06:12:00 on February 14, 2016 · (Permalink)
Repeating does not imply a limit, as I was taught. Repeating means repeating, eternally, with no end, infinitely.
glubness · 2 points · Posted at 06:47:28 on February 14, 2016 · (Permalink)
divide 999999999 by 3 four times and get 12345679
nxsky · 2 points · Posted at 08:23:58 on February 14, 2016 · (Permalink)
You don't need a proof for this. 0.9 and 0.3 recurring are decimal representations of a number. Whereas 1/3 and 1 are numbers.
What people really fail to see (and I don't blame them) is how mathematics can be very tricky without being complicated at all. For example, 2 is a complex number. Not easy to believe until you write it as 2 + 0i.
Naouak · 2 points · Posted at 09:29:07 on February 14, 2016 · (Permalink)
It can be also explained as :
Two numbers are different if you can write a number between them.
x<>y only if there is a z such as x<z<y or x>z>y.
Dude13371337 · 2 points · Posted at 11:20:53 on February 14, 2016 · (Permalink)
Not in the hyperreals.
Whats_Up4444 · 2 points · Posted at 03:58:09 on February 25, 2016 · (Permalink)
If you havin' math problems I feel bad for you son
I got 98.9 repeating problems but .9 repeating is 1
hawkman561 · 3 points · Posted at 04:44:06 on February 14, 2016 · (Permalink)
Only in certain number fields. The hyperreals are defined such that .9999 (repeating) ≠1.
jywn4679 · 2 points · Posted at 00:11:36 on February 15, 2016 · (Permalink)
Not exactly, 0.99...=1 in the hyperreals. Don't ask me to explain why.
redditisadamndrug · 5 points · Posted at 21:22:43 on February 13, 2016 · (Permalink)
What annoys me about this is that I pretty much never see people actually explain this. They either assume that 1/3 = 0.333... or assume that you can treat infinite sums like regular sums and do 10S - 9S.
You have to define what an infinite sum means rigorously and the simplest definition for a convergent infinite sum is that it equals the limit which in this case gives 0.999... = 1 which is like saying that when you walk across a room you've walked half way plus a quarter plus and eighth and so on.
175gr · 11 points · Posted at 21:59:43 on February 13, 2016 · (Permalink)
I like to use the fact that every two distinct real numbers have another distinct real number between them. What's between .999... And 1?
Thinks_Too_Logically · 2 points · Posted at 10:39:04 on February 14, 2016 · (Permalink)
.999... does equal 1, but the burden of proving there's no counterexample is on you.
I could answer: "Let A = .999..., B = 1, and C = A + B / 2. If A = B, then A = C = B; if A != B then A < C < B. I don't know what C is, but if A != B then I've found the number between A and B."
My problem with the "find the counterexample" proof is that I can't think of a way to show that "there can't be a C such that A < C < B" without the logic "A = B, therefore there is no number C such that A < C < B." If you can really show that there is no C between A and B without relying on A = B, then you've shown that A = B. I don't know how you'd do that though.
dreinn · 0 points · Posted at 14:25:46 on February 14, 2016 · (Permalink)
Easy. 0.00....1
Peazy.
That is, an infinite number of zeros, then a one. Lemon squeezy.
175gr · 1 points · Posted at 15:35:16 on February 14, 2016 · (Permalink)
Not their difference, the thing between them.
EccentricWyvern · 3 points · Posted at 22:38:35 on February 13, 2016 · (Permalink)
1-.999... = 0.0000.... = 0
1-.99999... =0
1=.99999
Not formal but this is how I think of it.
bik1230 · 2 points · Posted at 00:42:22 on February 14, 2016 · (Permalink)
Why are you mentioning infinite sums? That proof doesn't involve any infinite sums.
thmsoe · 10 points · Posted at 02:05:45 on February 14, 2016 · (Permalink)
When you write 0.9999..., you implicitly talk about the limit of the convergent series 0.9 + 0.09+0.009+...+9*10-n, whose limit is 1. Really, this problem all comes down to definitions.
bik1230 · 0 points · Posted at 02:53:24 on February 14, 2016 · (Permalink)
Ok, I could have been a bit clearer. I don't think it makes sense to talk about 0.9... as a convergent infinite sum when any number with predictable digits can be written as one.
Captain-Griffen · -5 points · Posted at 23:01:00 on February 13, 2016 · (Permalink)
Ultimately yes. It is an assumption. But it makes things tidy and has no actual practical downside, so why not? Mathematics is a tool, nothing more.
The correct thing to take away from it is that mathematics cannot and does not need to represent an infitessimal.
nmuna · 2 points · Posted at 04:38:44 on February 14, 2016 · (Permalink)
A lot of proofs here aren't wrong but there's a much simpler and arguably more correct way to do it. For any 2 distinct real numbers a and b, if we without loss of generality assume a<b, there exists a c such that a < c < b. There are infinitely many such c's in fact. In short there's a real number between any 2 real numbers but it's easy to see that theres no number between 0.99999... And 1. Therefore they're the same number.
Thinks_Too_Logically · 2 points · Posted at 10:26:11 on February 14, 2016 · (Permalink)
It's hard (in the sense that as a human I don't know how to do it) for me to find a number between 0.999999... and 1. But it's also hard for me to find a number between A and B where A is 1/(G64) and B is 1/(G64 with a random digit I don't know about replaced) where G64 is Graham's number.
I don't like this proof because it seems like you need to prove that A = B before you can say "There is no C such that A < C < B". And I don't really like the whole proof by "it's easy to see there's no counterexample" when there's no work showing that there's no counterexample.
nmuna · 2 points · Posted at 12:53:34 on February 14, 2016 · (Permalink)
That's a very good point. I think that it requires breaking .9999... down into the summation 910-1+910-2+9*10-3+... And see that if any change is made to any of the 9s in the number becomes less than .999... So to find a greater number requires us to start with a c*100 term. I think that would be enough to do it. I studied math in undergrad so I never got past intro to analysis so I could be wrong.
Thinks_Too_Logically · 1 points · Posted at 17:36:36 on February 14, 2016 · (Permalink)
That's a good argument for this particular problem. It actually shows that there is no counterexample.
HlfCntaur · 0 points · Posted at 06:33:10 on February 14, 2016 · (Permalink)
Like saying 2 is basically 3 if you are measuring in inches from a ruler placed on earth from the sun.
Not true, just seems so from our field of reality.
.9999...is not 1. It's damn close but it isn't one. Same as .6667 x 3 is not 2. Because .666666 is VERY close to .667. Does that mean we just round all .66666 to .667 and call it 2/3? Because it is so close? Or should it be .668. So now we can say .665 x 3 is now 2 also?
nmuna · 1 points · Posted at 12:58:47 on February 14, 2016 · (Permalink)
What I said is a property of real numbers though. The same doesn't apply to integers (what you were using in your inches example). .999999... and 1 are real numbers though where that property holds.
distactedOne · 1 points · Posted at 07:43:29 on February 14, 2016 · (Permalink)
If a < b, then there exists c such that a < c < b
If you believe .999... < 1, you are obligated to either disprove the above statement or name your c.
If you think I'm just making shit up:
https://en.wikipedia.org/wiki/0.999...
HlfCntaur · -1 points · Posted at 07:52:49 on February 14, 2016 · (Permalink)
Ok....99999... Plus .999999 plus .9999999 .9999 etc one billion times where do you find your discrepancy?
The more times you do it the farther from the same with the number 1 you get.
If a scientist does math on .3333... Vs 1/3 hundreds of times his math will eventually hit a point where the answers are different.
Though I should stop arguing. I see no proof .999 is 1. Why should I try to prove 1 is .9999. It's all conjecture and without a proof isn't math.
distactedOne · 1 points · Posted at 07:54:35 on February 14, 2016 · (Permalink)
.999... * ftfy
.999000... is obviously not equal to 1 and nobody thinks it is
https://en.wikipedia.org/wiki/0.999...#Algebraic_proofs
https://en.wikipedia.org/wiki/0.999...#Analytic_proofs
https://en.wikipedia.org/wiki/0.999...#Proofs_from_the_construction_of_the_real_numbers
HlfCntaur · 0 points · Posted at 09:14:31 on February 14, 2016 · (Permalink)
So these don't exist?
https://en.m.wikipedia.org/wiki/Infinitesimal
distactedOne · 1 points · Posted at 09:24:03 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Infinitesimal#Number_systems_that_include_infinitesimals
"Real numbers" is absent from this list.
You want to talk about surreal or hyperreal numbers, that's a totally different conversation.
e: OH ALSO
https://en.wikipedia.org/wiki/Infinitesimal#Infinitesimals_in_teaching
HlfCntaur · 0 points · Posted at 09:57:17 on February 14, 2016 · (Permalink)
Idk man. You are a karma whore and a dick. You just want to be right. Downvoting me and all that shit just to look better.
I was just arguing.
Anyways you are still considering .9999 to be a real number. 1/3 is but if you divide them you never complete the problem. You will be deciding infinitely.
I just see no documented proof from scholars saying it's true. Just that it is how it is taught to undergrads for grasping the concept.
And I'm not missing ellipses. In on a phone, and anything repeated 3 times should basically indicate infinity in this context.
Go on. If you really want to believe it I don't mind.
distactedOne · 2 points · Posted at 10:05:50 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Psychological_projection
I haven't downvoted you once.
https://en.wikipedia.org/wiki/0.999...#Algebraic_proofs
https://en.wikipedia.org/wiki/0.999...#Analytic_proofs
https://en.wikipedia.org/wiki/0.999...#Proofs_from_the_construction_of_the_real_numbers
Do you. Not see the word "proof" in these links?
Here, maybe another person can explain it better, since I'm just a huge karma dick. http://qntm.org/pointnine
distactedOne · 1 points · Posted at 07:56:27 on February 14, 2016 · (Permalink)
i think maybe you're missing the ellipsis that indicates "repeats infinitely"???
ace_urban · 3 points · Posted at 05:17:50 on February 14, 2016 · (Permalink)
by this logic, 0.0...1 (that's a 1 in the infinitieth place) should equal zero.
Edit: Is there a mathematical way to write that number I just made up?
raugturi · 1 points · Posted at 05:31:00 on February 14, 2016 · (Permalink)
No. If there are infinite 0's then the 1 at the supposed end never exists.
ace_urban · 1 points · Posted at 05:34:26 on February 14, 2016 · (Permalink)
Well, if 0.9999... has infinite 9's then you could say the same about that extra 1 that you'd need to add to the 9 in the infiniteth place to make it hit the ceiling. That's my point. From a sheer philosophical perspective, 0.9999... is never going to hit one. I'm trying to illustrate that by doing it in the opposite direction.
raugturi · 3 points · Posted at 05:44:28 on February 14, 2016 · (Permalink)
You don't have to add 1 to it at any supposed infinitieth place to make it look like 1. 0.999.... is the same as 1 but represented differently.
ace_urban · 1 points · Posted at 16:21:28 on February 14, 2016 · (Permalink)
So you're basically saying the asymptote touches the line. I see the proof and cannot refute it. That said, logically it makes no sense...
raugturi · 2 points · Posted at 21:44:43 on February 14, 2016 · (Permalink)
No, 0.999... is not a curve, it's a single value which is exactly equal to 1.
ace_urban · 1 points · Posted at 23:22:37 on February 14, 2016 · (Permalink)
What I meant is that it's curve-like if you consider how all the 9's keep getting closer to 1. 0.9 != 1. 0.99 != 1, but it's closer. On and on into infinity. Same concept as an asymptote. It will never equal one. (Well, it shouldn't, but somehow that proof says it does...)
raugturi · 1 points · Posted at 08:06:28 on February 15, 2016 · (Permalink)*
I'm going to try to use latex, so you might want a plugin for that like this: TeX The World
So, I think what you're saying is this:
[;\lim_{x \to \infty} \sum_{n=1}^{x} \frac{9}{10^n} = 1;]
I'm not sure how rigorous this proof is, but it appears to me that a) we don't need the limit, an b) it only approaches 1 because [;0.\overline{9} = 1;]. Let me see if I can demonstrate. Let's start with 1/9. If you do that via long division you'll see this:
[;\frac{1}{9} = \frac{1}{10} + \frac{1}{100} + \frac{1}{1000} + \cdots = \sum_{n=1}^{\infty} \frac{1}{10^n} = 0.\overline{1};]
If we did it as a limit the number it's approaching is actually [;0.\overline{1};], the same as the result of the sum of the infinite series itself. And since we can multiply either side by a constant:
[;\frac{k}{9} = \sum_{n=1}^{\infty} \frac{k}{10^n};]
Set k = 9 and you get:
[;\frac{9}{9} = \sum_{n=1}^{\infty} \frac{k}{10^n} = 0.\overline{9} = 1;]
Here is how wiki shows to prove it with limits and infinite series though: https://en.wikipedia.org/wiki/0.999...#/Infinite_series_and_sequences
Phantom1thrd · 1 points · Posted at 06:09:21 on February 14, 2016 · (Permalink)
No, that is not logically equivalent.
zhivago · 1 points · Posted at 10:47:29 on February 14, 2016 · (Permalink)
This is only true of number systems without infintessimals.
scobot · 1 points · Posted at 10:52:00 on February 14, 2016 · (Permalink)
But is .999.... an integer? If not, then this is just a lexical coincidence, no?
Ltbsd · 1 points · Posted at 14:34:35 on February 14, 2016 · (Permalink)
No it doesn't! Proof: https://m.youtube.com/watch?v=wsOXvQn3JuE
Phantom1thrd · 1 points · Posted at 14:42:49 on February 14, 2016 · (Permalink)
For any bystanders, that's an April fools video.
TaftintheTub · 1 points · Posted at 14:40:21 on February 14, 2016 · (Permalink)
I get this, and it makes sense for all intents and purposes, but isn't 1>.999.... by an infinitesimally small amount?
Phantom1thrd · 1 points · Posted at 14:48:42 on February 14, 2016 · (Permalink)
Fun video running down the proofs. https://youtu.be/TINfzxSnnIE
toasterstove · 1 points · Posted at 14:48:17 on February 14, 2016 · (Permalink)
Would that mean 99.9 would equal 100? If so, time to sue Lysol for false advertising.
Phantom1thrd · 2 points · Posted at 15:07:49 on February 14, 2016 · (Permalink)
99.9 no. 99.999... infinitely, yes. The repeating part is key.
Phone8675309 · 1 points · Posted at 00:56:38 on February 14, 2016 · (Permalink)
Eh. Not really. I mean sort-of. But basically this statement is because the 'repeating' notation is just a way for us to express things that go on forever without using something that goes on forever.
Supersnazz · 2 points · Posted at 02:32:33 on February 14, 2016 · (Permalink)
Until you get to hyperreals, then you can have infinitely small numbers.
popisfizzy · 3 points · Posted at 02:46:05 on February 14, 2016 · (Permalink)
Actually, it really depends. There is not a single canonical choice for what .999... is in *R, and depending on your choice the result may or may not still be true.
kogasapls · 2 points · Posted at 08:30:25 on February 14, 2016 · (Permalink)
He did say "can."
Splinter1591 · 1 points · Posted at 03:43:35 on February 14, 2016 · (Permalink)
:)
once-and-again · 1 points · Posted at 03:11:37 on February 14, 2016 · (Permalink)
Even in the hyperreals, 0.999999... = 1.
[deleted] · 1 points · Posted at 05:49:13 on February 14, 2016 · (Permalink)
no.
0.999999....... DOES NOT FUCKING EQUAL TO 1.
Stop spreading that shit.
jorellh · 1 points · Posted at 04:45:03 on February 14, 2016 · (Permalink)*
Is there an equivalent number 1.0000...1 ?
something like 1+(1-0.9repeating) ?
My guess is that there isn't but if it did it would also equal 1.
raugturi · 1 points · Posted at 05:30:23 on February 14, 2016 · (Permalink)
There is not because you can't have an infinite number of 0's followed by 1. The 1 never happens. If it did then a) the number of 0's is now finite, and b) the difference between that number and 1 is 0.<however many 0s you put in>1.
jorellh · 1 points · Posted at 15:13:40 on February 14, 2016 · (Permalink)
True it would just be 1+1/10infinity which is just 0
Kurochoplis · 1 points · Posted at 05:18:58 on February 14, 2016 · (Permalink)
I did an entire paper on this, I was given a low mark because my teacher didn't understand the concept of hyperreal numbers...
thestickystickman · -4 points · Posted at 20:02:08 on February 13, 2016 · (Permalink)*
Take x to equal 0.999...
10x = 9.999...
9x = 9
x = 1
Therefore, 0.999... = 1
Butt_Hunter · 1 points · Posted at 01:55:27 on February 14, 2016 · (Permalink)
You messed up on the second line.
thestickystickman · 1 points · Posted at 02:12:40 on February 14, 2016 · (Permalink)
Not anymore I didn't.
aoskunk · -8 points · Posted at 20:12:43 on February 13, 2016 · (Permalink)
but x doesnt equal 1 when the first thing you said was it equals 0.999..
or was this a joke that went over my head?
tetondon · 6 points · Posted at 20:38:53 on February 13, 2016 · (Permalink)
.9999.... is a different way to write 1.
They are equal.
regdayrF · 3 points · Posted at 20:35:30 on February 13, 2016 · (Permalink)
1/3 + 1/3 + 1/3 = 3/3 = 1
1/3 + 1/3 + 1/3 = 0.33333... + 0.33333... + 0.33333... = 0.99999....
Maybe that makes it easier for you to grasp the term.
Felix_Tholomyes · 4 points · Posted at 20:23:27 on February 13, 2016 · (Permalink)
Yes it does equal 1 since 0.9999… and 1 are the same.
kinectking · 2 points · Posted at 21:08:40 on February 13, 2016 · (Permalink)
Does this make it a little more clear?
X = 0.999...
10x = 9.999...
10x - X = 9.0 | (9.999... - .999...)
9x = 9
X = 1
0.999... = 1
thestickystickman · 1 points · Posted at 20:26:02 on February 13, 2016 · (Permalink)
Yes, it does. Because 0.999... = 1.
[deleted] · -14 points · Posted at 20:16:13 on February 13, 2016 · (Permalink)*
[deleted]
regdayrF · 5 points · Posted at 20:22:11 on February 13, 2016 · (Permalink)
1/3 + 1/3 + 1/3 = 3/3 = 1
1/3 + 1/3 + 1/3 = 0.33333... + 0.33333... + 0.33333... = 0.99999....
No difference at all.
[deleted] · -1 points · Posted at 20:25:32 on February 13, 2016 · (Permalink)
[deleted]
regdayrF · 4 points · Posted at 20:31:07 on February 13, 2016 · (Permalink)
That's what the points are for, this specific pattern will continue endlessly, so what I typed is not an approximation. If you were to read through some math-literature you notice, that points are often used for reocurring patterns. Therefore 1/3 = 0.333...3 . Just try to divide it by hand, no matter how many steps you were to follow, the next number would always be 3.
My two terms are just the thought behind 0.999...9 = 1 . Proving requires using positional notation and an infinite sum.
weebiloobil · 2 points · Posted at 20:36:34 on February 13, 2016 · (Permalink)
They are not approximations, they are equivalent to their fraction representations. An approximation would be 0.333...33 for some finite number if 3s.
We can see their equivalence by writing 0.333... as Σ3*10-n for n from 1 to infinity, which is a geometric series and can be summed in the usual way.
thestickystickman · 1 points · Posted at 20:43:25 on February 13, 2016 · (Permalink)
lol
Acemcbean · 1 points · Posted at 20:48:35 on February 13, 2016 · (Permalink)
Hey, I wasn't lying ;)
[deleted] · 1 points · Posted at 20:44:15 on February 13, 2016 · (Permalink)
Cant trust you on this when mathematicians say otherwise and you admit you dont know enough
Acemcbean · 1 points · Posted at 20:50:17 on February 13, 2016 · (Permalink)
Then dont, because Lord knows I was mistaken. Made an edit to my original post that basically said "Yeah, I dun diddly fucked up"
thestickystickman · 1 points · Posted at 20:33:54 on February 13, 2016 · (Permalink)
Ignoring the countless different proofs that are out there.
Felix_Tholomyes · -1 points · Posted at 20:23:54 on February 13, 2016 · (Permalink)
1/∞=0
epursimuove · 3 points · Posted at 22:07:38 on February 13, 2016 · (Permalink)
1/∞ is undefined. Lim_{x-> ∞} 1/x is 0, however.
Felix_Tholomyes · 1 points · Posted at 22:25:08 on February 13, 2016 · (Permalink)
Yeah I clarified in the next reply
[deleted] · -3 points · Posted at 20:27:14 on February 13, 2016 · (Permalink)
[deleted]
weebiloobil · 2 points · Posted at 20:41:38 on February 13, 2016 · (Permalink)
YOU CAN'T DIVIDE BY 'INFINITY' LIKE THAT!!!
Even if you're using the Extended Reals (where you have an element x s.t. n<x for all real numbers n) it's not actually dividing by infinity. What *is* correct is that in the Reals 1/x -> 0 as x -> infinity
Felix_Tholomyes · 4 points · Posted at 20:50:39 on February 13, 2016 · (Permalink)
No no no. Wrong.
First of all we can't write 1/∞ as ∞ is not a number. However if we take the limit of 1/x as x approaches ∞ then that limit is equal to zero. Not infinitesimally near 0, it's exactly equal to zero.
If you actually believe that the limit 1/x as x approaches ∞ is greater than zero then I invite you to write that limit on the form 0.000…0001 and tell me the number of decimal points in that number.
regdayrF · 0 points · Posted at 20:55:25 on February 13, 2016 · (Permalink)
Isn't he right to a certain degree ?
1/x = 0 , x --> ∞ doesn't behave like 0 in every way. Thus it is not exactly equal to zero.
1/x * x2 = x = ∞ , x --> ∞
0 * x2 = 0 , x --> ∞
VoteLobster · 0 points · Posted at 22:30:07 on February 13, 2016 · (Permalink)
You're just proving why 0.999...=1. Conceptually, 1/∞ = 0 and if two numbers have a difference of zero they're the same number.
Johanson69 · 0 points · Posted at 03:28:16 on February 14, 2016 · (Permalink)
Showing this was part of our Analysis I exam... I just didn't get it and thought I had come to a contradiction. Good thing I'm studying physics and rarely need limits... Oh wait.
gnorty · -1 points · Posted at 23:04:53 on February 13, 2016 · (Permalink)
anone who doubts this should be asked to write down what they think is 1-0.9999''. Anyone who starts writing 0.11111 should be cast straight to hell, everyone else will very soon stop doubting!
aecarol1 · 0 points · Posted at 00:31:31 on February 14, 2016 · (Permalink)
This was the very first proof I learned in pre-algebra class in Jr High. I was blown away with the idea. I’ve been into ‘hobby’ mathematics ever since.
shawndamanyay · 0 points · Posted at 02:24:23 on February 14, 2016 · (Permalink)
So infinity repeating in 9's equal 1.
canoe123 · 0 points · Posted at 04:23:23 on February 14, 2016 · (Permalink)
That really depends on what the number is representing. I could write down .999 repeating to mean a number infinitely close to 1, but necessarily not.
g-spot_adept · -1 points · Posted at 03:09:39 on February 14, 2016 · (Permalink)
No, it doesn't
Phantom1thrd · 2 points · Posted at 03:23:36 on February 14, 2016 · (Permalink)
Then, there must be a number that's bigger than .9999... but smaller than 1. Care to share?
g-spot_adept · 1 points · Posted at 07:47:30 on February 14, 2016 · (Permalink)*
yes, the number you seek is the difference in these two, i.e. subtracted from each other, which is an infinitely small number approaching zero!
or put another way, the number you seek that's "bigger than .9999... but smaller than 1" is (1 - (1/∞))
g-spot_adept · 0 points · Posted at 03:41:48 on February 14, 2016 · (Permalink)
the .9999.....number, does get "infinitely" close, but just never quite gets there, dang it!
TooMuchPants · 3 points · Posted at 04:53:00 on February 14, 2016 · (Permalink)
That's not correct. .999... and 1 are two different ways to write the same number just like .5 and 1/2 are two different symbols for the same number.
g-spot_adept · -1 points · Posted at 04:59:12 on February 14, 2016 · (Permalink)*
nah, you are infinitesimally close, but just a wee bit off!
TooMuchPants · 2 points · Posted at 05:25:13 on February 14, 2016 · (Permalink)
yup, and it can be proven mathematically
g-spot_adept · 1 points · Posted at 07:17:26 on February 14, 2016 · (Permalink)*
for the sake of doing a math problem or a proof, you can say that .999 repeating forever = 1 because it nearly does, and being infinitely close, they are as good as interchangeable, but they are not truly equal, a better way to say it would be that the limit of the difference of these two amounts approaches zero
TooMuchPants · 2 points · Posted at 07:44:23 on February 14, 2016 · (Permalink)
Again, you are just wrong. They are literally equal and it can be proven. Part of the problem is that calculus is a little counterintuitive, but you're thinking about it wrong:
The number .999... isn't "moving" anywhere. It doesn't get closer or further away from anything over time. It's not like someone is writing all the ones one at a time and each time you write one it gets closer to one, they already all exist. And there's infinitely many of them. Just like Pi. The name ".999..." is a name of a specific number that can be placed on a number line in a specific place. ANd it is provably equal to 1.
here's the actual proof, if you want it:
The number .999... is actually just an infinite sum. .9 + .09 + .009 + .0009 + .00009 etc. Another way to write that is (9/10) + (9/100) + (9/1000) etc.
This can be re-written as a power series "the sum" from 0-infinity of (9/10)(1/10)n.
This is a special kind of power series known as a "geometric series" which is known to equal a/1-r. a in this case is 9/10, r is 1/10. Just plug them in and do the arithmetic:
(9/10)/(1-1/10)=(9/10)/(9/10) = 1.
That is a mathematical proof right there. When you take Calc 2, you do this proof by hand and you can't argue with it.
.999... and 1 are the same number. Literally the same. Not so close we might as well call them the same. Not approaching the same. Not the same for the purposes of doing this problem. They are the exact same number.
g-spot_adept · 1 points · Posted at 08:17:56 on February 14, 2016 · (Permalink)*
Actually, I am not wrong, just a lot more educated than you are, I have a PhD in math. I'm sorry that you never made it much past Calc 2, but had you continued, you would have discovered advanced number theory, after about 5 more years of solid math (once you get into graduate school majoring in math)
The .9999 =1 problem a highly debated point in higher math circles, and illustrates why many conventional mathematical proof models fall apart when it comes to infinite series, I suppose you are one who has also fallen for that 100 year old hoax that 1 + 2 + 3 + 4 + ...., = -1/12 too?
TooMuchPants · 1 points · Posted at 08:35:53 on February 14, 2016 · (Permalink)
I really don't think this is highly debated in higher math circles. I've studied these types of problems in an academic setting and I've never met a phd who thought .999... didn't equal 1. Please enlighten me, though:
How does advanced number theory change what I wrote above? Are you saying that infinite sum isn't a geometric series? Or that geometric series don't equal a/1-r? The more detail the better, please.
g-spot_adept · 1 points · Posted at 09:21:45 on February 14, 2016 · (Permalink)*
well it is not an ELI5 subject, or it wouldn't be doctorate level, but hyperreals and infintesimals are interesting (if you are geek) - here is a paper on teaching younger students, and if you can wade through it all the way through, you will start to see that .999... < 1 and also that it just falls short by 1/∞ and perhaps rather than saying .999... = 1, math teachers should actually be saying lim .999... = 1
for the sake of simplicity in calculus, for example, we teach that .999... = 1, even though it really doesn't, so we can get on with class and get the rest of the course taught!
AcellOfllSpades · 3 points · Posted at 21:17:26 on February 14, 2016 · (Permalink)
.999... is a single number. There's nothing to take the limit of. An infinite decimal is defined as the limit as the number of digits goes to infinity of its truncations. By definition, .999... is exactly 1.
Also, 1/∞ is not a thing. .999... is a real number; 1 is a real number. Reals are closed under addition.
TooMuchPants · 1 points · Posted at 09:54:03 on February 14, 2016 · (Permalink)
I'm not trying to call you a liar, but a lot of people on reddit claim to have phds in lots of subjects. And your phrasing is just sloppier than I would expect from a math phd (calling zeta function regularization "a hoax" or using limits in sloppy ways).
I'm not saying it's impossible you have a phd, I just have to conclude you don't know what you're talking about. Feel free to prove me wrong if you want.
g-spot_adept · 0 points · Posted at 16:05:31 on February 15, 2016 · (Permalink)
people often dismiss concepts that go over their head as "he doesn't know what he is talking about" - it's a mental way of battling insecurity, but that is psychology and we were discussing mathematics.
PS - as I am not insecure, I have no need to feel as if I have to prove you wrong - the intelligent folks reading this will do their due diligence and dig deep enough, and that alone will will prove you wrong ;)
TooMuchPants · 1 points · Posted at 16:39:33 on February 15, 2016 · (Permalink)
I'm not sure we are talking about mathematics, though. I was. I gave you mathematical argument that .999...=1. Instead of actually refuting it, you said "I have a phd. Trust me, if you knew what I know, you would understand that .999...<1."
And all I'm saying is that what you have written in this thread gives me no indication to actually believe you. Here's the kind of thing I mean:
This statement, as its written, doesn't make mathematical sense. You can't take the limit of a number.
I have a degree in mathematics. Not a phd, but I've worked with math phds before and in my experience they're the most precise people around who are very clear about what they mean. I'm trying to give you the benefit of the doubt, but I just can't imagine one of them writing something like that.
g-spot_adept · -1 points · Posted at 18:42:01 on February 15, 2016 · (Permalink)*
apparently you didn't thoroughly read the pdf paper I linked to in its entirety and FYI, you certainly can take the limit of most any number that has in infinite number of digits (normally a series) - I didn't write the entire nomenclature out as a series (which this number actually is) because I thought you could figure out the concept, perhaps I over estimated you.
when someone abbreviates to save time, that doesn't make them sloppy, it just means they have better things to do than dig out all of the appropriate fonts and symbols to get a point across, a relatively easy to comprehend point at that.
TooMuchPants · 2 points · Posted at 19:06:39 on February 15, 2016 · (Permalink)*
No you can't. You can take the limit of a sequence or a series or a function. A number with infinite digits is defined as the limit as n approaches infinity of some series. That doesn't mean you are taking the limit of the number. Those are different things and a math phd would understand the difference.
You're not abbreviating. You're mixing up concepts.
i didn't even click on the pdf and I'm glad I didn't because it seems like it would be a waste of my time. Like I said, respond to the proof I posted above and be clear about which part you disagree with.
g-spot_adept · -3 points · Posted at 17:31:51 on February 16, 2016 · (Permalink)
see, this is why your knowledge of math is limited to the calculus level, because when someone presents a paper that might expand your knowledge past high school level, you don't even want to look at it - that's sad
TooMuchPants · 1 points · Posted at 17:55:34 on February 16, 2016 · (Permalink)*
It's not that, I love having my mind expanded. But I only have 24 hours in a day and have to budget the time wisely.
When someone who doesn't even understand basic calculus links me to a paper they claim will expand my mind, but refuses to give me an overview of it, it's probably not a great use of that time.
I've been begging you this whole time: explain to me in some condensed form how the proof I posted above is incorrect. Which part specifically is untrue and why. I'll even repost the proof for you:
Don't give me any bullshit about your "phd" or link me to some esoteric paper. Just explain which premise is wrong in there any why.
g-spot_adept · -1 points · Posted at 19:39:35 on February 16, 2016 · (Permalink)
I don't have time to rewrite the paper for you here, if you are too lazy to read and educate yourself!
TooMuchPants · 2 points · Posted at 21:11:38 on February 16, 2016 · (Permalink)
I'm not asking you to rewrite a paper. I'm asking you to refute a proof. Would take less time then writing your last 5 comments did.
But your silence speaks volumes by itself
g-spot_adept · 1 points · Posted at 01:01:09 on February 17, 2016 · (Permalink)
you are just insecure and intimidated and afraid you will not understand the paper - but you can do it! - just go slow :)
TooMuchPants · 1 points · Posted at 02:16:43 on February 17, 2016 · (Permalink)
Lol I'm really not though. I love math and I love learning new math.
I think you got caught exaggerating your knowledge and now are trying to cover that by insulting me.
Either way, .999...= 1. I proved it and you haven't even acknowledged the proof in the dozens of comments here.
Maybe your arrogant and dismissive tone is preventing you from learning something? I dunno, either way I'm done with this. Next time you pretend to have a phd, you should probably make sure you actually understand the fundamentals of the subject you're lying about. Just a thought.
Have a good one, man.
g-spot_adept · 1 points · Posted at 02:33:39 on February 17, 2016 · (Permalink)*
you only "proved it" using the low grade math that is down at your speed - i.e. calc 2 - when you learn higher levels, you'll find that the elementary level "proof" we provided you, doesn't hold
however you are scared to learn more, because you are scared of what you don't know
reminds me of how republicans deal with science - they only want there to be enough so that they can use their iPhone, and drive their car - otherwise, science is BS
and when you call them out - they quickly bail (like you did)
TooMuchPants · 1 points · Posted at 04:06:04 on February 17, 2016 · (Permalink)
Lol
TooMuchPants · 1 points · Posted at 07:48:08 on February 14, 2016 · (Permalink)
Also, Here's the wikipedia article on .999... if you don't want to believe me
The proof I posted is down the page a bit under "infinite series and sequences"
g-spot_adept · 1 points · Posted at 08:06:27 on February 14, 2016 · (Permalink)
I think you need to read the wikipedia article that you cited, and start at the paragraph titled Infantesimals and read on from there to the end.
This is a highly debated point in higher math circles, and illustrates why many conventional mathematical proof models fall apart when it comes to infinite series, I suppose you are one who has fallen for that 100 year old hoax that 1+2 + 3 + 4+ ...., = -1/12 too?
Phantom1thrd · 2 points · Posted at 04:04:53 on February 14, 2016 · (Permalink)
Well again, they are actually equal. You don't have to believe me though. I get this from mathematicians.
g-spot_adept · 1 points · Posted at 08:44:55 on February 14, 2016 · (Permalink)
you're talkin to one, actually :)
Phantom1thrd · 2 points · Posted at 11:01:05 on February 14, 2016 · (Permalink)
No offence, I find it hard to believe, since what you say contradicts what I've learned in school...
pinkfloyds · -1 points · Posted at 23:25:57 on February 13, 2016 · (Permalink)
Meh...
Noy2222 · 1271 points · Posted at 20:06:13 on February 13, 2016 · (Permalink)*
7 > 4 [citation needed]
Edit: Let's dispel the notion numbers aren't equal to themselves. They equal EXACTLY to themselves.
EmpireOfTheTsun · 1209 points · Posted at 23:10:10 on February 13, 2016 · (Permalink)*
3 = 4 for extremely large values of 3.
EDIT: Thanks for the first gold!
chateau86 · 45 points · Posted at 02:22:02 on February 14, 2016 · (Permalink)
3 = 4 evaluates to true.
3 == 4, however...
Narida_L · 14 points · Posted at 07:04:59 on February 14, 2016 · (Permalink)
2 + 2 == 5, according to this great stackoverflow thread
[deleted] · 4 points · Posted at 09:31:38 on February 14, 2016 · (Permalink)
"and God said "let 2+2=5 in 2+2"
[deleted] · 10 points · Posted at 05:30:05 on February 14, 2016 · (Permalink)
[deleted]
TheGatesofLogic · 4 points · Posted at 06:37:16 on February 14, 2016 · (Permalink)
Wait, why? Am I missing something? Does it have something to do with the way variables are stored? That confuses the hell out of me...
[deleted] · 10 points · Posted at 08:07:39 on February 14, 2016 · (Permalink)
[deleted]
reddit__scrub · 2 points · Posted at 08:59:05 on February 14, 2016 · (Permalink)
Woah... I mean, I can see the performance being improved, but that sounds like some pretty potentially dangerous undefined behavior... Is it really worth it?
lw9k · 3 points · Posted at 09:04:34 on February 14, 2016 · (Permalink)
Yes, because small integers are used a lot and this prevents a lot of needless allocations.
You don't use is very much in idiomatic python, it is actually pretty rare, and anyone using it is likely aware of this.
BTW None is None, which is actually faster than using == IIRC
TheGatesofLogic · 1 points · Posted at 16:55:11 on February 14, 2016 · (Permalink)
Ah that actually makes sense. Thanks.
reddit__scrub · 1 points · Posted at 07:08:36 on February 14, 2016 · (Permalink)
I think he's bullshitting us. I ran it through an online compiler and posted the results as a reply to his
lw9k · 1 points · Posted at 08:07:47 on February 14, 2016 · (Permalink)
See my answer.
BLARGLFLARG · 7 points · Posted at 01:24:28 on February 14, 2016 · (Permalink)
3 > 4
[deleted] · 3 points · Posted at 00:38:06 on February 14, 2016 · (Permalink)
Wait.. What
[deleted] · 53 points · Posted at 02:13:10 on February 14, 2016 · (Permalink)
It's a joke about rounded values. It's not mathematically true.
Usually it goes 2 + 2 = 5 for sufficiently large values of 2 and sufficiently small values of 5. For example 2.4 + 2.4 = 4.8, which would be rounded to 2 + 2 = 5.
IAmA_Catgirl_AMA · 1 points · Posted at 12:05:31 on February 14, 2016 · (Permalink)
I know it as π = 3, for sufficiently small π and large 3.
IBStupid · 10 points · Posted at 00:54:34 on February 14, 2016 · (Permalink)
3.999999999999 Is close enough to 4 that it can be considered 4 while still being 3
[deleted] · 27 points · Posted at 00:56:43 on February 14, 2016 · (Permalink)
But then, that's not 3. That's 3.999999999999, which is between 3 and 4 but is neither.
InsaneZee · 9 points · Posted at 01:31:30 on February 14, 2016 · (Permalink)
Be meant 3.999, repeating of course.
jaskamiin · 8 points · Posted at 03:48:45 on February 14, 2016 · (Permalink)
Is that a fucking leroy jenkins reference
InsaneZee · 2 points · Posted at 03:49:47 on February 14, 2016 · (Permalink)
Ayy, someone got it!
[deleted] · 2 points · Posted at 05:50:31 on February 14, 2016 · (Permalink)
I may have missed the reference, but at least I have chickens!
[deleted] · 1 points · Posted at 02:16:16 on February 14, 2016 · (Permalink)
Doesn't really matter. 3.999... = 4, but in no way is it 3. That's just plain wrong. And the only way we ended up with this mess is because someone was trying to retell a joke about rounding that they never actually understood in the first place.
InsaneZee · 1 points · Posted at 03:18:03 on February 14, 2016 · (Permalink)
Yeah he's wrong for that second part.
[deleted] · 1 points · Posted at 01:34:58 on February 14, 2016 · (Permalink)
Regardless of what he meant, he didn't write 3.9 recurring, or 3.999..., or anything in that vein. He wrote 3.999999999999, which is rational.
Also, regardless of whether he meant 3.9 recurring, that still wouldn't be 3. It would be 4, but definitely not 3.
InsaneZee · 1 points · Posted at 01:37:18 on February 14, 2016 · (Permalink)
Yeah he's wrong for that second part.
SlapNuts007 · 10 points · Posted at 00:58:38 on February 14, 2016 · (Permalink)
Oh no, don't start this whole .99999999 = 1 argument up again.
[deleted] · 26 points · Posted at 01:02:01 on February 14, 2016 · (Permalink)*
My argument wasn't so much that 0.9 recurring isn't 1. I think it is 1. But I strongly disagree that 3.9 recurring is 3.
And additionally, he didn't say 0.9 recurring, he said 0.999999999999, which is rational and is not 1.
ShoggothEyes · 6 points · Posted at 02:50:31 on February 14, 2016 · (Permalink)
Isn't 0.999... rational too, since it can be represented as 1/1?
su5 · 1 points · Posted at 04:31:39 on February 14, 2016 · (Permalink)
Pi is exactly 3!
[deleted] · -3 points · Posted at 01:49:24 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 3 points · Posted at 01:52:38 on February 14, 2016 · (Permalink)
Did I say that? No. I said the literal exact opposite, and confirmed what you said. What I said was that 3+1 != 3.
[deleted] · 2 points · Posted at 01:57:12 on February 14, 2016 · (Permalink)
oops, apparently I didn't read the comment very well
[deleted] · 1 points · Posted at 02:02:54 on February 14, 2016 · (Permalink)
Well I was a smarmy asshole in my reply to you, so I guess we both suck :>
chronogumbo · 7 points · Posted at 02:24:02 on February 14, 2016 · (Permalink)
It's not an argument, its a provable fact
SlapNuts007 · 3 points · Posted at 02:28:00 on February 14, 2016 · (Permalink)
I know that, but it doesn't mean people won't argue.
[deleted] · 4 points · Posted at 02:15:04 on February 14, 2016 · (Permalink)
There is no argument. There's just people who know that .999... = 1 and people who don't understand why and refuse to accept that maybe they're just dumb.
SlapNuts007 · 2 points · Posted at 02:17:39 on February 14, 2016 · (Permalink)
Oh I know--but that's not going to stop the comments.
columbus8myhw · 1 points · Posted at 01:15:27 on February 14, 2016 · (Permalink)
S/he forgot the "dot-dot-dot"
[deleted] · 3 points · Posted at 02:14:07 on February 14, 2016 · (Permalink)
That's not 3 in any sense of any of the words involved. 3 = 4 is a bad version of the joke, because no one actually rounds that way. It should be something like 1 + 1 = 3.
Mr_s3rius · 1 points · Posted at 02:54:37 on February 14, 2016 · (Permalink)
Except for prices. See a $3.99 price tag? Yea, that's 3 bucks.
[deleted] · 1 points · Posted at 03:53:51 on February 14, 2016 · (Permalink)
That's just being gullible and terrible at rounding. If I see a number that starts with 3 in a store, I just assume it's closer to 4. 99% of the time it's true.
IAMA_dragon-AMA · 3 points · Posted at 02:30:52 on February 14, 2016 · (Permalink)
At least, I think Java does automatic casting. It's been a while.
yawkat · 1 points · Posted at 10:08:08 on February 14, 2016 · (Permalink)
Nah, it won't do lossy casting like your example
VOMIT_ON_MY_DICK · 1 points · Posted at 02:53:30 on February 14, 2016 · (Permalink)
http://youtu.be/-70FqBXPUuw
ReaderWalrus · 1 points · Posted at 03:48:37 on February 14, 2016 · (Permalink)
That's hilarious!
Where is it from?
EmpireOfTheTsun · 1 points · Posted at 08:57:57 on February 14, 2016 · (Permalink)
Maths teacher humour!
[deleted] · 1 points · Posted at 03:54:37 on February 14, 2016 · (Permalink)
lim_3->4 3 = 4
Areakiller526 · 1 points · Posted at 04:02:25 on February 14, 2016 · (Permalink)
Wat
[deleted] · 1 points · Posted at 19:52:38 on February 20, 2016 · (Permalink)
that sounds like microeconomics
thestickystickman · 336 points · Posted at 20:49:43 on February 13, 2016 · (Permalink)
Time to write a 160 page paper.
CIearMind · 10 points · Posted at 22:05:24 on February 13, 2016 · (Permalink)
Or 362.
1100101000 · 3 points · Posted at 01:37:08 on February 14, 2016 · (Permalink)
Depends on the logic used. You can prove this in Lambda Calculus in just a few pages using Church Numerals and Peano arithmetic.
Star-spangled-Banner · 2 points · Posted at 02:15:40 on February 14, 2016 · (Permalink)
That tenure isn't gonna' prolong itself.
The_Butters_Worth · 1 points · Posted at 04:38:02 on February 14, 2016 · (Permalink)
300 page book*
[deleted] · 1 points · Posted at 17:03:05 on February 14, 2016 · (Permalink)
This guy fucks.
cowboyecosse · 103 points · Posted at 21:01:30 on February 13, 2016 · (Permalink)
Yeah that depends on the values of 7 and 4. I hope you're right though.
Urgullibl · 15 points · Posted at 22:26:58 on February 13, 2016 · (Permalink)
That depends on the meaning of "to be".
[deleted] · 8 points · Posted at 23:12:39 on February 13, 2016 · (Permalink)
Hey! Vsauce. Michael here
[deleted] · 14 points · Posted at 01:02:47 on February 14, 2016 · (Permalink)*
[deleted]
TestZero · 3 points · Posted at 07:39:15 on February 14, 2016 · (Permalink)
I thought ghosts ate ghoul-ash.
qwertyasdef · 2 points · Posted at 04:47:20 on February 14, 2016 · (Permalink)
But who is Michael, and how much does "here" weigh?
[deleted] · 4 points · Posted at 23:56:41 on February 13, 2016 · (Permalink)*
[removed]
Urgullibl · 3 points · Posted at 02:22:33 on February 14, 2016 · (Permalink)
I did not have a sexual relationship with that woman.
thatJainaGirl · 2 points · Posted at 23:17:45 on February 13, 2016 · (Permalink)
It really depends on what the meaning of "is" is.
OlorinTheGray · 4 points · Posted at 23:27:15 on February 13, 2016 · (Permalink)
It's totally weird when you're hearing linear algebra at university, using fields and stuff and occasionally you come along lines like
"If we assume that in the current body 1 = -1 then the following is true..."
Like, what?
Hoo-ray for Z(mod 2Z) and stuff...
franciscocorrales · 5 points · Posted at 01:59:32 on February 14, 2016 · (Permalink)
I don't understand...
Stuhl · 5 points · Posted at 02:14:20 on February 14, 2016 · (Permalink)
I have a truly marvellous proof of this, which this comment section is to narrow to contain.
blackhotchilipepper · 1 points · Posted at 05:49:12 on February 14, 2016 · (Permalink)
reference game 5/7
DrewsephA · 2 points · Posted at 01:44:11 on February 14, 2016 · (Permalink)
5=7
SquidgyTheWhale · 1 points · Posted at 23:46:15 on February 13, 2016 · (Permalink)
Even for large values of 4?
Dremora_Lord · 1 points · Posted at 13:21:50 on February 14, 2016 · (Permalink)
I believe it is 5=7.
CKYKOK · 1 points · Posted at 19:04:34 on February 14, 2016 · (Permalink)
5/7 this is the coolest math fact on here.
jorge_the_awesome · 1 points · Posted at 19:17:53 on February 14, 2016 · (Permalink)
True in Z mod 3
HungryChemist · 1 points · Posted at 13:52:19 on February 15, 2016 · (Permalink)
Didn't Kia get all the greatest minds together to work this one out?
ersils · 1 points · Posted at 03:35:15 on February 14, 2016 · (Permalink)
5/7=10/10
Drews232 · -2 points · Posted at 03:16:46 on February 14, 2016 · (Permalink)
5 out of 7 = 9 out of 10
aahdin · 317 points · Posted at 20:37:56 on February 13, 2016 · (Permalink)*
Euler's identity always seemed ridiculous to me.
ei*x= cos(X) + i*sin(x)
ei*pi = -1
You just take random constants that seem like they have nothing to do with each other, and then somehow they do. The proofs I've seen don't really explain much either, other than "the math works out".
Edit: Wow, ton of great responses and explanations. After reading most of this I actually feel like I've got a decent understanding of how it all works.
Jorlung · 64 points · Posted at 22:05:40 on February 13, 2016 · (Permalink)
Proving it using the Taylor Series definition for eix , sinx, and cosx is pretty easy to understand.
aahdin · 17 points · Posted at 23:06:49 on February 13, 2016 · (Permalink)
So both of the common proofs for it are easy enough to do, but they both left me without any kind of intuitive reason why they should work out or what's actually going on.
The closest I've been able to get is that eix is actually a way of rotating your function around the imaginary axis, which is even more confusing.
Jorlung · 11 points · Posted at 23:26:21 on February 13, 2016 · (Permalink)
I don't know if there's an intuitive way to think about it to be honest, maybe there is, but I've always just kind of taken it as something that's true.
If you ever take course in Quantum Mechanics or Control System you start getting a lot more comfortable bouncing around from complex exponential and the s-domain to sins and cosines.
healynr · 13 points · Posted at 01:47:20 on February 14, 2016 · (Permalink)
Have you seen this? http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/
MisterJose · 1 points · Posted at 04:47:31 on February 14, 2016 · (Permalink)
Lol, I linked the same thing higher up.
Jess_than_three · 1 points · Posted at 06:46:12 on February 14, 2016 · (Permalink)
Man, betterexplained is great. Having not had a math class in a decade and a half and having never gotten into calculus, I still don't understand it entirely, but I feel like it's something I could understand - not, as the author says, simply some magical incantation that just works because it works and doesn't inherently mean anything.
(Which, coincidentally, is why I quit math to begin with...)
aahdin · 3 points · Posted at 23:32:23 on February 13, 2016 · (Permalink)
I actually started googling around after reading your first comment, and I found this video.
I'm still trying to wrap my head around it, but it's making a lot more sense to me now than it did an hour ago.
[deleted] · 2 points · Posted at 02:41:00 on February 14, 2016 · (Permalink)
I had a lot of problems with trying to understand the visualisation, but the formulas make sense to me. If you have a spare half an hour, watch this lecture. It requires some basic understanding of calculus though (so does eπi = -1 though)
AllUltima · 1 points · Posted at 03:34:40 on February 14, 2016 · (Permalink)
Think about the definition of ex. It is 1 + x + x2 /2 + x3 /6 ... for a reason. When you take the derivative of the series, each term becomes the previous term and you end up with the same series. That's what makes this particular infinite series special enough to warrant its own name.
eix was defined in a similar way in order to mimic this property as closely as possible. And indeed, we end up with -eix which is at least close to its own derivative. This helps complex exponentiation be as natural an extension of the real numbers as possible, it's why calculus works so similarly on complex equations.
(By the way, people needs to stop calling these "proofs"! Euler's formula is a definition, it is the foundation of complex exponentiation. You cannot prove definitions, you can only prove that the definition carries desirable properties.)
ReidZB · 1 points · Posted at 03:47:57 on February 14, 2016 · (Permalink)
If you have a copy of Needham's Visual Complex Analysis (hint hint, look at the search results...!), then he tries to explain Euler's formula in an intuitive sense on page 10.
It also says there are "deeper" explanations later in the text, but I haven't looked at the text in such a long time that I don't really remember where; my complex analysis course was a while ago now.
However, I can recommend Needham's text for a "visual" explanation of many topics in complex analysis. Sometimes, they are more intuitive than the symbolic approach, though definitely not always. In my complex analysis course, we essentially came to the conclusion that Needham's text would be an excellent companion for a real, rigorous text on the subject, but that it couldn't really stand alone for a rigorous complex analysis study.
VacuouslyUntrue · 1 points · Posted at 09:22:18 on February 14, 2016 · (Permalink)
I think about it algebraically. The numbers of the form e2pi/n are called the roots of unity, and these are numbers whose nth power is equal to 1. ei*pi is a second root of unity because (-1)*2 = 1.
If you google the phrase, you'll see the geometry of the roots of unity, all of which are complex except 1, and -1, and it'll hopefully give a more satisfying depiction of what's going on.
AmadeusMop · 1 points · Posted at 17:48:56 on February 14, 2016 · (Permalink)
The derivative of eix is ieix.
That means that the change in the position is in a direction perfectly 90° from the position itself.
At x = 0, ex = 1. In vector terms, that's →.
Its derivative is 1 times i, which is just i. As a vector, i is ↑.
If the change in position is always 90° from the position itself, it'll trace out a circle.
zwhenry · 2 points · Posted at 02:07:45 on February 14, 2016 · (Permalink)
Exactly
AllUltima · 2 points · Posted at 03:15:46 on February 14, 2016 · (Permalink)
That isn't a proof though. Technically Euler's formula cannot be "proven" at all, since it is a definition-- that is, it is defined to equal that series in the first place. All you can do is prove that certain properties of this definition hold, which validates the definition is well chosen. The people creating complex numbers wanted the system to have certain properties, such as being an extension of the real numbers.
Think about what properties we'd want ei*x to have when defining it for the first time. Well, in the reals, ex is its own derivative-- that's kind of why ex was named in the first place. Can the complex extension have a similar property?
For the reals, ex was defined as a particularly useful infinite series which has the nifty property that taking the derivative of each term gives you the previous term in the series, which conspires to give you the exact same series you started with, making it its own derivative!! In trying to simulate this clever property, we might try defining eix in a similar way with a similar series in the most intuitive way possible. Sure enough, we get -ei*x as the derivative, which is highly reminiscent. And helps give rise to a concept of complex exponentiation where calculus is very consistent along real and complex axes. Complex analysis is really only possible because this definition was well chosen. (And of course, if you scoop up the terms from the -ei*x series definition, you end up with cosx + isinx)
Really anyone could create their own extensions of the real numbers with differing definitions, they'd just either likely be less useful, or in some sense "boil down" to something that already exists, such as complex numbers. But that's not a guarantee, there are likely many useful mathematical constructions that have yet to be discovered.
heavyish_things · 1 points · Posted at 03:18:27 on February 14, 2016 · (Permalink)
That's the much more useful and interesting one, unfortunately it's not used by most people so maths fans (as opposed to maths users) care more about the pretty one they don't care to understand.
corpuscle634 · 13 points · Posted at 21:30:09 on February 13, 2016 · (Permalink)
It didn't really click for me until I took differential equations, and then I was like "oh, duh."
iluvkfc · 6 points · Posted at 00:29:07 on February 14, 2016 · (Permalink)
Another one I like related to Euler's identity: ii = e-π/2
[deleted] · 7 points · Posted at 02:43:48 on February 14, 2016 · (Permalink)
The four most important mathematical constants all in one beautiful identity.
e, i, π and 1. It makes me happy.
nyrotagor · 8 points · Posted at 05:59:10 on February 14, 2016 · (Permalink)
Don't forget zero, it's also important.
[deleted] · 3 points · Posted at 14:36:51 on February 14, 2016 · (Permalink)
eπi - 1 = 0
:)
NanduDas · 15 points · Posted at 22:13:38 on February 13, 2016 · (Permalink)
I prefer it written as epi*i + 1 = 0.
brainandforce · 14 points · Posted at 02:20:10 on February 14, 2016 · (Permalink)
I prefer it written ei*tau = 1
BlackBloke · 8 points · Posted at 02:49:37 on February 14, 2016 · (Permalink)
You should write a +0 at the end.
mattuff · 3 points · Posted at 20:33:42 on February 14, 2016 · (Permalink)
Tau is the laziest, most unimportant shorthand but people have such diehard opinions for or against it.
[deleted] · 2 points · Posted at 02:47:12 on February 14, 2016 · (Permalink)
Wouldn't that be tau/2?
brainandforce · 4 points · Posted at 02:56:48 on February 14, 2016 · (Permalink)
No, because tau represents a full rotation from (1,0) and back. Pi takes you halfway around the unit circle.
[deleted] · 2 points · Posted at 03:00:37 on February 14, 2016 · (Permalink)
Oh, I didn't see the positive one there. My bad.
[deleted] · 3 points · Posted at 00:52:31 on February 14, 2016 · (Permalink)
For costheta+isintheta = a+bi, look at the geometry of the triangle OAP on an Argand diagram where P is the point (a, b)
You can show via Maclaurins' series' that eitheta = costheta+isintheta = a+bi
The Euler identity is substituting theta = pic into eitheta = costheta+isintheta. Hope I helped
skysurf3000 · 2 points · Posted at 00:07:13 on February 14, 2016 · (Permalink)
I have always preferred to see those as the definitions of cos/sin and pi.
cowgod42 · 2 points · Posted at 04:45:56 on February 14, 2016 · (Permalink)
What are exponential functions? They are just functions that are some multiple of their own derivative.
For example, the derivative of e3x is 3e3x; that is, just 3 times itself.
Going the other way around, if I told you that the derivative of a function f(x) was 5 times itself, it would be possible to show that f(x) is just an exponential function with "5x" in the exponent.
Now, what's the derivative of cos(x) + i*sin(x)? It's just -sin(x) + i*cos(x). Since i2 = -1, after factoring out an i, we see that the derivative of cos(x) + i*sin(x) is just "i" times itself. Therefore, this function must be an exponential function with "ix" in the exponent.
Halalsmurf · 1 points · Posted at 19:00:46 on February 15, 2016 · (Permalink)
This is a really good, intuitive explanation. I'm a physics student and use this equation all the time but this is the first time I really 'got' it.
cowgod42 · 1 points · Posted at 19:47:40 on February 15, 2016 · (Permalink)
Cool! Thanks!
JONNy-G · 1 points · Posted at 02:01:38 on February 14, 2016 · (Permalink)
Thank you! I scrolled way too far down looking for this one.
sansoomer1 · 1 points · Posted at 03:16:12 on February 14, 2016 · (Permalink)
Here's a very interest video explaining it in an unconventional way.
[deleted] · 1 points · Posted at 03:53:54 on February 14, 2016 · (Permalink)
There's a great explanation here.
kcazllerraf · 1 points · Posted at 04:02:17 on February 14, 2016 · (Permalink)
There's a great video by 3blue1brown on youtube explaining in terms of stretching and sliding. Essentially, instead of thinking of numbers as counting objects, think of them as marking an infinite line. In this system, adding 3 moves zero to where 3 used to be, multiplying fixes 0 and moves 1 to where 3 used to be, and exponents stretch in such a way that adding and then stretching is the same as stretching and then adding.
You can then extend this to the imaginary ( i ) plane by thinking of the real numbers as the horizontal axis and the imaginary numbers as the verticle axis. The same rules apply, except now exponents with imaginary components rotate the plane so what used to be the real axis is now in the complex space. Because of how pi is defined (half the circumference of a circle), an exponent of i pi rotates all the way around to -1.
MisterJose · 1 points · Posted at 04:46:59 on February 14, 2016 · (Permalink)
This is the best easy-to-understand explanation I've seen: http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/
goldistastey · 1 points · Posted at 05:23:55 on February 14, 2016 · (Permalink)*
Here's a way to prove it:
eix is complex so eix = A(x) + i*B(x) where A and B are real functions. A can simply be zero, or a function.
As stated above, one of the definitions of e is that derivative of ex is ex. By this definition, the similar special attributes of e's and the sin/cosine's derivatives are what make them related.
d/dx(eix ) = ieix,
so d/dx(A(x)+iB(x)) = iA(x) - B(x).
Now, since A(x) and B(x) are in themselves real, d/dx(B(x))=A(x) and d/dx(A(x)) = -B(x).
A=cos(x) and B=sin(x) fit this derivative behavior perfectly.
tldr: eix and the sine functions are related in that they both simply change signs when being taking the derivative of (forever).
_Psyki · 1 points · Posted at 05:32:42 on February 14, 2016 · (Permalink)
It may not be very intuitive, but you should look into Taylor Series expansions for ex , sinx, and cosx. This then leads into proving that complex numbers expressed in polar form r(cosθ+isinθ) can also be expressed in exponential form reiθ .
eiπ can then be shown to be a complex number with modulus (distance from 0) 1 and argument (anticlockwise angle from positive real axis on an Argand Diagram) π, i.e. cosπ + isinπ = (-1) + i(0) = -1.
The only other time the complex number has no imaginary part (so is a real number) is at θ = 0, but this just gives e0 = 1 which is hardly surprising.
jaspersgroove · 1 points · Posted at 06:28:57 on February 14, 2016 · (Permalink)
Salman Khans video on khanacademy regarding Euler's Identity is what cemented my love for math, it's great to watch.
underr_ · 1 points · Posted at 06:59:07 on February 14, 2016 · (Permalink)
Had to prove this as my uni for our first test. Had never seen it before, had about 4 hours to stare at it. Most gruesome thing I think I've done at that school.
IZ3820 · 1 points · Posted at 08:14:03 on February 14, 2016 · (Permalink)
So if you root the formula, the answer is i?
SigmaStarman · 1 points · Posted at 08:44:53 on February 14, 2016 · (Permalink)
"The math works out" is what my chem professor uses to explain everything that doesn't make immediate sense
aahdin · 1 points · Posted at 08:48:38 on February 14, 2016 · (Permalink)
I always hated it when professors did that.
AlphaQuin · 1 points · Posted at 09:01:15 on February 14, 2016 · (Permalink)
Okay, best way to think of it: Rotation around the complex plane (in terms of radians). Cos(x) would define the x part of a point on this circle with radius 1. Sin(x) is the y part. i is that awesome variable that doesn't mesh nicely with the real numbers, so it pushes the real numbers, which you know to be on a number line, now onto a number plane! (Want to read more? "Argand diagram".) If you can accept cos(x) being the x direction now and isin(x) being the y (which is clear because of the i part), we can move on! So by adjusting x, we move around this circle, cool, but why is that eix? If you multiply complex numbers together, their angles on the complex plane add up and their lengths multiply. If you force the length to be 1, then, multiplying by more length 1 points, lying on this circle I brought up, you can accomplish rotation. This is incredible that multiplying gives of rotation, so let's reason through it. Positive real numbers multiplied by themselves stay positive. This makes sense because this number is at 0 rotation, and adds 0 rotation to itself. Now take and negative and do the same thing. This makes a positive, which makes sense because negative numbers are a half rotation from positive ones, and two halfs make a whole rotation back to positives. Now, last one: ii. An imaginary squared. That is negative! Positive Imaginary numbers are a quarter rotation, so two quarter rotations make the number just negative! So taking a complex number, one with the real and i parts, to an exponent makes a rotation if the distances are 1. Great! So why e? E is the natural numbers, so think: Natural growth! If the number was 3ix, it would multiply to go out further than one, and if it was 2, it would shrink, but e keeps the exact distance of one around the axis going! And that exponent causes rotation, so eix makes a circle around the complex plane, as does cos(x)+isin(x), so they are the same! Using this, pi is a half rotation, a half rotation from 1 is -1, so ei*pi is -1! It's late for me, so this explanation might feel complicated, but here: TL;DR: cos(x)+isin(x) makes a circle of radius one, simply by rules of trig. Multiplying complex numbers rotates them. eix always has a distance/magnitude of 1, and is complex with exponent, so rotation occurs. Both then have to be equal since they are same thing!
floormanifold · 1 points · Posted at 09:18:12 on February 14, 2016 · (Permalink)
Imagine a particle in the complex plane moving along the path e{it}. The velocity of the particle is the derivative of position with respect to time which is ie{it}. Now multiplying a complex number by i corresponds to rotating it counterclockwise by 90 degrees, so the particle's velocity is always perpendicular to its position. But this is exactly motion along a circle of radius 1, so e{it} = cos(t) + i sin(t)
Bashar_Al_Dat_Assad · 1 points · Posted at 10:30:56 on February 14, 2016 · (Permalink)
It helps a lot more to understand what's going if you know the imaginary definitions of sin and cosine can be defined exponentially over the complex numbers
For example sin(θ) = (eiθ-e-iθ)/2i
Now it seems more intuitive that π can be related to e and i.
mattbin · 1 points · Posted at 14:46:01 on February 14, 2016 · (Permalink)
Last day of first year calculus the prof dropped this on us. It blew my tiny undergraduate English major mind.
ArcaneCraft · 1 points · Posted at 04:20:38 on March 3, 2016 · (Permalink)
u = cos(θ) + isin(θ)
du/dθ = -sin(θ) +icos(θ)
du = i(cos(θ) + isin(θ))dθ
du = i(u)dθ
(i/u) du = idθ
integrate, and
ln u = iθ
eiθ = u,
eiθ = cos(θ) + isin(θ)
eiπ = cos(π) + isin(π)
eiπ = -1 + 0
LudoRochambo · 0 points · Posted at 14:22:19 on February 14, 2016 · (Permalink)
e,1,0,i,pi are hardly random constants. the beauty is exactly opposite of what you said. its that these ARE related and they are hardly random.
Atheist_Simon_Haddad · 21 points · Posted at 02:48:32 on February 14, 2016 · (Permalink)
Student's t-distribution for statistical analysis of small sample sizes was invented to manage quality control for Guinness beer.
https://en.wikipedia.org/wiki/William_Sealy_Gosset
https://en.wikipedia.org/wiki/Student's_t-distribution
thatcanadian92 · 1141 points · Posted at 21:06:42 on February 13, 2016 · (Permalink)
You only need to know pi to the 39th digit, anything more isnt practical. With 39 you can calculate the circumference of the universe.
coolkid1717 · 1739 points · Posted at 22:57:17 on February 13, 2016 · (Permalink)
The circumference of the observible universe accurate to the width of a hydrogen atom.
Evil_Toilet_Demon · 917 points · Posted at 00:28:38 on February 14, 2016 · (Permalink)
The fact is pretty much useless without this info
dj0 · 67 points · Posted at 02:21:29 on February 14, 2016 · (Permalink)
I could just as easily "calculate" it by taking pi as 3
IGotSkills · 2 points · Posted at 16:12:33 on February 14, 2016 · (Permalink)
Gtfo
PM_girl_peeing_pics · 12 points · Posted at 04:13:11 on February 14, 2016 · (Permalink)
Yeah, you don't need that many digits to calculate the circumference of the observable universe accurate to the width of the observable universe.
slutvomit · 2 points · Posted at 09:43:56 on February 14, 2016 · (Permalink)
You can calculate the circumference of he universe (+/- 1 universe)
[deleted] · 2 points · Posted at 01:36:32 on February 14, 2016 · (Permalink)
"Pretty much" useless with this info.
sluuuurp · 1 points · Posted at 08:12:19 on February 14, 2016 · (Permalink)
I mean I could calculate the circumference of the observable universe using pi = 2. It wouldn't be very accurate though.
[deleted] · 1 points · Posted at 13:18:25 on February 14, 2016 · (Permalink)
But what if we need to calculate the circumference of the observable universe to the width of a planck length?
chesterjosiah · 603 points · Posted at 03:31:37 on February 14, 2016 · (Permalink)
BUT YOU WOULD NEED TO KNOW PI TO 40 DIGITS TO ACCURATELY MEASURE THE CIRCUMFERENCE OF YO MOMMA!!
ChannelSaidin · 16 points · Posted at 04:30:24 on February 14, 2016 · (Permalink)
Rekt.
RandomMagus · 5 points · Posted at 11:26:13 on February 14, 2016 · (Permalink)
Wow, that diet really paid off if she's so small we need the 40th digit for an accurate calculation
PickThymes · 3 points · Posted at 19:15:25 on February 14, 2016 · (Permalink)
The circumference of yo momma accurate to the width of a single Twinkie nucleus.
Moltk · 2 points · Posted at 08:50:59 on February 14, 2016 · (Permalink)
With no regard for human life (within the observable universe)
-duvide- · 2 points · Posted at 10:21:53 on February 14, 2016 · (Permalink)
all caps did it for me ... have an upvote
_____D34DP00L_____ · 2 points · Posted at 01:32:43 on February 14, 2016 · (Permalink)
How many digits are needed to calculate this to Planck Length?
coolkid1717 · 8 points · Posted at 02:29:57 on February 14, 2016 · (Permalink)
There are aproximatly 10 trillion trillion Planck lenghts in the width of a hydrogen atom. So I would guess you would need about 24 more decimal places.
sswitch404 · 1 points · Posted at 03:45:59 on February 14, 2016 · (Permalink)
To take it one step further than the size of a hydrogen atom: the circumference of a circle the size of the observable universe accurate to the size of a proton would only need 43 digits.
WeAreGlidingNow · 1 points · Posted at 07:46:44 on February 14, 2016 · (Permalink)
Can you cite a source? On Wikipedia's entry for pi, the 'talk' page had discussion on this very issue.
youav97 · 1 points · Posted at 11:33:47 on February 14, 2016 · (Permalink)
probably still pretty big for experiments like LIGO.
TrainsareFascinating · 1 points · Posted at 12:04:56 on February 14, 2016 · (Permalink)
How many digits would you need to resolve the circumference to within a Planck length?
Gobuchul · 1 points · Posted at 16:19:46 on February 14, 2016 · (Permalink)
Which is the GEO600 experiments (lately known for participating in finding gravitational waves) precision compared to the distance of sun to earth. Down to the diameter of a single hydrogen atom.
[deleted] · 0 points · Posted at 02:35:47 on February 14, 2016 · (Permalink)
[deleted]
coolkid1717 · 2 points · Posted at 02:39:03 on February 14, 2016 · (Permalink)
See my other comment below.
Floyddit · 0 points · Posted at 03:05:53 on February 14, 2016 · (Permalink)
What if I need it accurate to planck length ?
ellingeng123 · -1 points · Posted at 06:25:42 on February 14, 2016 · (Permalink)
What if I want it to the width of a Plank length?
[deleted] · 509 points · Posted at 23:41:07 on February 13, 2016 · (Permalink)
I won $314.15 for winning a Pi Recitation contest! What do you mean "not practical"?
Simoneister · 527 points · Posted at 01:50:47 on February 14, 2016 · (Permalink)
They robbed you of a cent for not rounding $314.159 to $314.16
Cortical · 26 points · Posted at 03:49:44 on February 14, 2016 · (Permalink)
unless it was in Canada. We got rid of the penny, so $314.16 would be rounded to the nearest multiple of $0.05.
hypervelocityvomit · 7 points · Posted at 12:06:52 on February 15, 2016 · (Permalink)
e = 2.718281828...
eh = 2.70
V1per41 · 13 points · Posted at 03:53:52 on February 14, 2016 · (Permalink)
Real pi fans don't round
jam1garner · 2 points · Posted at 05:59:36 on February 14, 2016 · (Permalink)
Sue like Jonathan Lee Riches.
[deleted] · 2 points · Posted at 06:11:39 on February 14, 2016 · (Permalink)
i thought irrational numbers are not rounded.. anyone has any explanation for me?
Simoneister · 3 points · Posted at 06:39:39 on February 14, 2016 · (Permalink)
Irrational numbers go on forever. But most of the time we don't need infinite numbers.
If we only need a number 5 digits long, then we start by looking at the sequence (3.141592653…) and we pick the closest 5 digit number to it. In this case, 3.14159… is much closer to 3.1416 than 3.1415 (i.e. 59 is a lot closer to 60 than 50).
ChRoNicBuRrItOs · 1 points · Posted at 08:11:47 on February 14, 2016 · (Permalink)
But you always round down when it comes to money.
PotatoesAreUs · 2 points · Posted at 10:50:35 on February 14, 2016 · (Permalink)
Only when you're giving money away.
When people charge for something they tend to round up.
ElBiscuit · 1 points · Posted at 09:45:35 on February 14, 2016 · (Permalink)
Well, they robbed him of 0.9¢.
JayGogh · 1 points · Posted at 14:08:17 on February 14, 2016 · (Permalink)
He made out pretty well. He should've only won $3.15.
ma2is · 1 points · Posted at 15:55:05 on February 14, 2016 · (Permalink)
One cent!? I would've demanded $3,141.59
phantomtofu · 5 points · Posted at 01:42:02 on February 14, 2016 · (Permalink)
How many digits? I've got 70, but I've found that most people who put in the effort to memorize some digits stop at more "round" numbers. 100, specifically. I'd go for 314 but... That's just way too many for me.
[deleted] · 14 points · Posted at 01:53:45 on February 14, 2016 · (Permalink)
Used to know over 1,000. Only recited 611 for the competition.
Mikeismyike · 9 points · Posted at 02:01:21 on February 14, 2016 · (Permalink)
I stopped at 314, and only have 200 ingrained into long term memory.
Nirheim · 7 points · Posted at 02:28:18 on February 14, 2016 · (Permalink)
Holy damn.....that a lot of numbers.
Mikeismyike · 0 points · Posted at 06:22:07 on February 14, 2016 · (Permalink)
It's a neat party trick especially because someone eventually calls you out by saying "Oh you're probably just making up numbers." So I've got a recording on my phone that I'll whip out and recite the digits in sync with the recording.
JPK314 · 1 points · Posted at 06:55:22 on February 14, 2016 · (Permalink)
I should also do that
Hoppi164 · 3 points · Posted at 02:39:38 on February 14, 2016 · (Permalink)
Should have gotten $314.16 if they're rounding up. Mate you got ripped off $0.01
arbitrageME · 2 points · Posted at 03:50:10 on February 14, 2016 · (Permalink)
more like $0.0092 ...
Parco44 · 2 points · Posted at 02:43:39 on February 14, 2016 · (Permalink)
How many times did people ask how far you went?
[deleted] · 2 points · Posted at 02:47:24 on February 14, 2016 · (Permalink)
Too many.
Side-note: Thanks for being the first comment that didn't ask how far I went. :P
ShadesOfDarkness · 2 points · Posted at 03:00:13 on February 14, 2016 · (Permalink)
Any tip on how to remembering the Numbers? I also have a contest coming up
[deleted] · 2 points · Posted at 03:03:53 on February 14, 2016 · (Permalink)
Nope, sorry. I just have a good memory I guess, I don't use any strategies.
UceOnOCE · 1 points · Posted at 09:36:11 on February 14, 2016 · (Permalink)*
I remember them in chunks of about 4 or 5. When I recite them in my head it kind of has a melody to it.
Quaisy · 1 points · Posted at 01:44:58 on February 14, 2016 · (Permalink)
How far did you memorize up to?
[deleted] · 6 points · Posted at 01:53:03 on February 14, 2016 · (Permalink)
I used to know like over a 1,000 but forgot most of it then I heard about this competition the day before so I only managed to memorize up to like 611. (Which sounds like a lot but it's not since it's all kinda in the back of my memory since I used to know it)
Quaisy · 5 points · Posted at 01:59:45 on February 14, 2016 · (Permalink)
Ah wow, when I was in elementary school I memorized up to 28 digits and as I grew older I became less and less interested in mathematics but those digits have always stuck with me. 28 is enough to impress people though!
TromboninHoes · 1 points · Posted at 01:59:27 on February 14, 2016 · (Permalink)
How deep did you go?
[deleted] · 5 points · Posted at 02:00:45 on February 14, 2016 · (Permalink)
611, would have memorized more if I didn't hear about the competition the day before. I used to know 1000+
Derf_Jagged · 2 points · Posted at 02:45:02 on February 14, 2016 · (Permalink)
From the sound of it, balls deep from winning the competition.
TheSwissArmy · 1 points · Posted at 02:05:39 on February 14, 2016 · (Permalink)
How many digits did you get to?
[deleted] · 2 points · Posted at 02:06:02 on February 14, 2016 · (Permalink)
611.
SoldierofNod · 1 points · Posted at 03:26:30 on February 14, 2016 · (Permalink)
That reminds me of a story a friend of mine told me about.
His middle school had this "Recite pi for pie!" competition. The idea being, whoever could recite the most digits would earn a pie. He wanted the pie, so he got to work and memorized 200 digits.
The thing is, he didn't know how many digits other people had memorized.
The second place competitor had memorized pi to 10 digits.
The pie sucked.
[deleted] · 1 points · Posted at 03:29:35 on February 14, 2016 · (Permalink)
That's kinda how I felt because second place only memorized like 300 digits.
.....money didn't suck though. :P
SoldierofNod · 1 points · Posted at 03:34:12 on February 14, 2016 · (Permalink)
How many did you know?
[deleted] · 1 points · Posted at 03:40:56 on February 14, 2016 · (Permalink)*
Six hundred eleven. Used to know 1000+ though.
TUoT · 1 points · Posted at 03:34:45 on February 14, 2016 · (Permalink)
You should have won $314.16!
[deleted] · 2 points · Posted at 03:40:48 on February 14, 2016 · (Permalink)
I'll never forgive them!
TinBryn · 1 points · Posted at 03:52:01 on February 14, 2016 · (Permalink)
This is why tau is better because then you would have won $628.31
[deleted] · 1 points · Posted at 03:59:04 on February 14, 2016 · (Permalink)
Or they might've been pricks about it and given me $62.83. :P
Whitespider331 · 1 points · Posted at 04:18:08 on February 14, 2016 · (Permalink)
How many digits did you recite?
[deleted] · 1 points · Posted at 04:18:44 on February 14, 2016 · (Permalink)
Recited 611. Used to know 1000+ though.
Whitespider331 · 1 points · Posted at 04:19:43 on February 14, 2016 · (Permalink)
Here i was thinking i was cool for knowing 100
WobbleWobbleWobble · 1 points · Posted at 04:44:35 on February 14, 2016 · (Permalink)
How many digits did you recite?
[deleted] · 1 points · Posted at 04:49:05 on February 14, 2016 · (Permalink)
611.
peachlobe · 1 points · Posted at 06:48:30 on February 14, 2016 · (Permalink)
how many digits do you know?
gunther-centralperk · 1 points · Posted at 07:03:43 on February 14, 2016 · (Permalink)
What did you do with the rest of the $0.009265358?
TestZero · 1 points · Posted at 07:41:25 on February 14, 2016 · (Permalink)
How many digits did you recite?
timndime · 1 points · Posted at 09:52:52 on February 14, 2016 · (Permalink)
shouldn't it have been $314.16?
I mean, we all know what comes after the 5
idleactivist · 1 points · Posted at 20:21:26 on February 17, 2016 · (Permalink)
In university I got a 2-4 of beer for reciting it to 62 digits. That's about a $40 value.
I'd have to say between you and I, I got the better deal ~ $0.64/digit vs $0.51/dgt
[deleted] · 1 points · Posted at 21:12:53 on February 17, 2016 · (Permalink)
Ya, but if I try again next year and get up to 1,000 and something (not sure the exact amount) I get bragging rights for being the most memorized in the University of Waterloo Pi Recitation contest ever... the only question is whether or not it's worth it. Also, I don't really like beer much.
CIearMind · 101 points · Posted at 22:10:47 on February 13, 2016 · (Permalink)
The observable universe.
TrillianSC2 · 14 points · Posted at 02:08:15 on February 14, 2016 · (Permalink)
Given that the circumference of the observable universe is increasing, how long before we need another digit?
natufian · 3 points · Posted at 03:12:49 on February 14, 2016 · (Permalink)
Asking the real questions.
zarraha · 20 points · Posted at 23:43:45 on February 13, 2016 · (Permalink)
You only need to know pi to the 3rd digit, anything more isn't practical. Any calculation that requires more precision than that is going to be a nightmare to do without a calculator, which knows more for you.
Sleekery · 1 points · Posted at 06:05:39 on February 14, 2016 · (Permalink)
Just type in "np.pi". Boom, problem solved.
[deleted] · 5 points · Posted at 23:39:56 on February 13, 2016 · (Permalink)
I don't like this one. If I make a life decision based on the 40th digit of pi, I have found a real physical application for it (I just prodded someone because it was odd). Pi has applications outside of circles and chaotic systems can 'resolve' circles to higher precision than this. Yes I'm being pedantic but welcome to the world of maths.
ScLi432 · 8 points · Posted at 23:59:51 on February 13, 2016 · (Permalink)
Or be an engineer rather than a mathematician in which case pi ~ 3ish
CoffeeAndSwords · 3 points · Posted at 22:54:02 on February 13, 2016 · (Permalink)
...what is the circumference of the observable universe?
assertiveguy · 12 points · Posted at 23:10:29 on February 13, 2016 · (Permalink)
I'd calculate it for you, but first I need to know pi to the 39th digit, apparently.
[deleted] · 6 points · Posted at 23:09:39 on February 13, 2016 · (Permalink)
The same circumference as your mom
Hitlerdinger · 8 points · Posted at 23:31:11 on February 13, 2016 · (Permalink)
http://www.wrightfuneralservices.net/
[deleted] · 0 points · Posted at 00:22:56 on February 14, 2016 · (Permalink)
dae think OP'mom is a fat whore xddddd
Nerdybeast · 2 points · Posted at 23:19:10 on February 13, 2016 · (Permalink)
I don't know about that, I think knowing out to 100 or so is pretty practical as a "why do you have no life?" conversation starter.
SleepTalkerz · 2 points · Posted at 23:39:33 on February 13, 2016 · (Permalink)
Someone else in this thread said you only need 20 digits of pi to do this. WHO DO I BELIEVE?
[deleted] · 2 points · Posted at 01:05:01 on February 14, 2016 · (Permalink)*
What if I want to discuss the circumference of a hypothetical universe scaled from ours by an arbitrarily large constant? :(
Govanator · 2 points · Posted at 01:21:50 on February 14, 2016 · (Permalink)
Pi≈3
1100101000 · 2 points · Posted at 01:44:12 on February 14, 2016 · (Permalink)
No one practically needs to know the circumference of the universe to within the width of a hydrogen atom.
logicalthinker1 · 2 points · Posted at 02:01:59 on February 14, 2016 · (Permalink)
How accurately can you calculate it?
[deleted] · 1 points · Posted at 02:53:49 on February 14, 2016 · (Permalink)
[deleted]
logicalthinker1 · 2 points · Posted at 04:31:31 on February 14, 2016 · (Permalink)
I mean how accurately can you calculate the universe?
Alljay_Everyjay · 2 points · Posted at 02:52:35 on February 14, 2016 · (Permalink)
I just read that it's only 20
Alkadron · 1 points · Posted at 01:28:00 on February 14, 2016 · (Permalink)
This is why I barely believe in irrational numbers.
I mean, I understand mathematically that they exist, and the decimal expansions thereof are non-repeating and non-terminating. I just... don't care.
This is what happens when a combinatorialist tries to do analysis.
TheCSKlepto · 1 points · Posted at 03:29:07 on February 14, 2016 · (Permalink)
I can do that with a whole lot less numbers: It's big
Just saved you some maths
servohahn · 1 points · Posted at 03:44:42 on February 14, 2016 · (Permalink)
Huh. So I guess Life + Everything = 3.
phx-au · 1 points · Posted at 04:05:37 on February 14, 2016 · (Permalink)
3 is within 5% of pi. Just use that.
JitGoinHam · 1 points · Posted at 04:12:20 on February 14, 2016 · (Permalink)
You can actually calculate the circumference of the universe with only two or three digits of pi.
Roller_ball · 1 points · Posted at 04:27:58 on February 14, 2016 · (Permalink)
Knowing more than 6 decimals of pi really isn't that practical.
I_too_amawoman · 1 points · Posted at 04:29:19 on February 14, 2016 · (Permalink)
People are so smart it's just shocking
thesymmetrybreaker · 1 points · Posted at 06:00:04 on February 14, 2016 · (Permalink)
I work on a particle physics project, and recently I found some of our code has the wrong value for pi in the 5th decimal place (3.14156 instead of 3.14159), it's not rounded it's just wrong, and while I can't imagine it has any real effect it's still bugging the crap out of me because there doesn't seem to be any reason for it.
[deleted] · 1 points · Posted at 06:03:58 on February 14, 2016 · (Permalink)
I have 39 digits of pi, where do I go from here
noplace_ioi · 1 points · Posted at 06:05:55 on February 14, 2016 · (Permalink)
still not accurate enough to measures OP's mom's waist
NotInVan · 1 points · Posted at 06:06:28 on February 14, 2016 · (Permalink)
Let's see:
Well, looks like I'm golden.
Toni_W · 1 points · Posted at 09:10:37 on February 14, 2016 · (Permalink)
Aww... I only know 25 digits :(
What can I calculate?
Ihavenofriendzzz · 1 points · Posted at 09:32:17 on February 14, 2016 · (Permalink)
Holy shit. I just tested how many digits of pi I knew and it was exactly 39. I'm not even lying.
raverbashing · 1 points · Posted at 09:34:32 on February 14, 2016 · (Permalink)
Unless you want to find the secret message...
quasielvis · 1 points · Posted at 13:27:05 on February 14, 2016 · (Permalink)
I'm surprised how many upvotes you got for this, it barely makes any sense.
jam11249 · 1 points · Posted at 13:47:38 on February 14, 2016 · (Permalink)
In numerical work I do there's no point having pi to huge precision at all since the integrals in the calculations are only accurate to 6 significant figures.
Similarly in "real world science" you're unlikely to know your measurements to more than 4 significant figures.
Pegguins · 1 points · Posted at 01:33:39 on February 14, 2016 · (Permalink)
Assuming pi only occurs linearly, sure. What if you have pi to some power?
Sknowman · 0 points · Posted at 03:30:31 on February 14, 2016 · (Permalink)
I'd like people to start memorizing either tau (2*pi) or sqrt(2). Both are equally as interesting as pi.
popejubal · 0 points · Posted at 03:41:52 on February 14, 2016 · (Permalink)
That assumes pi stays constant over large areas.
[deleted] · 0 points · Posted at 14:39:13 on February 14, 2016 · (Permalink)
You have no idea what you're talking about.
[deleted] · 18 points · Posted at 22:58:42 on February 13, 2016 · (Permalink)
Some mathematicians in the 16th century toyed around with the idea of taking the square root of a negative number and almost 4 centuries later it was discovered that system they had made to calculate this perfectly described the mathematics of an alternating currency circuit.
[deleted] · 5 points · Posted at 17:24:39 on February 14, 2016 · (Permalink)
current?
corntastic · 1 points · Posted at 11:21:31 on February 14, 2016 · (Permalink)
Can you tell me more?
Backlists · 6 points · Posted at 13:15:12 on February 14, 2016 · (Permalink)
Explained like you're about 15:
They named the square root of -1 the number i. I is for imaginary (in electronics they use j because I is used for current). Think of it like a new counting system, we have real numbers and we have imaginary numbers. It's best to picture it on an argand diagram - a graph whereby the imaginary numbers are shown on the y axis and the real numbers on the X axis.
We now can imagine a point off the axis and we say that it is a complex number - it has a real and an imaginary part.
For example, 2 in the real domain, 4 in the imaginary domain is expressed as 2+4i.
Well it turns out all complex numbers (and therefore purely real and purely imaginary numbers) can be expressed in terms of sine and cosine.
Turns out in AC electronics, components can also be thought of in this way, whereby the resistance is a complex number. It's called impedance.
Remember the argand diagram? When dealing with electronics, it's not called a phasor.
We have a projection (meaning value) on x (real) and a projection on y (imaginary).
A resistor has a y projection of 0. A capacitor has a positive y projection and an inductor has a negative y projection.
We can plot the current and voltage on the argand diagram, where the village is at an angle with the positive x axis. We can then add the sinusoidal part in and increase this angle (called the phasor angle). This can predict values for voltage and current at certain points in the cycle, by taking the real value.
corntastic · 3 points · Posted at 06:56:33 on February 15, 2016 · (Permalink)
Thank you, that was very interesting. I guess I'll need to brush up on my mathematics once we get to more advanced electrical theory.
FreezerPizza · 21 points · Posted at 04:12:41 on February 14, 2016 · (Permalink)
I figured out in High School somewhat of a shortcut for finding the square of a number.
Say you need to know 142 but don't have a calculator- I realized you could use the square of 13 (132=169) the add the sum of 13+14=27 so you'd end up with 169+27=196.
Another example: Finding 212 - 202=400. 20+21=41. 400+41=212
Does that make sense? I tried write a formula but wasn't able to.
arbok_guy · 7 points · Posted at 04:17:03 on February 14, 2016 · (Permalink)*
I did the same thing in high school, and the formula is: (x+1)2 - x2 = x2 + 2x + 1 - x2 = 2x+1 = x + (x+1)
FreezerPizza · 3 points · Posted at 06:40:53 on February 14, 2016 · (Permalink)
Thank you!
Vaspir · 1 points · Posted at 14:14:44 on February 14, 2016 · (Permalink)
See what he described is vastly easier to read for me than for formula. I know what the formula is but it...just isn't easy to read.
thegreatdune · 3 points · Posted at 06:22:08 on February 14, 2016 · (Permalink)*
(X+1)2 =X2 +[X+(X+1)]
So:
42 = 32 +(3+4)
16 = 9 + 7
I also figured this out in school, but never tried to write a formula until now.
fmlfr · 1 points · Posted at 14:05:47 on May 31, 2016 · (Permalink)*
Basically what you did can also be explained with any number:
(X+Y)2 = X2 + Y2 + 2XY
(20)2 = 132 + 72 + (2 * 13 * 7)
(20)2 = 132 + (13+7) + 7(20)
This is because the real formula of what you said is:
(X+1)2 = X2 + (1 * X) + 1(X+1)
(21)2 = 202 + (1 * 20) + (1 * 21)
OfTheWater · 38 points · Posted at 21:24:21 on February 13, 2016 · (Permalink)
Continuous functions that are nowhere differentiable are in fact fairly typical of continuous functions general. Look up Weierstrass functions when you get a chance.
johnnymo1 · 6 points · Posted at 23:52:34 on February 13, 2016 · (Permalink)
"Fairly typical" is an understatement. Almost all continuous functions are nowhere differentiable.
OfTheWater · 1 points · Posted at 05:31:05 on February 15, 2016 · (Permalink)
I was being very loose in my use of adjectives and adverbs.
[deleted] · 2 points · Posted at 01:12:34 on February 14, 2016 · (Permalink)
Ah, the Monsters of Real Analysis! Largely the cause of the modern pure/applied division.
[deleted] · 2 points · Posted at 01:34:51 on February 14, 2016 · (Permalink)
In more ways than one! The set of continuous functions had measure zero in the Weiner measure ( from Brownian motion). And they are nowhere dense in the supremum topology
[deleted] · 9 points · Posted at 02:49:55 on February 14, 2016 · (Permalink)
"Classical Wiener Measure" is the most giggle-inducing math phrase in my undergraduate-limited experience. Close up would be the Cox-Zucker Algorith or the Tits Group.
[deleted] · 6 points · Posted at 03:08:42 on February 14, 2016 · (Permalink)
There is also the Cuntz Algebra.
nyando · 3 points · Posted at 09:35:44 on February 14, 2016 · (Permalink)
So I've been sitting in front of the Wikipedia article about "Classical Wiener Space" for a solid minute just giggling to myself. Well done.
OfTheWater · 3 points · Posted at 05:32:27 on February 15, 2016 · (Permalink)
Don't forget the Hardy–Littlewood maximal operator!
[deleted] · 1 points · Posted at 05:35:36 on February 15, 2016 · (Permalink)
It's actually size-doesn't-matterwood...
Low_discrepancy · 1 points · Posted at 10:06:25 on February 14, 2016 · (Permalink)
You mean C0 on non compacts right for the nowhere dense part, right?
[deleted] · 1 points · Posted at 12:58:21 on February 14, 2016 · (Permalink)
Right
xiape · 1 points · Posted at 09:44:50 on February 14, 2016 · (Permalink)
Also all functions are "almost" continuous (Lusin's theorem)
Schuler001 · 51 points · Posted at 00:38:42 on February 14, 2016 · (Permalink)
Each digit of the number 3,816,547,290 is evenly divisible by the number of digits counted from left to right to that number.
3/1 = 3 38/2 = 19 381/3 = 127 3816/4 = 954
[deleted] · 8 points · Posted at 04:45:21 on February 14, 2016 · (Permalink)
And did you notice that 3,816,547,290 is 0123456789 mixed up?
VacuouslyUntrue · 2 points · Posted at 09:19:55 on February 14, 2016 · (Permalink)
From a mathematical perspective, this isn't that cool. It just seems like a random coincidence.
Ardub23 · 9 points · Posted at 10:52:43 on February 14, 2016 · (Permalink)
Yeah, I could come up with another such number right now.
1412586450
Just start with any digit and append whatever digits keep the property true.
[deleted] · -4 points · Posted at 05:26:37 on February 14, 2016 · (Permalink)
this is the coolest mathematical fact you know?
MoistTacos13 · 908 points · Posted at 21:42:33 on February 13, 2016 · (Permalink)
5318008 in an upside down calculator
chief_dirtypants · 413 points · Posted at 23:17:43 on February 13, 2016 · (Permalink)*
Take 1 girl who's 16 and do 69 with her 3 times.
11669 x 3. Flip it over and you find out what she is afterwards.
Edit A, yes 16 years old. I learned it when I was 14 so it would've been a step up, go fuck yourself you puritanical freaks. B, loose metaphorically not physically, get a clue.
Jellooooo · 194 points · Posted at 00:35:50 on February 14, 2016 · (Permalink)
And now you're on a list.
Undercover_NSA-Agent · 11 points · Posted at 03:40:24 on February 14, 2016 · (Permalink)
Don't worry, we put him on our list a looong time ago.
TheScienceSpy · 3 points · Posted at 05:32:01 on February 14, 2016 · (Permalink)
Am I on your list?
[deleted] · 3 points · Posted at 07:15:47 on February 14, 2016 · (Permalink)
You are now.
intensely_human · 5 points · Posted at 03:17:17 on February 14, 2016 · (Permalink)
Sir I think we may have located Chief Dirtypants.
ColinPascoe · 5 points · Posted at 03:53:46 on February 14, 2016 · (Permalink)
adam johnson wishes that one girl was 16
JamEngulfer221 · 5 points · Posted at 08:55:07 on February 14, 2016 · (Permalink)
Only in America
[deleted] · 5 points · Posted at 02:29:17 on February 14, 2016 · (Permalink)
Half the world is going to be on that list, so he's in good company.
Undercover_NSA-Agent · 6 points · Posted at 03:42:18 on February 14, 2016 · (Permalink)
Actually it's about 75%
S_B_B · 2 points · Posted at 05:45:08 on February 14, 2016 · (Permalink)
i thought this said, "And now you're an idiot" at first glance. Which describes how I felt after I just punched this into my calculator
Baldazar666 · 1 points · Posted at 13:09:25 on February 14, 2016 · (Permalink)
16 is legal in a lot of countries.
574N13Y · 1 points · Posted at 14:48:46 on February 14, 2016 · (Permalink)
not just a lot but the sensible ones
egtemp · 42 points · Posted at 01:25:22 on February 14, 2016 · (Permalink)
There is no penetration in that position tho
EmpororPenguin · 38 points · Posted at 03:11:33 on February 14, 2016 · (Permalink)
Do you expect the highschoolers that came up with this to know that
kingofvodka · 6 points · Posted at 09:25:03 on February 14, 2016 · (Permalink)
They told me that they bang hot girls every day
TurquoiseLuck · 11 points · Posted at 03:47:15 on February 14, 2016 · (Permalink)
To everyone else commenting confused - girls get loose when they're turned on. Generally giving a girl oral pleasure turns her on, therefore loosens her up.
Cahillguy · 8 points · Posted at 08:40:33 on February 14, 2016 · (Permalink)
This guy clearly fucks.
memeship · 24 points · Posted at 01:13:25 on February 14, 2016 · (Permalink)
( ͡° ͜ʖ ͡°)( ಠ_ಠ)[deleted] · 10 points · Posted at 02:06:45 on February 14, 2016 · (Permalink)
It looks like your guy had a stroke.
NC-Lurker · 6 points · Posted at 09:44:58 on February 14, 2016 · (Permalink)
Legal in most countries, even more so if you're about the same age. 'Murican prudes...
ElBiscuit · 1 points · Posted at 09:47:18 on February 14, 2016 · (Permalink)*
Actually, 16 is legal in the majority of US states, too. Some have it at 17, but only a dozen or so set it at 18.
NC-Lurker · 3 points · Posted at 10:11:45 on February 14, 2016 · (Permalink)
Then why is he ( ಠ_ಠ)'ing?!
Also thanks for the info :p
autocol · 10 points · Posted at 02:00:14 on February 14, 2016 · (Permalink)
Except... There's no penetration in a 69. Why would she end up loose?
CthulhuHatesChumpits · 15 points · Posted at 03:18:44 on February 14, 2016 · (Permalink)
Even if there was penetration, she still wouldn't...
dellaint · 5 points · Posted at 04:00:26 on February 14, 2016 · (Permalink)
Loose is generally a metaphorical term, no?
sonyka · 2 points · Posted at 11:07:47 on February 14, 2016 · (Permalink)
Well if it's that kind of loose (and we're 16 and judgy), she'd have been loose to begin with.
Brownt0wn_ · 2 points · Posted at 03:38:30 on February 14, 2016 · (Permalink)
What does that say?
GingerWithFreckles · 3 points · Posted at 01:46:56 on February 14, 2016 · (Permalink)
Made me try it out and giggle. Not telling my students this.
GrayOctopus · 2 points · Posted at 00:46:21 on February 14, 2016 · (Permalink)
Adam Johnson is that you?
Darkohuntr · 6 points · Posted at 01:52:56 on February 14, 2016 · (Permalink)
16 is legal in the UK.
MrFrimplesYummyDog · 1 points · Posted at 03:48:43 on February 14, 2016 · (Permalink)
No, but If he said "I punch those numbers into my calculator, it makes a happy face" he'd be Cave Johnson...
[deleted] · 2 points · Posted at 01:38:28 on February 14, 2016 · (Permalink)*
[deleted]
ubercanucksfan · 1 points · Posted at 02:12:49 on February 14, 2016 · (Permalink)
I'm still lost. What is it?
_____D34DP00L_____ · 2 points · Posted at 02:19:54 on February 14, 2016 · (Permalink)
Loose
bunker_man · 1 points · Posted at 07:00:32 on February 14, 2016 · (Permalink)
Do people even make that type of association to oral sex? I've only heard it for dicks.
NvizoN · 1 points · Posted at 08:49:37 on February 14, 2016 · (Permalink)
I haven't heard of, or done this, since middle school. Thank you for bringing that memory back.
timndime · 1 points · Posted at 10:07:01 on February 14, 2016 · (Permalink)
That reminds me of "55378008" eh?
bobbinika · 1 points · Posted at 10:36:31 on February 14, 2016 · (Permalink)
A girl had 69 boobs and that's too too too many. So she went to see Doctor X on 51st street and he went crazy and ate them all. Now she's boobless. 6922251x8= flip that over
Ronald-McFondled · 1 points · Posted at 13:12:55 on February 14, 2016 · (Permalink)
Sorry if you've seen this a ton already. Your equation reminded me of something.
Pamela Anderson's were 69 pounds, and that was 2 2 much so she went 2 51st street to see doctor X. After 8 weeks on treatment, she was left...
6922251x8
BlueberryPhi · 1 points · Posted at 13:59:31 on February 14, 2016 · (Permalink)
ExPddll?
StaleTheBread · 1 points · Posted at 15:11:00 on February 14, 2016 · (Permalink)
You must have a big tongue then
Jomo_sapien · 1 points · Posted at 17:08:21 on February 14, 2016 · (Permalink)
There was a girl with a 69 size bra which was 2 2 2 big, so she went to 51st to visit mister X who gave her 8 pills, now she's boobless! 6922251x8 = 55378008
hashtagwindbag · 1 points · Posted at 07:10:40 on February 14, 2016 · (Permalink)
How on Earth does a girl become loose after a 69?
Am I doing them wrong?
enriquex · 3 points · Posted at 07:59:24 on February 14, 2016 · (Permalink)
if a girl gets horny enough her vag will be looser
KSKaleido · 0 points · Posted at 03:01:35 on February 14, 2016 · (Permalink)
69ing doesn't involve penetration, though... or have I been doing it wrong?
[deleted] · 5 points · Posted at 23:45:51 on February 13, 2016 · (Permalink)
Why do people keep saying this when you can write 80085 and not have to turn it upside down?
[deleted] · 6 points · Posted at 01:17:49 on February 14, 2016 · (Permalink)
boobies != boobs
DantesEdmond · 3 points · Posted at 04:07:45 on February 14, 2016 · (Permalink)
There was a woman who was 69 years old and her boobs were 2, 2, 2 big so she had to take 51 pills a day for 8 days until she was 55378008
6922251 x 8
ITouchMyselfAtNight · 2 points · Posted at 07:07:58 on February 14, 2016 · (Permalink)
A woman's boobs weighed 69 pounds. They were 2 2 2 big. So she went to 51st street to doctor X and had 8 operations. She came out...
ceelo_purple · 2 points · Posted at 09:11:05 on February 14, 2016 · (Permalink)
I learned it as:
There was once a girl who was thirteen her breast size was eighty four but she wanted it to be forty five. She went to the doctor and the doctor said "Oh, take these pills two times a day" but she took them four times a day because she wanted smaller breasts and she ended up...
13844502 x 4 x 1 = 55378008
ToxDoc · 2 points · Posted at 01:34:53 on February 14, 2016 · (Permalink)
Can't...turn...iPhone...screen...over. Head going to explode.
tabascojones · 1 points · Posted at 05:02:12 on February 14, 2016 · (Permalink)
55378008 :-(
1MoAgain · 1 points · Posted at 06:33:25 on February 14, 2016 · (Permalink)
Upvote for boobs
akimbocorndogs · 1 points · Posted at 07:26:21 on February 14, 2016 · (Permalink)
I'm a fan of 53045 3080
JeBalon · 1 points · Posted at 07:37:38 on February 14, 2016 · (Permalink)
Omg...I always thought it was 55318008 for boobless. I never thought of boobies. Amazing
TestZero · 1 points · Posted at 07:43:05 on February 14, 2016 · (Permalink)
a 69-year old woman thought she was too too too fat, so she went to 51st street and saw dr X, had 8 operations and came out...
Murphenstien · 1 points · Posted at 10:35:59 on February 14, 2016 · (Permalink)
Finally. Something I understand
daanjderuiter · 1 points · Posted at 12:36:42 on February 14, 2016 · (Permalink)
This started getting boring quickly by the time we had to swith to graphical calculators
narenare658 · 0 points · Posted at 03:34:10 on February 14, 2016 · (Permalink)
This is way too far down in this thread.
[deleted] · 587 points · Posted at 20:11:58 on February 13, 2016 · (Permalink)
Monty Hall problem
Still makes no sense to me, it's one of those things that computer experiments shows to be true, but it has fooled mathematicians and also often makes no intuitive sense (though there are particular ways of thinking about it or framing it that can make better intuitive sense).
https://en.wikipedia.org/wiki/Monty_Hall_problem
jmt222 · 1468 points · Posted at 20:34:35 on February 13, 2016 · (Permalink)
If your strategy is to always switch:
If you initially chose correctly (1/3 chance), then you always lose by switching.
If you initially chose incorrectly (2/3 chance), then you always win by switching.
aixenprovence · 252 points · Posted at 22:38:07 on February 13, 2016 · (Permalink)
I've never seen it put so concisely. Nice.
memeship · 12 points · Posted at 01:16:15 on February 14, 2016 · (Permalink)
I remember when I was young in college having trouble grasping the concept, so I wrote a program to calculate it for me to prove that it was true. It was.
That was fun. I probably still have the web page I built that simulated the game somewhere online.
abedneg0 · 6 points · Posted at 02:53:17 on February 14, 2016 · (Permalink)
I won $20 by betting my programmer friend that the answer is 1/3, not 1/2. He took the bet and wrote the code -- and paid me.
ScrewAttackThis · -3 points · Posted at 09:21:09 on February 14, 2016 · (Permalink)*
The answer to what? Not switching? Cause switching is a 2/3 chance. Not switching is a 1/3 chance of getting it right, but that's usually not the part that people disagree on. Most people argue that switching doesn't matter. They incorrectly assume that their odds of winning remain 1/3.
So I'm not sure if you just had a typo or misexplained, but it sounds like you owe your programmer friend some cash.
abedneg0 · 1 points · Posted at 19:52:23 on February 14, 2016 · (Permalink)
He said that switching and not switching both had 50% chance of winning. I couldn't convince him he was wrong until he himself coded up a simulation.
NC-Lurker · -1 points · Posted at 09:50:27 on February 14, 2016 · (Permalink)
Yes, it is. Because the people who get it wrong will tell you that they have a 1/2 chance of getting it right (because there are only 2 doors left), when it's still 1/3. So he makes perfect sense to me.
ScrewAttackThis · 0 points · Posted at 09:56:54 on February 14, 2016 · (Permalink)*
If your strategy is to always switch doors, you will win 2/3 of the time. Not switching will result in winning 1/3 of the time.
Like I said, the part that people typically disagree on with this problem is whether switching increases your chances of winning. The answer is "switching increases your odds of winning."
So I'm not sure why you would bet someone "the answer is 1/3." They either argued a part of the problem that was never meant to be argued, or the person just made a flub in their comment.
The reason why you wouldn't argue "not switching is a 1/3 chance of winning" is because the answer is very intuitive.
Saying switching the doors increases your odds of winning to 50%, while still wrong, is closer to being correct than saying they remain the same. This is because it'll lead you to the correct strategy of always switching. The reason people think this is because they assume that the odds only matter when you're switching (you're either going to win or lose). That's not correct, though, since it ignores the fact that you had to make an initial 1/3 probability guess.
NC-Lurker · -2 points · Posted at 10:17:34 on February 14, 2016 · (Permalink)
You're just formulating the question differently.
Again, assuming he didn't typo or anything of the sort; at some point during this typical argument, the other person will say "but there are only 2 doors remaining, it's a 50/50!" In other words, "there's a 1/2 chance of my door being the good one!".
I assume that the OP replied "no, you only have a 1/3 chance of winning if you keep your door". At this point, they bet. 1/3 wins the bet, 1/2 loses it.
This whole "initial 1/3 probability" remaining relevant is what people fail to grasp, as they usually equate 2 doors remaining to a coin flip.
ScrewAttackThis · 0 points · Posted at 10:23:02 on February 14, 2016 · (Permalink)*
Hey man, I really don't feel like arguing something that's been argued to death for multiple decades.
https://en.wikipedia.org/wiki/Monty_Hall_problem
The Monty Hall Problem:
And what people usually assume:
Note how the problem is asking "should you switch." This is equivalent to saying "what are the odds of winning if you switch?" Certainly you can understand why I'm confused that someone would bet "the answer is 1/3" and consider themselves the winner. It's not the correct answer.
If the OP and their programmer friend were really just arguing what the odds of picking the correct door out of 3 possibilities are (not the Monty Hall problem), then I'm surprised it required a computer simulation.
NC-Lurker · -1 points · Posted at 10:39:18 on February 14, 2016 · (Permalink)
I'm not arguing the problem itself, we both understand how it works and what the correct answer is. Do take a second to read the previous posts before you criticize someone and tell them they owe money to their friend. Spend an additional second on the context if necessary.
Which is basically the same thing as asking "should you keep". As I said, you're getting crazy about a simple difference in formulation. To people who get it wrong (and as you pointed out, answer "it doesn't matter") it literally does not matter. Whether you ask "keep" or "switch", it's the same thing.
Put in mathematical terms, their answer is strictly equivalent to "I have a 1/2 chance of winning by keeping my door". To which you'd logically reply, "no, it's only 1/3."
Again, they're (supposedly) arguing their odds AFTER a door has been opened, which is exactly what the problem is about. They just happen to be talking about keeping the initial choice (1/3) rather than the switching possibility (2/3).
ScrewAttackThis · -1 points · Posted at 10:43:32 on February 14, 2016 · (Permalink)
"Should you keep" is literally the exact opposite of "should you switch." The answer is, unsurprisingly, completely different.
Not sure why you're trying to argue this so much. Their post was confusing. I asked for clarification. You're incapable of giving that clarification, so why are you still commenting?
Are you the person I responded to? No. So perhaps you shouldn't answer for them, since I was asking them exactly what you're trying to say is "supposedly" what they originally argued.
NC-Lurker · -1 points · Posted at 10:51:50 on February 14, 2016 · (Permalink)
From the point of view of someone who didn't get the problem, no, it's exactly the same thing - and their answer is the same; "it doesn't matter".
Again, the original post was fine, and in context, easy to understand. You're the one making a fuss about it.
I was capable of clarifying and did so. You appear to be unable to grasp it, don't blame it on me. Next thing we know it'll be the teacher's fault that you landed in a special needs class.
I took pity on your lack of understanding and tried to give the explanation you asked for (or rather, whined about). I'm starting to wonder whether you were really clueless enough to misunderstand the OP, or whether you just decided to troll and play dumb. Either way I'm done with you.
ScrewAttackThis · -1 points · Posted at 10:57:14 on February 14, 2016 · (Permalink)
So in the context of the Monty Hall problem, I'm supposed to know that they were arguing something that's not the Monty Hall problem? There's something wrong with asking them what they were arguing? What the hell are you smoking?
Seriously, you're just being a bit dumb about this.
[deleted] · 5 points · Posted at 03:55:47 on February 14, 2016 · (Permalink)
Hey, me too!
I was a beginner programmer; excuse my ugly code.
Bembu · 2 points · Posted at 17:44:26 on February 15, 2016 · (Permalink)
And here's a Python one! :) https://gist.github.com/bembu/7ff5afcd374e3b948358
jacybear · -42 points · Posted at 01:53:25 on February 14, 2016 · (Permalink)
This sounds an awful lot like a /r/humblebrag.
You also make it sound like a program to simulate that is hard to write. It isn't.
memeship · 12 points · Posted at 02:01:33 on February 14, 2016 · (Permalink)
Humble brag? I wrote this when I was in college. Any CS student would be able to write a program to simulate the Monty Hall experiment. There's nothing to brag about here.
Simply relating to the problem, and how I personally came to understand it better.
Here are the relevant bits if you'd like (Javascript):
As you can see, the comparison in the
didChooseCorrectly()function illustrates pretty well how the results rely on whether or not you chose correctly first, which you have only a 1/3 chance of doing.[deleted] · 8 points · Posted at 02:20:31 on February 14, 2016 · (Permalink)
"G-G-Guys, I can do this too! Guys, see, I can do it too! Me! I can do it! Me too!"
chill bruh
jacybear · -13 points · Posted at 02:28:36 on February 14, 2016 · (Permalink)
I actually didn't say that, nor did I imply it. I'm quite chill.
0raichu · 9 points · Posted at 04:26:48 on February 14, 2016 · (Permalink)*
jacybear · -7 points · Posted at 04:47:23 on February 14, 2016 · (Permalink)
k
Gehalgod · 1 points · Posted at 08:37:12 on February 14, 2016 · (Permalink)
There should be a subreddit celebrating this sort of thing.
Like, /r/conciseexplanationporn or something. Or just /r/conciseporn. Anyone want to mod it up with me?
Judo_John_Malone · 1 points · Posted at 12:52:03 on February 14, 2016 · (Permalink)
Nice idea, but leave "porn" out of the name.
Gehalgod · 1 points · Posted at 17:20:55 on February 14, 2016 · (Permalink)
Why? It's obviously not referring to actual porn.
[deleted] · 1 points · Posted at 08:46:44 on February 14, 2016 · (Permalink)
[deleted]
ScrewAttackThis · 1 points · Posted at 09:39:56 on February 14, 2016 · (Permalink)
Well they left out pretty much everything except for the answer.
rankinrez · 1 points · Posted at 13:51:28 on February 14, 2016 · (Permalink)
Agreed just read the whole wikipedia article and this explains it much better!
DemeaningSarcasm · 44 points · Posted at 00:07:21 on February 14, 2016 · (Permalink)
For people who are still confused.
With the stay condition, you must initially pick the winning door.
With the switch condition, you must initially pick the losing door.
Psycho_Robot · 23 points · Posted at 03:07:16 on February 14, 2016 · (Permalink)
A way to explain the problem that everybody understands is to just increase the number of doors. Instead of three doors, there are now a hundred doors. You pick a door at random and Monty then opens up every other door except one. Either the prize is in the door you picked first, or it's in the door that's left unopened. Which should you pick? Everyone knows that they probably didn't pick the right door at the start, and so it becomes much clearer why switching is the better strategy.
coinpile · 5 points · Posted at 03:58:58 on February 14, 2016 · (Permalink)
I couldn't understand it until I read something similar. Increase the number of doors to one million, choose one, and eliminate 999,998 incorrect doors. The odds of my choosing the correct door were one in a million. I know one of the two remaining doors is the correct door, and the odds are overwhelmingly in favor of it being the remaining door I did not choose.
ScrewAttackThis · 1 points · Posted at 09:46:44 on February 14, 2016 · (Permalink)
I like explaining it backwards. Based on the rules of the problem, you have 3 possible initial selections. Based on each proposed strategy, these are the following ways to lose:
Always switch:
Never switch:
Now just consider the odds of those happening. Remember there's 3 total initial possibilities for each strategy. If you always switch, you have a 1/3 chance of losing. If you never switch, you have a 2/3 chance of losing.
[deleted] · 19 points · Posted at 22:47:10 on February 13, 2016 · (Permalink)
[deleted]
sklos · 34 points · Posted at 23:09:17 on February 13, 2016 · (Permalink)
The door opened being never the correct one is the entire point. Thus, if you originally chose one of the two incorrect ones switching is a winning move, and if you originally chose the one correct one switching is a losing move.
AbysmalWhip · 11 points · Posted at 23:06:48 on February 13, 2016 · (Permalink)
The game show host knows which one is correct. He always opens up the one which is not correct.
Merlyn_LeRoy · 5 points · Posted at 23:08:38 on February 13, 2016 · (Permalink)
If they choose the door randomly, then yes, switching doesn't change things because 1/3 of the time it will uncover the prize -- but the problem specifies that a door known to not have the prize is opened.
The easiest way to show that switching wins in the normal case is to change the game in two steps:
Step 1: After showing a non-prize door, offer to trade both remaining doors for their original selection -- since one is worthless, this doesn't change the game in any real way.
Step 2: Now just point out that you know of a door you can open to show that it doesn't have the prize, and the player knows this too, so you don't have to actually open any door -- and now, offer to trade both closed doors for their original selection.
HiddenKrypt · 3 points · Posted at 03:01:54 on February 14, 2016 · (Permalink)
The original show never actually had the option to switch. That was a later addition to make it into an interesting problem. The thought experiment was named after the game show just because of the "pick one of three doors" idea.
And yes, your confusion is one of the core reasons people argue about this thing. If the host opens doors at random and happens to open a door with a goat, your odds are 50:50. If the host knows what door the prize is in and always opens the door with a goat, then your odds are 1/3 win if you stay, 2/3 win if you switch.
Which just makes the whole thing more mysterious! The knowledge and actions of the host affect the probabilities!
SQRT2_as_a_fraction · -2 points · Posted at 02:30:02 on February 14, 2016 · (Permalink)
That doesn't really change anything. Either the host opens the door with the car and it cannot possibly matter what you do, or he opens a door with a goat and you have 2/3 chances if you switch.
[deleted] · 1 points · Posted at 08:38:18 on February 14, 2016 · (Permalink)*
[deleted]
DoesntWearEnoughHats · 5 points · Posted at 23:20:47 on February 13, 2016 · (Permalink)
This is by far the most elegant solution I've ever seen.
krazay88 · 3 points · Posted at 02:07:37 on February 14, 2016 · (Permalink)
I finally understand!!!!!
unMasqed · 3 points · Posted at 02:06:09 on February 14, 2016 · (Permalink)
Damn...that's actually a super solid summary. Well done friend.
tadair919 · 2 points · Posted at 08:35:55 on February 14, 2016 · (Permalink)
You don't always win by switching. You could still switch to the wrong door.
jmt222 · 2 points · Posted at 13:28:35 on February 14, 2016 · (Permalink)
If your strategy is always switch and your first choice was wrong, then the host eliminates the other wrong door. There is only one door to switch to, which must be the winner.
tadair919 · 2 points · Posted at 13:43:39 on February 14, 2016 · (Permalink)
Oh I get it. It's because if you switch you get the benefit of your host disqualifying one of the doors. If you don't switch then you lose that advantage. If the host never shows a door between rounds then it would be even odds either way. But since he does, he works for you.
iamnewsorry · 1 points · Posted at 00:42:18 on February 14, 2016 · (Permalink)
Perfect
joeykip · 1 points · Posted at 03:49:16 on February 14, 2016 · (Permalink)
This is the perfect response, and perfectly sums up the five-minute, convoluted explanation I always attempt to give when this question comes up.
[deleted] · 1 points · Posted at 04:01:45 on February 14, 2016 · (Permalink)
[deleted]
jmt222 · 1 points · Posted at 13:32:16 on February 14, 2016 · (Permalink)
No. My initials are J.M.T.
[deleted] · 1 points · Posted at 06:11:21 on February 14, 2016 · (Permalink)
HOW. THERE IS A 50 PERCENT CHANCE OF GETTING THE WRONG DOOR.
[deleted] · 1 points · Posted at 06:27:30 on February 14, 2016 · (Permalink)
Okay, ignore the rest of the problem. There are three doors and one car. You pick a door at random. What are the odds that you picked the wrong door?
[deleted] · 2 points · Posted at 06:29:18 on February 14, 2016 · (Permalink)
2/3!!
[deleted] · 2 points · Posted at 06:59:39 on February 14, 2016 · (Permalink)
Right, so say there’s a strategy that gives you these results:
As you’ve just said, the odds that you picked the wrong door are 2/3, so a strategy like this would give you better-than-even odds. Agreed?
[deleted] · 1 points · Posted at 15:47:22 on February 14, 2016 · (Permalink)
The part I don't get is since it's still a 50% chance of getting a wrong door.
I understand what you're saying and why, but also whyyyy.
[deleted] · 2 points · Posted at 16:32:46 on February 14, 2016 · (Permalink)
Where are you getting 50%? If you pick 6/49 lotto numbers, the odds that you won are 1/13,983,816. Telling you 13,983,814 picks that lost based on what you picked, after you picked (maybe this is the part you’re missing? the host doesn’t open the preview door randomly) does not increase the odds that you won. Sure, if the number of options were reduced to 2 before you picked, then you would have a 50% chance. But it’s after.
Clyzm · 1 points · Posted at 07:14:41 on February 14, 2016 · (Permalink)
This is probably the most succinct way I've ever seen this explained.
akimbocorndogs · 1 points · Posted at 07:31:20 on February 14, 2016 · (Permalink)
But since you're deciding again, isn't it 50/50? The choices are basically, if you originally picked door number one and he puts down door three, do you pick door one or door two? Since he offers you another guess, you're making a new choice. That's what bothers me about it.
SkorpioSound · 1 points · Posted at 10:18:41 on February 14, 2016 · (Permalink)
The odds are based on your initial choice. You have a 1/3 chance of picking the correct door initially, right? If one of the wrong doors is then removed, do you suddenly have a 1/2 chance of your initial choice having been the correct door?
A good way to think about it is that the doors are not removed, they're just marked as incorrect but you can still pick them if you want (even though you know they're incorrect). So you pick a door (1/3 chance of it being right), a door is marked as wrong but is still there (so you still have a 1/3 chance of being correct) - you'd be stupid to pick the one you know is wrong so the only real choice is do you switch to the other unknown door or keep what you've got. Now, you have a 1/3 chance of you initial pick being right, so a 2/3 of it being wrong. You know for a fact that one of the doors is wrong, but there's still three doors so the odds still have to make 3/3. So if your initial choice was 1/3, and one door is known to be wrong, that 2/3 has to be behind the door you didn't initial pick and that hasn't been marked as wrong.
Hopefully that helps.
akimbocorndogs · 1 points · Posted at 17:02:06 on February 14, 2016 · (Permalink)*
Yes, because although when you picked it initially it was 1/3, you are now making a new choice: door number one or two? Picking door number three at this point is as good as picking door number four: since you know that won't get you the prize, you know picking it gives you a 0/3 chance of getting the prize. If door number one remains as 1/3 when door three is marked as incorrect, then door two also remains as 1/3. Before, the prize had an equal chance of being behind any of the three doors. Now there's only two (relevant) doors, and you have to decide if you want to stay on one or pick two. But, at that point, you're making a new decision: door one or door two? If you came on the show and were only offered two doors, it would be the same situation, pick one or the other.
What about this: you come on the show, there's four doors. Before you even make an initial choice, he tells you that door four will be an incorrect choice. Are your odds still one in four? Not to me, because you can make the informed decision of ruling out door four, so it's really just one of three doors. You know it's behind one of the three. 1/3, even when there's four doors. So, with the original problem, it's 1/2, even when there's three doors. Your information makes it 1/2 for you.
SkorpioSound · 1 points · Posted at 18:26:39 on February 14, 2016 · (Permalink)
Here are all the possible outcomes for the problem in a table. The door Monty opens doesn't affect your choice and doesn't give you any new information - there's no way for you to know whether the door that's being opened is being opened because it's the only one that both doesn't have the prize AND isn't one you picked, instead of just being one that doesn't have the prize (this is why, where possible, the door that Monty opens is "x or y").
The reason you're getting stuck is because you're "ignoring" the information you have at the start and are treating the two different choices as independent, when in reality the second choice is dependent on the first: whichever door you pick initially has a 1/3 chance of being the one with the prize but a 2/3 chance of NOT having the prize. Removing a door doesn't change the odds of the decision you've already made - if you chose an incorrect door initially (2/3 chance) then the prize MUST be behind the only remaining option once an incorrect door has been removed. If you chose the correct door initially (1/3 chance) then you are guaranteed to lose if you switch, regardless of which door is removed. So 2/3 of the time you'll have picked a losing door initially and switching will be a win, whereas 1/3 you'll have picked the winning door initially and switching will be a loss.
The whole thing is a statistical illusion.
akimbocorndogs · 1 points · Posted at 18:44:35 on February 14, 2016 · (Permalink)
So, if you're doing it multiple times it's best to always switch, because 2/3 of the time you'll get the prize, but if you only doing it once, which is what I assumed because that's how game shows usually work, it's just as likely that switching will get you the prize as not switching. Say the prize is behind door 1. You initially pick door 1. He puts down door 3. Now, it's always been a 100% chance that it is behind door 1. But to you, it was a 1/3 chance for any door, and after he reveals that it isn't behind door 3, it's now a 1/2 chance for either door. I'm talking about making a decision based on what you know. Since you don't know if it's behind door 1 or 2, you have to make a decision that's still uninformed: door 1 or 2?
Now the table: since you're only picking once, only one of these rows is going to get played out. If you pick door one, and he opens door 3, how would you know if you're in row one or two? It's going to be one or the other, and it's 50/50 between winning and losing. If it were a show where you pick nine doors and you get a switch offer each time, then you could expect to see results similar to the table. But that's not what I'm talking about.
SkorpioSound · 1 points · Posted at 19:22:02 on February 14, 2016 · (Permalink)
Why would doing it multiple times be any different to just doing it once? If you do it multiple times then each time is independent of the rest. The decisions you make in the first attempt don't have any effect on the odds in the second attempt, or the third, and so on. If you do it multiple times it's exactly the same as only doing it once - it isn't 2/3 of the time it's better to switch if you do it multiple times but it's still 50-50 if you only do it once, because if it was 50-50 how would it end up at 2/3 of the time if you repeat it?
You don't, you just have to go by how likely it is, but you're using the statistics badly here. If you pick door 1 then he can open door 3 potentially 2/3 times (there are three lines where you pick door 1, two of which have door 3 as an option for him to open). From this, there's there only 1/3 times where him picking door 3 AND you switching results in a loss.
Just because one of the choices is removed, leaving you with one choice, doesn't mean that the odds are 50-50.
I'm going to give a slightly modified example below. Break it down at tell me where you agree and where you disagree.
Imagine there are one hundred doors instead of three. One has a prize car, the other ninety-nine have goats. You pick one, the host removes ninety-eight doors with goats and then you are given the choice to switch or stay with you current door.
Your initial pick has a 1/100 (1%) chance of being the car and a 99/100 (99%) chance of being a goat. The host removes ninety-eight goats, but your initial pick will still have only been a car 1% of the time, yes? So if your initial pick was the car 1% of the times then 99% of the times it must have been a goat, it follows that this is still true once the host has removed ninety-eight goats, because while the host revealing goats is new information to you it doesn't make the choice you've already made any different.
Now you have two doors remaining - one with a car and one with a goat. If you have a car and you switch you're guaranteed (100%) to get a goat instead, and if you have a goat and switch you're guaranteed (100%) to get a car instead. So 99% of the time you'll have a goat, meaning if you switch every time then 99% of the time you'll win a car. 1% of the time you'll have a car from your initial pick, so if you switch then 1% of the time you'll get a goat. So 99% of the time, switching is the better option, versus 1% where you lose. You don't know which applies to you, so it makes sense to switch every time.
akimbocorndogs · 1 points · Posted at 20:17:11 on February 14, 2016 · (Permalink)
I think it's because I'm not looking at it as "door I initially picked vs. doors I didn't pick", I'm looking at it as "door 1 vs. door 2". No matter how many doors there are, if there are only two doors left, then it's one or the other. You are more likely to be wrong that right on the initial guess, but after it becomes a one-or-the-other decision, you now have just as much of a chance of being wrong as being right. It's a new decision, and your initial decision becomes irrelevant.
It makes more sense with the 100 door example, but because it's only 3 doors, it's different. If it were four doors, and two were opened by the host, then it would make more sense to me. But, with the three door example, maybe I'm getting thrown off by it having something be unique about each door: one door is initially chosen by you, one is discarded by the host, and one is left alone by both of you. Any more doors and that wouldn't happen, the host would discard more doors. The idea of picking the one you didn't initially pick works in situations where there are more than three doors, but when there's just three, it stops making sense to me.
With regards to the table being independent thing, I was talking about results you could expect. Overall, by switching every time, you could expect to win 2/3 of the time, but in each individual round, it's going to end up being a 50/50 shot of winning or not if you have to decide between the 2 doors. Yes, your initial pick has a 1/3 chance of being right, but your second pick has a 50/50 chance of being right. Look at the first three rows of the table, where you always pick door 1 initially. After the host puts down a door, it will always end up being one of two possibilities, the third is discarded. For example, you start with a 1/3 chance of being correct. The host puts down door 3. Now the third row is out of the equation. It becomes a new table: first column is you pick 1 for both rows. Second column is it's either in 1 or 2. N/A for third column because he won't open the other bad door. Fourth and fifth columns have Win/Lose and Lose/Win respectively.
I feel like I should talk more about the 100 door example. Say, for simplicity's sake, you pick door 1 initially and the prize is in door 2. The host puts down all the doors except for door 2. The thing is, if you picked door 2 initially, that would be just as uninformed as picking any other. If he put down all doors except #1, and you actually chose correctly initially, then you'd lose if you chose 1. Now, if you did this for 100 rounds, you could expect to win 99 times if you always switched. You could also expect to see one round where not switching would have been the better option. The thing is, you don't know if you're in that round or not. If you made the same table but for the 100 door round, you would still be left with it being "you pick door 1, prize is in door 1, host puts down doors 3-100. Stay=win, switch=lose" and "you pick door 1, prize is in door 2, host puts down 3-100, stay=win, switch=lose". Maybe in the next round it would look like: "you pick door 1, prize is in 3, host puts down 2 and 4-100, switch = win stay = lose". When the goal is to win as many times as possible in 100 rounds and it doesn't matter if you lose one, then it's smart to go with the odds and switch every time. But when the goal is to win every single time when you're only playing once, then it's left up to luck.
I'm not saying it's smarter to not switch, I'm saying that either way, especially in the 3 door game, you're making a random, uninformed guess, and neither choice would be smart.
SkorpioSound · 2 points · Posted at 21:40:20 on February 14, 2016 · (Permalink)*
It is a new decision, but the initial decision is still very much relevant because what door is revealed is dependent on your initial choice. Choosing whether to keep the door you've chosen or to switch is obviously dependent on you having already chosen a door, too. The whole point of the game is to make people think it's a 50-50 chance of the prize being behind either door, when in reality switching is always the better choice, statistically, because the second decision is very much dependent on the first. Look at the table I posted a couple of comments ago again: if you pick door 1, regardless of which door is revealed you will win in two of the 3 situations if you switch.
The number of doors changes your odds (more doors is better for you) but it doesn't change how the problem works. There are n doors, you pick one, the host removes n-2 incorrect doors (leaving one winning door and one losing door), you are given the chance to switch. If you switch you'll have (n-1)/n chance of winning, if you don't you'll have 1/n. This is true while n is any natural number.
The problem here is you're only looking at part of the data, which skews it. The doors that the host decides to reveal isn't an independent variable (i.e. isn't a choice made by you) so looking for a specific value in that subset won't give any usable results. If you did want to use door 3 being opened as something to examine, you'd need to take the first and fifth rows as a "half loss" (because both are only a 50% chance of door 3 being opened so they can't count for a full loss each) and take the second and fourth rows as a "full win". And if you do that, you'll get two wins versus one loss in the switch column. The host opening door 3 specifically isn't useful information to you, though - you pick door 1, he opens door 3, but how does that influence your decision? You've still got the switch/not switch choice to make. You have to look at all of the potential outcomes where you pick door 1 initially for it to be statistically valid.
The problem with statistics is that the universe doesn't give a shit about statistics. If you flip a coin one hundred times, the chance of you actually getting exactly 50 heads isn't 1/2, as you might expect (as demonstrated by Wolfram Alpha). On average you'd expect about 50 heads, but the chances of that happening every time are pretty low, and the chances of the results being HTHTHTHT... (which is what you'd expect if you were going by statistics only- you'd expect that with two coin tosses you'd get a heads and a tails, then repeat that fifty times for one hundred tosses) are very low. So while on average you'd expect to win ninety-nine out of one hundred rounds, it's possible that you could win two hundred times in a row before you lost, and it's also possible that you could only win ninety out of those one hundred rounds. There is no "one round" where you're more likely to lose, because every single round has the same chance of you winning or losing - they're all completely independent of each other.
Again, you'd need to look at every single possibility that could stem from you picking door 1, not just the two where door 1 and door 2 are the only ones remaining. You'd need to look at your second choice being between keeping door 1 or switching to door 3, keeping door 1 or switching to door 4, keeping door 1 or switching to door 5, etc. as well. Just because there's only two possible outcomes (WIN or LOSE/NOT WIN) doesn't mean that there's an equal chance of both happening, just like how when you get on a plane the outcomes are either "you get off alive" or "you die on the plane"/"you don't get off alive" but the latter is far less likely.
Those 100 rounds are made up of one hundred single rounds. Again, they're independent of each other, so it always matters if you lose one. Playing once is no different to playing one hundred times, or one thousand, or more - the odds are still the same, and you still want to win.
As I said above, the 3-door game is only different in the odds, the way it works is still the same, so switching is still the smarter choice. Your guesses can definitely be informed - knowing that (in the 3-door game) you're twice as likely to win if you switch than if you don't makes you pretty informed. Luck still comes into it, but you can still be informed.
EDIT: replying to your other comment here, too.
I've kind of already covered this above. There is no point trying to decide when tossing a coin because it's always a 50% chance of you getting it right, unlike with the Monty Hall problem, where there certainly are different odds if you choose to switch over choosing to stick with what you've already picked. This part specifically is wrong:
Coin flips are, again, independent of each other. Just because you got 50 heads doesn't mean the rest of the flips will be tails, it's still a 50% chance to be heads on each toss. It's not better to call the same one each time, either, because there's a 50% chance that you'll be wrong, regardless of what you pick.
You can always be smart when it comes to probability, but coin tossing isn't a good example of that. There's no being smart when it comes to tossing coins - the next toss isn't any more predictable because of the last, or because of the last hundred. It's 50-50 every time. The Monty Hall problem isn't 50-50 ever, so you can always be smart about it when it comes to the round you're playing, but looking at past rounds won't help at all because the results of the past round won't influence the results of the next, just like the chance of specific lottery numbers coming up isn't any higher because they didn't come up last week.
The main problem with all of your errors so far seems to be differentiating between dependent and independent probabilities.
akimbocorndogs · 1 points · Posted at 23:19:38 on February 14, 2016 · (Permalink)
Yeah, you're right about all the independent stuff. I still don't get how choosing the other door is better. I get it from a mathmatical standpoint, but the logic doesn't click with me. One of two doors has the prize, pick one. Sure, you have a 2/3 chance of being wrong when you initially pick. You have a 2/3 chance of it being another door. One of them is taken away, so the other door has a 2/3 chance of having the prize, while the door you initially picked retains its 1/3 chance. I get the idea, I just feel like there's more to it. How does the door with a 1/3 probability go up to 2/3 when you take the other door away?
I know the initial decision does impact it, it gets rid of one possibility. However it still leaves two possibilities, and you don't know which is the right one. So I was saying the initial decision is irrelivant because the initial pick no longer has its probability of 1/3. Now it's either the one that happened to be the initial pick or the other one. Yes, it does influence which door gets put down, but because of the chance of the initial pick being correct, you don't know if the other one that you didn't pick that's standing is the prize door or not. Seriously, if you were on a show, and you had one round to guess the door with the prize, and you went through the scenario, how would it not be a 50/50 shot when you made your final decision? Ultimately you're left with two doors, and you don't know what's behind either. It would be the same as not having any third door at all.
It seems like it's a technical issue. Technically you have better odds when you pick the non initial door, but it isn't "initial or non initial", it's "one or two". The game changes when the host discards the door. It goes from a 1/3 game to a 1/2 game. You say the problem isn't 50/50 ever, but if it's a choice between two equally random outcomes, I'd call that 50/50. The game has 9 possible outcomes before anyone does anything. Then after you pick a door, there's 3. Then after the host puts one down, there's two. It would be equally reasonable to change your mind and pick number two than to not change your mind and stay on one, because you wouldn't really be staying, either one is a choice. Your first choice only affected which door got discarded by the host, it doesn't lock in your choice as having a 1/3 probability even when there's only two doors. The door the host revealed is no longer an option. Since the possibility of the host discarding the other door you didn't pick is gone, the table goes from having the three outcomes, where two wins are on switch while only one is on stay, to two outcomes, where one win is on switch and one win is on stay. Again, switch and stay aren't really the right words since its a new choice. The host could say after putting a door down "are you going to switch or stay?", but he could also say, "now, will you choose door one or door two?" as if there were only two choices to begin with. The only difference is you're approaching it as a new decision rather than as an alteration to a previous decision.
And I know the difference between expected outcome and actual outcome. You could do the coin flip thing and get 70 tails, and you wouldn't have to be surprised.
Also, just curious, what would you do if there were four doors but he still only discarded one?
SkorpioSound · 1 points · Posted at 12:43:59 on February 15, 2016 · (Permalink)
The probably of the door having the prize doesn't go up. You take your initial pick at 1/3 odds, then between them the other two doors combined have a 2/3 chance of the prize being behind one of them - i.e. you have a 2/3 chance of being wrong on your first guess. So then one of those other two doors is removed, leaving you with a 2/3 chance of having been wrong on your first guess but only one door that it's realistic to pick, because you know that the one that was removed was wrong.
Imagine I roll a six-sided die, and tell you to guess whether it's going to be three or higher OR less than three. The first option will give you a win 2/3 of the time (if the die lands on a 3, 4, 5 or 6) whereas the first will give you a win only 1/3 of the time (if it lands on 1 or 2). There's two possible outcomes - WIN or LOSE - but one of the options has much better odds for you. It's random, but the chances aren't equal, so it makes sense for you to pick the better odds.
There's never two, because you never know whether the host opened the door because it was the only one he could open or because he randomly selected that from two options. And because you never know that, knowing that door 3 was removed isn't useful information to you at all - door 2 being removed would have been just as useless. Because of the "2 or 3" part of the table, you have to take door 2 being opened into account in the odds as well. So it's only ever three possible outcomes, never two, although two of the three outcomes will result in a win.
So you pick door 1 (1/4 chance of being on the prize, 3/4 chance of being wrong). The host removes an incorrect door, leaving two doors plus the one you initially picked. Those two doors between them now have a 3/4 chance of having the prize behind them. You have to split this 3/4 chance up between the two doors, meaning each has a 3/8 chance of having the prize behind it, versus your 2/8 chance of having picked it initially. So you still switch, but you chances of winning are a lot lower than in the three door version, or in a version where all of the unpicked doors except one are removed.
The formula for your chance to win if you switch when the host only opens a single door instead of n-2 doors is (n-1)/((n-2)*n), where n is the number of doors. As long as (n-1)/((n-2)*n) > 1/n you always want to switch. And it always will be greater. The host removing a door makes it so switching is always in your favour.
akimbocorndogs · 1 points · Posted at 17:06:01 on February 15, 2016 · (Permalink)
Yes, it could have been that he had no choice or one other choice. That's only two possibilities, which are dependent on the question of whether the prize is behind the door you picked or the other remaining door. It would be the same if he put door two down, you'd have one possibility of it being behind your initial door and he put a random door down, or you have the other possibility of it being behind another door and he had only one choice of a door to put down. It's one of those two scenarios every time. If door one and door two are left standing, then either they have a 1/2 chance of being correct or a 1/3, either way they're both equal. Each door has always had a 1/3 chance of being correct, from the start. When you pick a door, the other doors each, individually, have a 1/3 chance of being correct.
akimbocorndogs · 1 points · Posted at 20:29:07 on February 14, 2016 · (Permalink)
Let me throw out this example, maybe it'll make sense: a coin toss. You call heads or tails, and if you call it right you win. There's no point in trying to decide, because it's one or the other. But, if the game is flipping it 100 times, it's best to pick one and call it until it comes up 50 times, then call the other one until it's over. Or maybe it's better to call that one every time, I don't know. The point is, you can be smart about choosing when it becomes a game of using probability to get the maximum amount of wins possible, but when it's only one chance, and you get one choice, then there's no way to be smart about it. Calling heads is just as random as calling tails.
SkorpioSound · 1 points · Posted at 21:52:23 on February 14, 2016 · (Permalink)
Check my edit to my reply to your other comment for my reply to this :)
jmt222 · 1 points · Posted at 13:45:16 on February 14, 2016 · (Permalink)
If you adopt a strategy of always switch, then the only choice you make is your initial one and for the rest of the game you are following your strategy: If you initially chose 1, the host shows you 2, then by following your strategy, there is no guess made here: you pick door #3.
akimbocorndogs · 1 points · Posted at 16:50:12 on February 14, 2016 · (Permalink)
But then if you always pick door number one initially, and the host always puts down door number two, then you're really just always picking door number three. You have no chance of getting the prize if it's behind door number one. The lower odds don't make it impossible for it to be behind door number one, so by always switching you're cutting out the possibility of getting door one every time.
jmt222 · 1 points · Posted at 17:07:34 on February 14, 2016 · (Permalink)
Right. If you initially chose the correct door, then always switching will result in a loss. But you initially chose the correct door 1/3rd of the time so you lose 1/3rd of the time with this strategy.
There is no strategy which guarantees a win, but using the strategy of always switching will always result in a win whenever your initial choice was wrong and always result in a loss whenever your initial choice is correct.
intensely_human · -4 points · Posted at 03:24:26 on February 14, 2016 · (Permalink)
However the degree to which you lose by switching is twice as large as the degree to which you win by switching.
If you have chosen wrong, by switching you gain a 50% chance of getting the right thing.
If you have chosen correctly, then by switching you lose a 100% chance of getting the right thing.
So you take the total probability that you have already chosen correctly, times the expected value of a switch in that case, so 1/3 * -1, then add that to the total probability that you have not already chosen correctly, times the expected value of a switch in that case, so 2/3 * 0.5.
Add those together for the total value of a policy of always switching:
(1/3 * -1) + (2/3 * 0.5) = 0
So your intuition is correct - there is nothing to be gained from switching.
Except I just remembered the Monty hall thing has them eliminating one incorrect box after you make your choice, right? So never mind what I just said.
pixbox · -15 points · Posted at 23:56:46 on February 13, 2016 · (Permalink)
The chances aren't out of three, they're out of two.
ThePantsParty · 17 points · Posted at 00:31:22 on February 14, 2016 · (Permalink)
Jesus Christ. There are 3 doors. Therefore the chance that your initial door was the winner is 1/3.
pixbox · 0 points · Posted at 05:30:53 on February 14, 2016 · (Permalink)
I know there are three doors. If one door is opened, the chances of you choosing it are zero, so there is no point in it being included other than to increase the probability of picking the "correct" door.
ThePantsParty · 2 points · Posted at 05:51:11 on February 14, 2016 · (Permalink)
Yes. Which is exactly what it does, and literally the entire point of the entire Monty Hall problem. Because of the host always opening a goat door, switching gives you the odds of choosing both doors you didn't choose on the first guess, i.e. 2/3.
[deleted] · -1 points · Posted at 02:50:39 on February 14, 2016 · (Permalink)
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deikobol · 5 points · Posted at 02:56:47 on February 14, 2016 · (Permalink)
Does a graphic help? Image
If you always switch, 2 initial door choices lead to a prize and 1 leads to a goat.
ThePantsParty · 1 points · Posted at 03:14:46 on February 14, 2016 · (Permalink)
The comment above explained this already:
You will guess the prize 1/3 of the time: switching, you will lose.
You will guess the goats 2/3 of the time: switching, you will win.
Those are the only odds. 66% chance of winning when you switch. At no point in any scenario with any number of doors > 2 do you have a 50% chance.
AcellOfllSpades · 227 points · Posted at 21:40:05 on February 13, 2016 · (Permalink)*
We play a simple lottery with a million tickets. You buy one. I buy 999 999. I tell you before that I will throw away 999 998 of my tickets. The next day, I check the results. You don't see them yet. I pick a ticket to keep and burn the rest. (None of the ones I burn are winners, of course.)
Which ticket is more valuable? Yours or mine?
Now repeat with a lottery of 3 tickets.
Clementinesm · 27 points · Posted at 03:29:13 on February 14, 2016 · (Permalink)
The key is that the 999998 that you threw away are ones that you know for a fact are not winners.
AcellOfllSpades · 5 points · Posted at 03:30:33 on February 14, 2016 · (Permalink)
Exactly! (I edited to make it more clear that's what I meant - I can see how it would've been ambiguous.)
[deleted] · 8 points · Posted at 02:18:08 on February 14, 2016 · (Permalink)
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popejubal · 3 points · Posted at 03:49:42 on February 14, 2016 · (Permalink)
That is what always bothered me about the Monty Haul problem. It assumes that Monty knows what is behind a curtain and only ever eliminates a loser. I think that is a poorly articulated problem given the way that it is almost always stated. Because the way it is stated usually does not give you the fact that Monty k ows what is behind the doors and does not give you the fact that he eliminates only losing doors.
DemeaningSarcasm · 9 points · Posted at 04:36:45 on February 14, 2016 · (Permalink)
For the purpose of the problem, Monty always knows that the door he opens is empty (i.e. shows you an empty door). Whether or not he knows that the door is empty or not is irrelevant so long as you SEE that the door he opens is empty.
NC-Lurker · 1 points · Posted at 10:00:03 on February 14, 2016 · (Permalink)
Then that's not an issue with the problem, but with the people who incorrectly state it. I've always heard it carefully explained, saying that Monty deliberately chooses one of the "wrong doors" to be revealed.
[deleted] · 7 points · Posted at 01:50:32 on February 14, 2016 · (Permalink)*
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[deleted] · 21 points · Posted at 02:35:15 on February 14, 2016 · (Permalink)
He left out that the tickets thrown away were known to be wrong. We are now left with only 2 tickets and we know one of them is a winner. Odds are, the guy that picked 999,999,999 had the winning ticket, so his one left is the winner. So, it is beneficial for the guy that bought only one to trade tickets with the guy that bought 999,999,999 and threw away 999,999,998 that he knew were wrong.
Mr_s3rius · 4 points · Posted at 03:01:26 on February 14, 2016 · (Permalink)
Yea, that's kind of an important bit of information. Makes much more sense now.
jofwu · 2 points · Posted at 02:12:21 on February 14, 2016 · (Permalink)
Best explanation I've ever heard! Thanks.
AroundtheTownz · 2 points · Posted at 22:17:09 on February 13, 2016 · (Permalink)
wouldnt they be equally valuabe?
(there is like a 100% chance that i have no idea what i'm talking about)
AcellOfllSpades · 31 points · Posted at 22:18:14 on February 13, 2016 · (Permalink)
No. Remember, I saw the results before choosing which tickets to throw out.
nightfire36 · 26 points · Posted at 22:47:56 on February 13, 2016 · (Permalink)
I think you should mention that you looked at the results, then picked a ticket. Its ambiguous how you wrote it.
AcellOfllSpades · 2 points · Posted at 22:50:34 on February 13, 2016 · (Permalink)
Yeah, that was a bit ambiguous. Fixed!
President_SDR · 7 points · Posted at 22:54:46 on February 13, 2016 · (Permalink)
What makes the problem work is that the person in control of everything knows which ticket is the winning ticket. If you pick the wrong ticket, then the person controlling the lottery is purposefully going to discard all the other tickets except for the winning ticket because he knows the winning ticket. In this case the discarding actually does nothing and you're essentially picking between the set with your ticket and the set with every other ticket.
xereeto · 1 points · Posted at 04:01:21 on February 14, 2016 · (Permalink)
You need to mention that the tickets you burn are definitely not winners, otherwise it's confusing as all hell.
AcellOfllSpades · 1 points · Posted at 04:02:27 on February 14, 2016 · (Permalink)
I edited that in about half an hour ago.
xereeto · 5 points · Posted at 04:05:47 on February 14, 2016 · (Permalink)
Welp, that's what I get for tab hoarding... opened this page ages ago, only just got to it. Sorry.
AcellOfllSpades · 2 points · Posted at 04:06:46 on February 14, 2016 · (Permalink)
No worries, I've done the same thing several times. c:
A_S_D_F_ · 1 points · Posted at 04:07:38 on February 14, 2016 · (Permalink)
I've never seen it explained this way. Makes so much sense now, thanks!
AcellOfllSpades · 2 points · Posted at 04:08:49 on February 14, 2016 · (Permalink)
No problem! Plus, it makes the key to the problem immediately obvious - the host's knowledge is important too. If I burned 999 998 tickets, then there would be no benefit in swapping.
TheWoman2 · 1 points · Posted at 04:14:36 on February 14, 2016 · (Permalink)
That is the easiest to understand explanation of this I have ever heard.
BadBoyJH · 1 points · Posted at 04:23:45 on February 14, 2016 · (Permalink)
Almost missed this sentence "The next day, I check the results." which completely changes the answer.
Jaychillin · 1 points · Posted at 05:42:27 on February 14, 2016 · (Permalink)
Would both tickets be of equal value? I don't know anything about this paradox by the way
AcellOfllSpades · 1 points · Posted at 05:43:39 on February 14, 2016 · (Permalink)
Nope, mine would be more likely to win.
tanman334 · 1 points · Posted at 05:53:31 on February 14, 2016 · (Permalink)
Best explanation
dluminous · 1 points · Posted at 06:24:40 on February 14, 2016 · (Permalink)
But what I cant grasp is how given the new information (2 tickets) is not a new probability. Because if it is, then its 50/50.
AcellOfllSpades · 1 points · Posted at 06:39:46 on February 14, 2016 · (Permalink)
It's not 50/50, though. The two tickets are not equally likely to win.
Just because there are multiple outcomes doesn't mean that they're equally likely. If I draw a card from a standard deck, I'm more likely to draw a number than a letter - even though there are only two options, number or letter.
If it was picked randomly from the two tickets left over, then it would be 50/50. But it's not - it's picked at the beginning, then a ton of losing tickets are thrown away. Tickets being thrown away doesn't change the probability of one of my tickets winning versus one of yours winning; I only burnt them after the winner had been chosen! I've just moved all of my "probability mass" over to one specific ticket.
jtlcr777 · 58 points · Posted at 22:26:19 on February 13, 2016 · (Permalink)*
...what? It makes perfect intuitive sense! If you had a 100 doors, and you picked one, you're very likely to pick the wrong door first. Its better to switch when the host narrows it down to 2 doors.
So if there's three doors, theres a 2/3 chance you pick the wrong one first, so its better to switch when the host narrows it down to 2 doors.
Fake_Name_6 · 7 points · Posted at 00:50:41 on February 14, 2016 · (Permalink)
The fact that you understand it (and so do I) doesn't change the verity of OP's statement: many people get extremely confused by this problem.
samwise_420 · 2 points · Posted at 12:45:09 on February 14, 2016 · (Permalink)
It may be the fact that it is typically explained as a game show scenario - people may assume the game show host has chosen to offer the switch, knowing the contestant chose the right door first. However, in a scenario where you are always offered a second choice, it makes intuitive sense.
That is what had me confused when I first had the problem explained to me as above.
Xaxxon · 1 points · Posted at 03:00:17 on February 14, 2016 · (Permalink)
You just said that it's intuitive once it's intuitive.
Sadsharks · 1 points · Posted at 03:22:19 on February 14, 2016 · (Permalink)
So it's actually a sociological problem; it's a matter of analyzing the host's behaviour and intentions, not of understanding the math behind it.
rawling · 1 points · Posted at 08:33:18 on February 14, 2016 · (Permalink)
Yeah, you have to know in advance what the rules are, otherwise how do you know he's not only offering because he knows you picked the winning door?
Derren Brown did this as part of his stage show a while back. I was mad at the volunteer for not switching, as switching would've won, but the DB could've been bluffing since he didn't explain the switch option before the volunteer has chosen...
BabyLeopardsonEbay · -1 points · Posted at 03:13:27 on February 14, 2016 · (Permalink)
But 1 door is out of the equation after he reveals the 3rd door. So it's a 50/50 regardless if you switch. What am I missing? (to add, I guess I see that you had 33% chance the first time and now it's a 50% chance. That doesn't change the fact that there are 2 unknown doors remaining...)
mawhonic · 2 points · Posted at 04:05:09 on February 14, 2016 · (Permalink)
I took a while on this too. The way i think of it is by grouping the options
First, you have to assume the removed doors are definitely wrong.
Now, "chosen door" has a 33% chance of being correct. "Other doors" which has two doors has a 67% chance of being correct.
When one door is removed from "Other doors" the probability of the correct door being in that group doesn't change. Thus, the remaining door that was not chosen and not removed is most likely the correct answer with 67%.
jtlcr777 · 1 points · Posted at 03:15:40 on February 14, 2016 · (Permalink)
refer to my 100 door example...you still think its a 50/50 change once the host narrows it down to two doors?
BabyLeopardsonEbay · 1 points · Posted at 20:59:42 on February 14, 2016 · (Permalink)
Okay in your scenario, you're very likely to pick the wrong door first since you have a 1/100 chance, I'm with ya. The host then narrows it down to 2 doors (including your own), so obviously the door that the host leaves is way more likely to be the prize door than your 1/100 first pick. The host reveals 98 out of 100 doors, but only 98 out of 99 possible doors that he could reveal (since he can't reveal your door). So he has a 99/100 chance of having the winning door. So that's an obvious reason to switch doors. In the 3 door scenario, you start with a 1/3 chance of picking the right door. The host has a 2/3 chance of having the winning door, with a 100% chance of always having a loser. My point is that he will always reveal the loser no matter what, that leaves you with a 50/50. Let's say you start on the second phase and the host has already revealed the loser, let's also assume that your default pick is door A and now he asks if you want to switch to door B. In my mind that's 2 unknown doors of equal value, a 50/50. That differs from your 100 door scenario where the host has a 99% chance of picking the winner and leaving it for you to pick between his 99% chance or your 1% chance.
Ohhhhhhhhhhh I get it now.
In the 3 door, he has a 66% chance of having the winning door, and he will always eliminate 1 door. So it's his 66% chance pick that you're switching to. I got it! That took way too long for me to wrap my head around!! :)
NC-Lurker · 1 points · Posted at 10:06:28 on February 14, 2016 · (Permalink)
Other people have explained it, but here's a different point of view: the 2 remaining doors are not equivalent. The one you choose generally sucks: you chose it with a 33% chance.
We both know that one of the other doors is a "wrong" one (they cant both be "right"). So if the host shows you what's behind that door and you don't switch, effectively you haven't made a decision, you haven't made use of the new bit of information. You're exactly in the same state as you were before the reveal. Your odds are still 33%.
Now the last door, the one that wasn't revealed? That one is a winner. That one has the combined chances of the 2 doors you didn't pick - it's always the best of those 2. Maybe both are bad, in which case you started with the right door (again, 33%). But if either of them was good, then the remaining door has to be good. It "carries" the chance of both doors, i.e. 66%.
Curtalius · 8 points · Posted at 00:04:27 on February 14, 2016 · (Permalink)
like /u/etzophyer was saying elsewhere, I think the hidden key is that the host has 100% chance of revealing an incorrect door.
This means that you will always be left with one incorrect door and one correct door.
This means that switching doors will always switch whether or not you were a winner or a loser.
Finally, like /u/jmt222 said, you have a 2/3 chance of your first choice being incorrect, and 100% chance of switching to the correct door if you indeed did choose incorrectly.
Raijinili · 1 points · Posted at 12:29:27 on February 14, 2016 · (Permalink)
This is very key. The famous incident where mathematicians were yelling at vos Savant that she was wrong had an underspecified problem, so they were both technically wrong. If you don't know that the show ALWAYS opens a wrong door, the result won't be true.
If the show just opens a door at random, and it happened to be the the goat, it's 1:1 odds that your door has a car.
If the show only opens a door if you chose a car, then obviously you should not switch. (But who would watch that gameshow?)
If the show picks a door at random, and only opens it if it's a goat, then it's 1:1 odds.
By opening a wrong door with the "always opens a wrong door" strategy, the host is giving you new info. If you gain no additional information about the doors, the probability cannot change.
klawehtgod · 5 points · Posted at 23:41:45 on February 13, 2016 · (Permalink)
It's only confusing because Monty opening a door for you is a misdirect. Picture the game without Monty opening a door for you. Now the choices are to keep your one door, or switch to the other two doors.
Seen this way, you would never choose to have one door when you could have two.
GoCubsGo2016 · 2 points · Posted at 04:01:32 on February 14, 2016 · (Permalink)
This is the best explanation of it in my opinion
LightPhoenix · 1 points · Posted at 09:47:25 on February 14, 2016 · (Permalink)
Monty opening the door isn't a misdirect, it's a fundamental part of the concept. The contestant has no information and chooses randomly; Monty has information, when he opens a door now the contestant has information as well.
klawehtgod · 1 points · Posted at 14:27:10 on February 14, 2016 · (Permalink)
The information he gives you is that one of the doors you didn't pick is 100% a loser. This is a misdirect because it causes people to assume that the two remaining doors have equal probability of being winners. But it's precisely because Monty's choice of door is non-random that the game is a trick.
The odds when you pick a door are 1/3 - 1/3 - 1/3. Switching doors increases your odds to 2/3. If there's 3 equally likely options, as there are at the beginning, the only way to win 2/3 of the time is to pick two options. And I'm saying that switching "allows" you to pick the door Monty opened and the unopened you didn't select. Since you're now picking 2/3 doors, you have a 2/3 chance of winning.
LightPhoenix · 1 points · Posted at 18:48:49 on February 14, 2016 · (Permalink)
I see where you're coming from now, I think I just misunderstood. I don't think it's a misdirect per se, I think it's just taking advantage of people who understand the concept of basic stats (a random choice between two options is 50%) but don't understand the concept of information and logic in statistics.
TheOldHen · 6 points · Posted at 00:57:22 on February 14, 2016 · (Permalink)
You might be failing to realize: Monty knows which door has the prize behind it, and he never opens it (as a rule).
LightPhoenix · 1 points · Posted at 09:46:06 on February 14, 2016 · (Permalink)
This is the part people get hung up on in my experience. Most people have studied at least the basics of statistics. Most people have not studied the concept of information as it pertains to statistics and logic.
SerbianShitStain · 1 points · Posted at 19:51:18 on February 14, 2016 · (Permalink)
I believe one of the alternative versions of this, the "Monty Fall" problem, has a 50% chance to win whether you switch or not. In this version: Monty trips and opens a random door, revealing a goat.
I totally get the "Monty Hall" problem, but the "Monty Fall" problem drives me nuts. The situation ended up being the same (on the surface at least), but the probability is totally different.
worldnews_is_shit · 4 points · Posted at 21:54:42 on February 13, 2016 · (Permalink)
mryodaman · 19 points · Posted at 21:10:15 on February 13, 2016 · (Permalink)*
It's easier to think of this way: There are 100 doors, you pick one. The host opens 98 of the doors to reveal goats, and then gives you the option to swap.
You made the first guess with a 1% chance of being right.
When you swap think of it as a different choice; this time with 2 options instead of 100. So a 50% chance.
This logic applies to 3 doors just the same, but with different odds, but still so that it is advantageous to switch.
Edit: My Apologies, I've interpreted it as wrong as well. See replies to my comment for a better explanation
password_is_asdfghj · 19 points · Posted at 21:58:53 on February 13, 2016 · (Permalink)
In this scenario the hosts actually gives you 98% if you decide to switch.
In the original scenario, you have a 1% chance of being right, which you pointed out. When he shows you 98 doors, if you make the switch, you essentially picked 99 doors as your initial choice. But you have to realize that of the 99, only one of them will contain the prize
Curtalius · 5 points · Posted at 00:07:16 on February 14, 2016 · (Permalink)
99% chance actually. The only situation in which you don't win is if you initially choose the correct door (1% chance).
password_is_asdfghj · 2 points · Posted at 00:10:43 on February 14, 2016 · (Permalink)
I meant he gives you an additional 98% (because you were guaranteed 1%), for a total of 99%. So we're both right
ZincoX · 1 points · Posted at 01:10:07 on February 14, 2016 · (Permalink)
99%
lifelongfreshman · 6 points · Posted at 22:02:58 on February 13, 2016 · (Permalink)
50% should never enter into the Monty Hall problem unless the original number of doors is 2.
If the number of doors is greater than 2, your chance of being right is always less than 50%, and therefore your chance of being right if you switch is always greater than 50%.
In the 100 doors example, you pick a door, you have a 1% chance of being right and a 99% chance of being wrong. When the host reveals the 98 doors with goats behind them, you still have a 1% chance of being right and a 99% chance of being wrong. If you switch, you now have a 99% chance of being right and a 1% chance of being wrong. Knowing what's behind some of the doors does not change the probability of what's behind the rest of the doors, or the probability of you being correct versus incorrect with your initial guess, unless there is exactly 1 door whose contents you do not know.
geweldigzinloos · 0 points · Posted at 00:46:38 on February 14, 2016 · (Permalink)
The classic problem has 3 doors. That means 3 choices for the prize, and 3 choices for your guess. Total of 9 possibilities.
It's impossible for a 50% chance because out of 9 options, that would mean 4.5 times you win and 4.5 times you lose.
RadicalDog · 2 points · Posted at 01:35:45 on February 14, 2016 · (Permalink)
But this is missing the real confusion; where did all these goats come from?
Can I keep the goat?
Ashhel · 4 points · Posted at 22:25:56 on February 13, 2016 · (Permalink)
But this is incorrect. When you switch in the 100 door case, you have a 99% chance of winning. Similarly, when you switch in the 3 door case, you don't have a 50% chance of winning -- you have a 66% of winning.
aixenprovence · -3 points · Posted at 22:40:22 on February 13, 2016 · (Permalink)
I think I like this explanation the best.
President_SDR · 3 points · Posted at 22:58:46 on February 13, 2016 · (Permalink)
It's wrong, though. The common misconception is that you're left with two doors so it doesn't matter which door you pick, so there's a 50% chance of winning, and his explanation is exactly this misconception. The way the problem works is that you're giving new information because of how the doors are revealed.
aixenprovence · 1 points · Posted at 13:55:00 on February 14, 2016 · (Permalink)
Ah, thanks.
atree496 · 2 points · Posted at 22:58:41 on February 13, 2016 · (Permalink)
What you have to remember is that the host knows what is behind each door. If he showed a random door, it wouldn't matter if you switched or not.
[deleted] · 2 points · Posted at 19:38:47 on February 14, 2016 · (Permalink)
Just a note about a few people who have told me it never fooled any mathematicians or where I got the idea from:
I had seen Marilyn Vos Savant make references to it, and that's where I first saw the problem. She had posed the problem in her column and had received some letters from people who disagreed with her, and some were professionals with masters and PhDs, including mathematicians and physicists, disagreeing with the correct solution, often quite strongly.
Unfortunately I can't find the quote I had read, I was speaking from memory, but the only one I found today is from wiki, where Marilyn quotes a psychologist as saying, "... no other statistical puzzle comes so close to fooling all the people all the time...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".
SerbianShitStain · 1 points · Posted at 19:45:28 on February 14, 2016 · (Permalink)
The truth is that the human mind is just fucking awful at doing statistics and probability. We have so many built in biases towards this kind of math that it takes a looooooooot of experience and education to be able to handle these well, and even then things can blindside you. That said: The actual math behind this is quite simple when broken down. You just need to actually be willing to set aside your first instincts and actually look at it.
What I think is interesting is people who don't understand this (a 100% true mathematical concept), and instead of saying "I don't understand this. Can you help me understand it?", they instead say "This is wrong!".
That kind of aggressive ignorance is really astounding.
Hitlerdinger · 5 points · Posted at 23:26:40 on February 13, 2016 · (Permalink)
anyone fooled by this should not be allowed to call themselves a "mathematician". it makes perfect intuitive sense
Sadsharks · 1 points · Posted at 03:24:05 on February 14, 2016 · (Permalink)
Come on. Are you seriously saying Paul Erdos didn't deserve to be called a mathematician?
Hitlerdinger · 1 points · Posted at 10:26:27 on February 14, 2016 · (Permalink)
well, he did understand it eventually so no
timgodfang · 1 points · Posted at 23:19:40 on February 13, 2016 · (Permalink)
If you want to be even more mindblown:
If the host does not know where the losing doors are, then opens a door at random and just happens reveals no prize, then it doesn't matter if you switch or not for your chance of winning.
The 2/3 from switching only occurs when the host knows which doors have the prize.
sniperFLO · 1 points · Posted at 01:32:40 on February 14, 2016 · (Permalink)
This explains it best for me actually.
DemeaningSarcasm · 1 points · Posted at 04:42:36 on February 14, 2016 · (Permalink)
This isn't true. So long as he opens the empty door and tells you whether or not to switch, you should switch because you have more information.
If you factor in the possibility that the host could possibly open the door with the prize behind it, then your stats change. But so long as you filter out the chances that he opens the grand prize door, then it's no different than monty knowing which doors are empty.
RoyalHorse · -2 points · Posted at 00:58:19 on February 14, 2016 · (Permalink)
That's not true. If the door opened is a goat regardless of the hosts knowledge you know that the remaining other door is twice as likely to be the car.
timgodfang · 3 points · Posted at 01:21:14 on February 14, 2016 · (Permalink)
No.
Simple Bayes theorem shows that the probability is 1/2. This behavior is referenced in the "Ignorant Monty" row of the table here
https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors
RoyalHorse · 1 points · Posted at 01:28:18 on February 14, 2016 · (Permalink)
Oh, now that's interesting.
I don't understand, if he accidentally always opens a goat door how is that functionally different from opening them with intent?
Oh! Wait nevermind, got it. Thanks for the link!
[deleted] · 1 points · Posted at 23:16:43 on February 13, 2016 · (Permalink)
My computer science class just got finished making an app to test this. It's really mind blowing how that works, when everything you think says directly otherwise.
ohrightthatswhy · 1 points · Posted at 23:53:24 on February 13, 2016 · (Permalink)
There's a 2/3 chance that you initially choose a goat.
Assume you have a goat
When Monty opens a door with another goat, then the other door must have a car (assuming you have a goat). It is then a no brainer to switch.
Now 1/3 of the time you have incorrectly assumed that you have a goat, so 2/3 of the time you win, 1/3 of the time you lose.
Korlus · 1 points · Posted at 01:24:54 on February 14, 2016 · (Permalink)
The best way to understand it is to know that the person who gives you the choice knows the position.
Since they cannot/will not pick the correct door, they effectively removed one option from the equation.
It's not that it makes your door any less likely than it was before (it remains just as likely), but you now know that every other door is ever so slightly more likely than the door you picked. This works only because the person knew what was behind each door - if they did it at random, they could potentially reveal the prize.
In the classic problem, you have a 1/3 chance of being right, and a 2/3 chance of being wrong. After the person reveals what is behind the other door, you know that had you picked your door (now), you would have a 1/2 chance of being correct.
However, that is not the case. You picked it before. He didn't make what was behind your door any more likely to be correct, meaning that every other door is now more likely to be the correct answer than yours is/was.
PressQWER · 1 points · Posted at 01:27:02 on February 14, 2016 · (Permalink)
66% chance of choosing wrong, and assuming you did choose wrong, switching means you have a 50% chance of choosing wrong.
ChickenNoodle519 · 1 points · Posted at 01:41:55 on February 14, 2016 · (Permalink)
I always find it illuminating to increase the number of goats and doors:
In the original problem, there are three doors: two with goats and one with a car.
In my version of the problem, there are 100 doors. There are goats behind 99 of the doors, and a car behind the last.
The participant chooses an arbitrary door (let's call it Door 37) and then the host opens up 98 of the remaining doors to reveal the goats behind them. Now, only Door 37 (the original choice) and Door 19 remain.
At that point, when the participant chose Door 37, they had a 1/100 chance of choosing a car. That doesn't change. Since the host knows where the car is, opening up all of the other doors means that there is then a 99/100 chance of there being a car (and not a goat) behind Door 19.
Obviously, the best strategy is to switch doors.
ghroat · 1 points · Posted at 02:21:21 on February 14, 2016 · (Permalink)
this makes intuitive sense. the most likeley scnenario is that your original guess was wrong. the host combines the two other doors into one guess by eliminating the other wrong door. the two doors you didnt pick become one option that had two goes at picking the right door
pickletoes1 · 1 points · Posted at 02:22:15 on February 14, 2016 · (Permalink)
Ugh I had to prove this for homework today... Thanks khan Academy
IAMA_dragon-AMA · 1 points · Posted at 02:24:29 on February 14, 2016 · (Permalink)
I didn't think to cap the post, but someone on 4chan once told a story about how, for a Statistics project, they made a quick test for this with a deck of cards (or rather, the 4 aces). They got 50 people to take part in the study, told them the rules (one of these cards is the Ace of Spades, choose one, I'll reveal two that are neither your card nor the correct card, you can choose to switch or keep your original guess), and kept track of who switched, for whom switching would be correct, and for whom staying would be correct. Naturally, the switch/stay correctness was a 3:1 ratio, but apparently only something like 3 people chose to switch, and all but one who switched admitted they'd heard of the Monty Hall problem before.
TheMightyDingo · 1 points · Posted at 02:27:00 on February 14, 2016 · (Permalink)
It made more sense to me once I thought of the two options as the complete range options. Staying leaves you with all 3 doors being unaffected, a range of Win Lose Lose, switching removes a losing door from the range because the door opened is always a losing one, the switch range becomes Win Lose.
GokuMoto · 1 points · Posted at 02:37:54 on February 14, 2016 · (Permalink)
you have 3 doors
A...B...C
you pick say door A
i reveal C to not be the winning pick and give you the option to switch. you now have a 66.67% chance of winning if you switch not 50/50
HiddenKrypt · 1 points · Posted at 02:57:56 on February 14, 2016 · (Permalink)
Just increase the numbers. There's a million doors, and one prize. You pick one door. The host knows where the prize is, and opens 999,998 doors that he knows do not have the prize.
When you started, your odds were one in a million that you were right. Inversely (because the odds of all possible results always add together to one), there was 999,999/1,000,000 odds that you were wrong the first time.
Now you can switch. The door you chose the first time (1 in a million), or the only door left after 999,998 doors were opened (999,999 ina million).
FuckBrendan · 1 points · Posted at 03:03:17 on February 14, 2016 · (Permalink)
This doesn't fool mathematicians... It makes perfect sense to lots of non mathematicians.
Bohnanza · 1 points · Posted at 03:03:18 on February 14, 2016 · (Permalink)
I actually saw someone botch this on Let's Make a Deal the other day. Although, to be precise, it was the Wayne Brady problem.
taboojump · 1 points · Posted at 03:42:55 on February 14, 2016 · (Permalink)
My probability professor literally gave us this problem today! This is insane
[deleted] · 1 points · Posted at 04:12:06 on February 14, 2016 · (Permalink)
So first, you choose one door. The chances you chose wrong is more likely than not (2/3). In such a case, the host eliminates the other wrong door leaving the one and only winning door. So in this more than likely scenario where you chose wrong at first, you guarantee yourself the winning door by switching.
drkitteh · 1 points · Posted at 04:17:35 on February 14, 2016 · (Permalink)
I still don't see how it works. Your odds are the same, whichever door you choose. Your decisions don't affect what's behind the door. Initially, you have a 1 in 3 chance. They reveal the zonk, and you have a 50/50. I don't see how one is any more likely than the other.
Volume999 · 1 points · Posted at 04:33:51 on February 14, 2016 · (Permalink)
A fine explanation i had was when there are not 3 but 100 doors
So you chose 5 and they opened every single one except 5 and 57
it is pretty wise to change to 57 then
Haltgamer · 1 points · Posted at 04:37:45 on February 14, 2016 · (Permalink)
I don't understand it either. What if I want the goat?
zetacentauri · 1 points · Posted at 04:54:46 on February 14, 2016 · (Permalink)
Remember, it only works because Monty wouldn't pick the one with the prize behind it, that's what makes the switch a 2/3 rather than 1/3. If he didn't know which one had the prize, you would still have a 1/3 chance for each door.
King_Kars · 1 points · Posted at 05:22:35 on February 14, 2016 · (Permalink)
The trick is to remember the odds don't actually change, I got frustrated for a long time when people try to say things like the odd change BECAUSE they reveal the second door, which isn't quite true. The host say to pick a door. Once you do, he essentially says, "do you want that one, or both of the other two?"
Sometimes its easier to see if you use a bigger number, say 100 doors. Pick one. Thr host opens a dud door, and asks if you want to keep your original pick. You say yes so he opens another dud door and asks again if you want to switch. Because the host will always open a dud door, you this 96 more times until there are two door left. So if you think about it its just one simple question, "do you want the first door you picked, or ALL the other doors?!" You had a 1% chance of guessing the right door at the beginning. Switching at the end would give you a 99% chance you get the prize.
Atmosck · 1 points · Posted at 05:25:16 on February 14, 2016 · (Permalink)
It's not exactly perplexing, it's not like computer experiments betray the existing mathematical theory.
drinks_antifreeze · 1 points · Posted at 05:49:35 on February 14, 2016 · (Permalink)
This finally made it make sense to me:
Imagine that, instead of 3 doors, you have 100 doors. You guess door #47, then all the doors except #47 and #62 open to reveal goats behind them. You are then offered a choice: Switch your door to #62, or stay with #47? Obviously, the probability that you correctly picked door #47 is really really small, and now you know for a fact that the prize is either behind that one or #62. Since #47 is almost certainly wrong, it's a no-brainer that you should go for door #62.
BurningMist · 1 points · Posted at 06:01:28 on February 14, 2016 · (Permalink)
Tables convinced me better than the explanations. https://math4uandme.files.wordpress.com/2013/02/monty_hall_problem_win_table1.png
[deleted] · 1 points · Posted at 06:34:40 on February 14, 2016 · (Permalink)
I never got it until a friend explained it to me in this way:
Let's say there are 100 doors, and behind 99 of them are goats. Behind one of them is a car. You pick on and the game show guy eliminates 98 goat doors. So there are two doors left, the one you picked and the other one that wasn't eliminated.
The reason you should switch is because you have to ask yourself, does the door that I randomly picked have a greater chance of having the car? Or does the other door that the game show host strategically chose not to eliminate have a greater chance? Out of all the doors besides yours to eliminate, he chose to leave this door. So, do you think your randomly picked door is more likely to have the car, or the other door that FOR SOME MYSTERIOUS REASON was not eliminated like the 98 others? The other door. Because that doors not random like yours.
bunker_man · 1 points · Posted at 07:02:25 on February 14, 2016 · (Permalink)
Think of it this way. If you switch, what you're actually getting is to open every other door. The more doors there are the more obvious it is why its better. But its still better if there's only 3 total, since then you get two instead of one.
horrorshowmalchick · 1 points · Posted at 07:06:04 on February 14, 2016 · (Permalink)
Imagibe there were a hundred doors and they openned all but yours and one more. Then would you switch?
Kn0wmad1c · 1 points · Posted at 07:13:45 on February 14, 2016 · (Permalink)
It's easier to understand if you scale it up.
For those who don't know the original idea:
So the original is there are three doors. Two of them have junk behind them and one has a new car. You pick door number 1. Monty then says, "Ok, well let's see what's behind door number 3!"
Surprise it's trash.
Now Monty asks you if you want to switch your door to door number 2. Should you do it?
Yes. You should. Why?
Let's scale it up. Let's say there are a million doors and you choose door number 23. Monty then takes away 1 door and asks if you want to switch your door. You say yes. And this continues until your door and two others are left. One has a car and the other two have junk. Monty takes away one other door, leaving yours and another. Do you switch? Well, obviously. I mean what were the chances that you just happened to choose the one door out of a million that had the car behind it?
VacuouslyUntrue · 1 points · Posted at 09:24:26 on February 14, 2016 · (Permalink)
When has this ever fooled mathematicians? It follows from the basic fact that the host gives you more information than you had. It updates what is called a 'filtration', and changes the probability space that your choice exists in.
Tuberomix · 1 points · Posted at 09:57:12 on February 14, 2016 · (Permalink)
I actually wrote a simple Java program myself once to confirm statisticians aren't bulshitting me.
DrMonsi · 1 points · Posted at 10:57:31 on February 14, 2016 · (Permalink)
Easiest way to understand it:
Imagine there being 100 doors (instead of 3). You choose one. The moderator opens 98 false ones (instead of one). You still think it's 50:50 that the door you chose has a probability of 50% being the right one now?
Think about it. It all became clear to me after i was presented this argument.
Coubsauce · 1 points · Posted at 13:21:37 on February 14, 2016 · (Permalink)
I get that 1/2 is better than 1/3. What always bothered me about this problem is that with EITHER the choice to change doors or stick to your door, you still making a 1/2 decision. If a person tossed a coin at this point would they not see heads half the time? And yet this seems like equivalent of saying always call heads.
steppe5 · 1 points · Posted at 15:25:05 on February 14, 2016 · (Permalink)
I hope it doesn't fool mathematicians, since I understood the concept in high school statistics.
achmonth · 1 points · Posted at 20:32:23 on February 14, 2016 · (Permalink)
THANK YOU!!! I have been wondering about this one for years, finally an explanation I understood.
adrianmonk · 1 points · Posted at 21:49:03 on February 14, 2016 · (Permalink)
What finally made it make sense to me is that Monty is giving away a huge amount of information by revealing the door with the non-prize. Probability is basically about making estimates based on available information. New information can and should change your estimates.
Let's think of it in terms of sets of doors, and the odds that the prize is behind one of the doors in that set. That gives us the following table:
In plain English, the odds are 1/3 that the prize is behind any given door. The odds that the prize is behind either one of two doors are 2/3. (And of course there's a 100% chance that the prize is behind one of the three doors.)
Now, you pick door #1. The odds that the prize is there are 1/3. The odds that the prize is behind door #2 or #3 are 2/3.
Monty reveals that the prize is not behind door #2. The odds that it was behind door #2 or #3 have not changed. There's still a 2/3 chance it's somewhere in that set of locations. But Monty has shown you it's not behind #2, so the odds "focus" on #3. By process of elimination you know that there's a 2/3 chance that it's behind door #3.
That's double your chances if you stick with door #1, so you should switch.
AnticScarab3 · 1 points · Posted at 23:33:44 on February 14, 2016 · (Permalink)
I think this is an instance of mathematics dealing with theory rather than reality. When you're talking about probabilities, you can phrase the question such that it sounds like switching is a better option, but if you were to actually go on the show and put that reasoning into practice, whether or not you switched wouldn't make a difference.
Here's how I'm thinking of it: Let's say we change the rules slightly. You pick one of three doors, and Monty reveals one of doors you didn't pick. However, he doesn't ask if you want to switch your answer. Instead, your original answer is discarded, and you are now asked to pick one of the remaining two doors. There are two unknown doors, 50% of which have a car behind them and 50% have a goat behind them. The third door is now irrelevant. Whichever door you pick, you have a 50% chance of getting the car.
This is essentially the same problem. "Not switching" is the equivalent of picking the first door you chose, and "switching" is the equivalent of picking the second.
[deleted] · 1 points · Posted at 09:44:55 on February 16, 2016 · (Permalink)
Source? I really doubt such a simple concept has fooled any rael mathematicians.
coolkid1717 · 0 points · Posted at 23:13:03 on February 13, 2016 · (Permalink)
It's really simple. When you first choose there are 3 doors and one prize. So there is a 1/3 chance you choose the correct door and a 2/3 chance you chose the wrong door. When the host removes a a door he always removes a door without the prize behind it. So the chances are in your favor to switch because its more likely that your first choice had no prize behind the door.
If you plot all of the choices you can see all the results of switching and not switching.
Let's look at if you do not switch. For picking each door 1 through 3. Let's say the prize is behind door number 3.
1) you pick door 1. The host removes door number 2. You do not switch. The prize is behind door 3. You lose
2) you pick door 2. The host removes door number 1. You do not switch. The prize is behind door 3. You lose
3) you pick door 3. The host removes door number 2 or 1 (it doesn't matter which. He always removes a door without a prize behind it). You do not switch. The prize is behind door 3. You win!
Now let's look at if you do switch
1) you pick door 1. The host removes door number 2. You switch to door 3. The prize is behind door 3. You win!
2) you pick door 2. The host removes door number 1. You switch to door 3. The prize is behind door 3. You win!
3) you pick door 3. The host removes door number 2 or 1. You switch to door 2 or 1 (which ever door the host did not remove). The prize is behind door 3. You lose.
In the case where you do not switch you only win if you pick the door with the prize behind it on your first try. That is a 1/3 chance or 33.33%.
In the case where you switch you win if your first choice is a door without the prize behind it. That is a 2/3 chance or 66.66%.
So it is always in your best interest to switch.
I never understood why people say that it took mathematicians so long to solve the problem. It's really pretty straight forward.
geweldigzinloos · 1 points · Posted at 00:48:15 on February 14, 2016 · (Permalink)
I guess it took them very long to convince normal people of it. And still there's tons that say 50%.
ophello · 0 points · Posted at 09:10:08 on February 14, 2016 · (Permalink)
Ugh... I will never understand why people don't get this.
If a door is opened to you by the host, you've just been given more information. Your odds are now different. You did not pick the prize door because otherwise they would have revealed that you won.
JoshuaZ1 · 62 points · Posted at 20:51:32 on February 13, 2016 · (Permalink)*
I don't know what the coolest is, but I'll try to list a few neat ones that haven't been mentioned yet:
Call a rotation "periodic" if when you keep doing that rotation one eventually gets back to where one started. So for example, on a circle a rotation of 90 degrees (in radians Pi/2) is periodic because you can do it four times and get every point on the circle back where it started. It turns out in two dimensions if you compose two rotations which are periodic you get a third rotation which is periodic (so for example, if I do a 60 degree rotation and a 90 degree rotation I'll have a 150 degree rotation which I can repeat 12 times). Now here's the cool fact: this isn't true on a sphere. I can do two periodic rotations so that I compose them and don't get a periodic rotation. For example, if I rotate 30 degrees on a sphere around a vertical axis and then 30 degrees around an axis that is perpendicular to that axis, you get a rotation across a new axis which is not periodic. (Proving this requires a little linear algebra where you look at the eigenvalues of the corresponding matrix.)
There are the same number of rational numbers as integers. But there are more real numbers than there are rational numbers. (Here I'm using cardinality as the notion of size.)
The number of primes numbers less than or equal to x is very closely approximated by x/ln x. This is the prime number theorem.
We know that one of e+pi and e pi is irrational, but we don't know which (we strongly suspect that both are irrational). (EDIT: Correct version of statement is transcendental for both per comments by /u/tcampion and /u/sniffnoy .)
Here's an "almost" fact. 31, 331, 3331, 33331... are all prime. (Fun programming exercise: make a program to find where this breaks down. Fun number theory exercise: without using any calculator or computer, find a counterexample.)
1729 is the smallest positive integer representable as the sum of two perfect cubes in two different ways. That is 93 +103 = 1729 and 13 + 123 = 1729. There's a famous story about this. Also, worth noting that 1729 is also a Carmichael number.
[deleted] · 4 points · Posted at 01:07:46 on February 14, 2016 · (Permalink)
Upvote for not indulging in Group Theory in polite society. :)
heap42 · 4 points · Posted at 00:02:18 on February 14, 2016 · (Permalink)
The numbers of primes less than or equal to x thing( x/ln x) was conjectured by Gauss when he was FUCKGIN 15 YEARS OLD FUCKING 15... when i was 15 i was looking up boobs on internet. FUCK THAT GUY.... WHAT A LEGEND!!!!
dude_pirate_roberts · 1 points · Posted at 08:32:21 on February 14, 2016 · (Permalink)
What? You can find boobs on the internet?!
Roland_B_Luntz · 1 points · Posted at 14:14:49 on February 14, 2016 · (Permalink)
He was 19 (Born in 1777, conjectured it in 1796). Gauss was without a doubt a genius but this accomplishment isn't thaaaat impressive. It's actually kind of obvious if you know what prime numbers are (only divisible by 1 and themselves).
And by obvious I mean logical that as the number increases there is a higher probability of finding another smaller number that it is divisible by, thereby making prime numbers rarer and rarer. Now if he would have PROVED it at 15 (or 19), yeah, that's impressive.
JoshuaZ1 · 1 points · Posted at 17:33:16 on February 14, 2016 · (Permalink)
Um, people knew well before Gauss that primes got rarer as they got larger. What is impressive is figuring out the exact rate at which that happens, and yes that was pretty damn impressive.
tcampion · 3 points · Posted at 02:29:44 on February 14, 2016 · (Permalink)
Nice list! One quibble:
I think you mean transcendental, not irrational. I think it's not too hard to show that e and pi are irrational, and probably not so hard to show that they are linearly independent over the rationals. But transcendence is typically a very hard question.
JoshuaZ1 · 2 points · Posted at 02:38:34 on February 14, 2016 · (Permalink)
No. I think I meant irrational. I don't see any easy way to prove that e+pi is transcendental or that e pi is transcendental. Is there some way to do that? It doesn't follow in any obvious way from e and pi being transcendental.
analambanomenos · 6 points · Posted at 07:17:37 on February 14, 2016 · (Permalink)
(x-e)(x-pi)=x2-(e+pi)x+e pi. If e+pi and e pi were both algebraic, then this would show that e and pi are both algebraic. But they're not, so at least one of e+pi or e pi is transcendental.
JoshuaZ1 · 1 points · Posted at 13:13:40 on February 14, 2016 · (Permalink)
Ah yes. That works.
Sniffnoy · 2 points · Posted at 05:37:27 on February 14, 2016 · (Permalink)
Prety sure transcendental is correct here. If r+s and rs are both algebraic, then r and s must also be algebraic since you can solve a quadratic for them. So at least one of e+pi and e*pi must be transcendental (and in particular irrational).
I don't know how you'd get irrationality here without using transcendence; if r+s and rs are both rational, that doesn't necessarily mean rs is rational. (E.g. r=sqrt(2), s=-sqrt(2).)
[deleted] · 1 points · Posted at 05:45:31 on February 14, 2016 · (Permalink)
[deleted]
Sniffnoy · 2 points · Posted at 05:59:20 on February 14, 2016 · (Permalink)
Are you just claiming that the statement is correct with "irrational" (which I agree with, see above), or are you actually claiming that it is incorrect with transcendental? If the latter, would you mind pointing out the hole in my proof rather than just asserting that I'm wrong?
[deleted] · 0 points · Posted at 06:07:43 on February 14, 2016 · (Permalink)
[deleted]
JoshuaZ1 · 0 points · Posted at 13:14:06 on February 14, 2016 · (Permalink)
His comment looked completely calm to me.
CaesarTheFirst1 · 2 points · Posted at 22:48:18 on February 13, 2016 · (Permalink)
Number theory approach: 3*(10n +10n-1 ...+10)+1= 30*(10n -1)/9+1=
(10*(10n -1)+3)/3 so we want a prime p != 3 so that there is n so that 10n+1 -7 is divisible by p. Is there an elementary argument to find such p that isn't brute force? I know that for almost all numbers they generate mod p for an infinite amount of p so that we know there is a prime p so that 10n for n=1...p-1 goes through all different values mod p (and 7 specifically), but that isn't elementary at all.
JoshuaZ1 · 2 points · Posted at 23:20:32 on February 13, 2016 · (Permalink)*
Actually, that's still open. That's the weak form of the Artin primitive root conjecture. But yes, one way is to find a prime that 10 is a primitive root which isn't 7 or 3. A slightly better way is to realize that since the nth term is (10(10n -1)+3)/3 and since 1030 is 1 mod 31 (by Fermat's Little Theorem), and for n=32 one must get a term divisible by 31 since the 2nd term was divisible by 31.
CaesarTheFirst1 · 1 points · Posted at 23:23:12 on February 13, 2016 · (Permalink)
Shit I'm stupid, how did I miss that 10n -1, I was focused on the general case (for any sequence your trick will work, when I say general I mean I've been pondering about artin's conjecture for the last few days) for some reason. What I meant is that there is much progress on Artin's conjecture, so for almost all values this is true.
JoshuaZ1 · 1 points · Posted at 23:27:14 on February 13, 2016 · (Permalink)
Yeah, Artin's conjecture is one of those things where we can't prove it, but given the work of Heath-Brown and Hooley, it is pretty clearly true (although I wouldn't be completely shocked if there's some subtle correction factor that actually changes the density of the primes for a given primitive root candidate a when a has a lot of distinct prime divisors).
iSeize · 2 points · Posted at 05:29:50 on February 14, 2016 · (Permalink)
wow that first one was described perfectly. im impressed!
ifarmpandas · 1 points · Posted at 21:51:56 on February 13, 2016 · (Permalink)
Aren't all rotations on a 2d plane periodic? Since you can just apply the rotation 360 times.
JoshuaZ1 · 2 points · Posted at 21:59:24 on February 13, 2016 · (Permalink)
Nope. Consider a rotation of sqrt(2)/180 degrees.
ifarmpandas · 1 points · Posted at 22:15:11 on February 13, 2016 · (Permalink)
I think I see?
So essentially, for a rotation of degree x, you want to find a coefficiant a such that ax ≡ 0 (mod 360) for a rotation to be periodic?
JoshuaZ1 · 2 points · Posted at 22:25:54 on February 13, 2016 · (Permalink)
Yes, so any rational multiple will work. Any irrational multiple will not work.
synthcheer1729 · 1 points · Posted at 00:38:33 on February 14, 2016 · (Permalink)
I knew about the 1729 thing! And some others.
ceriee · 215 points · Posted at 22:00:24 on February 13, 2016 · (Permalink)
Probably too late to the party. Any factor of 9's digital root will always be 9. (A digital root being the sum of all the digits) For example: 1 x 9 = 9 13 x 9 = 117, 1+1+7 =9 185 x 9 = 1665, 1+6+6+5 = 18, 1+8 = 9 194385 x 9 = 1749465, 1+7+4+9+4+6+5 = 36, 3+6 = 9
PhilMcgroine · 91 points · Posted at 22:50:39 on February 13, 2016 · (Permalink)
This works simply because we use base 10. For any number system with base n, the divsors of n-1 have this property.
For example, in hexadecimal (base 16), any factor of 15s digital root will always be 15.
LazyAHole · 9 points · Posted at 04:27:33 on February 14, 2016 · (Permalink)
You mean F
EpicCrab · 4 points · Posted at 05:04:07 on February 14, 2016 · (Permalink)
This is basically a property of mod n-1, where you write your numbers in base n. Essentially if you have a number with digits a, b, c,... z written abcdefghijklmopqrstuvwxyz base n or any other choose you choose, writing it as powers of n comes out to:
a * n24 + b * n23 + ... + x * n2 + y * n1 + z * n0
Now, because you're in mod n-1, (mod protip: any number in mod k is congruent to its remainder when divided by k - this is not how mod works, but it'll work for the purposes of this) n-1 is congruent to 0, and n is congruent to 1. So essentially,
abcdefghijklmopqrstuvwxyz
=a * n24 + b * n23 + ... + x * n2 + y * n1 + z * n0
=a * 124 + b * 123 + ... + x * 12 + y * 11 + z * 10 mod n-1
=a+b+c+d+e+f+g+h+i+j+k+l+m+o+p+q+r+s+t+u+v+w+x+y+z mod n-1
Where that whole mess is congruent to 0 if it's a multiple of n-1, or some whole number smaller than n-1 otherwise.
If any of you don't know much about modular arithmetic and want to know why it's not as simple as taking the remainder, then continue reading. Otherwise you're good to go.
Modular arithmetic is what happens when you write out the whole numbers and zero from 0 to m-1 inclusive, then cut it at either end, then glue the two ends together to make a loop. When you go past the one end, you end up on the other. There are exactly m numbers in your new number system; that's what the m in mod m refers to. This also implies no fractions; you can't divide anything in mod, because otherwise you have an infinite number of numbers in a system that can only contain m numbers (where m is a finite number; real math is already basically mod infinity). 2 + 6 mod 7 is congruent to 1. The reasoning for this is not just 2+6 = 8, 8/7 = 1 R1. The reasoning actually looks like 2 + 6 = 1 + 1 + 6 = 1 + 7, and 7 mod 7 is congruent to 0, so therefore 1 + 7 mod 7 is congruent to 1 + 0 mod 7.
You can still sort of divide, but there are some workarounds. In regular math, you divide by multiplying by the number's multiplicative inverse. You (technically, most people just skip this step and go straight to dividing) decompose 8/2 into 8 * 1/2 because 21/2 = 1, making them multiplicative inverses. Mod has a similar system, in which you identify the multiplicative inverse q of a number p such that pq is congruent to 1 mod k. This only works for numbers relatively prime to k; you can never, ever create a multiplicative inverse to 2 in mod 2k where k is any whole number, because there exists no number that you can multiply 2 by such that the result is congruent to 1.
You can also exponentiate, and this gets used to create RSA privacy: security based on the concept that you give somebody 2/3s of the system, and that nothing is worth the vast effort that it takes to find the remaining third.
[deleted] · 1 points · Posted at 05:24:15 on February 14, 2016 · (Permalink)
you mean f
Fattychris · 1 points · Posted at 13:54:55 on February 14, 2016 · (Permalink)
This response messed with my head the most. I always figured it was something about the number 9. I never think about other base systems.
ThumbForke · 4 points · Posted at 23:47:44 on February 13, 2016 · (Permalink)
I like to think of it like this: if you add 9 to something, it is basically adding 10 (thus increasing the digital root by 1), and then taking away 1 (thus decreasing the digital root by 1). So adding 9 to something doesn't change its digital root.
A multiple of 9 is just the number 9 with a load of 9's added onto it. So it must have a digital root of 9!
ravingprivatecyan · 1 points · Posted at 03:14:14 on February 14, 2016 · (Permalink)
You just wrinkled my brain.
ThumbForke · 2 points · Posted at 11:37:24 on February 14, 2016 · (Permalink)
That's a good thing, yeah?
ravingprivatecyan · 1 points · Posted at 11:56:28 on February 14, 2016 · (Permalink)
Definitely!
zxcvbnmmssdh · 4 points · Posted at 23:27:00 on February 13, 2016 · (Permalink)
So that's pretty much the fancy way of putting the way you check if something is a multiple of 9
pasqualy · 2 points · Posted at 23:58:47 on February 13, 2016 · (Permalink)
On a similar note, the digital root of every multiple of 3 is a multiple of 3.
You can do a similar (but more complicated) process (that I cannot remember atm) to multiples of 7 as well.
Lord_Binky · 6 points · Posted at 02:01:08 on February 14, 2016 · (Permalink)*
Was going to mention that about 3 but you beat me to it. It's logical since 9 is 32.
However, I can refresh your memory on digital roots of 7.
Take any number. Remove the last digit entirely. Double it and subtract it from the remaining digits of the original number. If the difference is a multiple of 7 then the original number is rooted in 7. If it is not then it is not rooted in 7. If you are unsure then repeat the process.
Example 1:
Let's use a simple multiple first: 14.
Step 1: Drop the last digit.
Step 2: Double that dropped digit.
Step 3: Subtract from the remaining digits.
-7 is of course a multiple of 7 (7 × -1) therefore the number 14 is a multiple of 7.
Example 2:
Let's try 49 (7 × 7).
Step 1: Drop the final digit.
Step 2: Double it.
Step 3: Subtract from remaining digits.
-14 is the product of (-1 × 2 × 7). It is rooted in 7.
Try one more? How about... 343?
Step 1 : Drop the final digit.
Step 2 : Double that dropped digit.
Step 3 : Subtract from the remaining digits.
Hm, I'll play dumb. Is 28 divisible by 7? I'm not sure. Let's do that again.
Step 1 : Drop the final digit.
Step 2: Double that dropped digit.
Step 3: Subtract from the remaining digits.
Aha! 343 is divisible by 7! (It's 73 in fact).
publius101 · 3 points · Posted at 06:59:28 on February 14, 2016 · (Permalink)
you can also do a similar thing for multiples of 11 - add up all the odd-position digits and the even position digits and subtract the two.
e.g. 132: 1+2=3, 3-3=0 - multiple of 11. or 1716: 6+7=13, 1+1=2, 13-2=11 - multiple of 11.
Lord_Binky · 1 points · Posted at 13:08:15 on February 14, 2016 · (Permalink)
Yep. Both that and 7 blew my mind the first time I learned them.
skyzich · 2 points · Posted at 09:21:37 on February 14, 2016 · (Permalink)
And you can test for a multiple of 6 as well, if it fits the conditions for a multiple of three and is also an even number.
MrPRambo · 1 points · Posted at 13:32:07 on February 14, 2016 · (Permalink)
Half life 3 confirmed
Starsy · 1 points · Posted at 01:28:20 on February 14, 2016 · (Permalink)
Works for 3 and 6 as well.
IAMA_dragon-AMA · 1 points · Posted at 02:36:47 on February 14, 2016 · (Permalink)
And for 18, just show it's a multiple of 9 and that it's even.
carlthecubsfan · 1 points · Posted at 01:39:02 on February 14, 2016 · (Permalink)
https://youtu.be/Q53GmMCqmAM
Redbird9346 · 1 points · Posted at 05:29:27 on February 15, 2016 · (Permalink)
That's where I learned about it. Square One TV.
ud0ntknowme · 1 points · Posted at 04:04:45 on February 14, 2016 · (Permalink)
This generalizes to all other bases too. For example, consider base 8 number systems. In this case, the special property of 9 is replaced by 7. Examples (the numbers below are in base 8):
1 x 7 = 7 7 x 7 = 61, 6 + 1 = 7 123 x 7 = 1535, 1 + 5 + 3 + 5 = 16, 1 + 6 = 7
[deleted] · 1 points · Posted at 04:24:42 on February 14, 2016 · (Permalink)
Any multiple of three adds up to be 3 6 or 9
AsidK · 1 points · Posted at 05:34:30 on February 14, 2016 · (Permalink)
I think you mean multiple, not factor
mamyt1 · 1 points · Posted at 05:48:11 on February 14, 2016 · (Permalink)
As a non-mathy geek this has always been my favorite.
workerdrones · 1 points · Posted at 05:57:13 on February 14, 2016 · (Permalink)
I finally learned that this weird mental tic I do has a name. Huh.
OPreco · 1 points · Posted at 07:14:22 on February 14, 2016 · (Permalink)
Actually super useful if you are trying to quickly determine if a large-ish number can be evenly divided by 3!
MayhemMessiah · 1 points · Posted at 07:56:43 on February 14, 2016 · (Permalink)
You can always tell if a number is divisible by three, no matter how big, if you sum all of it's digits untill you get a 1 digit number and it's 3, 6, or 9.
14376=> 1 + 4 + 3 + 7 + 6 = 21 => 2 + 1 = 3
14376/3 = 4792
bassinastor · 1 points · Posted at 08:36:28 on February 14, 2016 · (Permalink)
I imagine this is a result of the divisible by 3 trick? Any number who's digits add up to three (or a multiple of three) is divisible by three.
Jasonwfranks · 1 points · Posted at 09:05:22 on February 14, 2016 · (Permalink)
I think you meant any multiple of 9?
AKA_Squanchy · 1 points · Posted at 15:27:04 on February 14, 2016 · (Permalink)
Woah! I just posted similar but not as advanced as yours! Neat!
DrSchaffhausen · 278 points · Posted at 22:10:55 on February 13, 2016 · (Permalink)*
X2 = (X-1)*(X+1)+1
1x1 = 1 while 0x2 = 0
2x2 = 4 while 1x3 = 3
3x3 = 9 while 2x4 = 8
4x4 = 16 while 3x5 = 15
5x5 = 25 while 4x6 = 24
6x6 = 36 while 5x7 = 35
And so on. ..
synthcheer1729 · 53 points · Posted at 00:41:29 on February 14, 2016 · (Permalink)
This is the difference of squares equation with one added to it. It's still pretty interesting though.
Midas_Warchest · 20 points · Posted at 04:50:51 on February 14, 2016 · (Permalink)
You can use this to do other stuff as well. How can you quickly multiply 38 x 42. The number in between the two numbers is 40 -- 38 + 2 = 40 & 42 - 2 = 40. 402 is 1600. 22 = 4. (The two is taken because it is the difference between 38 and 40 and 40 and 42). 1600 - 4 = 1596. 38 x 42 = 1596.
What is 64 * 56? The middle number is 60. 602 = 3600. 42 = 16. 3600 - 16 = 3584. 64 * 56 = 3584.
DrSchaffhausen · 3 points · Posted at 06:01:39 on February 14, 2016 · (Permalink)
That is a neat addition. I never considered trying to expand the gap before.
Nindzya · 6 points · Posted at 06:18:40 on February 14, 2016 · (Permalink)
Neater formatting for convenience.
102 = 100
11*9 = 100-12 (99)
12*8 = 100-22 (96)
13*7 = 100-32 (91)
14*6 = 100-42 (84)
15*5=100-52 (75)
pfoxeh · 1 points · Posted at 09:41:58 on February 14, 2016 · (Permalink)
I learned this doing the Math and Science competitions in Texas, many many moons ago. Tricks like this are always fun to show off! :D
callahandler92 · 9 points · Posted at 02:07:01 on February 14, 2016 · (Permalink)
(x+1)(x-1)= x2 - x + x - 1 = x2 - 1
Therefore (x+1)(x-1) + 1 = x2 -1 + 1 = x2
Tetradrachm · 23 points · Posted at 03:09:42 on February 14, 2016 · (Permalink)
foiled again!
thgril · 5 points · Posted at 02:42:02 on February 14, 2016 · (Permalink)
More generally, x2 - a2 = (x - a)(x + a), which means that memorising square numbers can make multiplication a lot easier.
Zobtzler · 1 points · Posted at 16:13:11 on February 14, 2016 · (Permalink)
Wow, this formula has been in front of my face for years, I have never made this connection until now
maxdoss · 10 points · Posted at 01:28:32 on February 14, 2016 · (Permalink)
Before I read that I somewhat figured that out in 4th grade.
Fake_Name_6 · 7 points · Posted at 01:00:21 on February 14, 2016 · (Permalink)
This is great because anyone with a decent grasp of algebra can proove and understand it but it seems so cool. It is great to introduce non-mathematical people to the beauty of numbers.
plus4dbu · 2 points · Posted at 05:07:43 on February 14, 2016 · (Permalink)
I like this! I hope this will help me when doing mental math.
hijomaffections · 1 points · Posted at 04:28:14 on February 14, 2016 · (Permalink)
This would've been great for elementary
The_gray_ghost · 1 points · Posted at 04:57:41 on February 14, 2016 · (Permalink)
I find this especially interesting for some reason
pikaras · 1 points · Posted at 05:10:40 on February 14, 2016 · (Permalink)
(x-1)*(x+1) + 1 = x(x-1)+(x-1)+1 = x2 -x +x -1 +1 = x2
hotbrokemess · 1 points · Posted at 07:21:17 on February 14, 2016 · (Permalink)
I'm high right now and this is blowing my mind.
ForeignTorque · 1 points · Posted at 07:24:38 on February 14, 2016 · (Permalink)
(x+1)(x-1)+1 X2-x+x-1+1 x2
captain__knuckles · 1 points · Posted at 07:31:33 on February 14, 2016 · (Permalink)
n2 is also equal to the sum of n odd integers. So for example 22 = 1+3 and 82 = 1+3+5+7+9+11+13+15
fofbacon · 1 points · Posted at 07:58:59 on February 14, 2016 · (Permalink)
even works for (i+1)*(i-1)
bassinastor · 1 points · Posted at 08:32:44 on February 14, 2016 · (Permalink)
This one is also very easy to prove. (X+1)(X-1) is equal to X2 - 1. You add a 1 and you're left with X2 .
feo_ZA · 1 points · Posted at 14:59:18 on February 14, 2016 · (Permalink)
This one is interesting when you put numbers to it but algebra wise, it's pretty simple.
Voxel_Brony · 1 points · Posted at 02:22:18 on February 15, 2016 · (Permalink)
x2 = (x - a)(x + a) + a2
12tales · 0 points · Posted at 04:45:32 on February 14, 2016 · (Permalink)
So, you can find X2 by squaring X, subtracting X, adding X, subtracting 1 and adding 1?
Shocking.
DrSchaffhausen · 1 points · Posted at 05:57:19 on February 14, 2016 · (Permalink)
I somehow knew posting a simple formula on Reddit would draw negative comments.
Your comment doesn't match the formula, by the way.
12tales · 1 points · Posted at 06:17:31 on February 14, 2016 · (Permalink)
It does. Your formula is (X-1)(X+1) + 1. That can be simplified to (X x X) + (X x 1) + (-1 x X) + (-1 x 1) +1. Simplified further, that's X2 + X - X - 1 + 1.
I'm just saying, that formula is only cool to the extent that it obfuscates the trivial mathematics going on behind it.
popejubal · 0 points · Posted at 03:41:09 on February 14, 2016 · (Permalink)
That's pretty neat. I never thought of using (x2 - 1) + 1 to do work. That is very clever.
dluminous · 0 points · Posted at 06:27:27 on February 14, 2016 · (Permalink)
Fuck why cant teachers show us this. Why do teachers suck? While I knew the above, its sooooo easy when you see this.
zekilki · 49 points · Posted at 21:20:48 on February 13, 2016 · (Permalink)
That there are more numbers in the segment [0,1], a subset of the real numbers than there are all integers. I enjoy that: 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... equals 2 but 1 + 1/2 + 1/3 + 1/4 + 1/5 + ... is infinite. Infinite!!
AcellOfllSpades · 38 points · Posted at 21:46:24 on February 13, 2016 · (Permalink)
Proof for the last one:
1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8...
is more than
1 + 1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 + 1/16...
which is the same as
1 + (1/2)+ (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8)+ (1/16...)
which is the same as
1 + 1/2 + 1/2 + 1/2 + ...
which clearly is infinite.
[deleted] · 12 points · Posted at 01:17:13 on February 14, 2016 · (Permalink)*
Infinitely many mathematicians walk into a bar: the first one says "I'll have a beer!"; the second one says "I'll take half a beer!"; the third asks for a quarter of a beer...
Bartender shakes his head, pours two pints, and says:
"C'mon guys! Know your limits..."
I'll go ahead and show myself out. I mean, I'd love to tell you the one about the group that commutes. But you've probably heard it abelian times by now...
thmsoe · 3 points · Posted at 02:26:26 on February 14, 2016 · (Permalink)
There is more :)
If in your sum : 1+1/2+1/3+1/4+1/5+... you exclude all numbers which contain 9 as a digit, then your sum actually converges. I believe it works for any combination of digits : for example, if you exclude all numbers that contain '101467' in their digits, then the sum converges.
Even crazier is this : the sum of all 1/p where p are the prime numbers diverges towards infinity. You can thank Euler for that one !
REMagic42 · 1 points · Posted at 10:38:15 on February 14, 2016 · (Permalink)
However, if you only take every 10th element, it is infinite:
1 + 1/10 + 1/20 + 1/30 + 1/40 + ... = infinite
Thinks_Too_Logically · 1 points · Posted at 18:16:29 on February 14, 2016 · (Permalink)
The reasoning behind the "exclude all the numbers with 9" is that 9 becomes more common in numbers as you get larger.
How many numbers between 1 and 10 have a 9 in them? 1. So there's a 10% chance of there being a 9 in the first 10 numbers. What about between 1 and 100? 9,19,29,39,49,59,69,79, 89,90,91,92,93,94,95,96,97,98,99. That's 19. So there's a 19% chance of there being a 9 in the first 100 numbers, and you can see how the ratio to numbers with a 9 vs total numbers is increasing.
Another way to look at is this: Randomly generate a number with N digits. What is the chance that none of those digits is a 9? We have a 9/10 chance of the first digit not being a 9, a 9/10 chance of the second digit being a 9, and so on. So there's a (9/10)N chance of every digit not being a 9. Since 9/10 < 1, then as N goes to infinity, (9/10)N goes to 0.
heap42 · 1 points · Posted at 00:03:59 on February 14, 2016 · (Permalink)
Wait... is the first one right?... Can someone else confirm? I am not really good with Cardinals ordinals and infinities... and someone in an other comment said that this is not true.. or maybe i am confusing somethign.
corpuscle634 · 3 points · Posted at 00:50:50 on February 14, 2016 · (Permalink)
n = 1 + 1/2 + 1/4 + ...
2n = 2 + 1 + 1/2 + 1/4 + ...
2n - 2 = 1 + 1/2 + 1/4 + ...
2n - 2 = n
n = 2
tero1414 · 1 points · Posted at 02:05:50 on February 14, 2016 · (Permalink)
[https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument]
[deleted] · 403 points · Posted at 19:08:03 on February 13, 2016 · (Permalink)
the derivative of ex is ex.
DanTheTerrible · 366 points · Posted at 19:54:07 on February 13, 2016 · (Permalink)
I never thought of that as amazing, that's just the definition of e. Its like saying if you divide the circumference of a circle by its diameter you get pi.
ThereOnceWasAMan · 232 points · Posted at 20:15:24 on February 13, 2016 · (Permalink)
Well, it's a bit more cool because it's ONE of the definitions of e, and it's not immediately obvious why those definitions are equal to eachother.
[deleted] · 14 points · Posted at 02:31:50 on February 14, 2016 · (Permalink)
It's also pretty cool that such a number even exists. It's not immediately obvious that there would exist any number at all for which it holds true.
DonGateley · 6 points · Posted at 07:18:39 on February 14, 2016 · (Permalink)
Another way to think about is to realize that there must be some function which is the derivative of itself and this happens to be the one.
red_trumpet · 4 points · Posted at 14:17:25 on February 14, 2016 · (Permalink)
I don't think it's that obvious
And even less obvious, that this should be unique (which it is)
[deleted] · 2 points · Posted at 23:26:36 on February 14, 2016 · (Permalink)
Proving that it must be unique is much easier than proving that it must exist.
Suppose you have two functions f and g such that f' = f and g' = g. and f(0) = g(0) = 1.
Then (f/g)' = (f'g - fg')/g2 = (fg - fg)/g2 = 0
so f/g is a constant and since f(0)/g(0) = 1, then f = g
ThereOnceWasAMan · 2 points · Posted at 16:41:56 on February 15, 2016 · (Permalink)
Whoa, I've never seen that before. I really like it!
SorrowOverlord · 2 points · Posted at 14:17:12 on February 14, 2016 · (Permalink)
why must there be such a function?
[deleted] · 1 points · Posted at 23:33:16 on February 14, 2016 · (Permalink)
Because of the Picard–Lindelöf theorem, of course.
But seriously, you can think of differential equations as the continuous analogue to sequences defined recursively.
In the latter, each new value is defined using the previous values.
In the former, at each point, you can think of f'(x) as (f(x+h)-f(x))/h, where h is a small number. The differential equation now gives you a relation between f(x) and f(x+h), that allows you to figure out f(x+h), then f(x+2h) and so on. And as you make the h smaller and smaller, you get a function that gets closer to a solution of the differential equation.
VacuouslyUntrue · 2 points · Posted at 09:28:05 on February 14, 2016 · (Permalink)
You are wrong, because differentiation is a linear operation on a function space, avoiding going into details here.
So there will be functions that are preserved by the operator, basically exactly like eigenvectors for a regular old matrix, but of course differentiation is an operator on an infinite dimensional vector space.
UnchainedMundane · 2 points · Posted at 03:04:31 on February 14, 2016 · (Permalink)
Is it obvious in some way which isn't immediate?
VacuouslyUntrue · 3 points · Posted at 09:28:46 on February 14, 2016 · (Permalink)
Yes, because differentiation is linear, and so there are 'eigenvectors' of differentiation and ex is one of them.
SidusKnight · 2 points · Posted at 10:14:25 on February 14, 2016 · (Permalink)
Well, it also has to have eigenvalue of 1 (otherwise we'd be off by some coefficient).
VacuouslyUntrue · 1 points · Posted at 00:25:22 on February 15, 2016 · (Permalink)
I suspect, though I don't know, that the existence of such an eigenvector is guaranteed by the kind of space differentiation acts on. which is a Hilbert space with (uncountably) infinite dimensions.
[deleted] · 2 points · Posted at 04:27:44 on February 14, 2016 · (Permalink)*
[deleted]
ThereOnceWasAMan · 8 points · Posted at 04:32:10 on February 14, 2016 · (Permalink)
There are many. The two other most used ones are:
and
Kered13 · 3 points · Posted at 14:40:16 on February 14, 2016 · (Permalink)*
Also you can define the exponential function as the inverse of the natural logarithm (which is itself defined as the integral of 1/x from 1 to x). e itself is defined as exp(1) in this approach.
This is how we did it in my analysis class.
sorif · 2 points · Posted at 04:39:54 on February 14, 2016 · (Permalink)
ELI5 for the other definitions and the reason why they're all equal?
fnybny · 2 points · Posted at 07:51:50 on February 14, 2016 · (Permalink)
It is not a definition because e is not the unique complex number with this property. 0'=0
ThereOnceWasAMan · 1 points · Posted at 08:51:15 on February 14, 2016 · (Permalink)
Eh. Mathematicians get around this by in the usual way -- tack on a "...is the only non-trivial function s.t. ..." within the definition.
fnybny · 2 points · Posted at 18:09:55 on February 14, 2016 · (Permalink)
Or sometimes an odd prime.
[deleted] · 1 points · Posted at 23:35:40 on February 14, 2016 · (Permalink)
The full definition is f' = f and f(0) = 1
drinks_antifreeze · 2 points · Posted at 06:00:32 on February 14, 2016 · (Permalink)*
Right. Any student just starting out in ODE can easily derive ex using the differential equation y=dy/dx; i.e., "Some function 'y' is equal to its derivative 'dy/dx'." For anyone who's curious...
y = dy/dx
dy/y = dx
∫dy/y = ∫dx
ln(y) = x
e[ln(y)] = ex
y = ex
However, you can also derive e as the following limit:
lim n->∞ (1+1/n)n
Add on a little less to 1 every time, but exponentiate it another time too. This sequence of numbers converges to e (although don't ask me to prove it).
The number e is also transcendental, meaning that it can never be the root of a polynomial with rational coefficients, which essentially says that you can't construct this number with algebra. Numbers that aren't transcendental are, fittingly, called algebraic numbers. Even the imaginary number i is algebraic (x2 + 1 = 0), so transcendental numbers are very special set of numbers indeed. (Fun fact though: Transcendental numbers are uncountably infinite and the algebraic numbers are only countably infinite, meaning that most real numbers are in fact transcendental. It's just really hard to prove that a number is transcendental, which is why it's sort of special.) In fact, the transcendence of e was used to prove that π is also transcendental using Euler's identity eiπ + 1 = 0.
Basically what I'm trying to say is that e is a really neat number.
ConfusedMandarin · 3 points · Posted at 14:02:10 on February 14, 2016 · (Permalink)
Well, when you integrate the equation you're using the knowledge that the derivative of lnx is 1/x, and this comes from the knowledge that the derivative of ex is ex. So you can't really use that proof without already knowing about ex. ie you can't actually find the value of ex like that
Kered13 · 1 points · Posted at 14:42:20 on February 14, 2016 · (Permalink)*
Not necessarily. You can also go in the other direction: ln(x) can be defined as the integral of 1/x from 1 to x, and you can then define exp(x) as the inverse of ln(x).
ConfusedMandarin · 1 points · Posted at 15:02:43 on February 14, 2016 · (Permalink)
Hmm. That doesn't seem like it gets you anywhere. All you're getting from that is "assume the integral of 1/x from 1-x is defined, and give it a name without figuring out what it actually is. Then the derivative of its inverse (assuming that exists) is its inverse"
In my mind, e has to come from the limit definition
e = lim[x->INF](1 + 1/x)x
Because that value makes sense without using e or ln anywhere in it, and it makes sense why the differentiation property holds.
Kered13 · 1 points · Posted at 15:19:43 on February 14, 2016 · (Permalink)*
Here's a good page that shows you how this approach works, (it was posted elsewhere in this thread for unrelated reasons). Note that while this page starts by talking about properties of logarithms, it doesn't define the logarithm by these properties. It proves the properties after defining the logarithm as the integral of 1/x.
I think part of your problem with this is that you feel like e is the more basic concept, and that it therefore must be defined without the exponential function or the natural logarithm. I would argue that this is wrong. That limit (and other limits that make e) is useful in a few circumstances, but the natural logarithm and exponential function are far more universal. Indeed, you'll almost always find e being used as part of one of these two functions. Furthermore, there's no obvious reason why that limit is important, while both the natural logarithm and exponential function are obviously important from just their definition and basic properties, without even getting into e. Therefore it makes the most sense to define e in terms of one of those two functions. Essentially all rigorous calculus courses do this. (Incidentally, pi is also usually defined as something like the smallest positive x such that sin(x) = 0, since this doesn't require geometry, and even then the circle definition only works in Euclidean geometry).
The next choice is which of the two functions to use. The natural logarithm approach is very natural if you start with integrals before derivatives, while the exponential function is natural if you start with derivatives (most calculus classes do derivatives first, but it's easy to go from the other direction instead). Starting with the natural logarithm is also arguably simpler: The natural logarithm can be defined as a simple definite integral, while the exponential function must be defined as a differential equation. By corollary, this also arguably makes the natural logarithm easier to calculate: The natural logarithm can be calculated using Riemann sums over 1/x, while if the exponential function is defined first it has to be calculated using Euler's method. (Remember, when you've just defined these functions these are the only methods you have to calculate them. Power series and other approximations have to be proved later.)
NukeDukem1 · 2 points · Posted at 08:10:36 on February 14, 2016 · (Permalink)
Proof for lim n -> ∞ (1 + 1/n)n
y = lim n-> ∞ (1+1/n)n
ln(y) = lim n-> ∞ ln((1+1/n)n )
ln(y) = lim n-> ∞ (n)ln(1 + 1/n)
ln(y) = lim n-> ∞ [ln(1+1/n)]/(1/n) (evaluates to 0/0, thus use L'Hopital's rule)
ln(y) = lim n-> ∞ [(-1/n2 )/(1+1/n)]/(-1/n2 )
ln(y) = lim n-> ∞ (1 + 1/n)
ln(y) = 1
y = e1
L'Hopital's rule states that if the limit evaluates to the indeterminant form of 0/0, then the limit can be substituted with the derivative of the top over the derivative of the bottom.
Atmosck · 1 points · Posted at 05:26:34 on February 14, 2016 · (Permalink)
It is a bit remarkable in that it's not obvious that the function that's it's own derivative is exponential.
flaming_plutonium · 1 points · Posted at 14:53:04 on February 14, 2016 · (Permalink)
And the other definitions are convenient for other problems
klod42 · 1 points · Posted at 16:54:09 on February 14, 2016 · (Permalink)
I never understood why those definitions are equal to each other.
Dinkir9 · 90 points · Posted at 21:23:42 on February 13, 2016 · (Permalink)
Know why this is the case? ex can be defined as 1 + x + x2 /2! + x3 /3! + x4 /4! and so on. Thing is when you derive x4 /4! or something in that vein... It gets knocked down to the term before it. Since the pattern repeats indefinitely, the sequence doesnt get distorted when you derive it and it stays the exact same proving that ex =ex
Btw this was extremely difficult to write out on a phone.
acolourfulmind · 19 points · Posted at 23:56:28 on February 13, 2016 · (Permalink)
Just FYI, the word for taking a derivative is "differentiate", not "derive". Derive means something totally different,
Dinkir9 · -14 points · Posted at 00:35:20 on February 14, 2016 · (Permalink)
Thats math grammer. The general point is still understood by everybody, doesnt matter if I said differentiate or derive, in the context of the post it was clear what I meant by derive and, it seemed to be pretty well understood. Consider it with literary grammer, the fact that I put a comma in the wrong place or, hell, dont have one isn't gonna change the fact that what I was writing about is still understood almost universally. Only the really anal grammer professors are gonna get confused and that's just because they are trained to do so.
Oh and by the way, I put "grammer" on purpose to get the point across.
hbutcher · 5 points · Posted at 03:06:10 on February 14, 2016 · (Permalink)
Pretty well understood that you sound dumb... jk just don't get so salty. Chill ;-)
p_kell · 3 points · Posted at 23:19:00 on February 13, 2016 · (Permalink)
Gotta love your Maclaurin polynomials
kaps1 · 3 points · Posted at 02:23:49 on February 14, 2016 · (Permalink)*
Is that the Maclaurin series expansion for ex?
ChessClue · 2 points · Posted at 22:44:22 on February 13, 2016 · (Permalink)
Isn't it also because when you derive exponential function you multiply times ln(a)
so d/dx of ax = ln(a)*ax
so with ex = ln(e) * ex
but ln(e) is just 1 so it's just ex
auralucario2 · 4 points · Posted at 00:32:51 on February 14, 2016 · (Permalink)
That's a result of the proof that the derivative of ex is itself. As a result, you can't use it to prove that d/dx(ex) = ex
Nettius2 · 1 points · Posted at 02:28:50 on February 14, 2016 · (Permalink)
The exponential is usually defined using limits (as tetondon did). This is the Taylor series expansion. They are equivalent.
Gobuchul · 1 points · Posted at 16:32:07 on February 14, 2016 · (Permalink)
So there still is a use for keyboard based computers!
Dinkir9 · 1 points · Posted at 17:18:10 on February 14, 2016 · (Permalink)
Damnit you're right.
auralucario2 · 1 points · Posted at 21:50:52 on February 15, 2016 · (Permalink)
But don't you need to know the derivative of ex to determine it's Maclaurin expansion? Therefore, you can't prove it that way.
tetondon · 82 points · Posted at 20:42:24 on February 13, 2016 · (Permalink)
e is the limit of (1 + 1/n)n as n approaches infinity.
Felix_Tholomyes · 36 points · Posted at 22:22:00 on February 13, 2016 · (Permalink)*
Let f(x)=ax where a is a real number
We want to find a such that f(x)=d/dx(f(x))
f'(x)=lim h->0 (f(x+h)-f(x))/h
=lim h->0 ( ax+h - ax )/h
=lim h->0 ( ax * ah - ax )/h
=lim h->0 ( ah - 1 )ax / h
=lim h->0 ax * (ah - 1)/h = f(x) = ax
<=> lim h->0 (ah - 1)/h = 1
<=> lim h->0 ah = lim h->0 h+1
<=> lim h->0 (h+1)1/h = a
We let n=1/h. h->0 <=> n->∞
lim n->∞ (1/n+1)n = a = e
Thus the definition is equivalent to yours.
[deleted] · 1 points · Posted at 01:33:20 on February 14, 2016 · (Permalink)
Can you explain how you got this step lim h->0 (h+1)1/h = a
Felix_Tholomyes · 3 points · Posted at 01:45:53 on February 14, 2016 · (Permalink)
I corrected a mistake in my post, but if you solve lim h->0 (ah - 1)/h = 1 for a, you get that.
Multiply both sides by h, add 1, raise to the 1/h power
[deleted] · 1 points · Posted at 19:40:56 on February 14, 2016 · (Permalink)
Since you seem pretty knowledgeable about e, do you know the mathematical explanation for the maximum of x1/x occurring at x= e?
Felix_Tholomyes · 1 points · Posted at 22:00:57 on February 14, 2016 · (Permalink)*
I can't offer any profound explanation to why it's e, other than that it follows from a property of exponential functions. I can however show how to find the derivative of x1/x in which a logarithm term appears which explains why x=e is an extreme point.
Let f(x)=x1/x x>0
xx = eln( x1/x ) where ln is the natural logarithm with base e
You could choose any base for the logarithm but as we are about to differentiate, this would be unnecessarily complicated and we would still get a logarithm term with base e.
eln( x1/x ) = e1/xln(x)
d/dx(f(x)) = ( -ln(x)/x2 + 1/x2 )e1/xln(x) =
= x1/x / x2 (1-ln(x)), x>0
We set the derivative equal to zero
x1/x / x2 (1-ln(x)) = 0
1-ln(x) = 0
x = e
There probably is a way to do this where you use the definition of a derivative and reduce the problem to the same as above, thus avoiding the use of logarithms, which would be neater.
jaynay1 · 41 points · Posted at 21:56:48 on February 13, 2016 · (Permalink)
No, e is the value to which the sum from 0 to infinity of 1/n! converges.
datorangeguy · 6 points · Posted at 23:34:06 on February 13, 2016 · (Permalink)
ummm, actually e is the number which when taken to the power of n, subtracted by one, then divided by n, approaches 1 as n approaches 0.
katycat737 · 13 points · Posted at 22:08:49 on February 13, 2016 · (Permalink)
It's both actually, and some more too
jaynay1 · 30 points · Posted at 22:12:23 on February 13, 2016 · (Permalink)
I know. I was joking about how many different definitions of e there actually are.
I've only done the proofs for one of those implying the other two though.
aixenprovence · 8 points · Posted at 22:51:59 on February 13, 2016 · (Permalink)
Whoosh!
T-Rex96 · -8 points · Posted at 23:54:24 on February 13, 2016 · (Permalink)
Comment of the year.
LBJSmellsNice · 1 points · Posted at 03:10:40 on February 14, 2016 · (Permalink)
No, e is the number which, when raised to the i*pi = -1
InfanticideAquifer · 1 points · Posted at 06:32:24 on February 14, 2016 · (Permalink)
Actually, e to the power of any odd integer also satisfies that.
[deleted] · 2 points · Posted at 22:58:34 on February 13, 2016 · (Permalink)
e is also the infinite sum of all the reciprocals of the factorial products, 1/0! (by convention, 0! = 1) + 1/1! + 1/2! +1/3!...
BadBoyJH · 1 points · Posted at 04:32:29 on February 14, 2016 · (Permalink)
But this definition comes from exponential growth, and (to me) is like saying pi is the area divided by the radius squared, instead of the circumference divided by the diameter.
MacBookMinus · -1 points · Posted at 01:46:28 on February 14, 2016 · (Permalink)
But e isn't 1
New_World_Era · 15 points · Posted at 20:41:08 on February 13, 2016 · (Permalink)
It's amazing when you first learn about it, because you don't really know how fundamental "e" is at that point.
CaesarTheFirst1 · 3 points · Posted at 21:36:50 on February 13, 2016 · (Permalink)
I don't think that's exactly the best analogy. Consider this, why should there be a function that is it's own derivative? On the other hand it's obvious the ratio between the circumference of a circle by its diameter is a number (That doesn't depend on the diameter).
ananori · 1 points · Posted at 22:06:05 on February 13, 2016 · (Permalink)
Why shouldn't be there a function that describes its own rate of change?
CaesarTheFirst1 · 5 points · Posted at 22:10:04 on February 13, 2016 · (Permalink)
I think the burden of proof is on you, why should there? That's not at all a trivial condition, a derivative is a limit, it contains a lot of information about the function. Let's try and build such a function, so arbitrarily set f(0)=0, how do we continue?
Maybe it's intuitive for you, I don't quite see why there should be such a function. For example there is no continuous function which maps rationals to irrationals and irrationals to rationals.
Alpha_sc2 · 1 points · Posted at 01:37:22 on February 14, 2016 · (Permalink)
In your case the problem would be solved pretty easily by choosing f as the constant zero-function f(x) = 0 for all x.
But if you are familiar with the Taylor-series you can actually construct it pretty easily for any arbitrary value of f(0):
So, we want to get a function f with f'(x) = f(x) and f(0) = a for some number a.
According to Taylor, f(x) ist equal to the infinite sum f(0)/0! + f'(0)/1! * x + f''(0)/2! * x² + f'''(0)/3! * x³ + ... on the sums radius of convergence. Because of f'(x) = f(x) it also holds that f''(x) = f(x) and so on.
Thus, we get f(x) = a + a * x + a/2 * x² + a/6 * x³ + ... = a * sum(xk / k!, k=0..infinity).
The last sum converges for every real number x, and so f(x) = a * sum(xk / k!, k=0..infinity) for all x. That sum by the way is equal to ex , so f(x) = a*ex.
CaesarTheFirst1 · 3 points · Posted at 07:20:29 on February 14, 2016 · (Permalink)*
Why does the sum converge? Why is the derivative the same as taking the derivative of every term? Why is the function even differentialable?
Alpha_sc2 · 1 points · Posted at 10:51:06 on February 14, 2016 · (Permalink)
There are a number of ways to show that the sum converges. For example when using the ratio test, you get:
lim[k->inf] ( (xk+1 / (k+1)!) / (xk / k!) ) = lim[k->inf] (x / (k+1)) = 0 < 1 for every x.
We assume, that we have a differentiable function f with the given properties and then show what f has to look like. This assumption is okay because then function we get IS in fact differentiable with these properties.
You can differentiate an infinite sum term by term at any point if the sum converges absolutely at this point (which our sum does).
CaesarTheFirst1 · 1 points · Posted at 18:14:52 on February 14, 2016 · (Permalink)
You have to prove that last thing. What I'm trying to say is that it isn't obvious why such a function exists, when you learned about functions, even when you learned about what is a derivative, did you immediately think that it can be represented by an infinite polynomial?
At this stage I can easily build a function that is its own derivative, but when I learned about what a function is, I did not. I am not saying it takes an incredible genius to think of one, but it is certainly not "just the definition of e".
Kered13 · 1 points · Posted at 14:44:35 on February 14, 2016 · (Permalink)
It's not immediately obvious that that ratio is a constant though (indeed, it's only constant in Euclidean geometry).
CaesarTheFirst1 · 1 points · Posted at 18:18:45 on February 14, 2016 · (Permalink)
I think it's pretty obvious when you define the circumference.
Kered13 · 1 points · Posted at 20:35:19 on February 14, 2016 · (Permalink)
Famous last words of many a math student. It's no more obvious than the existence of a solution to y'=y.
CaesarTheFirst1 · 1 points · Posted at 20:56:57 on February 14, 2016 · (Permalink)
You define circumference as the limit of putting a bunch of triangles, if you accept similar triangles as obvious it follows.
Kered13 · 1 points · Posted at 21:13:29 on February 14, 2016 · (Permalink)
But similar triangles are equally non-obvious. They also fail in non-Euclidean geometry.
I mean, yes, you can prove this, but taking it as obvious is a mistake. You can also prove the y'=y has a solution with some pretty simple math.
CaesarTheFirst1 · 1 points · Posted at 21:42:20 on February 14, 2016 · (Permalink)
Yes you're certainly right it takes work to prove, I think it is much more intuitive though, if you take a triangle and magnify it, than all sides grow by the same factor.
CaesarTheFirst1 · 2 points · Posted at 21:36:33 on February 13, 2016 · (Permalink)
I don't think that's exactly the best analogy. Consider this, why should there be a function that is it's own derivative? On the other hand it's obvious the ratio between the circumference of a circle by its diameter is a number (That doesn't depend on the diameter).
poizan42 · 1 points · Posted at 23:09:50 on February 13, 2016 · (Permalink)
The fact that the function which satisfies f(x)'=f(x), f(0)=1 is exponentiation with an transcendent base may be a bit surprising.
skysurf3000 · 1 points · Posted at 00:09:41 on February 14, 2016 · (Permalink)
There are a few things like that that we use as definitions but that are actually not that rigorous at the level they are introduced.
Divide the circumference by the diameter to get pi. Why is it a constant?
exp is the function that is 1 at 0 and such that exp'=exp. Why does that exist?
bafoon90 · 1 points · Posted at 01:57:14 on February 14, 2016 · (Permalink)
Am I the only still amazed by pi?
ThePharros · 1 points · Posted at 05:14:22 on February 14, 2016 · (Permalink)
Another reason why it's pretty amazing is the intuitive approach of what that implies. ex being its own derivative implies that the slope of the tangent line at any given point in said function is equal to the value of the function at that given point. I'm sure this can be expanded upon, but I find that initial approach amazing enough.
diabolical-sun · 1 points · Posted at 06:19:38 on February 14, 2016 · (Permalink)
I think it gets cool when you work through it. Like differentiate ex the same way you would 3x
[deleted] · 1 points · Posted at 08:26:57 on February 14, 2016 · (Permalink)
Well its because e is just an integer. This is true for all integers.
Bashar_Al_Dat_Assad · 1 points · Posted at 10:11:05 on February 14, 2016 · (Permalink)
That's not the definition of e. It's a property of e. There's a huge distinction there and those are not at all the same thing. You can't derive the value of e from f(x) = df(x)/dx.
LudoRochambo · 1 points · Posted at 14:26:52 on February 14, 2016 · (Permalink)
yes, but now can you PROVE to me that when you divide the circumference by the diameter for ANY circle, its a constant value? which ends up being pi.
Kered13 · 1 points · Posted at 14:47:05 on February 14, 2016 · (Permalink)
If a mathematics course is advanced enough to define e as exp(1) and exp(x) as the function that is it's own derivative, then it's probably advanced enough that pi is not defined as the ratio of a circle to it's diameter. Pi would probably be defined as the smallest positive number x such that ex*i = -1 (or equivalently, the smallest positive number x such that sin(x) = 0).
CaesarTheFirst1 · 0 points · Posted at 21:36:55 on February 13, 2016 · (Permalink)
I don't think that's exactly the best analogy. Consider this, why should there be a function that is it's own derivative? On the other hand it's obvious the ratio between the circumference of a circle by its diameter is a number (That doesn't depend on the diameter).
Zartregu · 20 points · Posted at 23:39:40 on February 13, 2016 · (Permalink)*
ex and a constant function are having a nice stroll.
Suddenly they see a differential operator walking toward them.
"Yikes, he's going to nullify me!" screams the constant function as she runs away.
ex smiles and greets the differential operator.
"Hi, I'm ex"
"Why hello, I'm d/dy..."
bisbyx · 9 points · Posted at 04:25:05 on February 14, 2016 · (Permalink)
I told that joke on the first date with my wife. 8 years later and she still tells people how lame I was on our first date.
Zartregu · 2 points · Posted at 10:48:54 on February 14, 2016 · (Permalink)
I think this is close to being the archetypal nerd joke...
Glad it turned out fine for you!
[deleted] · 5 points · Posted at 02:44:26 on February 14, 2016 · (Permalink)
y = ex
lny = lnex
lny = x*lne
lny = x
1/y*dy/dx = 1
dy/dx = y
dy/dx = ex
[deleted] · 2 points · Posted at 06:47:49 on February 14, 2016 · (Permalink)
Now show that the derivative of lnx = 1/x, without using the derivative of ex.
[deleted] · 2 points · Posted at 12:57:27 on February 14, 2016 · (Permalink)
Best I can do in this format:
lim(h->0) (ln(x+h)-ln(x))/h
lim(h->0) ln((x+h)/x)/h
lim(h->0) 1/h * ln(1+h/x)
lim(h->0) ln(1+h/x)1/h
u = h/x
lim(u->0) ln(1+u)1/ux
1/x * lim(u->0) ln(1+u)1/u
1/x * ln [ lim(u->0) (1+u)1/u ]
1/x * ln e
1/x
slaerdx · 3 points · Posted at 03:18:52 on February 14, 2016 · (Permalink)
relevant pic
PlasmicDynamite · 21 points · Posted at 19:08:56 on February 13, 2016 · (Permalink)
And the integral of ex is ex + C
themasterofallthngs · 2 points · Posted at 07:15:16 on February 14, 2016 · (Permalink)
That is basically saying the exact same thing, if you know the Fundamental Theorem of Calculus.
[deleted] · 1 points · Posted at 03:06:12 on February 14, 2016 · (Permalink)
That'd be the antiderivative.
drawingdead0 · 0 points · Posted at 22:09:16 on February 13, 2016 · (Permalink)*
For me, ex + ex = a lot to drink
datorangeguy · 1 points · Posted at 23:35:55 on February 13, 2016 · (Permalink)
...oh
Well have a happy valentines day, bud!
Alexanderdaawesome · 3 points · Posted at 03:02:36 on February 14, 2016 · (Permalink)
But what about the antiderivative?
jkgao · 2 points · Posted at 04:38:20 on February 14, 2016 · (Permalink)
ex + c
Alexanderdaawesome · 1 points · Posted at 07:21:10 on February 14, 2016 · (Permalink)
thx boo
von_Hytecket · 2 points · Posted at 01:44:23 on February 14, 2016 · (Permalink)
The function describes at what rate the function itself grows.
This always amazes me.
[deleted] · 2 points · Posted at 04:39:52 on February 14, 2016 · (Permalink)
The more interesting part of that is that there exists a number such that the derivative of it raised to the xth power is it raised to the xth power.
Once that's proven, it's got to be e, since the definition of e is that it's the number such that the derivative of ex is ex
intensely_human · 1 points · Posted at 03:26:08 on February 14, 2016 · (Permalink)
In other words, when you take ecstasy, you feel ecstasy.
Dezpool · 1 points · Posted at 05:44:05 on February 14, 2016 · (Permalink)
What's more weird is you can think of it as a graph of ex to x. The slope of every single point on the graph, will be the value of the point itself.
CBtheDB · 1 points · Posted at 08:41:21 on February 14, 2016 · (Permalink)
The derivative of (ex x girlfriend) is bitch
georgeo · 1 points · Posted at 23:38:25 on February 13, 2016 · (Permalink)
and the integal of 1/x is log x.
SmellySlutSocket · 5 points · Posted at 02:25:19 on February 14, 2016 · (Permalink)
No, it's ln(x) + C
smurphatron · 1 points · Posted at 03:42:23 on February 14, 2016 · (Permalink)
Pedantry
xereeto · 1 points · Posted at 04:26:36 on February 14, 2016 · (Permalink)
The integral of 1/cabin is a houseboat... log cabin, then add the c
[deleted] · 1 points · Posted at 23:33:57 on February 13, 2016 · (Permalink)*
No it's not. The derivative is 7. Some guy proved that a while back. The derivative of 7, however, is 7.
There is more to this as well. The natural logarithm of 7 is 7. Or actually it is 6.98989898. Experts are still trying to find out why that is the case; i.e. why it is not exactly 7. Could be proof of a deep error in the way we understand numbers.
If you raise 7 to the 7th power 7 times, what you get is actually not a natural number. It is either irrational or transcendent - nobody knows for sure. Some think it might be divisible by 0.
If you solve the equation 'x + 7 = 0', you get 'x = -7' which is impossible, because the derivative of 'x + 7' is 7 and not 0, which you get on the right-hand side, suggesting complex numbers are somehow involved.
The Riemann zeta-function for even natural numbers can be written as a rational number times a power of 'pi', but there is no similar expression for odd numbers; not even for 7, as one would expect. The numerical value is also no-where near 7.
While the mystery of 7 is way beyond me, I have tried to come up with some answers. 7 is 5 + 2. 2, 5 and 7 are three numbers, giving the sequence 2, 3, 5 and 7 - the first four prime numbers. The derivative of 7 is 7.
That's all I got so far.
TaytosAreNice · 2 points · Posted at 01:20:10 on February 14, 2016 · (Permalink)
This is like Terryology brought to the next level.
somadIcanteven · 1 points · Posted at 03:32:25 on February 14, 2016 · (Permalink)
That was fantastic.
[deleted] · 1 points · Posted at 20:45:45 on February 14, 2016 · (Permalink)
This is a joke btw.
[deleted] · 1 points · Posted at 23:35:17 on February 13, 2016 · (Permalink)
So e to the power of a variable is invariably 7? Its a curve, so why would it have a constant derivative?
CaptainOrnithopter · -1 points · Posted at 03:00:49 on February 14, 2016 · (Permalink)
woosh
Ganjisseur · 0 points · Posted at 06:19:47 on February 14, 2016 · (Permalink)
"All I gotta do is put my mind to this shit, Cancel out my ex I put a line through that bitch."
aqwertd · 385 points · Posted at 20:43:01 on February 13, 2016 · (Permalink)
An interesting application of this theorem is that an any given time, there must be a location on Earth where the wind speed is zero.
chilly-wonka · 195 points · Posted at 22:02:19 on February 13, 2016 · (Permalink)
What theorem
Why must it be so?
EccentricWyvern · 159 points · Posted at 22:41:48 on February 13, 2016 · (Permalink)
Hairy ball theorem.
ghroat · 7 points · Posted at 02:27:26 on February 14, 2016 · (Permalink)
lol
mlkk22 · 1 points · Posted at 05:44:22 on February 14, 2016 · (Permalink)
theres a plethora of references in this thread
[deleted] · -2 points · Posted at 06:02:51 on February 14, 2016 · (Permalink)
so meta
karma3000 · 1 points · Posted at 12:00:31 on February 14, 2016 · (Permalink)
Nice try but most redditors are too young.
ThumbForke · 9 points · Posted at 23:38:44 on February 13, 2016 · (Permalink)
Imagine trying to rub all the fur on a sphere the same direction. The direction of the fur corresponds to the wind direction. So if you rub the fur down the whole way around the equator, and then continue to rub the fur in the same direction all over the sphere, the north and south poles will have no direction. There'll be like a little swirl around them, but right at the pole, you'll have the fur pointing in no particular direction.
This isn't a proof, just something to give you a bit of an intuition about it.
aixenprovence · 6 points · Posted at 22:49:55 on February 13, 2016 · (Permalink)
I think they meant to reply to this. See the Wikipedia article for the bit about the wind.
awhaling · 1 points · Posted at 15:41:07 on February 14, 2016 · (Permalink)
The hair ball theorem. Because all of the hairs on my balls may not gracefully blow in the same direction without a cowlick forming.
ophello · 0 points · Posted at 09:12:47 on February 14, 2016 · (Permalink)
Swirls. The center of a swirl is zero wind speed. It's impossible to arrange vectors on the surface of a sphere without a swirl somewhere.
JStealthy · 235 points · Posted at 21:49:55 on February 13, 2016 · (Permalink)
Hairy Ball Theorem?
Valetudo83 · 9 points · Posted at 02:57:19 on February 14, 2016 · (Permalink)
You are awarded no points. You must phrase your answer in the form of a question.
intensely_human · 7 points · Posted at 03:27:37 on February 14, 2016 · (Permalink)
What is the hairy ball theorem?
And no it doesn't because the atmosphere is not a surface it is a volume.
Dude13371337 · 0 points · Posted at 11:27:44 on February 14, 2016 · (Permalink)
Volume is just a stack of surfaces.
intensely_human · 3 points · Posted at 16:39:10 on February 14, 2016 · (Permalink)
Not true. Higher dimensional spaces have options that lower dimensional ones do not.
For example this is why printed circuit boards require two sides to function: it allows lines to cross.
Knots only exist in three and more dimensions.
In the case of wind it means that a given surface might have "zero speed" points but the wind is still moving there it's just moving up or down, ie outside of the "plane" of that surface.
Theorems true in 2D don't necessarily generalize to 3D.
The_Butters_Worth · 3 points · Posted at 04:43:40 on February 14, 2016 · (Permalink)
I think you were looking for Harry Baal.
MengerSpongeCake · 1 points · Posted at 21:00:22 on February 14, 2016 · (Permalink)
I'm Ron Burgundy?
Dexaan · 25 points · Posted at 23:32:40 on February 13, 2016 · (Permalink)
What is the Hairy Ball Theorem? I'll take Mathematics for 1200, Alex.
pikaras · 12 points · Posted at 00:05:28 on February 14, 2016 · (Permalink)
Or is blowing vertically (up/down)
jillyboooty · 4 points · Posted at 22:37:39 on February 13, 2016 · (Permalink)
Also, for any great circle of the earth (cross section through the middle), there are two points opposite each other with the same temperature. Pretty sure that's how it goes.
3_14159 · 8 points · Posted at 23:30:25 on February 13, 2016 · (Permalink)
This comes from the Intermediate Value Theorem!
TwoFiveOnes · 2 points · Posted at 04:12:27 on February 14, 2016 · (Permalink)
No? How so? I'm pretty sure it's the Borsak Ulam theorem, which is waaay hader than IVT
3_14159 · 2 points · Posted at 04:22:25 on February 14, 2016 · (Permalink)
Glad you asked! You can see the solution here: http://math.stackexchange.com/questions/715777/there-exist-two-antipodal-points-on-the-equator-that-have-the-same-temperature, where the solution also refers to the Borsak Ulam Theorem.
TwoFiveOnes · 1 points · Posted at 11:08:45 on February 14, 2016 · (Permalink)
Aah thanks, I guess that theorem is a sledgehammer here then. Much nicer with IVT!
rawling · 1 points · Posted at 08:28:14 on February 14, 2016 · (Permalink)
Same temperature and wind speed, or whatever.
sluuuurp · 3 points · Posted at 08:16:58 on February 14, 2016 · (Permalink)
Well that isn't really true because velocities of air particles do not quite behave like a 2 dimensional differentiable vector field.
Shnezzberry · 1 points · Posted at 23:31:37 on February 13, 2016 · (Permalink)
Hairy Ball Theorem?
PeNetrator15 · 1 points · Posted at 03:47:03 on February 14, 2016 · (Permalink)
Holy fucking shit. Mind=blown
A_Booger_In_The_Hand · 1 points · Posted at 05:07:48 on February 14, 2016 · (Permalink)
Says who?
[deleted] · 1 points · Posted at 05:22:57 on February 14, 2016 · (Permalink)
could be a single point at the center of a tornado though.
Zomplexx · 1 points · Posted at 05:31:54 on February 14, 2016 · (Permalink)
I'm not sure I understand... I've been outside many times when there was absolutely no wind. Do I live in a vortex? I'm not smart. I don't know what a vortex is.
bassinastor · 1 points · Posted at 08:30:14 on February 14, 2016 · (Permalink)
Technically yes, but that's not very useful. Speed is defined as distance over time, so at any point in time the wind vectors must be 0 at some point, but that point could be moving just as fast as the wind is.
Baldazar666 · 1 points · Posted at 13:16:36 on February 14, 2016 · (Permalink)
Are you sure about that? The earth is not a perfect sphere?
[deleted] · 1 points · Posted at 15:18:56 on February 14, 2016 · (Permalink)
Only the horizontal component
thatJainaGirl · 81 points · Posted at 23:17:14 on February 13, 2016 · (Permalink)
If you have a pizza with the radius z and the thickness a, its volume is calculated pi(z*z)a.
Jotakob · 4 points · Posted at 12:01:02 on February 14, 2016 · (Permalink)
Alternatively, for a pizza with radius z pi*z*z = A is also true
An0therB · 4 points · Posted at 07:07:50 on February 14, 2016 · (Permalink)
Pizza pi
nietzschetsefly · 5 points · Posted at 09:30:35 on February 14, 2016 · (Permalink)
What a splendid buy, pizza pizza pie, every minute every second buy buy buy buy buy
everyoneknowsabanana · 1 points · Posted at 15:20:31 on March 2, 2016 · (Permalink)
Yay for Murderous Maths!
dbers92 · 34 points · Posted at 02:14:46 on February 14, 2016 · (Permalink)
As lame as it may sound, last semester in an abstract algebra class we proved:
Anything * 0 = 0
&
A negative * A positive = A negative
22 years old and many years of schooling (aimed toward an applied math degree) and I finally was shown the proof of what is considered trivial by most people.
Obyeag · 29 points · Posted at 04:54:44 on February 14, 2016 · (Permalink)
Proof for those wondering:
x*1=x because 1 is the multiplicative identity.
x+0=x because 0 is the additive identity
A*(b+c)=A*b+A*c due to the distributive property
Prove A*0=0
A*1=A=A*(1+0)=A+A*0
A=A+A*0
Thus A*0=0
dbers92 · 5 points · Posted at 05:15:30 on February 14, 2016 · (Permalink)
I probably should have included this in the original post. Thanks for adding it!
Abomm · 2 points · Posted at 07:36:22 on February 14, 2016 · (Permalink)
Looks a lot like my coq homeworks
[deleted] · 0 points · Posted at 08:44:39 on February 14, 2016 · (Permalink)*
[deleted]
REMagic42 · 7 points · Posted at 10:42:09 on February 14, 2016 · (Permalink)
There you go.
[deleted] · 2 points · Posted at 05:29:50 on February 14, 2016 · (Permalink)
proof requires definition
fib16 · 87 points · Posted at 20:02:44 on February 13, 2016 · (Permalink)
I asked this a ways back. Really interesting answers.
https://www.reddit.com/r/AskReddit/comments/2owi8k/what_is_a_an_interesting_mathematical_fact_or_a/
G-O-single-D · 10 points · Posted at 23:46:24 on February 13, 2016 · (Permalink)*
Fixed the equation, looks a bit weird still but should be understandable.
n is greater than or equal to 1.
[ (0123...(n-1)) x 9 ] + n = sum{i=1->n}(10i-1)
(0 x 9) + 1 = 1
(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
Edit: Fixed equation.
The only thing I can figure out myself:
When n is greater than or equal to 11 you have to throw in (n-10) amount of zeroes between the outside digits.
1234567890 x 9 + 101 = 11,111,111,111
12345678901 x 9 + 1002 = 111,111,111,111
1234567890123 x + 10003 = 1,111,111,111,111
And so on. I'm guessing something will change once n=20 or 21.
Hedgehogs4Me · 3 points · Posted at 01:24:50 on February 14, 2016 · (Permalink)*
sum{i=1->n}(10i-1) would work for the right side, but it's not exactly elegant.
Edit: similarly, n+9(sum{i=1->n}((i-1)10n-i)) works for the left side but at that point I start to hate myself
narbris · 2 points · Posted at 05:45:57 on February 14, 2016 · (Permalink)
You messed it up after the 9th row.
(1234567900 x 9) + 11 =0 The reason is when you add 10 to the 1 is carried over to the 9 which becomes 10 and carries over a 1 to the 8 which becomes 9.
pikaras · 2 points · Posted at 10:06:12 on February 14, 2016 · (Permalink)
I'm sure you mean 123456780 x 9 and 1234567801 x 9....
The 10 carries over into the next digit and when added to 9 makes it 0. The 11,12,13... also carry over a 1 but add it to the ones place of the last number so it appears to simply skip the 9 and start over
G-O-single-D · 1 points · Posted at 22:55:37 on February 14, 2016 · (Permalink)
123456780 x 9 and 1234567801 x 9 don't work either.
The only thing I can figure out myself:
When n is greater than or equal to 11 you have to throw in (n-10) amount of zeroes between the outside digits.
1234567890 x 9 + 101 = 11,111,111,111
12345678901 x 9 + 1002 = 111,111,111,111
1234567890123 x + 10003 = 1,111,111,111,111
And so on. I'm guessing something will change once n=20 or 21.
noggin-scratcher · 10 points · Posted at 23:53:49 on February 13, 2016 · (Permalink)
I really quite like Cantor's diagonal argument, to show that there are more real numbers (or even, more real numbers between 0 and 1) than there are integers, even though both are infinite.
If you start out assuming that there's only one kind of infinity, then there's the same infinite number of integers as there is of reals. Hence also there must be some way to count all the real numbers, and make a 1-to-1 mapping from integers to reals and vice versa. So then if that's true you should be able to line them up in order.
For example, you could have a mapping like this:
#1 : 0.84385748398853492...
#2 : 0.32458735438291454...
#3 : 0.75649302034359684...
...
#n : 0.xxxxxxxxxxxxxxxxx...
and naively we might think that because there are infinite integers, every real number will end up somewhere in that list, even if we just assign them at random - there's an infinity of each type of number so no matter how many reals we think of we're never going to run out of integers to assign to count them with.
But then along comes Cantor and highlights a diagonal line down those rows of digits, to pick out the first digit of #1 and the second digit of #2 (and so on), and says "Consider the real number that we can construct by looking at the nth digit in the nth real and then picking any different digit to be the nth digit of our new number... where does that appear in the numbered list?"
But it can't appear in the list, because it's by-definition different from every entry in the list; different by at least that one digit that was deliberately set to be different from the nth digit of #n. Therefore there are too many reals to count, because we didn't count that one.
[deleted] · 2 points · Posted at 12:58:31 on February 14, 2016 · (Permalink)*
[deleted]
noggin-scratcher · 3 points · Posted at 16:23:09 on February 14, 2016 · (Permalink)
Hmm, you have a point that I'm not sure how to answer... in the general sense that numbers with different digits can nonetheless be equal, so demonstrating differing digits doesn't absolutely prove differing value.
It's a well established enough argument that I would be surprised if there were no answer to that, but being a distant admirer rather than a proper mathematician, I'm not going to be able to furnish you with that answer.
HumanAllergy · 2 points · Posted at 16:49:54 on February 14, 2016 · (Permalink)
It's because the list has to be an infinite attempt to list all numbers. You are creating a subset of this set that, by your definition, is countable.
[deleted] · -1 points · Posted at 17:21:45 on February 14, 2016 · (Permalink)*
[deleted]
HumanAllergy · 1 points · Posted at 18:19:51 on February 14, 2016 · (Permalink)
Does the number .2 exist on your list anywhere?
By your construction, it does not. Thereby you did not attempt to list all numbers, but listed a subset of them.
I'm fully aware of mathematical notation, thank you.
1, 2 ,3, 4, 5, ... Is an infinite list. Countable.
.1, .11, .111, .1111, .. Is an infinite list. I'm fairly certain it, too, is countable.
Cantor's argument is about uncountability. A different type of infinity.
[deleted] · -2 points · Posted at 18:24:42 on February 14, 2016 · (Permalink)*
[deleted]
HumanAllergy · 1 points · Posted at 18:32:17 on February 14, 2016 · (Permalink)
Again, I'm fully aware of this, having studied mathematics.
My point was that one of your premises was wrong for utilization of Cantor's proof.
I'm also impressed by you utilization of ad hominem during this discussion.
If you can't win, just insult. It's a surefire way to prove yourself right. Good on you!
aezart · 1 points · Posted at 08:20:17 on February 14, 2016 · (Permalink)
I've never understood this one. I do understand that there are different infinities, but I don't understand how that diagonal number can't be on the list.
noggin-scratcher · 3 points · Posted at 10:20:04 on February 14, 2016 · (Permalink)
It can't be the same number as #1 because it has a different 1st digit to #1
It can't be the same number as #2 because it has a different 2nd digit to #2
It can't be the same number as #3 because it has a different 3rd digit to #3
...
It can't be the same number as #n because it has a different nth digit to #n
The way that it's defined makes it different to every number in the list, no matter how you assign the numbers.
arbok_guy · 12 points · Posted at 04:02:50 on February 14, 2016 · (Permalink)
The Rule of 9's: You can determine if a number is divisible by 9 by adding up all the digits in the number. If the sum of the digits is divisible by 9, so is the original number. So for 81, 8+1=9 so 81 is divisible by 9. But for 719384715, 7+1+9+3+8+4+7+1+5 = 45, and 45 is divisible by 9, so 719384715 is too. And if you don't know 45 is divisible by 9, all you have to do is 4+5=9 and you know 9 is divisible by 9 (this matters more for super large numbers).
This can also be generalized, so for a base 6 system the same is true for determining if a number is divisible by 5. It works for n-1 in any base n system.
[deleted] · 9 points · Posted at 01:01:20 on February 14, 2016 · (Permalink)*
When you have two complex numbers (which are "real" numbers added to an "imaginary" number (5 + 3i; sqrt(2) + (pi)i; 0 + 0i; etc.) you can describe them (because they are essentially two-dimensional coordinates) as arrows, determined by length and their angle from the positive x axis. When you multiply two complex numbers, their length multiply, and their angles add. So when you multiply complex numbers, they rotate!
An example: 1 + i is a complex number with a length of sqrt(2) and a, angle of 45 degrees from the x-axis: (1+ i)2 = (1+ i)(1+ i) = 12 + 2i + (i)2 = 1+2i-1=2i
Note that 2i has length 2 and an angle of 90 degrees!
edit: exponents in reddit's text environment don't obey order of operations.
heavyish_things · -2 points · Posted at 03:32:18 on February 14, 2016 · (Permalink)
That's a circular argument. You're saying it's cool that complex numbers can use vector mathematics but that's only true because complex numbers are a representation of vectors.
[deleted] · 3 points · Posted at 05:55:18 on February 14, 2016 · (Permalink)*
I really hope you're making a pun with "circular argument". Besides, my point isn't that they are a vector space. I bring that up only to call attention to representing them in polar form. The point is that rotation (one of the dare I say "transcendental" ideas in mathematics) is built into that vector space! In the complex plane rotation is a totally diagonalizable transformation, and accomplished through multiplying by a unimodular constant!
bryceguy72 · 9 points · Posted at 02:55:25 on February 14, 2016 · (Permalink)
It's possible to ride a square-wheeled bicycle so that your ride is perfectly smooth (your center of mass doesn't bob up and down at all). You have to ride the bike on an upside down catenary curve, which is the curve formed by a rope or chain suspended at both ends (it's not a parabola). Here's CGI of such a bike: https://www.youtube.com/watch?v=0BtZcmEkFsI
tahitiisnotineurope · 1 points · Posted at 04:12:42 on February 14, 2016 · (Permalink)
Catenary Curve = canadian roads
[deleted] · 59 points · Posted at 20:02:27 on February 13, 2016 · (Permalink)
The nr of possible orders in which the 52 cards in a stack of cards can be stacked:
80658175170943878571660636856403766975289505440883277824000000000000
So, each time you stack cards, it's very likely that it's the first time in history in which the cards have been stacked in that exact order. Of course, you can never know for sure, but it's still pretty cool.
Solopete_HD · 39 points · Posted at 22:51:09 on February 13, 2016 · (Permalink)
...aaaaaaand I still get the worst cards.
waiting_for_rain · 9 points · Posted at 01:43:24 on February 14, 2016 · (Permalink)
RNGsus
-LiberaMeFromHell- · 4 points · Posted at 00:05:18 on February 14, 2016 · (Permalink)
Never lucky
The_Enemys · 5 points · Posted at 01:51:00 on February 14, 2016 · (Permalink)
Other people have already had the good combos
0876 · 6 points · Posted at 23:21:21 on February 13, 2016 · (Permalink)
Saw this posted above which will help to demonstrate the incomprehensible enormity of that number.
noggin-scratcher · 5 points · Posted at 23:33:57 on February 13, 2016 · (Permalink)
If your shuffle is truly random, in the sense that each possible ordering of the cards is equally likely. If you start with a new in-order deck and do one or two quick shuffles then you'll be much more likely to duplicate an order that someone else created before by doing the exact same thing.
aezart · 1 points · Posted at 08:11:01 on February 14, 2016 · (Permalink)
According to numberphile, 7 good riffle shuffles is sufficient.
IAMA_dragon-AMA · 3 points · Posted at 02:14:25 on February 14, 2016 · (Permalink)
Yes, but the probability is much higher than your comment seems to suggest. IIRC, when computerized card games first started up, some people familiar with those games IRL thought the computer was cheating, since they were dealt hands with different frequencies than occurred IRL - of course, the computer's shuffle was close enough to random distribution that the more likely explanation was that real shuffled cards resulted in less varied patterns.
bunker_man · 2 points · Posted at 07:07:55 on February 14, 2016 · (Permalink)
Unless you're really shitty at shuffling.
chief_dirtypants · 1 points · Posted at 23:19:46 on February 13, 2016 · (Permalink)
What a joker.
jayfeather314 · 1 points · Posted at 18:58:22 on February 14, 2016 · (Permalink)*
If you shuffle perfectly, it's extremely likely nobody has ever gotten that combination of cards in that order before. I'm on mobile so I don't feel like linking but check out VSauce's most recent video to see just how huge 52! is.
[deleted] · 1 points · Posted at 19:16:26 on February 14, 2016 · (Permalink)
Dude did you even read my comment?
jayfeather314 · 1 points · Posted at 21:48:09 on February 14, 2016 · (Permalink)
Why do you ask?
makemerepete · 26 points · Posted at 04:57:21 on February 14, 2016 · (Permalink)
Combo math / biology fact: average number of heartbeats per lifetime is a constant among mammals.
crusoe · 12 points · Posted at 05:37:39 on February 14, 2016 · (Permalink)
But all mammals no matter their size take about 20 seconds to empty their bladder completely. From the shrew to the elephant..
Kjbcctdsayfg · 6 points · Posted at 06:33:49 on February 14, 2016 · (Permalink)
This is actually not the case.
Source: http://biomedgerontology.oxfordjournals.org/content/62/2/149.long
[deleted] · 1 points · Posted at 15:30:05 on February 14, 2016 · (Permalink)
This paper doesn't mention resting/active heart rate at all...
Kjbcctdsayfg · 1 points · Posted at 15:42:51 on February 14, 2016 · (Permalink)
The overall metabolic rate has been argued as the underlying factor that links life spans with heart rate. In the paper, the authors conclude that there is no significant correlation.
For more direct counter-examples, see also https://www.reddit.com/r/todayilearned/comments/1jmimk/til_all_mammals_have_around_one_billion/cbg8lj3
Total heartbeats per lifetime is far from 'a constant' unless you allow for a variation of more than 50%.
candlecrusher · 21 points · Posted at 20:33:30 on February 13, 2016 · (Permalink)
I never quite understood why, but my calc prof told my class that if your sum all numbers 1 - Infinity in different orders you get different answers.
almightySapling · 11 points · Posted at 22:42:39 on February 13, 2016 · (Permalink)
We should speak more carefully.
If you add "all numbers from 1 - Infinity" which I can only presume means "the natural numbers" then this is a false statement. No matter how you arrange the terms, the series diverges to infinity.
Also, there are plenty of convergent sequences that also don't have this property.
What he should have said is "given an infinite sequence of numbers whose series converges but does not converge absolutely, and given any real number r, the sequence can be rearranged such that the sum is r."
For this to work, your sequence of numbers needs to have infinitely many positive numbers and infinitely many negative numbers.
candlecrusher · 2 points · Posted at 23:00:50 on February 13, 2016 · (Permalink)
Ahhhh, that makes more sense. I imagine that's exactly what he said. This was around 2 years ago and I always thought it was along the lines of what I posted and wondered how that made sense. I just assumed he knew much more then I did.
I'll show myself out.
F-0X · 15 points · Posted at 22:04:27 on February 13, 2016 · (Permalink)
Riemann Rearrangement theorem
481x462 · 2 points · Posted at 23:05:54 on February 13, 2016 · (Permalink)
"in different orders you get different answers" can be easier seen if we take the sum: 1 - 2 + 3 - 4 + 5 - 6 + 7 ...
(1 - 2) + (3 - 4) + (5 - 6) + (7 ... = -1 + -1 + -1 ... tends to negative infinity.
1 + (3 - 2) + (5 - 4) + (7 - 6) ... = 1 + 1 + 1 ... tends to infinity.
All the same terms summed in a sufficiently clever order can land on any number you want in between.
REMagic42 · 1 points · Posted at 10:40:36 on February 14, 2016 · (Permalink)
Even 0.5 or 0.12083109, right?
481x462 · 1 points · Posted at 02:27:10 on February 15, 2016 · (Permalink)
Yea. I think.
I could do it easily if I just slip in terms of +a -a that would cancel each other out, and have the sum converge to a.
Without those sneaked in, but using the type of summation that says 1 - 1 + 1 - 1 + 1... = 0.5, I could arrange the sum to equal any real number.
PKMNtrainerKing · 0 points · Posted at 21:32:33 on February 13, 2016 · (Permalink)*
1+3+2= 6
3+2+1= 6
Do that but with every number
Edit: the reason adding every number from 1 to infinity in a different order will give you the same answer is because it doesn't matter what gets added first, i was trying to give an example
Second edit: in my defense i failed high school algebra. I'm not good at math. Sorry i was wrong
candlecrusher · 7 points · Posted at 21:42:37 on February 13, 2016 · (Permalink)*
Yes but what I'm saying is that if you change the order of the number while going to infinity the answers will be different. Yours are the same. It doesn't work with a set amount of numbers. It's something to do with limits and summation series.
Edit: Don't worry bud. My wording made me wrong too. Lets just quietly leave and leave the math to the math people.
Duuhh_LightSwitch · 1 points · Posted at 21:52:50 on February 13, 2016 · (Permalink)
?
22fortox · 1 points · Posted at 22:44:27 on February 13, 2016 · (Permalink)
That isn't what he said, he said it will give you different answers if you change the order.
anthli · 8 points · Posted at 04:30:00 on February 14, 2016 · (Permalink)
Mentally squaring any number with 5 in the ones digit.
Example: 65. 52 = 25. Then, take the 6 and multiply it by itself plus 1, so 6 * (6 + 1) = 6 * 7 = 42. Take the 42 and put it in front of 25, resulting in 4225 = 652.
[deleted] · 269 points · Posted at 22:10:33 on February 13, 2016 · (Permalink)
Well, look into my eyes and it's easy to see, 1 and 1 makes 2, 2 and 1 makes 3. It was destiny.
aixenprovence · 50 points · Posted at 22:55:45 on February 13, 2016 · (Permalink)
Once every hundred thousand years or so, when the sun doth shine and the moon doth glow...
aaronclements · 31 points · Posted at 23:21:18 on February 13, 2016 · (Permalink)
And the grass doth growwww...
Therose86 · 29 points · Posted at 00:06:26 on February 14, 2016 · (Permalink)
It's needless to say, the beast was stunned.....
gansmaltz · 25 points · Posted at 00:42:01 on February 14, 2016 · (Permalink)
Whip crack went his whuppet tail!
CethinFusasaki · 22 points · Posted at 01:14:49 on February 14, 2016 · (Permalink)
And the Beast was done.
The_Great_Kal · 22 points · Posted at 02:10:19 on February 14, 2016 · (Permalink)
He asked us, snort, be you angels?
shmameron · 22 points · Posted at 02:57:42 on February 14, 2016 · (Permalink)
And we said "Nay,
We are but men."
ROCK!
Albert_Cole · 16 points · Posted at 03:53:00 on February 14, 2016 · (Permalink)
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOON!
OOOOOOOOOOOOOOON!
OOOOOON!
TsMAmp · 13 points · Posted at 04:37:10 on February 14, 2016 · (Permalink)
OOOOOoooOOOOOOOooooooh. This is not the greatest song in the wo-orld.
mybustersword · 7 points · Posted at 04:56:26 on February 14, 2016 · (Permalink)
This is just a TRIBUTE
Dcoil1 · 7 points · Posted at 05:01:12 on February 14, 2016 · (Permalink)
Couldn't remembe-e-er, the greatest song in the wor-horld!
starkinmn · 4 points · Posted at 11:30:32 on February 14, 2016 · (Permalink)
This is a trib yoooooot
[deleted] · 2 points · Posted at 17:23:19 on February 14, 2016 · (Permalink)
oooooh, to The Greatest Song in the World,
Mr_Bubbles69 · 3 points · Posted at 07:21:39 on February 14, 2016 · (Permalink)
Yea. No. This is just a tribute.
ChRoNicBuRrItOs · -1 points · Posted at 08:22:21 on February 14, 2016 · (Permalink)
Doned*
Nathan-Sharp · 1 points · Posted at 07:35:31 on February 14, 2016 · (Permalink)
Is it not forked tail (with forked pronounced as forkèd)?
gansmaltz · 2 points · Posted at 15:25:28 on February 14, 2016 · (Permalink)
Not according to the Vevo video's lyrics
Nathan-Sharp · 1 points · Posted at 15:53:19 on February 14, 2016 · (Permalink)
My bad then
dude_pirate_roberts · 1 points · Posted at 08:00:54 on February 14, 2016 · (Permalink)
Did gire and gimble in the wabe!
ajschm · 2 points · Posted at 00:26:32 on February 14, 2016 · (Permalink)
And the grass doth grow-ooooohhhhhh
GuTTeRaLSLaM · 1 points · Posted at 23:21:40 on February 13, 2016 · (Permalink)
And the grass doth groooooooooow
abedneg0 · 1 points · Posted at 02:55:00 on February 14, 2016 · (Permalink)
Is this somebody's convoluted way of asking for a threesome?
Zaev · 1 points · Posted at 04:22:19 on February 14, 2016 · (Permalink)
One and one don't make two; one and one make one.
[deleted] · 1 points · Posted at 06:24:59 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 20:16:51 on February 14, 2016 · (Permalink)
Indeed.
Triquetra4715 · 1 points · Posted at 21:18:16 on February 14, 2016 · (Permalink)
Did you say that out loud?
[deleted] · 1 points · Posted at 00:40:47 on February 15, 2016 · (Permalink)
No, of course not, well I mean maybe, possibly, well in retrospect it's quite possible, well it makes sense.... yes, okay yes i did
elimisteve · 8 points · Posted at 01:36:12 on February 14, 2016 · (Permalink)
1/81 is 0.012345679 repeating, which is ALMOST digits 0 through 9 in order, except the 8 is missing.
[deleted] · 2 points · Posted at 01:45:16 on February 14, 2016 · (Permalink)
Numberphile talks about this:
https://www.youtube.com/watch?v=daro6K6mym8
mikefightmaster · 7 points · Posted at 02:43:42 on February 14, 2016 · (Permalink)
That every second that passes, we as the human race collectively experience about 237 years.
theluckkyg · 2 points · Posted at 16:21:07 on February 14, 2016 · (Permalink)
It really fucks me up every time I look at a YouTube video's statistics and it says how many years have been spent watching the video.
47dniweR · 8 points · Posted at 02:59:27 on February 14, 2016 · (Permalink)
Probably more of a trick than a fact, but most numbers 2 digits or larger, revert back to 9 in just a few steps by adding them together then subtracting the result from the original number. No idea why this works. Sometimes an additional step is required.
14...1+4 is 5, 14-5=(9)
35... 3+5 is 8, 35-8=27, 2+7=(9)
1154... 1+1+5+4=11, 1154-11=1143, 1+1+4+3=(9)
RamThe3rd · 3 points · Posted at 03:05:03 on February 14, 2016 · (Permalink)
This is the first time math has ever left me in awe.
47dniweR · 3 points · Posted at 03:13:08 on February 14, 2016 · (Permalink)
This has always fascinated me. Must be something special about the number 9.
orcscorper · 2 points · Posted at 05:24:07 on February 14, 2016 · (Permalink)
It's special because it's one less than ten. If humans had eight fingers, we would probably use base-8. Then seven would be special.
Problem119V-0800 · 3 points · Posted at 07:00:03 on February 14, 2016 · (Permalink)*
It's a variation on the "casting out 9s" trick, which I learned as a way to check whether a number is divisible by 9 (or 3): add all the digits together, if the sum has multiple digits do it again, and if the final result is 9 the original was a multiple of 9; if the final result is 3,6,9 the original was a multiple of 3. In general the final result has the same remainder when divided by 9 as the original number did.
To see why this works, think of the number 7154 as 7000 + 100 + 50 + 4, that is, consider each digit's value separately. Now think about what happens if you have a number like 7000 and remove the last 0: you've removed a 10*700, and added 1*700, or in other words, you've subtracted 9*700. Whatever the digit is, 9*X00 is a multiple of 9. So if you lop off all the trailing zeroes, you've subtracted a multiple of 9. Meaning the remaining number has the same residue (remainder) mod 9 as the original. That residue is kept when you add up the digits, and also when you repeat the process until you are left with a single digit.
In your trick, the first time you do the subtraction, you subtract [a multiple of 9 plus a residue equal to the original number's residue] from your number, leaving you with a number with no residue, that is, it's guaranteed to be a multiple of 9. After that you're just subtracting more multiples of 9 until you reach a single-digit multiple of 9, which can only be 0 or 9.
This also explains why 9 is special for tricks like this. It's one less than our number base, and when you lop off a zero, you're involving the number base.
diablo-solforge · 8 points · Posted at 04:41:21 on February 14, 2016 · (Permalink)
If you start with the number 41, and add 2, then 4, then 6, then 8, etc., to obtain the sequence 41, 43, 47, 53, 61, etc., then the first 40 numbers in this sequence are all prime numbers.
Source: mathematician guy in the 90s PC game Rama (based on the Arthur C. Clarke book).
WeAreGlidingNow · 2 points · Posted at 11:40:37 on February 14, 2016 · (Permalink)
I believe the source is even older. The Polish mathematician Stanislaw Ulam was doodling in the 1960s, and came up with his famous spiral. I think the idea of starting at 41 is a derivative of his work.
EDIT: I am wrong! Wow, learn something new everyday. Wikipedia says...
In a passage from his 1956 novel The City and the Stars, author Arthur C. Clarke describes the prime spiral seven years before it was discovered by Ulam. Clarke did not notice the pattern revealed by the prime spiral because he never actually performed the experiment.
diablo-solforge · 1 points · Posted at 12:42:57 on February 14, 2016 · (Permalink)
Cool, TIL!
Hedgehogs4Me · 6 points · Posted at 01:20:18 on February 14, 2016 · (Permalink)
Holy smokes, has no one taken the best one yet, or at least the one with the best source? I imagine someone has but I can't find it with ctrl-f in the top 200 comments.
ii (sqrt(-1) to the power of sqrt(-1), to be clear) is about 0.208.
And now, the source (nsfw).
Magiwarriorx · 6 points · Posted at 02:38:01 on February 14, 2016 · (Permalink)
The Banach-Tarski paradox. It states that you can take a mathematical spheres, cut it into a finite number of pieces, and with a finite number of rotations, assemble two spheres identical to the first. Not half as small, not similar. Two spheres identical to the first. This means you can make an infinite number of mathematical spheres from only one sphere. The reason for this is that, unlike a physical sphere, a mathematical sphere is an infinitely dense set of points. When you assemble the two daughter spheres, each is half as dense as the first. However, since the first sphere is infinitely dense, the resulting spheres are ∞/2 dense, which is still ∞. Thus, the daughter spheres are identical to the parent sphere.
iluvgrannysmith · 1 points · Posted at 02:48:31 on February 14, 2016 · (Permalink)
Is this that whole situation where you can split up a pea and make it equal to the size of the earth?
Magiwarriorx · 3 points · Posted at 03:18:45 on February 14, 2016 · (Permalink)
Absolutely! To quote Wikipedia:
"A stronger form of the theorem implies that given any two "reasonable" solid objects (such as a small ball and a huge ball), either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox"."
hbcproeagle · 6 points · Posted at 03:13:32 on February 14, 2016 · (Permalink)
26 is the only natural number sandwiched between a perfect square and perfect cube.
fortheloveofscience_ · 5 points · Posted at 10:19:00 on February 14, 2016 · (Permalink)
A quick and easy way to convert Miles to Kilometers using the Fibonacci sequence.
0, 1, 1, 2, 3, 5, 8, 13
all approx: 3mi = 5km 5mi = 8km 8mi =13km
Michafiel · 1 points · Posted at 10:20:51 on February 14, 2016 · (Permalink)
Oh damn this is pretty cool.
ecco311 · 1 points · Posted at 10:24:42 on February 14, 2016 · (Permalink)
I live in Europe, so I will not need it that often...
But damn :O That's so good
Never ever realized how close 1 mile/km is to the golden ratio
DerrickCreamer · 1 points · Posted at 21:48:19 on February 14, 2016 · (Permalink)
Now if only I could remember which one is bigger.
Scarecrow1779 · 5 points · Posted at 14:48:34 on February 14, 2016 · (Permalink)
Here's an algebra trick i learned in middle school.
x = 1 , y = 1
x = y
xy = y2
xy - x2 = y2 - x2
next you factor both sides.
x (y-x) = (y+x) (y-x)
then you cancel out the common factors on both sides.
x
(y-x)= (y+x)(y-x)x = y+x
1 = 2
Tada!
The trick is that when you cancel out (y-x) from both sides, you are actually dividing both sides by y-x (which is equal to zero). This is an easy-ish way to show somebody why you aren't allowed to divide by zero.
[deleted] · 28 points · Posted at 21:39:23 on February 13, 2016 · (Permalink)
9+10=19. Not 21, you fucking idiots. Let that meme stay in 2015 where it belongs.
NoesHowe2Spel · 17 points · Posted at 02:12:15 on February 14, 2016 · (Permalink)*
Similarly: 1.3 billion/300 million is 4, not 4 million (to one significant figure). Some people didn't understand that
bazir03 · 6 points · Posted at 06:42:10 on February 14, 2016 · (Permalink)
Maybe they used real billions and not the false ass amerikanski helldog ones
Scuderia · 2 points · Posted at 06:36:51 on February 14, 2016 · (Permalink)
It's actually 0.00433333333 b/m.
heap42 · 5 points · Posted at 00:04:35 on February 14, 2016 · (Permalink)
a Perfect 5/7
[deleted] · 1 points · Posted at 00:04:53 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 00:38:02 on February 14, 2016 · (Permalink)
Look up "21 Vine"
perseenliekki · 11 points · Posted at 21:56:35 on February 13, 2016 · (Permalink)
If you have a conditionally convergent series (that is, a series which converges but the sum of the absolute values of the terms diverges), then you can rearrange the terms to make it converge to any real number.
For example, the series 1–1/2+1/3–1/4+... converges to ln(2), but by rearranging the terms it can be made to converge to 1,000,000.
heap42 · 9 points · Posted at 23:17:08 on February 13, 2016 · (Permalink)*
There are some... one is probably, Gödels Incompleteness Theorem... Even though i dont understand it, its still awesome.
EDIT: I understand what the theorem states and I undetand the implications, i just dont understand or rather i cannot follow Gödels Proof itself. The enitire thing with his Numbering etc... it just is to much for me... maybe at a later point in time.
[deleted] · 7 points · Posted at 05:45:59 on February 14, 2016 · (Permalink)
I'll give it a quick shot.
A formal logic consists of a set of strings. Theorems, for lack of a better word. Mathematics is then about deciding whether each of these strings is true or false.
Given a finite set of axioms (strings which are assigned a truth value to start) and laws of inference (which allow us to extract a truth value from another strings truth value). We'd like to be able to say the following.
for all strings x, x can never be proven to be both true and false. for all strings x, x can always be proven to be either true or false.
For this would mean that Mathematics is never in vain.
We'd like to, but for any formal logic which is sufficiently complex to allow you to enumerate the theorems of the logic itself (which is much less complex than you'd think), it is impossible.
The proof is a lot more detailed than this, but the result is worth knowing on its own.
heap42 · 1 points · Posted at 15:30:47 on February 14, 2016 · (Permalink)
yea i understand... but can you proof it, thats what i have trouble with... it makes sense, and i understand what it says... but i wouldnt be able to prove it to you.
MrWoohoo · 2 points · Posted at 06:47:09 on February 14, 2016 · (Permalink)
I came looking for this answer and found it at the bottom of the page. :( My lay understanding is that it says that in any logical system (capable of expressing arithmetic) there will be statements/theorems/conjectures you can make but never prove true or false. His proof essentially starts with the statement "this statement is unprovable" and then uses math to prove its true. Badass math there. Again, that's my lay understating.
In the book "Pi in the Sky" (a fun overview of math history) the author points out that if you define a religion as a belief system where there are things you simply have to accept on faith because you can't prove them true or false them mathematics is a religion and the only one that can actual prove it's a religion with rigorous logic.
karma3000 · 2 points · Posted at 12:10:20 on February 14, 2016 · (Permalink)
Thank God for that!
heap42 · 1 points · Posted at 15:28:12 on February 14, 2016 · (Permalink)
I understand what it says... and i understand the implications... i just dont understand the proof itself.
MrWoohoo · 1 points · Posted at 05:38:57 on February 15, 2016 · (Permalink)
I was mostly writing it for others. I've toyed with the proof. My vague hand-waving sense is that the Godel numbering thing lead to a proof by paradox similar to the proof there is no largest prime. I never understood how his numbering system discerned between valid statements and gibberish of symbols, or even if it is required for the proof.
endorphins12 · 11 points · Posted at 23:17:17 on February 13, 2016 · (Permalink)
Tupper's Self-Referential Formula.
That's a 7 minute video describing the formula and what it is (and it describes it better than I'll ever be able to). Essentially it's a bitmap (106 x 17 pixels) that will eventually display every possible sequence of pixelated images when given the correct starting 'y' coordinate.
[deleted] · 1 points · Posted at 03:24:15 on February 14, 2016 · (Permalink)
So, what's the plot in the book showing?
kogasapls · 2 points · Posted at 08:58:48 on February 14, 2016 · (Permalink)
It's Tupper's formula, but upside down and backwards and it says "Matt was 'ere" in it.
https://imgur.com/h9HVUPn.jpg
endorphins12 · 1 points · Posted at 19:08:31 on February 14, 2016 · (Permalink)
I don't know. Don't have the book so I can't check.
incathuga · 11 points · Posted at 01:30:04 on February 14, 2016 · (Permalink)
Somewhere on the earth, there are two points which are diametrically opposed (ie, exactly opposite of each other) that have the same temperature and air pressure. This is the three-dimensional case of the Borsuk-Ulam Theorem. The really interesting part is that while real-valued functions are typically the realm of the branch of math known as analysis, it is easier prove this theorem using topology, a very different branch of math.
-Reddit_Account- · 26 points · Posted at 22:01:17 on February 13, 2016 · (Permalink)
(Credit to Vsauce)
The size of the number 52!
(The permeation a of cards in a deck)
Imagine you had a timer that counted down 52! seconds. How long would that be?
Let's say you stood on the equator. Every billion years, you take one step foreward. Once you made it around completely, you take one drop out of the Pacific Ocean. You continue doing this untill the pacific is empty. When the pacific is empty, you put one piece of paper on the ground. You refill the ocean and repeat this process untill the stack of paper reaches the sun.
And that would have barely made a dent in the time.
You would have to repeat this process 3,000 times to even come close to 52! seconds.
Edit: another cool math fact!
You take a standard piece of paper and you rip it in half and stack it, making a stance that is two pieces tall.
You do this again... 49 times.
The stack is now (paper)x250 pieces of paper thick.
To where would that reach? The roof, maybe? A story or two? A skyscraper? The clouds? The moon? Nope. It would reach to the sun.
NovaRunner · 5 points · Posted at 01:40:12 on February 14, 2016 · (Permalink)
This reminds me of this from "The Shepherd Boy" by the Brothers Grimm:
DrummerVim · 1 points · Posted at 07:49:27 on February 15, 2016 · (Permalink)
Personally, I think that's one hell of a bird!
[deleted] · 2 points · Posted at 01:02:03 on February 14, 2016 · (Permalink)
I think I'm retarded because it's not clicking
grandtorino · 2 points · Posted at 06:28:34 on February 14, 2016 · (Permalink)
About the second part, wouldn't I just have a stack of 100 sheets, or are you ripping the entire stack in half each time?
-Reddit_Account- · 2 points · Posted at 12:57:32 on February 14, 2016 · (Permalink)
You're not just adding a new sheet every time, you're doubling the stack. So it would look like this;
So, by doubling a single piece of paper 50 times you end up with a stack that is 1 quadrillion pieces of paper thick, which could reach the sun with ease.
Here's a graph
grandtorino · 1 points · Posted at 15:14:40 on February 14, 2016 · (Permalink)
Ok, thanks for clarifying.
-Reddit_Account- · 3 points · Posted at 15:16:50 on February 14, 2016 · (Permalink)
No problem :)
[deleted] · 1 points · Posted at 01:09:36 on February 14, 2016 · (Permalink)
Do you have a link to the video? Thanks.
[deleted] · 1 points · Posted at 02:50:28 on February 14, 2016 · (Permalink)
A google search would probably be faster than writing that comment.. ohay look at this
-Reddit_Account- · 1 points · Posted at 03:55:49 on February 14, 2016 · (Permalink)
https://m.youtube.com/watch?v=ObiqJzfyACM
Here you go
PlasmicDynamite · 66 points · Posted at 19:07:31 on February 13, 2016 · (Permalink)
0!=1
grawies · 225 points · Posted at 20:56:34 on February 13, 2016 · (Permalink)
I like how this reads as "0 factorial is 1" with my mathematics glasses on but "0 does not equal 1" with the programmer glasses - and both statements are true! :)
dj0 · 19 points · Posted at 02:36:14 on February 14, 2016 · (Permalink)
And 1=0! is like an absurd statement with an exclamation mark at the end to show it's not true
lw9k · 4 points · Posted at 08:14:54 on February 14, 2016 · (Permalink)
It's also a surprised person with a bowtie and an arrow on his head
AluminiumSandworm · 1 points · Posted at 08:27:45 on February 14, 2016 · (Permalink)
me_irl
Ardub23 · 1 points · Posted at 11:15:38 on February 14, 2016 · (Permalink)
11. 0-0-0!
samlee405 · 2 points · Posted at 06:43:00 on February 14, 2016 · (Permalink)
What I'm interested in knowing is what you thought of first. I'm working on degrees in math and computer science so I'm in sort of the same boat as you but for whatever reason I think I'll always consider the mathematical angle first.
grawies · 3 points · Posted at 13:48:49 on February 14, 2016 · (Permalink)
Me too! It must be the lack of monospace font.
Felix_Tholomyes · 59 points · Posted at 20:26:16 on February 13, 2016 · (Permalink)
That's just a definition, hardly an interesting result
vocamur09 · 37 points · Posted at 21:28:40 on February 13, 2016 · (Permalink)
I like the explanation that relates factorials to permutations. How many ways can arrange two objects? 2! = 2. How many ways can you arrange no objects? 0! = 1
The_Great_Kal · 5 points · Posted at 02:31:22 on February 14, 2016 · (Permalink)
And nothing can only be arranged one way.
37casper37 · 3 points · Posted at 08:45:17 on February 14, 2016 · (Permalink)
Ehm, I actually cannot arrange zero objects at all.
vucislav · 1 points · Posted at 03:29:59 on February 14, 2016 · (Permalink)
Exactly the way that I was taught
F-0X · 22 points · Posted at 22:01:13 on February 13, 2016 · (Permalink)
It's a definition if you are lazy.
It is a result if you define n! to be the number of bijections from a set of cardinality n to itself.
I agree it's not an interesting result, but it's not just a definition. By definition of a function (i.e., as a subset of a cartesian product) we are guaranteed a function from the empty set (which of course has cardinality 0) to any other set, the empty function. Consequently, there is one map from the empty set to itself; thus 0!=1.
AtomikTurtle · 4 points · Posted at 03:29:14 on February 14, 2016 · (Permalink)
You can also define factorials of real numbers through integration (gamma functions). The result 0! = 1 follows.
heap42 · 2 points · Posted at 23:55:54 on February 13, 2016 · (Permalink)
It also follows the pattern: n! =(n+1)! /(n+1)
datorangeguy · 2 points · Posted at 00:03:25 on February 14, 2016 · (Permalink)
which every programmer behind a factorial calculator vary much is.
KellogsHolmes · 3 points · Posted at 01:34:07 on February 14, 2016 · (Permalink)
From an Algebraian's point of view it makes sense that the empty product is equal to the neutral element of multiplication (and the empty sum is equal to the neutral element of addition) and since 0! is equal to the empty product thus it is equal to 1.
Really_Schruted_It · 2 points · Posted at 23:23:13 on February 13, 2016 · (Permalink)
Much more interesting when you write 1=0!
trampabroad · 1 points · Posted at 08:03:41 on February 14, 2016 · (Permalink)
ZERO! ....equals one.
Bashar_Al_Dat_Assad · 1 points · Posted at 10:37:10 on February 14, 2016 · (Permalink)
Yeah.. Because it's defined to be.
reddevilvaibs · 1 points · Posted at 18:29:04 on February 14, 2016 · (Permalink)
Nah. There is only one way to choose nothing.
reddevilvaibs · 1 points · Posted at 18:29:59 on February 14, 2016 · (Permalink)
It is more intuitive if you think that there is only one way to choose nothing.
zeta12ti · 10 points · Posted at 15:44:43 on February 14, 2016 · (Permalink)
I'd like to nominate Yoneda's Lemma. To really understand it, you're going to need some background. So here goes...
Categories
A category is a way to organize structures in mathematics. Essentially a structure is represented by an "object" or "point" and a connection between two structures is represented by a "morphism" or "arrow" between the two objects.
For example, the category of sets has as objects sets (such as the collection of natural numbers {0,1,2,3,4,...} or {Hillary, Bernie, Donald, Ted}). The arrows between sets are functions. For example, there is a function {Hillary, Bernie, Donald, Ted} -> {0,1,2,3,4,...} taking each person to their age in years: Hillary -> 68, Bernie -> 74, Donald -> 69, Ted -> 45.
More generally, between any two sets S and T, there is a set of functions denoted Hom(S, T) from S to T.1 In fact this holds for all categories: for any two objects x and y, there is a collection of morphisms Hom(x, y) from x to y.2
Generally speaking, the categories used most frequently used in math are "sets with structure" as objects and "structure preserving functions" as morphisms. For example, consider the category of magmas. A magma is a set with a way of multiplying two elements together to get a third element. For example, the real numbers with their standard multiplication form a magma. A morphism between to magmas M and N is a function f from the set M to the set N such that for a and b in M, f(a*b) = f(a)*f(b).
However, categories are much more general than just sets with structure. The arrows could be something completely unrelated to functions. The set of natural numbers can be made into a category by making there be an arrow from a to b precisely when a ≤ b.
Now we're ready for the formal definition of a category. A category C is a collection of objects ob(C). For any two objects x and y, there is a collection Hom(x,y), called the morphisms from x to y. Additionally, we have a way to compose compatible morphisms. What this means is that we can take a morphism f from y to z and a morphism g from x to y and compose them to get a morphism f∘g from x to z.
This operation of composition has to satisfy
It's now possible to check that the category of sets and the category of natural numbers really do satisfy these properties. For natural numbers, this essentially follows from transitivity (a≤b and b≤c implies a≤c) and reflexivity (a≤a).
From now on I'll just work with arbitrary categories satisfying these properties. If you're really interested, it helps a ton to get familiar with the standard examples. If you aren't interested, just think of this as some crazy abstract math that falls way on the right in this picture.
Visualizing Categories
As I mentioned before, objects and morphisms in a category are sometimes called points and arrows. This refers to a standard way of visualizing a category, or some fragment of a category. For example, this image is a way of visualizing the composition of arrows. Whenever we have a picture like this, we say it commutes if we can compose along any path and get the same morphism either way. The example commutes because f∘g=f∘g. We'll get more technical commutative diagrams below when we talk about natural transformations.
Functors
The natural kind of morphism between two categories is called a functor. A functor is required to preserve all the structure of a category. Specifically, a functor F:C->D is a function on objects Ob(C) -> Ob(D) and morphisms Hom(x,y) -> Hom(F(x), F(y)). F must preserve identies: F(idₓ) must be the identity for F(x).3 F must also preserve composition: whenever f∘g is defined, F(f∘g) = F(f)∘F(g).
I mentioned before that lots of categories contain sets with structure. Every category like this has whats called a "forgetful functor" to the category of sets. This functor takes every set with structure to the underlying set and every structure preserving function to the underlying function between sets.
We've already met the most important example of a functor: the Hom functor. Let C be a category and let a be an object in C. Using Hom, we get a functor Hom(a, -):C->SET (the category of sets). We already know what Hom(a, b) is (the set of morphisms from a to b), so we know what Hom(a, -) does to objects. What about morphisms? Let f:b -> c be a morphism in C. Hom(a, f) ought to be a function from Hom(a,b) to Hom(a,c), so given g:a->b, and f, how can we get a morphism from a to c? The answer is composition: [Hom(a, f)](g) is defined to be f∘g. You can check that this really does define a functor, since Hom(a, id) maps g to id∘g = g, so it's the identity function. Hom(a, f∘h) maps g to (f∘h)∘g=f∘(h∘g) = [Hom(a, f)](h∘g)=[Hom(a, f)]([Hom(a, h)](g)), so Hom(a, f∘h) = Hom(a, f)∘Hom(a, h).
Hom has two variables, so we can ask what happens when we have an object c and look at Hom(-, c). It turns out that this is also a functor, but somehow reversed. Hom(f∘g, c) = Hom(g, c)∘Hom(f, c), rather than the other way around. such a thing is called a contravariant functor. Equivalently, we can reverse the composition in the original category to get the category Cop. Cop has the same objects and morphisms as C, but the direction of every arrow is reversed. Composition is also reversed: f ∘op g in Cop is defined to be g∘f in C. Hom(-, c) turns out to be a functor from Cop to SET, since Hom(f ∘op g, c)=Hom(f∘g, c)=Hom(f, c)∘Hom(g, c), so the order ends up the way we want it.
Natural Transformations
Functors themselves are an object in a certain category. For categories C and D, we can for the functor category [C, D] which has a objects functors from C to D and as morphisms natural transformations. For functors F and G from C to D, a natural transformation α:F -> G is a collection of morphisms αₐ: F(a) -> G(a) for every object a in C. A natural transformation is required to satisfy the naturality condition: for every morphism f: a -> b, G(f)∘α = α∘F(f) (where the first α is the morphism F(a) -> G(a) and the second is the morphism F(b) -> G(b)). This picture is the vizualization of this (for functors Φ and Ψ and natural transformation η).
Naturality occurs all over in mathematics. For example, Adjoint functors and the Tensor-Hom Adjunction . Other examples are the isomorphism from a finite-dimensional vector space into its double dual and the idea that two functors are the "same" even if they're literally different (natural isomorphism).
The Yoneda Lemma
Finally you have the terminology to understand the Yoneda lemma. The statement is simple: Let F:Cop -> Set be a functor and let c be an object in C. There is a one to one correspondence between elements of the set F(c) and natural transformations from Hom(-, c) to F. Moreover, this correspondence is natural in the variable c. That's it. The cool part is how many different applications this has.
Cayley's Theorem
Every group can be realized as a subgroup of a group of permutations. A group is a way of organizing the symmetries of something (in particular, every object x in a category has a group of automorphisms Hom(x,x).4). This follows from Yoneda's lemma by considering a group as a category with one object x and letting Hom(x,x) be your group.
Isbell Duality
I won't claim to understand this fully, but Yoneda's lemma the reason that Isbell Duality works. Isbell duality is a huge statement of the duality between algebra and geometry.
Representable Functors
Sometimes a functor is naturally isomorphic to a functor like Hom(c, -). Using the Yoneda lemma, we can show that if c exists, it's unique up to isomorphism.
Yoneda Embedding
Any category C can be embedded into the category [Cop, Set] via c -> Hom(-, c). The Yoneda lemma implies that this embedding preserves essential properties of C. However, [Cop, Set] is generally much "nicer" than C. For example, it's complete and cocomplete.
An example of the Yoneda embedding is the embedding of the rational numbers into the (extended) real numbers. Similarly to our natural numbers example above, the rational numbers can be made into a category. [Cop, Set] happens to be isomorphic to the reals plus infinity and -infinity. Completeness gives us all the nice properties of the reals.
Further reading
Since I'm running out of space, check out here and here for some other cools stuff.
1 Hom here stands for homomorphism, which is also where the word morphism come from.
2 When this collection is actually a set for any two objects x and y, the category is called locally small. See here for the reason we can't just assume this.
3 Why does Reddit not support subscripts globally? Any for that matter, why does Unicode not have subscripts for every letter (notably missing a subscript 'y')?
4 Actually just the isomorphisms from x to itself. A morphism is an isomorphism if it has an inverse.
creampieguy49 · 7 points · Posted at 16:34:14 on February 14, 2016 · (Permalink)
Too long for me to read, but upvote for pure effort champ
HewloTherexP · 1 points · Posted at 05:51:25 on February 18, 2016 · (Permalink)
tl;dr?
zeta12ti · 1 points · Posted at 08:01:13 on February 18, 2016 · (Permalink)
TL;DR: Yoneda's Lemma is a simple fact that has some profound consequences.
The majority of what I wrote isn't directly related to Yoneda's Lemma, but is required to understand the language of the statement.
(It's like how if you didn't understand multiplication and decimal notation, 11111111*11111111 = 123456787654321 wouldn't make any sense, but once you understand, you can easily check it).
brandonmfree5 · 5 points · Posted at 01:49:58 on February 14, 2016 · (Permalink)
When any 3 digit number where all the digits are the same(111, 222, 333) is divided by the sum of the digits, the quotient is always 37.
Haus42 · 4 points · Posted at 01:53:48 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Four_color_theorem : roughly that on any 2D map, there's a way to code the "countries" with 4 colors, so that no two adjacent countries have the same color. It took almost 140 years to be proven, and it was the first major theorem to be proven using computer assistance.
benmac89 · 2 points · Posted at 08:42:48 on February 14, 2016 · (Permalink)
Spent 6 months writing a dissertation on this at university - the paper mathematically proved that it could be done with 5 and then concluded by saying "hey it could be done with 4 but it's too hard so deal with it"
Mewcancraft · 5 points · Posted at 13:36:46 on February 14, 2016 · (Permalink)*
Can't remember where I saw this, but the expression "(12 + 144 + 20 + 3 * sqrt(4)) / 7 + (5 * 11) = 81 + 0" is a limerick:
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
Swate- · 1 points · Posted at 13:37:59 on February 14, 2016 · (Permalink)
Oh man I love this one.
mykeuk · 5 points · Posted at 15:09:56 on February 14, 2016 · (Permalink)
Take three random, different numbers. Now you have a 3 digit number. Now reverse the number so now you have two 3 digit numbers, one the reverse of the other.
Subtract the smaller from the larger.
Now you have a new number. Again, reverse it to make a new number, one the reverse of the other.
Add the two together.
Your answer is 1,089.
Example:
831 makes 138. So 831-138 = 693.
693 + 396 = 1,089
You can use this for a magic trick. Either write down the number 1,089 or get a book, go to page 10 and find the word that's 8 lines down and 9 words in and write that down. Then get 3 people to pick 3 separate numbers and use patter to make it sound like their choices are all completely random. Then, when the answer is 1,089 get them to check your prediction or check the book, then check what you'd written down.
iPreemo · 40 points · Posted at 19:07:52 on February 13, 2016 · (Permalink)
Tangent is slope...not all that cool but it's the first thing that popped into my mind.
hayberry · 14 points · Posted at 22:37:04 on February 13, 2016 · (Permalink)
I think the first time you achieve a crystal clear understanding of derivatives and the basics of calculus is just the most amazing feeling
ILIKEFUUD · 7 points · Posted at 02:54:41 on February 14, 2016 · (Permalink)
I took a precalculus class last year, and didn't get a thing. Started taking calc this year and WOOOOSH it was so cool to see everything I've learned all throughout school fall into place as a kind of mathematics.
ngwoo · 2 points · Posted at 00:43:23 on February 14, 2016 · (Permalink)
Calculus is super easy to explain and understand until you start getting pesky numbers involved
datorangeguy · 1 points · Posted at 23:37:27 on February 13, 2016 · (Permalink)
I believe he's talking about the tangent function, though. Not a tangent line.
hayberry · 6 points · Posted at 23:42:19 on February 13, 2016 · (Permalink)*
It's all the same really. The tangent function is the slope of the line tangent to a circle as it turns:
http://www.mathwarehouse.com/animated-gifs/images/graph-of-tangent-from-unit-circle.gif
Or if this is what you meant, copying form wikipedia, the Opp/Adj Tan function is "ratio of the length of the opposite side to the length of the adjacent side: so called because it can be represented as a line segment tangent to the circle":
https://upload.wikimedia.org/wikipedia/commons/4/45/Unitcircledefs.svg
datorangeguy · 2 points · Posted at 00:34:01 on February 14, 2016 · (Permalink)
That doesn't make any sense, though. At pi/4 rad the tangent line would have a slope of -1, the secant line would have a slope of 1. Tangent is the slope of the hypotenuse, which isn't tangent to a circle.
hayberry · 2 points · Posted at 01:39:26 on February 14, 2016 · (Permalink)
You can see it as purely the slope of the angle going from pi/2 to 3pi/2 (which makes the original gif make more sense), but the actual relation is that the tangent function maps the length of a line tangent to a circle at an angle. Take a look at this gif:
http://i.imgur.com/oPa38Fo.gif
Look at the red tangent line. As you move around the circle, the angle of the hypotenuse line creates a triangle with the red tangent line, and the length of the red line side of that triangle is the length that is plotted onto the tangent graph at its angle. For example, at pi/4, if you extend the hypotenuse to make a triangle with the red tangent line, the length of the right red side of that triangle would be 1, which is tan(pi/4). Because of right triangle properties, the length of this length actually ends up being equal to the angle of the tan angle. Here's a video that goes over the trig:
https://www.youtube.com/watch?v=6-tsSJx-P18
datorangeguy · 1 points · Posted at 01:54:17 on February 14, 2016 · (Permalink)
I'm aware of the all of this, but the slope of a tangent line isn't what's being output by the tangent function, it's just related in a somewhat convoluted way. Trust me, all of this "clicked" for me years ago. I understand everything there is to understand about tangent lines and the tan(x) function. All I was saying is that when he said "tangent is slope", your comment about the feeling of finally understanding derivatives wasn't really relevant when he was talking about the tangent function outputting the slope of the hypotenuse. Your comment lead me to believe that you thought he meant tangent lines touching functions.
hayberry · 3 points · Posted at 01:59:41 on February 14, 2016 · (Permalink)
It's not convoluted, it's the definition of the tangent function, and a fundamental part of why trigonometry was invented as a tool for understanding astronomical relationships, namely, distances.
My interpretation of what he was saying is that a tangent line is just the slope of a line at that point, which is the same as a derivative, hence my comment about calculus. You're the one who brought up the tangent function which, again, is still about a tangent line, hence why it's called the tangent function. It wasn't named just to confuse people.
datorangeguy · 1 points · Posted at 04:45:26 on February 14, 2016 · (Permalink)*
I didn't bring up the tangent function, he did. The parent/root comment of all this. tan(x) means input angle, output slope. That's what he was saying when he said "tangent is slope." That's what he was commenting about. Your calculus/derivative comment wasn't relevant. I said you were thinking of tangent lines, which although they are undeniably connected at a very intricate level with the tangent function, they are not interchangeable meanings of the word tangent. In his comment, "tangent is slope" is implicitly saying that the tangent function gives you the slope of the line. There's no other meaning behind the word "tangent" given the context provided by his comment, that could possibly make sense; the only thing you've commented that has provided any relevance to what you've been saying is "my interpretation of what he was saying..."
Only after you explained yourself was there any relevance in what you were saying at first.
And yes, it is convoluted. It's the same thing as, for example, the sine integral function. You can show a function that waves up and down, with precise outputs given precise inputs. You can go on and on about the applications in engineering, and for years just tell people to use a calculator to do calculations for Si(x). You can develop entire fields of study on that function, and still not bother with the origins of its name. You see, it's called the sine-integral function not because of all of these millions of definitions for the word "integral" not just in math, but in english, not because of all of these millions of definitions of the word "sine" again, within ENGLISH, but because the function is defined as the area from 0-input under the function y=sin(x)/x, which in purely mathematical terms is y=integral(0,x)[sine(t)/t]dt, aka integral[sin(x)/x]. You have to go out of your way in order to connect its name with the origin of its name. Therefore it's convoluted. Yes, it has a very good reason to be called the sine integral function, but the only way to explain to someone exactly why it's the specific words "sine integral" and not literally anything else is through a convoluted explanation. Which is exactly why the tangent function has an exclusively convoluted connection to the other definitions of the word "tangent" that we all know and love. It took you 3 comments to explain it to someone who already knew it, because you continued to convince yourself that it needed further explanation. How does that not seem convoluted to you?
hayberry · 1 points · Posted at 05:14:11 on February 14, 2016 · (Permalink)*
He said, and I quote, "Tangent is slope". No mention of the tangent function.
But it doesn't matter, because both the tan function and tangent lines are slope--tangent line is the slope of the graph at that point, the tan function is derived from the tangent line to a circle at an angle of a circle at that point. I don't see how someone who understands "everything there is to understand about tangent lines and the tan(x) function" isn't getting that.
Convoluted: "extremely complex and difficult to follow." Perhaps for some, but that doesn't change the fact that it's the definition of the tangent function. Just because its actual usage and derivation is more complicated than the formula they teach you in middle school doesn't make it something else. Opp/Adj is just easier to digest for children, but that does not change what the function actually represents.
[deleted] · 1 points · Posted at 06:45:44 on February 14, 2016 · (Permalink)
Yes! I remember the first time I understand the concept of a derivative. I know exactly the feeling you're talking about.
BeaverCleaver69 · 3 points · Posted at 01:34:19 on February 14, 2016 · (Permalink)
Makes sense, considering tan X = (opposite / adjacent) and slope is (change in Y/change in X) and if you simply imagine a right triangle, the opposite side length = the change in Y, and the adjacent side length = the change in X
everyoneknowsabanana · 1 points · Posted at 15:23:15 on March 2, 2016 · (Permalink)
And slope is just the derivative at a point. It is in fact very cool; awesome algorithms for become easy to understand when you know this.
[deleted] · -10 points · Posted at 19:40:52 on February 13, 2016 · (Permalink)
[removed]
[deleted] · -3 points · Posted at 20:32:06 on February 13, 2016 · (Permalink)
Are you autistic? You keep repeating this inane, pointless comment.
Schniffbert · 8 points · Posted at 22:52:27 on February 13, 2016 · (Permalink)
That the busy beaber function grows faster than any computable function.
CurrentlySingle · 1 points · Posted at 07:46:55 on February 14, 2016 · (Permalink)
I don't like Canada either.
[deleted] · -1 points · Posted at 05:30:07 on February 14, 2016 · (Permalink)
woo good answer.
legendariers · 37 points · Posted at 00:33:05 on February 14, 2016 · (Permalink)
I have a lot of truly marvelous facts, which this comment is too small to contain.
brainandforce · 7 points · Posted at 02:23:24 on February 14, 2016 · (Permalink)
ah, Fermat's last theorem
Fermats_Last_Account · 10 points · Posted at 04:02:47 on February 14, 2016 · (Permalink)
You called?
brainandforce · 2 points · Posted at 04:29:15 on February 14, 2016 · (Permalink)
Oh yeah.
[deleted] · 2 points · Posted at 06:29:16 on February 14, 2016 · (Permalink)
And, given how the proof of the theorem turned out, you are moat likely full of shit
REMagic42 · 1 points · Posted at 10:45:44 on February 14, 2016 · (Permalink)
Eh, the abc - conjecture would reduce the proof to one page or so.
apierson2011 · 3 points · Posted at 23:07:52 on February 13, 2016 · (Permalink)
My first calculus professor demonstrated this for our class, but I've since forgotten the actual equation;
A simple variation of the sine wave can be used the determine the exact number of hours of daylight in each day during the year, and the derivative of this equation shows why, at some times during the year, you can tell that the number of hours of daylight is changing, and you can't at other times (rate of change).
Pretty simple, nothing mind-blowing, but although I've always enjoyed math that was the first time I really appreciated calculus!
loozid · 1 points · Posted at 08:18:42 on February 14, 2016 · (Permalink)
Every curve is smaller segments of line put together, proven by the rate of change. I always found that fascinating as well. It makes me picture zooming into a point on a graph and how to define a graph and the visualization of data, and the infinite amounts of points from which you can acquire the average rate of change, and makes one question what a line is, if it has ever existed in nature, idk makes me think of that.
NumberMuncher · 5 points · Posted at 01:54:05 on February 14, 2016 · (Permalink)
The sum of the alternating infinite series:
1-(1/3)+(1/5)-(1/7)+(1/9).......=π/4
The left side seems like a simple enough pattern, but equals a quarter the ratio of a circle's circumference and diameter.
tl;dr Proof: the Taylor series and the inverse tangent
[deleted] · 4 points · Posted at 02:51:08 on February 14, 2016 · (Permalink)
The natural number e (2.71828....) can be obtained by the infinite sum 1/(n!) for n = 0 -> infinity.
Waniou · 2 points · Posted at 06:16:20 on February 14, 2016 · (Permalink)
That's not as cool as why that's the case.
We know that ex is a function made so that the derivative is ex . So how can we make that sort of a function?
Well, we know that the derivative of x2 is 2x, x3 is 3x2 and, in general, the derivative of xn is nxn-1 .
So, we basically just make a function where, if you differentiate each term, you get the previous one. So we start with 1, because the derivative of 1 is 0. The next term will be x, because its derivative is 1. Then we need x2 / 2. The derivative of x2 again is 2x, so we get 2x/2 = x. Again, the derivative of x3 is 3x2 so we need to divide our x2 / 2 by 3 so that it'll differentiate into it. In other words, x3 / 2*3 = x3 / 6 = x3 / 3!
From here, it's pretty easy to show that, to get the previous term in the equation when you differentiate, you just have xn / n!, and in other words, you get an infinite sum, xn / n! for n = 0 -> infinity. Or, in other words, ex = x0 / 0! (Or 1) + x1 / 1! (Or x) + x2 / 2! + ... + xn / n! + ... forever. If you differentiate each term in that, you always get the previous one.
And, of course, to get the actual natural number, 2.71828, you just let x = 1 and obviously get 1/(n!).
[deleted] · 1 points · Posted at 17:54:24 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 05:49:55 on February 15, 2016 · (Permalink)
You can get as picky as you wan't with the definitions, but the reason e is commonly referred to as "the natural number" is because it is the base of the natural logarithm.
[deleted] · 1 points · Posted at 11:37:54 on February 15, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 15:52:13 on February 15, 2016 · (Permalink)
I respectfully accept your insult. Note, I am not a mathematician, but I have had my fair share of math as an aerospace engineering PhD.
[deleted] · 3 points · Posted at 04:57:36 on February 14, 2016 · (Permalink)
[deleted]
dedcupid · -1 points · Posted at 05:21:09 on February 14, 2016 · (Permalink)
9x=8.99........ x=.999
Bluefire262 · 4 points · Posted at 05:05:33 on February 14, 2016 · (Permalink)
Its a joke, but still math related so ill throw it in here.
What does the middle initial of Benoit B. Mandelbrot stand for? Benoit B. Mandelbrot.
Dyne4R · 5 points · Posted at 14:42:23 on February 14, 2016 · (Permalink)
It's a basic one, but you can quickly tell if any number is divisible by three by adding the digits together. If the resulting number is divisible by three, then the original number is also divisible.
5,146,752 is divisible by three (5+1+4+6+7+5+2=30)
802,465,367,987,236,592 is not.
ck2839 · 1 points · Posted at 14:45:09 on February 14, 2016 · (Permalink)
The same test works for divisibility by 9.
RowThree · 3 points · Posted at 02:13:19 on February 16, 2016 · (Permalink)
9 x (any number) = a sum of digits equaling 9
e.g.
9 x 3 = 27. 2 + 7 = 9
9 x 61 = 549. 5 + 4 + 9 = 18. 1 + 8 = 9
9 x 3498 = 31,482. 3 + 1 + 4 + 8 + 2 = 18. 1 + 8 = 9
9 x 45,685,442,387 = 411,168,981,483. 4 + 1 + 1 + 1 + 6 + 8 + 9 + 8 + 1 + 4 + 8 + 3 = 54. 5 + 4 = 9.
[deleted] · 45 points · Posted at 20:05:30 on February 13, 2016 · (Permalink)*
[deleted]
ThereOnceWasAMan · 38 points · Posted at 20:23:43 on February 13, 2016 · (Permalink)
aka "Why do programmers get Christmas and Halloween mixed up?"
[deleted] · 12 points · Posted at 20:24:57 on February 13, 2016 · (Permalink)
[deleted]
NanotechNinja · 61 points · Posted at 22:15:14 on February 13, 2016 · (Permalink)
Because Oct 31 = Dec 25, in case anyone reading doesn't know the answer.
[deleted] · 4 points · Posted at 23:36:17 on February 13, 2016 · (Permalink)
Still makes no sense
NanotechNinja · 17 points · Posted at 00:27:55 on February 14, 2016 · (Permalink)
Oct 31 means 31 in base 8, "Octal" which is expressed as 25 in base 10, "Decimal".
[deleted] · 1 points · Posted at 03:37:52 on February 14, 2016 · (Permalink)
Thank you
aixenprovence · 5 points · Posted at 22:59:19 on February 13, 2016 · (Permalink)
This always weird me out. It's like God's fucking with us, because that's man-made (English!) notation, and the people who invented the notation didn't have those basically randomly-assigned holiday dates in mind when they invented it.
NanotechNinja · 13 points · Posted at 23:04:43 on February 13, 2016 · (Permalink)
Eh, I think of it as Bible Code/pareidolia/confirmation bias type shit. You're always gonna notice the weird coincidences more than the 363 other days that don't mean anything.
[deleted] · 13 points · Posted at 00:46:44 on February 14, 2016 · (Permalink)
I was just reading about the Bible Code 363 days ago! That's so crazy!
eudamme · 1 points · Posted at 00:50:46 on February 14, 2016 · (Permalink)
???
Thistlefizz · 1 points · Posted at 01:30:22 on February 14, 2016 · (Permalink)
I still don't get it.
philly_fan_in_chi · 1 points · Posted at 02:54:18 on February 14, 2016 · (Permalink)
Let _n denote "base n".
OCT31 = 31_8 = 3 * 81 + 1 * 80 = 25_10 = DEC25
Royal-Ninja · 1 points · Posted at 18:39:15 on February 14, 2016 · (Permalink)
25 in base 10 (decimal) is 31 in base 8 (octal).
sephrinx · 1 points · Posted at 08:23:21 on February 14, 2016 · (Permalink)
I don't get it.
ELI am utterly stupid, because that's how I feel.
hayberry · 1 points · Posted at 22:38:13 on February 13, 2016 · (Permalink)
Do mathematicians deal with other number bases often?
philly_fan_in_chi · 1 points · Posted at 02:55:43 on February 14, 2016 · (Permalink)
Computers are all base 2, and base 16 is used for memory addressing.
hayberry · 1 points · Posted at 03:00:48 on February 14, 2016 · (Permalink)
I know, I'm a programmer, but I'm asking about actual mathematicians. I'm trying to see where base theory is applicable outside of machines.
shockbot943 · 1 points · Posted at 04:30:46 on February 14, 2016 · (Permalink)
Physics major here ( had to take my fair share of math). Not really, the only reason to use different bases is when it makes computation easier. But most mathematicians don't even work with numbers anyways... Mostly variables. We use base ten because for one reason or another it allows our brains to comprehend bigger numbers. I may be wrong though so if an actual math wiz sees this, please correct me.
Edit - we could probably Google this but I'm too lazy
chilly-wonka · 1 points · Posted at 22:02:58 on February 13, 2016 · (Permalink)
uh... why?
ThereOnceWasAMan · 7 points · Posted at 22:05:30 on February 13, 2016 · (Permalink)
"Why do programmers get Christmas and Halloween mixed up?"
"Because DEC25 == OCT31"
(ie 25 in base ten is equal to 31 in base 8)
epursimuove · 2 points · Posted at 22:12:43 on February 13, 2016 · (Permalink)
' Dec 25 = Oct 31'
i.e., 25 in the (regular) decimal system equals 31 in octal, base 8, since 3x8 + 1 = 25.
DoNotUpvoteTooMuch · 1 points · Posted at 02:48:44 on February 14, 2016 · (Permalink)
The joke here is that Octal 31 (which abbreviated looks like October 31st, Halloween) is equal to Decimal 25 (which abbreviated looks like December 25th, Christmas).
https://www.idtech.com/blog/part-i-top-10-programmer-jokes-explained-for-the-rest-of-us/
jillyboooty · 3 points · Posted at 22:38:48 on February 13, 2016 · (Permalink)
huh?
boweruk · 15 points · Posted at 23:22:02 on February 13, 2016 · (Permalink)
Oct 31 = Dec 25
(base 8, octal)31 is the same as (base 10, decimal)25
onlytoask · 1 points · Posted at 02:17:03 on February 14, 2016 · (Permalink)
Man, you're an angry little fucker, aren't you?
[deleted] · 1 points · Posted at 23:36:24 on February 13, 2016 · (Permalink)
What?
[deleted] · -9 points · Posted at 23:37:49 on February 13, 2016 · (Permalink)*
[deleted]
GoldenDude · 1 points · Posted at 00:59:52 on February 14, 2016 · (Permalink)
How? I just checked and that doesn't make sense
[deleted] · 22 points · Posted at 03:00:07 on February 14, 2016 · (Permalink)
Why was 6 afraid of 7?
Cuz 7 8 9.
dmo012 · 14 points · Posted at 05:07:01 on February 14, 2016 · (Permalink)
Cause 7 is a registered six offender
-WPD- · 3 points · Posted at 07:03:05 on February 14, 2016 · (Permalink)
Six hasn't been the same since he left Vietnam. Every time he closes his eyes, he's sees Charlie hiding in the darkness of the forest. Not that you could ever see those bastards, mind you. They were fast and they knew their way around the jungle. He remembers the looks on the boy's faces when they walked into that village and... oh Jesus. He shouldn't think about that now. Sometimes he still hears Tex's slow southern drawl. He remembers the smell of Brooklyn's cigarettes. He always had a pack of Luckys. But the boys are gone now... he knows that. It's--it's just that he forgets sometimes. And sometimes the way that seven looks at him... it makes him think. Sets him on edge. And he feels like he's back there... In the jungle... In the darkness.
mybustersword · 2 points · Posted at 04:57:10 on February 14, 2016 · (Permalink)
Not quite
https://www.reddit.com/r/FanTheories/comments/419zxr/why_is_6_afraid_of_7/
EpicGoats · 14 points · Posted at 20:42:13 on February 13, 2016 · (Permalink)
With 23 people in a room, there is a greater than 50% chance that two people have the same birthday. Tested this last night with 22 people, and we found out two people has the same birthday on November 10th!
KKMX · 2 points · Posted at 01:19:36 on February 14, 2016 · (Permalink)
Otherwise known as the birthday problem/paradox - https://en.wikipedia.org/wiki/Birthday_problem
[deleted] · 1 points · Posted at 02:47:56 on February 14, 2016 · (Permalink)
That's a surprisingly small amount of people.
Add to that that there are more and less favorable months for getting pregnant [citation needed] (from a social viewpoint; relations tend to form during summers, settle down during winters)
EpicGoats · 1 points · Posted at 03:44:02 on February 14, 2016 · (Permalink)
That's a good point. The two people had their birthday on November 10th, which we figured meant they were Valentines day babies
kogasapls · 1 points · Posted at 08:45:33 on February 14, 2016 · (Permalink)
This increases the probability by a very small amount.
Darth_Rasputin32898 · 1 points · Posted at 16:19:23 on February 14, 2016 · (Permalink)
That's not technically a valid test of the theorem's validity, since all it gives you is a probability, not a prediction.
RotWS · 1 points · Posted at 22:23:59 on February 14, 2016 · (Permalink)
That also happens to be my brother's birthday.
SherrickM · 14 points · Posted at 22:21:44 on February 13, 2016 · (Permalink)
If you shuffle a deck of cards properly, the order the cards are in has probably never been seen before.
[deleted] · 3 points · Posted at 03:19:56 on February 14, 2016 · (Permalink)
[deleted]
SherrickM · 2 points · Posted at 03:45:07 on February 14, 2016 · (Permalink)
From random order? Yeah, that's impossible.
I know, its not....but the odds of it happening in the lifetime of anyone that can read this today is infinitesimally small.
tanman334 · 2 points · Posted at 06:18:50 on February 14, 2016 · (Permalink)
And at the same time, every other specific combination is equally likely. It has to be one of them.
g-spot_adept · -1 points · Posted at 03:21:21 on February 14, 2016 · (Permalink)
No
raptorcop · 12 points · Posted at 00:36:05 on February 14, 2016 · (Permalink)
Assuming that the decimal of Pi extends infinitely, probability states that there has to be a length of digits that corresponds to the data forming a .jpeg of you making out with a polar bear.
1100101000 · 10 points · Posted at 02:01:49 on February 14, 2016 · (Permalink)
No need to assume, the decimal of Pi does extend infinitely, it is proven irrational. It's digits do not terminate or repeat. What is not proven is whether Pi is a normal number or not (though it is conjectured). If Pi is normal, then the idea in your comment is true.
MrWoohoo · 1 points · Posted at 06:53:52 on February 14, 2016 · (Permalink)
So which irrational numbers are normal vs, um, Abby normal? Is e normal? The golden ratio?
[deleted] · 6 points · Posted at 02:45:45 on February 14, 2016 · (Permalink)
Actually we do not know this yet. It is possible that every possible sequence of digits can be found in pi's expansion, but it's also possible that this is not true. An unanswered question, and if it's false then it's also interesting: What would be special about the sequences that do or don't appear in pi's expansion?
As an example of a decimal extension that that extends forever without repeating but does NOT include every possible sequence:
0.101001000100001000001...
Obvious pattern, but the sequence of digits never repeats itself in totality. Nothing but ones and zeros to be had, however.
GokuMoto · -1 points · Posted at 13:18:05 on February 14, 2016 · (Permalink)
gasp i thought i saw a 2
heavyish_things · 1 points · Posted at 03:21:39 on February 14, 2016 · (Permalink)
But the only way you can use this to encode x amount of information is by using y amount of information where y >= x.
kogasapls · 1 points · Posted at 08:50:19 on February 14, 2016 · (Permalink)
I want to encode the number 1415926535897932384626 in pi. It can be described as the cut of decimal digits 0 through 21 of pi. Your statement is true in that pi is longer than the excerpt I'm encoding, but if pi is known and constant between two computers, that long number can be encoded using just a label for pi and the start/end points of the desired cut.
AlwaysGnarlyAlways · 8 points · Posted at 01:18:39 on February 14, 2016 · (Permalink)
What the fuck am I doing in this thread?
youloo · 3 points · Posted at 21:31:21 on February 13, 2016 · (Permalink)
1 + 1/2 + 1/3 + 1/4 + 1/5 + ... is infinite diverges to infinity.
tiplinix · 1 points · Posted at 22:09:49 on February 13, 2016 · (Permalink)
Well, you can say that everything 1 + 1/2a + 1/3a where a <= 1 diverges to infinity. Whereas with a > 1 it converges.
jmt222 · 1 points · Posted at 22:10:47 on February 13, 2016 · (Permalink)
This has a fairly easy proof. Replace every 1/n in the series with 1/2k when
1/2k-1 < 1/n <= 1/2k
The resulting series has a smaller sum, but for every k>=1 there are 2k-1 summands 1/2k so the resulting series has sum
1+1/2+1/2+1/2+...
which diverges to infinity, so 1+1/2+1/3+1/4+1/5+... must also diverge.
410-915-0909 · 3 points · Posted at 22:23:43 on February 13, 2016 · (Permalink)
One of the applications of the Theorema Egregrium is a proof that a 2D model of a 3D object (such as the Earth) cannot simultaneously preserve both angle and area which is why on standard 2D maps Antartica becomes enormous
dobodlee · 3 points · Posted at 00:06:47 on February 14, 2016 · (Permalink)
I can't bother to check if this is already been posted but:
ii is a real number.
Specifically it equals e-pi/2
(That's one solution anyway.. But all solutions are real. )
pringlelover · 3 points · Posted at 01:31:26 on February 14, 2016 · (Permalink)
That the pine cone pattern follows fibonacci numbers.
zk3033 · 3 points · Posted at 01:48:55 on February 14, 2016 · (Permalink)
Generating functions
We all know the coefficients to (x+y)n give us binomials, or rather combinatorically "ways to pick n items from two piles." Of course, the y pile could be empty, so (x+1)n becomes ways to pick an item out of n total.
Similarly, (x+y+z)n coefficients give ways to pick n items out of 3 piles. Say if we want 8 items: 2 x's, 1 y, 5 z's; just expand out the expression to the 8th power, and look at the term x2 y z5 and the coefficient is the answer.
Generating functions is a way to use the power algebra to solve combinatorial problems.
it can be expanded to things as simple as "how many ways to assemble a bike from 4 handles, 6 frames, 3 front wheels, and 2 back wheels." Or even applied to recursive functions, famously the Fibonacci.
ksugama · 3 points · Posted at 03:05:28 on February 14, 2016 · (Permalink)
1/998001 spits out all the three digit integers from 0 to 999 EXCEPT 998. So it goes 1/998001 = 0.000001002003004 and so on until ...996997999 and then it restarts
There is a numberphile video explaining why this is and why it skips 998...
ArchitectGeek · 3 points · Posted at 03:34:25 on February 14, 2016 · (Permalink)
Every time you randomly shuffle a deck of playing cards you have created a sequence that has likely never existed, nor will ever existi again, in the entire history of the universe.
52! Is a HUGE number.
killersoda · 3 points · Posted at 03:56:36 on February 14, 2016 · (Permalink)
If a pizza has a radius Z and a depth A, that pizza's volume can be defined as Pi * z * z * a
Joelpher · 3 points · Posted at 04:22:00 on February 14, 2016 · (Permalink)
If you multiply a 2 digit number by 11, say 36-- if you add the 2 numbers-- 3 and 6, and place that sum between them-- you have the correct number. 11 X 42 is 462, because 4 + 2 = 6.
Dad2DnA · 2 points · Posted at 04:49:49 on February 14, 2016 · (Permalink)
396 for your first example, that's a good one!
FredFnord · 3 points · Posted at 04:26:32 on February 14, 2016 · (Permalink)
The integral z-squared dz
from 1 to the cube root of 3
times the cosine
of three pi over 9
is the log of the cube root of 'e'.
SenorGravy · 3 points · Posted at 04:54:49 on February 14, 2016 · (Permalink)
Reading these comments made my head hurt. Low IQ confirmed.
c3534l · 3 points · Posted at 04:58:11 on February 14, 2016 · (Permalink)*
Probably not as interesting as the others in this thread, but here are some things that kind of blew me away when I first learned about them:
Kuratowski's Theorem says if you draw a graph in two dimension, you know it can only be drawn with the lines crossing if it contains a subgraph that is K5 or the Utility Graph. That is, there's basically only two ways to draw a graph that cannot be untangled, save adding unnecessary tails and extra little nodes in there.
I forget the name of the theorem and I'm having trouble finding it online, but I also found it fascinating that we have a formula that tells us exactly how many un-disentanglable graphs there are in every dimension of space, but that really doesn't give us the least bit of clue as how to find what those graphs are. Like, you could say with absolute certainty that there are exactly 6 necessarily-crossing graphs in 19-dimensional space (I'm making those numbers up), but if someone asked you to draw one, you'd have no idea where to start.
I also like that Shannon's Source Coding Theorem gives us a hard limit as to how much data can be compressed and it's a great way of dispelling a lot of flim-flam in data compression by people who are sure they've developed an amazing new compression algorithm that cannot exist.
If you flip a coin bunch of times the probability of getting HHT is higher than the probability of getting HTT. (an explanation).
edit: can't figure out how subscript works on reddit
TheAdam_Bomb · 3 points · Posted at 04:58:17 on February 14, 2016 · (Permalink)
If you take the curve y = 1/x and create a solid body from it by revolving it around the x-axis from x=1 to x=infinity, you will get a solid with strange properties.
The volume of this shape is pi, yet the surface area is infinite. Thus, you could machine this solid from a relatively reasonable block of metal, but no amount of paint in the world could cover its entire surface.
dmo012 · 3 points · Posted at 05:10:17 on February 14, 2016 · (Permalink)
The Big Bang would have measured in the Richter scale as a 40.0 earthquake.
But, since the Richter scale increases exponentially, that means the Big Bang was 1040 times more powerful than a 10.0 earthquake.
tocaloni1 · 3 points · Posted at 05:16:36 on February 14, 2016 · (Permalink)*
It is more likely to win the lottery 800,000 times than to reconstruct a given HD-picture with random color pixels.
Edit: HD-picture means 1280x720, 24 bit color depth
zeusman123456 · 3 points · Posted at 05:18:29 on February 14, 2016 · (Permalink)
Okay..here it goes.....Compounding Interest
Two twins,both 20 years old. One of them socks away $200/month, every month for 6 years. Hypothetically making 10%. At age 26 the first twin stops investing and the second one starts. The second one invests in the same investment , $200/month as his brother from age 26 to 65. At 65 who has more money?? Answer ...its a tie....how much $2 000 000. Don't ask me for the proof Ive done it more times then i can count. This was shown to us in our Economics class in high school. It was meant to prove that you should always invest for the long term in quality high dividend paying companies and not chase the hot stocks. Also to realize the as young students we have the greatest thing going for us........TIME. well back to my margaritas.
04fuxake · 3 points · Posted at 05:58:25 on February 14, 2016 · (Permalink)
A prime number can be found either side of a multiple of six.
Roughdog · 3 points · Posted at 06:18:53 on February 14, 2016 · (Permalink)
I learned that Christmas and Halloween are really the same, since OCT 31=DEC 25
thepopcornwizard · 1 points · Posted at 07:06:03 on February 14, 2016 · (Permalink)
NIIIIIIIIIIIIIIIIICE
Shellova · 3 points · Posted at 07:31:33 on February 14, 2016 · (Permalink)*
If the total of all the digits in a number could be divided by 3, that number could be divided by 3.
278510367
2 + 7 + 8 + 5 + 1 + 0 + 3 + 6 + 7 = 39
3 + 9 = 12
1+ 2 = 3
278510367 / 3 = 92836789
[deleted] · 3 points · Posted at 07:58:13 on February 14, 2016 · (Permalink)
The sum of all integers, i.e. 1+2+3+... is equal to -(1/12).
this video explains it really well
ScottCurl · 3 points · Posted at 08:27:47 on February 14, 2016 · (Permalink)
Here's a good one for all the accountants out there or other people who have to add numbers from time to time:
Let's say you add up a bunch of numbers and you expect a certain result and there's a difference. Usually you would now spend a lot of time looking for the cause of that difference by going through the numbers one by one.
Here's the catch: when the difference you have is divisible by 9, the cause of your difference is that you mixed up two figures in your calculation.
Example: 123+456+789 = correct result: 1368
Say by mistake you mixed up two figures in the last one (123+456+879) = wrong result: 1458
The difference between 1368 and 1458=90 (divisible by 9)
Here's where it really gets cool: it even works, when you mix up two figures who are not next to each other.
123+456+987=1566 -> difference = 198 (divisible by 9)
Saved my ass SOO many times....
Damoss · 3 points · Posted at 10:07:25 on February 14, 2016 · (Permalink)
Not a fact but:
e.g. 11 = 1 + 1.
e.g. a = 1, b = 2
A grey elephant in Denmark.
deepsoulfunk · 3 points · Posted at 10:36:31 on February 14, 2016 · (Permalink)
2 + 2 = 5
Depending on who's in charge.
iHaveAgency · 3 points · Posted at 10:54:30 on February 14, 2016 · (Permalink)
A cool way of expressing the infinitude of infinity in English is to simply say, "Every number is smaller than most numbers."
inthelittleforest · 3 points · Posted at 11:54:23 on February 14, 2016 · (Permalink)
There's a 32.33% (Repeating of cause) of survival in that hatchling room! Y'know, the one in Upper Bedrock Spire!
Zoorom · 1 points · Posted at 19:33:24 on February 14, 2016 · (Permalink)
Leeeeeeeroy Jeeeeeenkins!
Poppamunz · 3 points · Posted at 12:32:54 on February 14, 2016 · (Permalink)
If you have a pizza with a radius of z and a depth of a, the volume of said pizza is pi*z*z*a.
Cpianti · 3 points · Posted at 12:52:31 on February 14, 2016 · (Permalink)
For some who has little to no grasp on mathematics outside of the badics, this is all at once the most fascinating and confusing thread I have ever read
barcodez · 3 points · Posted at 13:15:42 on February 14, 2016 · (Permalink)*
eiπ + 1 = 0
edit: It's called Euler's Identity
AncientMumu · 3 points · Posted at 13:27:59 on February 14, 2016 · (Permalink)
1+2=3
4+5+6=7+8
9+10+11+12=13+14+15
.... function this!
[deleted] · 3 points · Posted at 13:29:26 on February 14, 2016 · (Permalink)
Why do mathematicians confuse Halloween and Christmas? Because OCT 31=DEC 25!
AClassyNarwhal · 3 points · Posted at 13:35:38 on February 14, 2016 · (Permalink)
111,111 * 111,111 = 12,345,654,321
[deleted] · 3 points · Posted at 13:51:20 on February 14, 2016 · (Permalink)
To easily find the product of any two numbers times 11, just add the two digits and place the sum in the middle of the two digits:
23x11=253, (2+3=5, place the 5 between the 2 and 3)
52x11=572
36x11=369
44x11=484
If the two digits add up more than 9, just carry it over to the first digit:
56x11=616 93x11=1023
hornet330 · 3 points · Posted at 15:15:49 on February 14, 2016 · (Permalink)
1 = 0.99999..... (infinite number of nines, sorry I can find the right hat).
Proof:
10x = 9.9999999...
x = 0.9999999...
9x = 9 => x = 1.
Sounds like a trick but It isn't. It's real.
[deleted] · 3 points · Posted at 16:33:21 on February 14, 2016 · (Permalink)
A pizza that has a radius "z" and a height "a" is Pi•z•z•a
MWatson17 · 2 points · Posted at 17:53:16 on February 14, 2016 · (Permalink)
My kind of math.
Redbird9346 · 3 points · Posted at 05:33:02 on February 15, 2016 · (Permalink)
n2 is simply the sum of the first n odd integers (assuming n is an integer >= 1).
12 = 1.
22 = 1+3 = 4
32 = 1+3+5 = 9
42 = 1+3+5+7 = 16
52 = 1+3+5+7+9 = 25
…and so on.
unique_2 · 3 points · Posted at 22:35:10 on February 15, 2016 · (Permalink)
If you randomly shuffle a deck of cards (or anything really), what's the average number of cards that will be at the exact same spots as they were before?
Turns out it's 1. Doesnt even matter how many cards you started with.
somerandomguy02 · 8 points · Posted at 00:16:32 on February 14, 2016 · (Permalink)
Your sexual game is the lim of 1/x as x approaches infinity.
[deleted] · 4 points · Posted at 01:09:29 on February 14, 2016 · (Permalink)
Yours is the left-handed limit about zero. Boom!
somerandomguy02 · 1 points · Posted at 01:19:30 on February 14, 2016 · (Permalink)
Oooo, been so long. As in limit as x approches zero as in Does Not Exist?
lol, I hate you.
Edit: I graphed it and remember now. Negative Infinity. You bastard, nice one.
[deleted] · 2 points · Posted at 01:48:02 on February 14, 2016 · (Permalink)
If you take 1/x where x>=1 and rotate it in three dimensional space about the x-axis the resulting surface has infinite surface area but finite volume. That is to say you could fill it with a finite amount of paint, but you could never have enough paint to cover its exterior. This surface is known as the Gabriel's Horn or Torricelli's trumpet.
kogasapls · 1 points · Posted at 08:46:44 on February 14, 2016 · (Permalink)
So what you're saying is its existence can only be described as surreal?
(Or hyperreal? :p)
MacduffFifesNo1Thane · 67 points · Posted at 19:27:04 on February 13, 2016 · (Permalink)*
1+2+3+4+5+6+7+8+9… can be assigned a value under some system equal or near the amount known as -1/12.
Edit: People hate erroneous cases of applying equality.
thestickystickman · 37 points · Posted at 19:56:27 on February 13, 2016 · (Permalink)
What?
Felix_Tholomyes · 19 points · Posted at 20:05:31 on February 13, 2016 · (Permalink)
You can assign values to divergent sums and get some pretty confusing results
Fake_Name_6 · 5 points · Posted at 01:09:58 on February 14, 2016 · (Permalink)
It's not a randomly assigned value though. There is no other value but -1/12 that could be assigned to that sequence.
MacduffFifesNo1Thane · 10 points · Posted at 20:01:39 on February 13, 2016 · (Permalink)
How rude! I forgot to offer some sauce. http://youtu.be/w-I6XTVZXww
FawtyTwo · 1 points · Posted at 23:15:41 on February 13, 2016 · (Permalink)
That was awesome, but as soon as I finished the video I forgot the exact way in which it makes sense.
New_World_Era · 12 points · Posted at 20:34:27 on February 13, 2016 · (Permalink)
Yep, also 1+2+4+8+16+32....=-1
Infinite sums have a funny property where although they seem to diverge to infinity, you can assign values to them
laprastransform · 4 points · Posted at 01:10:54 on February 14, 2016 · (Permalink)
True in the ring of 2-adic integers
[deleted] · 3 points · Posted at 21:52:50 on February 13, 2016 · (Permalink)*
[deleted]
New_World_Era · 3 points · Posted at 22:13:01 on February 13, 2016 · (Permalink)
Not necessarily arbitrary. There are certain methods of coming to those answers.
+
-2×(1+2+4+8+16+32...)=-2S
1+(2-2)+(4-4)+(8-8)...=-S
S=-1
jaynay1 · 3 points · Posted at 22:14:44 on February 13, 2016 · (Permalink)*
There are methods of coming to those answers. There are different methods that yield different answers. That's where the arbitrariness comes in if you want to claim equality. Well, that, plus there not typically being a definition for a divergent infinite sum.
New_World_Era · 1 points · Posted at 22:19:17 on February 13, 2016 · (Permalink)
You know, I never thought of different methods leading to different sums. Do you have some examples or explanations?
jaynay1 · 1 points · Posted at 22:25:56 on February 13, 2016 · (Permalink)
Well, the first one I came to involved an error on my part involving forgetting that one of the 1's doesn't cancel, so I'm not sure that actually does happen.
bigb1 · 2 points · Posted at 06:58:05 on February 14, 2016 · (Permalink)*
Pegguins · 1 points · Posted at 01:38:08 on February 14, 2016 · (Permalink)
It's to do with various properties of infinite/divergent series.
Divergent series were considered nonsensical, even the creation of the devil according to some for quite a long time.
AcellOfllSpades · 94 points · Posted at 21:33:35 on February 13, 2016 · (Permalink)
NO.
NO NO NO NO NO.
There are many ways to assign values to infinite sums that normally go to infinity. As a bonus, those methods give the right answer for sums that do give a finite value. Two of the most popular ones (Ramanujan summation and Riemann Zeta analytic continuation) give -1/12 as the answer for 1+2+3... . In some contexts in string theory and various other parts of physics, you get infinite sums that sometimes go off to infinity; in those cases, using the other methods can give you a sensible result. However, it is not the actual sum; it's just a way to assign a value to a series. In other cases, it lines up with infinite summation, but they are not the same thing.
somadIcanteven · 3 points · Posted at 03:04:58 on February 14, 2016 · (Permalink)*
Terence Tao has an excellent blog post describing that the analytic continuation method of "summing" this series is the same as looking at asymptotic data for a sum where each entry "n" is replaced by "n times a smooth cutoff function". He also goes on to explain why the "values" of the series that you get, while meaningful for an individual series, tend to conflict with the "values" of other divergent series, because they are computing asymptotics of a different order.
Said post can be found here
MacduffFifesNo1Thane · 4 points · Posted at 21:42:56 on February 13, 2016 · (Permalink)
Umm.....I got lost. ELI5?
AcellOfllSpades · 15 points · Posted at 21:53:31 on February 13, 2016 · (Permalink)*
Infinite sums usually don't work. For example, 1+2+3+4... is infinite - not a number. You can use various special methods to fix that though. 1/2+1/4+1/8+1/16.. is 1; even when you use the special methods, they can still give the value "1" for the series without adding it up. The techniques also give you numbers for other series that don't usually work. Two common techniques both assign -1/12 to the series 1+2+3... . That doesn't mean that the sum is -1/12; it just means that it can be helpful in physics to treat it like it is. It can tell physicists that there's a hidden "hey, you need to use the Ramanujan sum here" in a formula rather than a regular sum. For working series, there isn't a difference; for series that shoot off to infinity, regular adding doesn't work but Ramanujan sums do.
So why don't we just call Ramanujan sums "adding"? Because there are several different methods that give values to normally divergent series. Frequently they conflict with each other. 1+2+3+4... is assigned -1/12 by two methods though.
MrShutCo · 1 points · Posted at 00:54:30 on February 14, 2016 · (Permalink)
This actually makes a lot of sense, thanks.
[deleted] · 1 points · Posted at 04:22:35 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 2 points · Posted at 04:23:18 on February 14, 2016 · (Permalink)
[deleted]
[deleted] · 1 points · Posted at 04:28:37 on February 14, 2016 · (Permalink)
[deleted]
toxictaru · 1 points · Posted at 04:16:49 on February 14, 2016 · (Permalink)
I might be wrong, but I feel like I remember reading that 1/2+1/4+1/8+1/16...=1 isn't actually correct, just that it tends closer and closer to 1.
AcellOfllSpades · 7 points · Posted at 04:21:45 on February 14, 2016 · (Permalink)
1/2+1/4+1/8+1/16... is a number.
Numbers don't "tend" to anything; they don't move.
It's exactly 1.
If you were talking about 1/2 + 1/4 + 1/8 + ... + 1/2n, with a finite amount of terms, then you could say that as n goes to infinity, that series approaches 1. But in the case of the single sum 1/2 + 1/4 + 1/8 + ..., nothing "changes".
professortweeter · 1 points · Posted at 02:51:32 on February 14, 2016 · (Permalink)
I think he was considering ramanujan considering he said "under some systems" rather than outright claiming the sum of the naturals was -1/12
AcellOfllSpades · 2 points · Posted at 02:54:38 on February 14, 2016 · (Permalink)
That's not what it said at first.
professortweeter · 1 points · Posted at 03:50:53 on February 14, 2016 · (Permalink)
Oh. Didn't know it had been edited. Keep knocking out that sum of N is -1/12 misconception. You're needed in this thread.
Obyeag · 1 points · Posted at 04:56:59 on February 14, 2016 · (Permalink)
Knew you'd be in here somewhere
daniel14vt · 35 points · Posted at 21:08:06 on February 13, 2016 · (Permalink)
This isn't true.
The video shows that if you arrange a specific infinite set of numbers, you can arrange it in a way so that it appears to sum to -1/12. This is useful when talking about comparing different infinite sums. BUT, 1+2+3+4... = infinity
MacduffFifesNo1Thane · 9 points · Posted at 21:29:44 on February 13, 2016 · (Permalink)
Physics thrives on summing infinite sequences.
daniel14vt · 3 points · Posted at 21:33:22 on February 13, 2016 · (Permalink)
yes, but those sequences would be convergent, not divergent. Using the = sign here is the main cause for concern
MacduffFifesNo1Thane · 2 points · Posted at 21:40:48 on February 13, 2016 · (Permalink)
As a historian, I will edit to what you mean.
daniel14vt · 9 points · Posted at 21:49:48 on February 13, 2016 · (Permalink)
Its not your fault, its that freaking Numberphile video that everyone and their mother has seen where they don't explain what they are doing
Wolfy21_ · 1 points · Posted at 01:32:36 on February 14, 2016 · (Permalink)
wait but what sign can u use for this though...
daniel14vt · 2 points · Posted at 02:45:27 on February 14, 2016 · (Permalink)
So the standard way for the Ramanujan series would be
=-1/12 (R)
But it's a curly R
Fake_Name_6 · 1 points · Posted at 01:06:18 on February 14, 2016 · (Permalink)
But the Ramanujan summation of 1+2+3... is actually -1/12, it is not something somebody pulled out of a hat.
daniel14vt · 3 points · Posted at 01:08:12 on February 14, 2016 · (Permalink)
Yes. But 1+2+3... Does NOT = -1/12
If you make it clear that your doing a special summation, sure you're fine. But if you don't then you're just confusing people
functor7 · 1 points · Posted at 04:52:49 on February 14, 2016 · (Permalink)
If you use the arbitrary method of summation that takes place on the real line. There are infinitely many different ways to assign values to infinite sums, and convergence on the real line is not special in any way.
Anesan2654 · 0 points · Posted at 21:38:35 on February 13, 2016 · (Permalink)
It can't equal infinity, because infinity isn't a number, it is a concept. Just like how 1-1/2-1/4-1/8... Does not equal "small".
Fake_Name_6 · 4 points · Posted at 01:07:36 on February 14, 2016 · (Permalink)*
Ramanujan summation is the system you are looking for (edit: Riemann zeta summation works too)
Exactly equal, in fact.
This is not made up, and you can't get this infinite sum to be anything else other than -1/12, or infinity depending on which system you are in.
[deleted] · 13 points · Posted at 20:55:13 on February 13, 2016 · (Permalink)
Please don't use = for this. Please.
1+4+9+16+25+... = 0 makes no sense.
functor7 · 1 points · Posted at 04:54:45 on February 14, 2016 · (Permalink)
Technically, we should use explicit limits for any infinite series, because adding together an infinite number of things is meaningless without explicitly stating how you're assigning values.
1+2+4+8+16+... = -1 in 2-adic convergence
[deleted] · 2 points · Posted at 08:13:14 on February 14, 2016 · (Permalink)
I'm not going to argue with an r/math regular in askreddit. (unless we fight over whether Zp means Z/pZ or the p-adic integers)
MacduffFifesNo1Thane · -3 points · Posted at 21:28:50 on February 13, 2016 · (Permalink)
Only going on what those mathematicians said.
A_Waskawy_Wabit · 0 points · Posted at 00:47:10 on February 14, 2016 · (Permalink)
If a mathematician said that they're doing it wrong. Physicists are the ones who get to say that
Goodnametaken · -3 points · Posted at 01:25:34 on February 14, 2016 · (Permalink)
No you're not. If you were talking to an actual mathematician they would have told you that the LIMIT of the series that you defined approaches -1/12. There is no = there. Nobody who knows what they are talking about would have said =.
somadIcanteven · 2 points · Posted at 03:29:10 on February 14, 2016 · (Permalink)
That's not the issue at all. Using an = sign for a series already implies taking a limit of some kind. Even taking this account, there are serious problems with claiming
1 + 2 + 3 + 4 + . . . = -1/12
from a mathematical standpoint. On the other hand, the number -1/12 is the result of a regularized sum, which is a whole other beast entirely.
angelsandbuttermans · 2 points · Posted at 20:58:48 on February 13, 2016 · (Permalink)
I feel like if you focus too hard on trying to wrap your head around that answer you'll just have an existential crisis.
MacduffFifesNo1Thane · 3 points · Posted at 21:29:24 on February 13, 2016 · (Permalink)
That caused my quarter life crisis. Which was weird.
mobius_stripe · 1 points · Posted at 22:09:24 on February 13, 2016 · (Permalink)
Ah. This is fascinating.
Awkward_moments · 1 points · Posted at 00:30:49 on February 14, 2016 · (Permalink)
I thought it was 1-2+3-4+5-6+7...
This makes even less sense.
TaytosAreNice · 1 points · Posted at 01:24:39 on February 14, 2016 · (Permalink)
That can be shown to equal 1/4 under certain summation methods.
Cremasterau · 1 points · Posted at 06:22:17 on February 14, 2016 · (Permalink)
This is something I found particularly cool.
The formula for summing sequential numbers is 1/2x(x+1) and if you plot this at Wolfram this is what you get).
If you calculate the small area under the x axis you get -1/12.
It seems if you take the area under the curve but above the x axis to the right and subtract it from the area to the left -1/12 is what you are left with.
muffley · 1 points · Posted at 01:04:25 on February 14, 2016 · (Permalink)
If you walk in one direction for 1 foot, then 2 more feet, then 3 more feet, etc. at infinity you will be 1 inch behind where you started.
Ok.
FMERCURY · 1 points · Posted at 03:10:13 on February 14, 2016 · (Permalink)
There is no "at infinity" though.
DiscoHippo · 1 points · Posted at 03:19:59 on February 14, 2016 · (Permalink)
That's true for a globe with infinity-1 inch circumference
smurphatron · 1 points · Posted at 03:51:10 on February 14, 2016 · (Permalink)
Actually infinity+1
DiscoHippo · 1 points · Posted at 03:52:42 on February 14, 2016 · (Permalink)
Wait... crap, I've been out of school for too long
SOwED · 0 points · Posted at 20:50:56 on February 13, 2016 · (Permalink)
1-1+1-1+1-1...=1/2
MacduffFifesNo1Thane · 1 points · Posted at 21:29:04 on February 13, 2016 · (Permalink)
Makes perfect sense. Takes the average of the two sums.
somadIcanteven · 1 points · Posted at 03:27:11 on February 14, 2016 · (Permalink)
At the same time, without first establishing what you mean by a series, why are you allowed to take the averages and claim it is "equal" to the value of the series.
The scenario you are describing is called Cesaro summation and is different from standard summation (among many other possibilities).
1 - 1 + 1 - 1 + ... is not equal to 1/2
However, the series is Cesaro summable and its Cesaro sum is 1/2.
ifarmpandas · 1 points · Posted at 21:41:31 on February 13, 2016 · (Permalink)
The sum doesn't converge to a single value, unless you're using non-standard operations and definitions, in which case, 1=2!
[deleted] · 0 points · Posted at 23:46:34 on February 13, 2016 · (Permalink)
Wrong.
TheFakeJerrySeinfeld · 0 points · Posted at 01:44:22 on February 14, 2016 · (Permalink)
This is the best one here because it's so simple but so mind blowing
slaerdx · 8 points · Posted at 03:13:30 on February 14, 2016 · (Permalink)
All positive integer powers of 26 (except for 0 and 1) end in the number 76. Example:
262 = 676
263 = 17576
264 = 456976
and so on
narbris · 3 points · Posted at 06:20:51 on February 14, 2016 · (Permalink)
3762 = 141376
3763 = 53157376
3764 = 19987173376
and so on
hayberry · 4 points · Posted at 22:18:56 on February 13, 2016 · (Permalink)*
2147483647, 231 -1, is a pretty cool number. It's the largest integer you can have on a 32-bit machine, which is why it's the highest score before things get wonky on a lot of old video games. It's also a prime, and the primeness of it was proven in a letter from Euler to Bernoulli. It's actually one of 49 known Mersenne primes, and one of four known double-Mersenne primes, both of which are tied to a bunch of other mathematical conjectures and used to derive other special numbers. As a programmer and general math nerd it holds a special place in my heart. (:
ben1996123 · 1 points · Posted at 23:18:16 on February 13, 2016 · (Permalink)
there are 49 known mersenne primes not 29
hayberry · 1 points · Posted at 23:19:48 on February 13, 2016 · (Permalink)
Typo, my bad.
davidjricardo · 5 points · Posted at 01:24:21 on February 14, 2016 · (Permalink)
0.999999.......... = 1
Not approximately equals, or converges to, but actually equals - like they are the same number.
somadIcanteven · 2 points · Posted at 03:15:23 on February 14, 2016 · (Permalink)
The number 0.999999... represents an infinite series, and saying
A) a series equals some finite number
and
B) a series converges to that finite number
are really the same thing. So yes, the two are equal, but "converges to" is not invalid language.
Billlll_Brasky · 3 points · Posted at 02:19:45 on February 14, 2016 · (Permalink)
Not sure if it's my fav, but I'm surprised no one has posted about Gabriel's Horn yet. It's a surface that has finite volume but infinite surface area. So you can fill with paint, but cannot paint it.
https://en.wikipedia.org/wiki/Gabriel%27s_Horn
[deleted] · 8 points · Posted at 21:48:02 on February 13, 2016 · (Permalink)
I'm getting stressed out reading this thread
Yonderen · 6 points · Posted at 01:35:43 on February 14, 2016 · (Permalink)
A pizza with depth a and radius z has a volume of pi z z a.
[deleted] · 8 points · Posted at 05:30:16 on February 14, 2016 · (Permalink)
[deleted]
hypervelocityvomit · 0 points · Posted at 13:20:42 on February 16, 2016 · (Permalink)
Hahah, I have 3.5 inches when it's floppy...
devishe · 4 points · Posted at 21:00:46 on February 13, 2016 · (Permalink)
I know I'm way late, but I always liked this explanation of the difference between a million and a billion: One million seconds is eleven and a half days.. One billion seconds is 31 and a half years.
truthinlies · 3 points · Posted at 00:27:19 on February 14, 2016 · (Permalink)
as of today im exactly 10,000 days old
GreyHexagon · 7 points · Posted at 00:40:53 on February 14, 2016 · (Permalink)
Well congratulations
truthinlies · 1 points · Posted at 00:58:16 on February 14, 2016 · (Permalink)
Thanks! I'm actually pretty excited about it
GokuMoto · 2 points · Posted at 13:38:09 on February 14, 2016 · (Permalink)
i am only 7584 days old
truthinlies · 1 points · Posted at 13:56:50 on February 14, 2016 · (Permalink)
young'en
ImAStupidFace · 2 points · Posted at 06:41:43 on February 15, 2016 · (Permalink)
You're old!
truthinlies · 1 points · Posted at 11:47:04 on February 15, 2016 · (Permalink)
please please, i prefer the term 'wise and smelly'
fucky_fucky · 4 points · Posted at 00:56:04 on February 14, 2016 · (Permalink)*
You can derive pi from a toothpick and some parallel lines which are drawn twice the length of the toothpick apart from each other. The probability that the toothpick will land on a line approaches 2/pi as the number of trials tends to infinity.
The strange thing about this is that pi is defined as the ratio of a circle's circumference to its diameter, which seems to have absolutely nothing to do with toothpick tossing.
Hedgehogs4Me · 1 points · Posted at 01:39:14 on February 14, 2016 · (Permalink)
That's... weird. I'm going to need an explanation for this one.
fucky_fucky · 2 points · Posted at 01:47:47 on February 14, 2016 · (Permalink)
It's actually fairly straightforward.
http://mste.illinois.edu/activity/buffon/
Hedgehogs4Me · 1 points · Posted at 01:54:23 on February 14, 2016 · (Permalink)
Huh. That makes a lot of sense, actually, thanks. That was certainly a lot easier for me to understand than Wikipedia's explanation!
eldencampbell · 6 points · Posted at 03:45:09 on February 14, 2016 · (Permalink)
When you type in 55378008 on a calculator and hold it upside down it says 'BOOBLESS'.
blazingparakeet · 1 points · Posted at 04:36:29 on February 14, 2016 · (Permalink)
Dolly Parton's boobs weighed 69 lbs., and that was too, too, too (222) much. So she walked down 51st st. And had Dr X remove her boobs 8 times.
6922251x8=80087355
[deleted] · 2 points · Posted at 22:21:08 on February 13, 2016 · (Permalink)
Kaprekar's constant
Definition from Wikipedia describes it well:
And for basically any four digit number, except 000, 1111, 2222, etc. (which will arrive at 0), will arrive at 6174.
Other sets of n numbers have similar properties but with convergences at multiple numbers.
Urgullibl · 2 points · Posted at 22:28:21 on February 13, 2016 · (Permalink)
The Banach-Tarski Paradox:
Nettius2 · 1 points · Posted at 02:37:15 on February 14, 2016 · (Permalink)
Non-rectifiable curves? No thanks.
Urgullibl · 1 points · Posted at 03:03:28 on February 14, 2016 · (Permalink)
Rect.
snypre_fu_reddit · 2 points · Posted at 22:50:35 on February 13, 2016 · (Permalink)
12 = 1
22 = 1+3
32 = 1+3+5
42 = 1+3+5+7
etc.
[deleted] · 2 points · Posted at 22:57:21 on February 13, 2016 · (Permalink)
There is no way to define a perfect circle with Bézier curves.
[deleted] · 2 points · Posted at 22:57:52 on February 13, 2016 · (Permalink)
The circles in % are not zeros – but o’s.
GustauveVIII · 2 points · Posted at 23:35:05 on February 13, 2016 · (Permalink)
A simple one.
To square any number that ends in 5, simply divide by 10, round down, and then multiply it by itself plus 1. Then you tack on 25.
For example, to square 205:
205 / 10 = 20.5 rounded down = 20
20 * (20 + 1) OR 20 * 20 + 20 = 420
42025
atarikid · 2 points · Posted at 00:01:34 on February 14, 2016 · (Permalink)
If you could hang a hammock with both lines being perfectly level with no sag (this is impossible, but stick with me), the force on the lines (and whatever they are attached to) would be infinite.
This is why you need to know how to hang a hammock properly, or you can pull down walls.
a_flying_walrus · 2 points · Posted at 00:07:28 on February 14, 2016 · (Permalink)
That the infinite sum: 1/12 + 1/22 + 1/32 + 1/42 + ... = pi2 /6
It's not the fact that the sum converges which is cool, it's the fact that such a seemingly simple sum converges to a value which is expressed in terms of pi. This is known as the Basel problem https://en.wikipedia.org/wiki/Basel_problem
wallysaruman · 2 points · Posted at 00:25:43 on February 14, 2016 · (Permalink)
0.99999999∞ = 1
llttss · 2 points · Posted at 01:20:58 on February 14, 2016 · (Permalink)
12343212343212343... can be split up to make every number using addition, and all of this is in order.
GaloisGroupie3474 · 2 points · Posted at 01:35:44 on February 14, 2016 · (Permalink)
My favorite theorem: A lobster is a reptile, and a snake is not a reptile.
diazegod · 2 points · Posted at 01:37:37 on February 14, 2016 · (Permalink)
Can you explain how that is math?
GaloisGroupie3474 · 3 points · Posted at 01:53:32 on February 14, 2016 · (Permalink)
Reptile is short for Repeating Tile. It means a shape that can be divided up into smaller versions of itself. Lobster and Snake are two polyiamonds – shapes created by arranging equilateral triangles side to side. Lobster looks like a lobster claw, two of them can be joined together to make a parallelogram, which can be tiled into a lobster shape. So it's a reptile. Trying to match up the ends of a snake however always results in an overlap, so it's not a reptile.
SunshineUponMyAnus · 2 points · Posted at 01:42:11 on February 14, 2016 · (Permalink)
Every integer can be expressed as a unique product of prime powers
This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, the factorization would not be unique, as, for example, 2 = 2×1 = 2×1×1 = ...
battering-ram · 2 points · Posted at 02:57:56 on February 14, 2016 · (Permalink)
111,111,111 × 111,111,111 = 12,345,678,987,654,321
ExtraSmooth · 2 points · Posted at 03:11:37 on February 14, 2016 · (Permalink)
ei*pi = -1
[deleted] · 2 points · Posted at 03:11:59 on February 14, 2016 · (Permalink)
At any given time, there is at least 2 point on Earth such that they are on complete opposite sides of the planet and have the exact same temperature.
https://www.youtube.com/watch?v=5Px6fajpSio
Handsinsocks · 2 points · Posted at 03:15:49 on February 14, 2016 · (Permalink)
If the sum of a numbers digits is dividable by 9 so is the original number.
e.g. 972 :. 9+7+2 = 18. 18 = 2x9 :. 972 can be divided by 9.
N0T_an_ape · 2 points · Posted at 03:23:33 on February 14, 2016 · (Permalink)
1/998001 = 0.000 001 002 003 004 005... You get the idea ...995 996 997 999 000 001.....
Wooper160 · 2 points · Posted at 03:28:02 on February 14, 2016 · (Permalink)
.999...=1 various proofs can be found here
Sharynm · 2 points · Posted at 03:30:52 on February 14, 2016 · (Permalink)
That 9x 6-10 is a reverse of the numbers of 9x 1-5. 9x1=9 9x2=18 9x3=27 9x4=36 9x5=45 9x6=54 (reverse 9x5) 9x7=63 (reverse 9x4) 9x8=72 (reverse 9x3) 9x9=81 (reverse 9x2) 9x10=90 (reverse 9x1)
[deleted] · 2 points · Posted at 03:41:12 on February 14, 2016 · (Permalink)*
If you take any number and double it or half it, then take the result and add numbers together repeatedly until you condense it into one number, it will follow a predictable pattern of 1,2,4,8,7,5 or 3,6, or repeating 9s.
For instance: 1
1*2 = 2
2*2 = 4
4*2 = 8
8*2 = 16 , 1+6 = 7
16*2 = 32, 3+2 = 5
32*2 = 64, 6+4 = 10 , 1+0 = 1
64*2 = 128, 1+2+8 = 11, 1+1 = 2... and so on
or 1 = 1
1/2 = 0.5, 0+5=5
0.5/2 = 0.25, 0+2+5 = 7
0.25/2 = 0.125 , 0+1+2+5 = 8
0.125/2 = 0.0625, 6+2+5 =13 , 1+3 = 4
0.0625/2 = 0.03125,= 3+1+2+5 = 11 , 1+1 = 2 .. and so on in the opposite direction
3=3
3*2 = 6
6*2 = 12, 1+2 = 3
12*2 = 24, 2+4 = 6 and so on.
Radius86 · 2 points · Posted at 03:43:06 on February 14, 2016 · (Permalink)
Do you want to know if a number is divisible by 3? Add up the digits.
For instance, 144. 1 + 4 + 4 = 9 which is divisible by 3. Therefore 144 is divisible by 3.
jfffj · 1 points · Posted at 10:24:44 on February 14, 2016 · (Permalink)
There's several of those.
If adding up all the digits is divisible by 9 then the whole number is divisible by 9.
Etc for powers of 3.
If the last digit is divisible by 2, then the whole number is divisible by 2.
If the last 2 digits are divisible by 4, then the whole number is divisible by 4.
If the last 3 digits are divisible by 8, then the whole number is divisible by 8.
Etc. for powers of 2.
But my favourite: If you add up alternate digits, i.e. digits 1,3,5,... and digits 2,4,6,... and those two sums are the same, then the whole number is divisible by 11. Example:
132 is divisible by 11 (1+2 = 3)
4369356585 is divisible by 11 (4+6+3+6+8 = 3+9+5+5+5)
OneTrueArthur · 2 points · Posted at 03:44:34 on February 14, 2016 · (Permalink)
I know I'm super late, but to square numbers whose ones digit is 5, excluding 5 itself, suppose the number before it is X. For example, 105. X here is 10. Then, take (X)(X+1) then put it right beside 25. So in this case, 11×10= 110, put that beside 25, the answer is 11025. Works with any number whose (X)(X+1) you can mentally calculate, if you wanna do it without a calculator
Coequalizer · 2 points · Posted at 03:47:27 on February 14, 2016 · (Permalink)
The curvature of a closed orientable surface tells you how many handles it has. This is essentially the Gauss-Bonnet theorem. Chern-Weil theory is a generalization of this idea, that curvature of a space tells you important geometric and topological information. Famous physicist Edward Witten developed Chern-Simons theory, a branch of topological quantum field theory, using these ideas. Interestingly, mathematician James Harris Simons, who discovered/invented the Chern-Simons form alongside S. S. Chern, later founded an investment firm and is now worth $14 billion.
Ryuzaki2 · 2 points · Posted at 03:49:00 on February 14, 2016 · (Permalink)
You only need 23 people in the same room for an approximately 50% chance that two of those people will share the same birthday.
Mausman · 2 points · Posted at 03:52:48 on February 14, 2016 · (Permalink)
Almost all numbers contain a 3 (or any other number of your choosing).
Smailien · 2 points · Posted at 03:53:19 on February 14, 2016 · (Permalink)
The digits of multiples of nine add up to nine, and also are a "palindrome."
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)
9x10= 90 (9+0=9)
VanillaIcee · 2 points · Posted at 03:53:43 on February 14, 2016 · (Permalink)
e ^ i pi = -1
decaturbadass · 2 points · Posted at 03:54:57 on February 14, 2016 · (Permalink)
Naught times naught equals naught - Jethro Bodine
lank3y · 1 points · Posted at 03:56:14 on February 14, 2016 · (Permalink)
finally something I can stand behind entirely.
jhawkins93 · 2 points · Posted at 03:55:49 on February 14, 2016 · (Permalink)*
If the digits of any number add up to a multiple of 3, then the number itself is a multiple of 3. Example: Take the number 171. 1+7+1=9. 9 is a multiple of 3. So 171 is also a multiple of 3 (57*3=171).
greenzr · 2 points · Posted at 03:56:29 on February 14, 2016 · (Permalink)
I know this is true for 9, but I didn't know for 3.
Skydiv3rLAS · 2 points · Posted at 03:56:43 on February 14, 2016 · (Permalink)
uhhh... If you write down from 0 to 9 and then from 9 to 0 you have the multiplication table of 9:
09
18
27
36
45
54
63
72
81
90
TheSixTen · 2 points · Posted at 03:57:32 on February 14, 2016 · (Permalink)
3-4-5⊿
It's an easy way to square up a room. From an inside corner measure 3' out on Wall 1. From the same corner measure 4' on Wall 2. Measure from point 1 to point 2 and it should be 5'. If you are under 5' your corner is acute and your wall will need to be pushed away from the room, if obtuse then need to bring wall into room.
For larger rooms just double the numbers.
ParallelResistance · 2 points · Posted at 03:59:18 on February 14, 2016 · (Permalink)
They just discovered the next largest known prime number
soulbribra · 2 points · Posted at 04:16:06 on February 14, 2016 · (Permalink)
The answer of any number multiplied by 9 can always be added together to equal 9. For example 9x3=27, 2+7=9. Or a more intense example 9x523=4707, 4+7+7=18 then 1+8=9. Definitely black magic involved here.
Undeadicated · 2 points · Posted at 04:16:58 on February 14, 2016 · (Permalink)
79% of statistics are made up on the spot
[deleted] · 2 points · Posted at 04:25:02 on February 14, 2016 · (Permalink)
.999... = 1
shit's cray
JungleJesus · 2 points · Posted at 04:28:16 on February 14, 2016 · (Permalink)
There are propositions which are undecidable: it's impossible to systematically answer yes or no. For example, there is no way in general to decide if two real numbers are equal.
reddit4rms · 2 points · Posted at 04:32:59 on February 14, 2016 · (Permalink)
9's multiplication table, you write from 0 to 9 in a row, and then on the row below you write from 9 to 0 in descending order.
0 1 2 3 4 5 6 7 8 9
9 8 7 6 5 4 3 2 1 0
xthemoonx · 2 points · Posted at 04:37:18 on February 14, 2016 · (Permalink)
1 2 3 4 5 6 7 8 = 9x2
1 2 3 4 5 6 7 8 = 9x3
1 2 3 4 5 6 7 8 = 9x4
1 2 3 4 5 6 7 8 = 9x5
8 7 6 5 4 3 2 1 = 9x6
8 7 6 5 4 3 2 1 = 9x7
8 7 6 5 4 3 2 1 = 9x8
8 7 6 5 4 3 2 1 = 9x9
ktkps · 2 points · Posted at 04:41:52 on February 14, 2016 · (Permalink)
I'm saving this!!!
[deleted] · 2 points · Posted at 04:55:17 on February 14, 2016 · (Permalink)
I'm late to the party. But I haven't seen anyone mention this yet, and it's probably crazier than anything else in here.
The sum of all of the whole numbers is -1/12.
canon3212 · 2 points · Posted at 04:56:29 on February 14, 2016 · (Permalink)
You need 4 dimensions to rotate in 3 dimensions
Dinosaur_Boner · 2 points · Posted at 04:57:15 on February 14, 2016 · (Permalink)
The circumfrence of the equater divided by the number of days in a year, divided again by the number of degrees in a circle, divided again by 1000 is exactly 1 foot.
philalether · 2 points · Posted at 04:58:21 on February 14, 2016 · (Permalink)
For y=ex, its value and its slope are the same.
fruitsj · 2 points · Posted at 05:02:28 on February 14, 2016 · (Permalink)
That 42 = Life, the Universe, Everything.
McFukinLovin · 2 points · Posted at 05:10:14 on February 14, 2016 · (Permalink)
0!=1
theevilempire · 2 points · Posted at 05:11:04 on February 14, 2016 · (Permalink)
To square a number ending in 5, take the part before 5, multiply by that +1, and tack on 25 to the end.
15 x 15 = 1 x 2 = 2 + 25 = 225 25 x 25 = 2 x 3 = 6 + 25 = 625 35 x 35 = 3 x 4 = 12 + 25 = 1225 Etc.
[deleted] · 2 points · Posted at 05:18:28 on February 14, 2016 · (Permalink)
You only need 23 people in a room to have a good chance of finding two people who share a birthday.
deadhead94 · 2 points · Posted at 05:19:05 on February 14, 2016 · (Permalink)
Not the coolest but my favorite.
1729 is the smallest positive integer that can be expressed as the sum of two cubes in two different ways, 13 + 123 and 93 + 103 . The digits also add up to 19 and when you divide it by 19 the answer is 91.
Sevengrizzlybears · 2 points · Posted at 05:20:10 on February 14, 2016 · (Permalink)
Didn't see this one on here and I find it pretty amazing. People used their own bodies to create the imperial system (Inches, feet, yards, mile, and whatever else).
1000 paces make up a mile. We call 1/8 of a mile a furlong (660 feet). 660 X 12 (inches in a foot) = 7920. There are 7920 miles if you measure the diameter of the Earth from the Tropic of Capricorn to the Tropic of Cancer. So the inch is relative to the furlong as the mile is to the Earths diameter. We are modeled after the Earth. 7920 is also a multiple of 72 which is significant, for that explanation you'll have to get into sacred geometry.
EssenceLumin · 1 points · Posted at 05:27:54 on February 14, 2016 · (Permalink)
Really big paces. 5.28 feet each.
Sevengrizzlybears · 1 points · Posted at 05:54:33 on February 14, 2016 · (Permalink)
Sorry, should have clarified, a pace if you count every time the same foot hits the ground. 2000 steps, 1000 paces.
MischeviousMacaque · 2 points · Posted at 05:23:04 on February 14, 2016 · (Permalink)
One of the most influential mathematicians of all time, Évariste Galois, did all of his work by the age of 20 when he died in a duel resulting from a dispute over a lady friend.
[deleted] · 2 points · Posted at 05:23:38 on February 14, 2016 · (Permalink)
[deleted]
Vortico · 2 points · Posted at 06:14:58 on February 14, 2016 · (Permalink)
1 is also the product of primes (exactly 0 of them)!
clever_cuttlefish · 2 points · Posted at 05:31:56 on February 14, 2016 · (Permalink)
eiπ + 1 = 0
An oldie but a goodie.
Newfoundplanet · 2 points · Posted at 05:35:28 on February 14, 2016 · (Permalink)
Adding all of the digits in a number until there's just one digit left will tell you if a number is evenly divisible by 3.
Example: 46865 becomes 4+6+8+6+5 = 29 which becomes 2+9 = 11 = 1+1 = 2. 2 isn't divisible by 3, therefore neither is 46865.
Save for a weird trivia question, I'll admit it's not very useful.
iluvgrannysmith · 2 points · Posted at 05:56:18 on February 14, 2016 · (Permalink)
It's great if you don't have a calculator. Also, the same trick works for 9. Look for divisibility by 9 instead though
hhtran91 · 2 points · Posted at 05:46:56 on February 14, 2016 · (Permalink)
20 people gathered in a room have a >50% chance that at least two share a birthday
[deleted] · 2 points · Posted at 05:50:44 on February 14, 2016 · (Permalink)
If one was able to imagine Grahams Number, their brain would collapse into a black hole
Enragedocelot · 2 points · Posted at 05:57:39 on February 14, 2016 · (Permalink)
111,111,111 x 111,111,111 = 12345678987654321
j0hnk50 · 2 points · Posted at 05:58:23 on February 14, 2016 · (Permalink)
The area of a four inch circle is equal to the circumference of a four inch circle
[deleted] · 2 points · Posted at 05:59:22 on February 14, 2016 · (Permalink)
11630 is the First Uninteresting Number, which is a paradox, because being the first uninteresting number makes it interesting
FrenchToast1047 · 2 points · Posted at 05:59:48 on February 14, 2016 · (Permalink)
2 multiplied by 2 is the same as 2 plus 2.
water_bottle_goggles · 2 points · Posted at 06:00:35 on February 14, 2016 · (Permalink)
Did you know?
0.9999999..... = 1
1 + 2 + 3 + ..... = -(1/12)
0! = 1
[deleted] · 2 points · Posted at 06:00:53 on February 14, 2016 · (Permalink)
.9999...=1
[deleted] · 2 points · Posted at 06:01:05 on February 14, 2016 · (Permalink)
I give zero fucks.
BulbStar · 2 points · Posted at 06:02:01 on February 14, 2016 · (Permalink)
I learned if you want to calculate the amount of water flowing down a river (Discharge). You calculate the cross sectional area of the river and multiply it by the rivers velocity. That's the basic idea of it.
Yasrynn · 2 points · Posted at 06:02:24 on February 14, 2016 · (Permalink)
There are many levels of infinity, some larger than others.
Edit: Oops! Cheers /u/mightbethrownaway
JFIVEK · 2 points · Posted at 06:02:41 on February 14, 2016 · (Permalink)
I always thought it was neat that...
1 = 1/2 + 1/4 + 1/8 + 1/16 + ... 1/2 = 1/3 + 1/9 + 1/27 + 1/81 + ... 1/3 = 1/4 + 1/16 + 1/64 + 1/256 + ... 1/4 = 1/5 + 1/25 + 1/125 + 1/625 + ...
And so on.
Reala27 · 2 points · Posted at 06:02:58 on February 14, 2016 · (Permalink)*
Base conversion between numbers an be done by dividing by the target number by the target base as represented in the current base, and encoding the integer remainders until you get a 0 for the quotient. For example, converting decimal to binary (base 2). Let's take, say.... 19.
19/2 = 9 with remainder of 1. Encode the 1.
9/2 = 4 remainder 1
4/2 = 2 remainder 0
2/2 = 1 remainder 0
1/2 = 0 remainder 1
10011(base 2) = 19(base 10)
Not convinced? Fine. Let's try... base 20(base 7) to base 9 (12 in base 7 unless I can't count, which is possible)
20(7)/12(7) = 1 remainder 5
1(7)/12(7) = 0 remainder 1
20(base 7) in base 9 = 15 according to Wolfram Alpha.
Reala27 · 1 points · Posted at 06:08:26 on February 14, 2016 · (Permalink)
Also a fun function that I just know exists is the Weierstrass set. https://en.wikipedia.org/wiki/Weierstrass_function This function is continuous everywhere but differentiable nowhere. It's a fractal that changes direction at literally every point, so you cannot possibly take its derivative.
thrylkyl · 1 points · Posted at 09:14:58 on February 14, 2016 · (Permalink)
This is great...I do base conversions differently but this is very interesting.
One thing I don't understand...why do you say according to Wolfram Alpha? Did you use Wolfram to check your answer?
Reala27 · 1 points · Posted at 17:58:17 on February 14, 2016 · (Permalink)
Yes. I forget how to count on occasion, so I ensured I remembered what I was doing.
moldren · 2 points · Posted at 06:05:50 on February 14, 2016 · (Permalink)*
9 times any number always will have an answer that equals 9 if you add the numbers in the answer together.
9 x 53 = 477
4 + 7 + 7 = 18
1 + 8 = 9
Or...
9 × 48215 = 433935
4 + 3 + 3 + 9 + 3 + 5 = 27
2 + 7 = 9
Works with any number multiplied by 9. Fun for the whole family.
Another fun fact about the number 9. Take any number and subtract the reversed version of said number. Now add the numbers in the answer.
518 - 815 = -297
2 + 9 + 7 = 18
1 + 8 = 9
Or...
47213 - 31274 = 15939
1 + 5 + 9 + 3 + 9 = 27
2 + 7 = 9
Works with any number. Go ahead and give it a try. The man in your life will love you for it.
6 + 6 + 6 = 18
1 + 8 = 9
Just had to...
drjimhill · 2 points · Posted at 06:20:15 on February 14, 2016 · (Permalink)
Write down the first three odd natural numbers twice each:
11 33 55
Separate them into two groups of three digits:
113 355
Divide the second by the first:
355/113 = 3.1415929203539825...
Here's pi:
3.141592653589793...
As approximations to pi go, 22/7 can Suck It.
ThePocketCat · 2 points · Posted at 06:20:24 on February 14, 2016 · (Permalink)
Grahm's number is so large that it is larger than the observable universe. It is used in a problem about hypercubes, a theoretical shape. It something I will probably never be able to wrap my head around.
[deleted] · 2 points · Posted at 06:22:07 on February 14, 2016 · (Permalink)
A dozen, a gross and a score. Plus three times the square root of four. Divided by seven. Plus nine times eleven Equals nine squared and not a bit more.
thepopcornwizard · 2 points · Posted at 07:04:45 on February 14, 2016 · (Permalink)
nice limerick
[deleted] · 1 points · Posted at 09:01:40 on February 14, 2016 · (Permalink)
And I'm pretty sure it's mathematically accurate.
bjjdoug · 2 points · Posted at 06:23:59 on February 14, 2016 · (Permalink)
The square root of 69 is 8 something.
mr1000111 · 2 points · Posted at 06:24:05 on February 14, 2016 · (Permalink)
Gabriel's Horn. It blows my mind that a cone can have an infinite internal surface area but a finite volume.
firedrake242 · 2 points · Posted at 06:26:48 on February 14, 2016 · (Permalink)
1112 creates a cycle of numbers that counts from 1 up to X-1 and back down again, with X being the number of digits. It looks like this:
1112 = 121
11112 = 12321
111112 = 1234321
And so on.
[deleted] · 2 points · Posted at 06:40:20 on February 14, 2016 · (Permalink)
The square of a number is always one more than the product of the two surrounding numbers.
TorazChryx · 2 points · Posted at 06:48:42 on February 14, 2016 · (Permalink)
There are FOUR LIGHTS.
Kaaaos · 2 points · Posted at 06:53:51 on February 14, 2016 · (Permalink)
you+me=<3
EnergyFX · 2 points · Posted at 06:54:38 on February 14, 2016 · (Permalink)
Fibonacci Sequence can be used as a rough conversion of miles into kilometers (after the 1s)
1,1,2,3,5,8,13,21,34
It's off by the same percentage no matter how high in the sequence you go.
darksingularity1 · 2 points · Posted at 06:59:34 on February 14, 2016 · (Permalink)
If you have a 4-legged stool that wobbles, within a 45 degree turn, you will find a place it does not wobble.
bryan49 · 2 points · Posted at 07:06:12 on February 14, 2016 · (Permalink)
e ^ (2 * pi * i) = 1
A very beautiful equation, combining two irrational constants as well as an imaginary number, and the answer is just 1!
fanalin · 1 points · Posted at 07:54:42 on February 14, 2016 · (Permalink)
I prefer the form ei*pi + 1 = 0. It's a very good choice!
Weacron · 2 points · Posted at 07:09:59 on February 14, 2016 · (Permalink)
I'll never use Intergral/cal 2 math in computer science on an everyday bases so I'm wasting my money in college.
NotYourAverageTomBoy · 2 points · Posted at 07:39:15 on February 14, 2016 · (Permalink)
That all my life math teachers would say, "It's not like you're going to be carrying calculators with you everyday, all day." 📱
thinksimple · 2 points · Posted at 07:45:54 on February 14, 2016 · (Permalink)
142857 is an amazing number. It cycles itself when multiplied by digits upto 6
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
And to easily remember it divide 999999 by 7
142857 * 7 = 999999
Nathanhoff · 2 points · Posted at 07:52:25 on February 14, 2016 · (Permalink)
YEEZY YEEZY JUST JUMPED OVER JUMPMAN
babrowski · 1 points · Posted at 08:13:04 on February 14, 2016 · (Permalink)
Yes sir
Ursidaelius · 2 points · Posted at 08:00:29 on February 14, 2016 · (Permalink)
1+1=WINDOW
Immortal_Scholar · 2 points · Posted at 08:05:06 on February 14, 2016 · (Permalink)
5318008 on a calculator, turned upside down, spells "Boobies". This amused me through all of my public schooling
anewwayoflearning · 2 points · Posted at 08:05:24 on February 14, 2016 · (Permalink)
The birthday problem.
If you have 23 people in a room there's a 50% chance 2 of them share a birthday.
At 70 people it's a 99.9% chance.
And at 367 people it's 100%
SmartWentCody · 2 points · Posted at 08:05:54 on February 14, 2016 · (Permalink)
If you a shuffle a 52 deck of cards, it's almost certain that what you're holding is the only time that order of cards has ever existed. If you were to create a new permutation every second since the moment the universe began (13.8 billion years ago), you would still be creating new permutations today, and for millions and millions of years to come. There are more ways to arrange the deck of cards than there are atoms on Earth. The number of possible arrangements is 52 factorial (52!) which is 8.065x1067.
Written out, this is: 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.
Source.
Faulknett · 2 points · Posted at 08:10:18 on February 14, 2016 · (Permalink)
i am an imaginary number
Nik_Tesla · 2 points · Posted at 08:11:43 on February 14, 2016 · (Permalink)
1/9 = 0.1111111111...
2/9 = 0.2222222222...
3/9 = 0.3333333333...
4/9 = 0.4444444444...
5/9 = 0.5555555555...
6/9 = 0.6666666666...
7/9 = 0.7777777777...
8/9 = 0.8888888888...
So it makes perfect sense that 0.999999... = 9/9 = 1
CarpeCyprinidae · 2 points · Posted at 08:48:10 on February 14, 2016 · (Permalink)
I never understood that before. Thanks Tesla!
Mickadoozer · 2 points · Posted at 08:18:01 on February 14, 2016 · (Permalink)
The sum of all positive integers is -1/12
InvaderZed · 2 points · Posted at 08:18:24 on February 14, 2016 · (Permalink)
3.5 = 4 just ask /r/nvidia
DrMubutu · 2 points · Posted at 08:18:49 on February 14, 2016 · (Permalink)
ei*pi+1=0
[deleted] · 2 points · Posted at 08:23:47 on February 14, 2016 · (Permalink)
The inner product space <f(x), g(x)> of a closed interval [a,b] is the integral of f(x)g(x) on [a,b]. (If I expressed that properly...)
I dunno why, but the fact that calculus and linear algebra tied so nearly together was kind of cool to me.
Linearts · 2 points · Posted at 08:24:41 on February 14, 2016 · (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.
Illustration from Wikipedia. Look at the central triangle between the circles.
[deleted] · 2 points · Posted at 08:28:05 on February 14, 2016 · (Permalink)
To date, nothing has been as controversial as Lopez Theorem.
Stated, succinctly: k = FU
Where k is Knowledge, and FU is theorized to represent "Fuel Units".
Xavier_OM · 2 points · Posted at 08:37:14 on February 14, 2016 · (Permalink)
You know multiplication is commutative, as in 3 * 2 = 2 * 3
It means that percentages are commutative too : 32% of 50 (hard to compute mentally) is 50% of 32 (easy, 16).
Because obviously (x/100) * y = (x * y) / 100 = x * (y / 100)
filiona · 2 points · Posted at 08:48:08 on February 14, 2016 · (Permalink)
If you mulitply all real numbers (except for zero) you get -1. That's because every number has an inverse (eg. 2 has 1/2, 3 has 1/3, pi has 1/pi and so on) and those pairs cancel each other to 1. -1 is the only number that is its own inverse, so it cant be cancelled to 1. Also works for complex numbers.
BenBro · 2 points · Posted at 08:48:45 on February 14, 2016 · (Permalink)
I tried to read this thread drunk. It hasn't gone well.
zawhiskey · 1 points · Posted at 09:01:07 on February 14, 2016 · (Permalink)
same
sh41 · 2 points · Posted at 08:50:15 on February 14, 2016 · (Permalink)
That 0.999... = 1.
Here are 9.999... reasons: https://www.youtube.com/watch?v=TINfzxSnnIE
adedade · 2 points · Posted at 08:56:41 on February 14, 2016 · (Permalink)
9*2 = 18 1+8 = 9
9*5 = 45 4+5 = 9
9*17 = 153 1+5+3 = 9
9*58 = 522 5+2+2 = 9
This works with every number multiplied by 9, sometimes you'll have to do some extra adding thought. Ex:
9*732 = 6588 6+5+8+8 = 27 2+7 = 9
Tehbeefer · 1 points · Posted at 09:49:05 on February 14, 2016 · (Permalink)
Came here to comment this. Anyone know why it works? I've yet to find a whole number where summing the digits twice doesn't work.
Pr0v3nD1sc1pl3 · 2 points · Posted at 09:05:37 on February 14, 2016 · (Permalink)
Vel'Koz gets 3.1415 AD per Level.
8AzO8 · 2 points · Posted at 09:12:30 on February 14, 2016 · (Permalink)
It is impossible to make a map of the Earth without distortions. The maps we use either show distances correctly or angles not both.
This was proven by Gauss: https://en.wikipedia.org/wiki/Theorema_Egregium
The very best theorems in math are about something being impossible. No other field of science has such power!
PyroStormOnReddit · 2 points · Posted at 09:13:13 on February 14, 2016 · (Permalink)
1*9+2=11
12*9+2=111
123*9+2=1111
1234*9+2=11111
12345*9+2=111111
123456*9+2=1111111
1234567*9+2=11111111
12345678*9+2=111111111
123456789*9+2=1111111111
JHuth · 2 points · Posted at 09:14:43 on February 14, 2016 · (Permalink)
Adding every integer between 0 and infinity equals -1/12
shyguybman · 2 points · Posted at 09:19:01 on February 14, 2016 · (Permalink)
This thread just reminds me of how little I actually remember from Math. A co worker of mine solves calc problems on his lunch break while he eats and I read reddit and watch people play video games on twitch......
UpgrayeDDoubleDose · 2 points · Posted at 09:26:22 on February 14, 2016 · (Permalink)
That 1 is the loneliest number.
reddrip · 2 points · Posted at 09:41:50 on February 14, 2016 · (Permalink)
Well, two can be as bad as 1.
GamerFan2012 · 2 points · Posted at 09:27:46 on February 14, 2016 · (Permalink)
On a TI switch the mode to Polar coordinates. Then graph 5sin(7theta). The result is a Marijuana leaf :)
Raikhyt · 2 points · Posted at 09:40:22 on February 14, 2016 · (Permalink)
The square of every prime number is one more than a multiple of 24.
CarpeCyprinidae · 1 points · Posted at 10:06:02 on February 14, 2016 · (Permalink)*
That can't be right. What about 1,2 & 3? Or am I missing something? Always possible, please educate me if so.
Raikhyt · 1 points · Posted at 13:31:23 on February 14, 2016 · (Permalink)
1 isn't a prime, and 2 and 3 are too small for that rule to work. Otherwise, it's always applicable.
CarpeCyprinidae · 1 points · Posted at 22:36:10 on February 14, 2016 · (Permalink)
My understanding of primes is simplistic - I thought that the definition "divides evenly only by itself and 1" would include 1. I can see that it works for 7 & 11 and cant be bothered to remember or square any higher primes!
PrescriptionCocaine · 2 points · Posted at 18:37:00 on March 7, 2016 · (Permalink)
1 is technically a prime but it isn't practical to use.
TinBitz · 2 points · Posted at 09:41:54 on February 14, 2016 · (Permalink)
The sum of all positive integers equals -1/12 i.e. 1+2+3+4 ... +n = -1/12 This video explains it well https://www.youtube.com/watch?v=w-I6XTVZXww
Drased · 2 points · Posted at 10:08:41 on February 14, 2016 · (Permalink)
Late to the party, as always, but: This guy has proven that Pythagorean trigonometric identity is wrong, which was the main subject of his PhD. He teaches at my University, and still only has master's degree - because comission decided not to give him his title, despite not being able to find any mistakes in his work. The unofficial reason is that did this because otherwise a lot of modern math would be rendered wrong as well.
Legend says that mr Pietraszko (his name) decided not to shave until comission accepts his work and finally gives him his PhD. That was quite a few years ago, as you might have noticed :)
EnkoNeko · 2 points · Posted at 10:16:43 on February 14, 2016 · (Permalink)
Ok I'm not sure if anyone's posted this yet or not, but Pi is actually fucking amazing. Since it is non-repeating yet infinite, every single digit, every single number combination - it's somewhere in Pi.
If you converted it into ASCII text, it would tell the story of your life.
Convert it into a BITMAP, and you would see your life played out.
Really interesting, but if I tried to calculate all that, my computer would most likely blow up.
MacLife
gindc · 1 points · Posted at 15:19:02 on February 14, 2016 · (Permalink)
Pi is irrational. But that doesn't mean it contains every number combination.
EnkoNeko · 1 points · Posted at 08:14:27 on February 15, 2016 · (Permalink)
Ok true, but it would contain a shit ton of them, no?
0.10100100010000100000...
[deleted] · 2 points · Posted at 10:17:30 on February 14, 2016 · (Permalink)
1x1=2. Thanks Terrence Howard!
SausageTape · 2 points · Posted at 10:28:16 on February 14, 2016 · (Permalink)
eiπ -1 =0 e, a completely irrational number. π, another irrational number. i, a number that doesn't actually exist. Put them together and take 1 it equals 0. To me that's almost proof of a god
Swarlsonegger · 2 points · Posted at 10:42:08 on February 14, 2016 · (Permalink)*
I know this is more of a engineering thing than a math thing but:
dB is NOT a unit. Bel stands for log(A/B) while dB is 10*log(A/B).
Why does it matter? well to DOUBLE the intensity of sound all you really do is add 3dB
10* log(2 * A/B) = 10 * log(A/B) + 10 * log(2)
Or to Hundredfold the intensity it's adding 20dB
10 * log(102 * A/B) = 10 * log(A/B) + 20 * log(10)
[deleted] · 2 points · Posted at 10:53:30 on February 14, 2016 · (Permalink)
1 + 2 + 3 + ... = -1/12.
The sum of all positive numbers is equal to minus one twelfth.
Used in physics all the time.
I_am_a_Wookie_AMA · 2 points · Posted at 10:55:24 on February 14, 2016 · (Permalink)
You have to understand that as far as Grandpa's concerned, you're both pieces of shit. Yeah... I can prove it mathematically. Actually, L-l-let me grab my whiteboard, this has been a long time coming anyway.
(Sorry, couldn't help myself.)
Invokationz · 2 points · Posted at 10:57:21 on February 14, 2016 · (Permalink)
cleopatra lived closer to the moon landing than the foundation of the pyramids
BADURAI · 2 points · Posted at 10:59:34 on February 14, 2016 · (Permalink)
So Ramanujan proves, that (hang on): 1+2+3+4+5+6+...+inf=-1/12 That's a very weird series. It can be proves, by the Riemann zeta function. This is also a result use in string theory. https://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Ramanujan_Notebook_1_Chapter_8_on_1234_series.jpg/440px-Ramanujan_Notebook_1_Chapter_8_on_1234_series.jpg
flyonawall · 2 points · Posted at 11:02:15 on February 14, 2016 · (Permalink)
My son, the math Ph.D. grad student.
Aturom · 2 points · Posted at 11:04:16 on February 14, 2016 · (Permalink)
Me plus no one equals a pretty bummed out Valentine's day
[deleted] · 2 points · Posted at 11:06:41 on February 14, 2016 · (Permalink)
e pi*i +1 =0. Eulers identity. Bear with me And just look at the equation. You have pi, the ratio of the circumfrence of a circle to its diameter; 3.1415927 etc. You have "e ", Eulers Constant, which is arguably as important as pi and describes fundamental growth in nature and mathematics. Of course you have 1, the beginning step of all mathematics, and 0 which is a fairly new understanding but an equally mind boggling concept.
Before I get to i , remember that e and pi are not only what are called irrational numbers, they are in fact transcendental numbers. Which means not only can you not describe them with ratios, you cant describe them as solutions to a polynomial with easy numbers. Whats more, integers like 0 and 1 are infinitely rare. For every integer there are uncountably many transcendental numbers. So if you put all the numbers into a hat and pulled one the chance you get an integer like 0 or 1, or even a number you can understand like 1/2, is literally 0. There is no chance of it hapoening in the same sense that there is no chance of you winning every raffle, lottery, game that has every taken place or will ever take place.
Then you have i, the imaginary number, the square root of -1. This was the number that allowed us to describe algebra thoroughly.
So Now you have the 5 fundamental thoughts of mathematics: fundamental growth, roundness, unity, nothingness, and the imaginary number. Two of these numbers are transcendental and would probably produce at least an irrational number. Two of these are integers and would probably produce an integer. But when you combine ALL FIVE THOUGHTS, the formula is so neat that all you need is those 5 thoughts.
in some sense the formula couldnt be anything else, in another sense the probability of the formula existing is 0. Its pretty neat. Check it out! Eulers identity.
CardiffBorn · 2 points · Posted at 11:07:10 on February 14, 2016 · (Permalink)
The equals sign (=) was created by a Welsh man because he was tired for having to write "is equal to" all the time
AdmiralPellaeon · 2 points · Posted at 11:10:48 on February 14, 2016 · (Permalink)
That 7 8 9.
AJockeysBallsack · 2 points · Posted at 11:28:08 on February 14, 2016 · (Permalink)
The fact that at any given time and place, if you tell me something about math, I won't get it.
paragonic · 2 points · Posted at 11:32:40 on February 14, 2016 · (Permalink)
/u/Bromskloss
Bromskloss · 1 points · Posted at 11:37:17 on February 14, 2016 · (Permalink)
Aww, thanks! ;-)
Yaz010 · 2 points · Posted at 11:36:46 on February 14, 2016 · (Permalink)
I have 0% chance on getting a cute girlfriend ;_;
[deleted] · 2 points · Posted at 12:10:42 on February 14, 2016 · (Permalink)
If you divide cos(506) by tan(35) you can see that math is not my strongpoint.
loptthetreacherous · 2 points · Posted at 12:22:50 on February 14, 2016 · (Permalink)
Do you know how, if you differentiate displacement you get velocity and if you differentiate velocity you get acceleration?
Well, it goes: Position, speed, acceleration, jerk, snap, crackle, pop.
doffensmush · 2 points · Posted at 12:24:32 on February 14, 2016 · (Permalink)
pie is 3.14
perhapslevi · 2 points · Posted at 12:24:52 on February 14, 2016 · (Permalink)
Get this... 12345679...multiplied by 8...
98765432.
Math.
Pohatan · 2 points · Posted at 12:58:34 on February 14, 2016 · (Permalink)
A litte late to the party, but the most non-intuitive mathematical result I know of is that if you add up all the natural numbers (i.e 1+2+3+4+...), the answer to the sum is -1/12. The result is even used in string theory (if i remember correctly).
toysjoe · 2 points · Posted at 13:13:44 on February 14, 2016 · (Permalink)
You can keep adding the digits of a long number to see if it's divisible by 3.
Take for example 111,111,111,111 is divisible by 3 because
1+1+1+1+1+1+1+1+1+1+1+1=12
1+2=3
3/3 is 1
So 111,111,111,111 is divisible by 3.
Jayco86 · 1 points · Posted at 13:19:17 on February 14, 2016 · (Permalink)
Holy shit this one is my favorite
Badya122 · 0 points · Posted at 13:20:51 on February 14, 2016 · (Permalink)
You can just take a look at the last digit and figure out? If it's 1,3,6,9 its divisible by 3. If it's 0 or 5, divisible by 5 etc
toysjoe · 1 points · Posted at 13:22:09 on February 14, 2016 · (Permalink)
31 is not divisible by 3
23 is not divisible by 3
16 is not divisible by 3
29 is not divisible by 3
The 0 and 5 rule works but I figure everyone knows that.
Ikhtionikos · 2 points · Posted at 13:20:13 on February 14, 2016 · (Permalink)
Does the fact that I didn't fail a math in high school, so I can go on living my life, almost completely void of math count?
Swate- · 2 points · Posted at 13:51:34 on February 14, 2016 · (Permalink)
Yes.
gives noogie
SBENDEV · 2 points · Posted at 13:27:04 on February 14, 2016 · (Permalink)
5/7 = 1.0000.....
Ava-cado · 2 points · Posted at 13:29:13 on February 14, 2016 · (Permalink)
Okay so 1/3+2/3=3/3=1 right? Well 1/3=.33 & 2/3=.66 and .33+.66 =.999 so then .999=1
DarkTron · 2 points · Posted at 14:41:31 on February 14, 2016 · (Permalink)
With certain fractions (e.g. 1/3), it's impossible to give the true decimal value. As such, you're merely approximating these numbers, rather than giving their true sum.
Ava-cado · 1 points · Posted at 14:51:58 on February 14, 2016 · (Permalink)
I know its only an approximation but it still blew my mind when my teacher showed me this a few years back
thatfatgamer · 2 points · Posted at 13:30:57 on February 14, 2016 · (Permalink)
U + Me >= 1
:D
Butterbean6 · 2 points · Posted at 13:31:45 on February 14, 2016 · (Permalink)
0.99999...= 1.0
Proof:
1/9 = 0.11111....
8/9 = 0.88888...
1/9 + 8/9 = 0.99999.....= 1.0
DarkTron · 1 points · Posted at 14:39:52 on February 14, 2016 · (Permalink)
Not really true. It's impossible to give the decimal value of certain fractions. Your fact is more the sum of 2 approximations to make a new approximation
Butterbean6 · 1 points · Posted at 14:42:54 on February 14, 2016 · (Permalink)
Here's some mathy talk on the subject.
Navel_Linty · 2 points · Posted at 13:35:36 on February 14, 2016 · (Permalink)
25 divided by 1/2 is 50
phrazel · 2 points · Posted at 13:49:17 on February 14, 2016 · (Permalink)
can prove that there exist two irrationals A and B such that A to the power of B is rational without actually having to know what A and B are. Consider the identity:
(sqrt(2)sqrt(2))sqrt(2) = 2
Now, let A = sqrt(2)sqrt(2) and B = sqrt(2). If A is irrational, then A and B are the two irrationals and the proposition is proven. If, however, A is rational, then A’ = B’ = sqrt(2) are such that A’ ^ B’ = A = rational, and the proposition is again proven, since sqrt(2) is irrational.
GatemouthBrown · 2 points · Posted at 14:02:08 on February 14, 2016 · (Permalink)
Halloween = Christmas
OCT31 = DEC25
sgshubham · 2 points · Posted at 14:10:18 on February 14, 2016 · (Permalink)
a real askreddit finally
CrakAndJaxter · 2 points · Posted at 14:14:19 on February 14, 2016 · (Permalink)*
The Rule of 72
Used as a shortcut to determine about how long it takes to double your investment at a certain interest rate.
For example, about how long does it take to double my investment at 5%?
72/5 = 14.4 years
Also, 1+2+3+4+5+4+3+2+1 = 5x5 = 25
arunnair87 · 2 points · Posted at 14:24:05 on February 14, 2016 · (Permalink)
Distributive property.
35 x 12 seems hard to do in your head. But what about
35 x (10 + 2)
(35 x 10) + (35 x 2)
350 + 70
420
Much easier, right?
finalarbiter9 · 1 points · Posted at 06:06:42 on February 15, 2016 · (Permalink)
Lol this is actually how I do most of my multiplication because I never learned my times tables
evilcheesypoof · 2 points · Posted at 14:36:42 on February 14, 2016 · (Permalink)*
Forget what this is called, but I thought it was interesting, it's been done on Mythbusters too.
There are 3 doors but only 1 of them has the prize behind it. You must first pick a door. But before it is opened, 1 of the 2 doors you did not pick is opened to reveal that nothing is behind it and it would have been an incorrect choice.
Now you're given an option
A. Do you open the door you initially picked?
or
B. Do you open the other door that was not yet opened?
At first thought, this might seem pointless because you would think you have a 50% chance of guessing the correct door...but you would be wrong.
The choice that is more likely to be correct is B.
When you make your first pick, there is a 1/3 or 33.3% chance that you've already chosen the correct door, but there is a 2/3 or 66.6% chance that one of the other two doors has the prize. When one of the two unchosen doors is revealed to be incorrect, the odds do not change. The door you initially picked is not all of a sudden more likely to be correct just because one of the incorrect options got taken away, and on that same point, the other two doors that were more likely to contain the prize now only have one option, still at 2/3 chance.
It's weird and it's cool. On Mythbusters they did a large sample size (hundreds of people) and the data came back that people who chose option B. were right more often than people who chose option A.
yerPalSal · 2 points · Posted at 16:22:34 on February 14, 2016 · (Permalink)
That is called the Monty Hall problem; named for the host of the game show Let's Make a Deal.
ck2839 · 1 points · Posted at 14:39:24 on February 14, 2016 · (Permalink)
You don't need to test this in real life like that; it's a mathematical fact, and you can't disprove it.
evilcheesypoof · 1 points · Posted at 14:46:38 on February 14, 2016 · (Permalink)
Some people like me didn't know about it and some people aren't so quick to trust it because it sounds wrong at first, testing it like that helps people understand it easier.
ck2839 · 1 points · Posted at 14:49:04 on February 14, 2016 · (Permalink)
If you switch doors, then you win if and only if you previously chose the wrong door (which has probability 2/3). So it's quite intuitive.
evilcheesypoof · 1 points · Posted at 14:52:33 on February 14, 2016 · (Permalink)*
I know, that's what I put in my first post. I'm just saying I've heard/seen people be puzzled by it. I know it didn't make sense to me at first.
huntinjj · 2 points · Posted at 14:36:59 on February 14, 2016 · (Permalink)
Stephen Curry is shooting 60% from 3pt range and the rest of the league is shooting 58% from 3ft or less.
edelweiss45 · 2 points · Posted at 14:48:29 on February 14, 2016 · (Permalink)
Euler's identity is the most beautiful mathematical equation, linking the numbers e, pi and i: eπ * i = -1
ben175 · 2 points · Posted at 14:48:33 on February 14, 2016 · (Permalink)
f(x) = ex f'(x) = ex
ex is its own derivative bc the derivatives with bases of e are: eu * u'
zeroone · 2 points · Posted at 15:12:56 on February 14, 2016 · (Permalink)
http://imgur.com/a/MvbNj
Z3NZY · 1 points · Posted at 15:37:08 on February 14, 2016 · (Permalink)
Whut?
SAGNUTZ · 1 points · Posted at 19:06:33 on February 14, 2016 · (Permalink)
Was "A" trying to logic break a bot("B")?
Dietorelle · 2 points · Posted at 15:39:30 on February 14, 2016 · (Permalink)
32 + 42 = 52
WilliamcoHolm · 2 points · Posted at 15:42:24 on February 14, 2016 · (Permalink)
Commenting so i can easily find this thread again
Ramroder · 2 points · Posted at 15:51:04 on February 14, 2016 · (Permalink)
82% of all statistics are bullshit.
r0r0r0 · 2 points · Posted at 16:04:09 on February 14, 2016 · (Permalink)
Binary counting makes a pretty good beat: https://vimeo.com/1639345
tas1495 · 2 points · Posted at 16:14:16 on February 14, 2016 · (Permalink)
ei*pi+1=0
Fibreoptix · 2 points · Posted at 16:26:38 on February 14, 2016 · (Permalink)
If the universe was a goggleplex light years acroos, as you travel you would hit a region of space where some one there not just looks like you but is a complete carbon copy of you. Mole for mole, hair for hair and DNA for DNA. There would be no distinguishable difference at all. Even down to your scars.
Blue_Dog_Democracy · 1 points · Posted at 17:39:25 on February 14, 2016 · (Permalink)
Is that on average, or would you really just run into an exact replica? I'm not sure I understand why that would be.
Fibreoptix · 2 points · Posted at 18:49:39 on February 14, 2016 · (Permalink)
the atom arrangements of the volume of space you occupy can only be so much regardless of the staggering number. I think it's 10 to the power of 100 to the power of 86 or something like that. And a Google plex is 10 to the power of 100 to the power of 100. So you'll hit a point where things just duplicate.
JinsChina · 2 points · Posted at 16:38:28 on February 14, 2016 · (Permalink)
eipi + 1 = 0
adamsvette · 2 points · Posted at 18:57:27 on February 14, 2016 · (Permalink)
0 time anything is how many valentines i have.
Ballistics · 2 points · Posted at 19:43:06 on February 14, 2016 · (Permalink)
Inverse square law. Pretty fascinating. Doubling the distance will halve the power of light, sound etc. It's obviously a lot more elaborate than that of course, but worth looking up.
iamaskier123 · 2 points · Posted at 20:33:33 on February 14, 2016 · (Permalink)
Can't believe I didn't see this one scrolling through: The sum of all of the counting numbers (i.e. you do 1+2+3+..... to infinity) = -1/12
Furthermore, the sum of all counting numbers squared (12 + 22 +....) = 0, same goes for any even numbered exponent on this series.
These both come from the Riemann Zeta function.
Good video here:https://www.youtube.com/watch?v=w-I6XTVZXww
Riemann Zeta Function:http://i.stack.imgur.com/q0XjQ.gif
[deleted] · 2 points · Posted at 07:40:37 on February 15, 2016 · (Permalink)
22222*55555 = 123454321
3geek14 · 1 points · Posted at 14:24:07 on February 15, 2016 · (Permalink)
You left out the 0 at the end. 22222*55555=1234543210
[deleted] · 1 points · Posted at 16:42:00 on February 15, 2016 · (Permalink)
Sorry mate. <3
RhusPeg · 2 points · Posted at 08:59:45 on February 17, 2016 · (Permalink)
9 times table on the fingers is a sweeeeeeeeet trick
Chattle · 2 points · Posted at 00:05:14 on February 19, 2016 · (Permalink)
You + me = us I know my calculus
teyxen · 2 points · Posted at 18:40:42 on February 19, 2016 · (Permalink)
ii = e-pi/2.
That's pretty out there for me.
dsmith1067 · 2 points · Posted at 22:39:08 on February 19, 2016 · (Permalink)
I recently learned that the number of possible shuffles of a deck of cards is so large, that it is likely that every shuffle of any deck of cards, since the invention of cards, is probably unique (despite the number of decks and shuffles happening all the time).
Link: Here
The whole video is cool, but this was astounding to me. I'm not even sure it counts as a math fact tbh.
cowboy_alien · 2 points · Posted at 19:39:13 on February 20, 2016 · (Permalink)
I am surprised nobody mentioned Euler's(pronounced Oiler) Identity:
http://wordpress.mrreid.org/wp-content/uploads/2012/07/euler-identity.png
Gauss once said of this,"If you can't appreciate its beauty in first glance, you can never become a mathematician". Seriously this one equation contains all the major mathematical constants from different fields. e= Euler's Number, basis of Natural Logarithms and used in Calculus.
i=square root of -1(Complex Numbers)
pi= Needs no introduction.
1 and 0
NowC204 · 1 points · Posted at 21:52:10 on February 22, 2016 · (Permalink)
Don't worry, someone did mention it. And thanks for your explanations
regular-normal-guy · 2 points · Posted at 23:07:03 on February 23, 2016 · (Permalink)
An algorithm was written to construct a series of theoretical books. The books contain the letters A through Z, spaces, commas, and periods in every permutation possible.
It's called the "Library of Babel"
These "books" contain: everything that has ever been written with those characters, everything that WILL ever be written with those characters, the exact date and time each of us were born, the exact date and time each of us will die. Your entire life can be found on pages inside books in this digital library (kind of...).
This portion of Vsauce's video can explain it much better. Messages For The Future 17:04
Whats_Up4444 · 2 points · Posted at 03:26:32 on February 25, 2016 · (Permalink)
Pi increased by 1337% = 42
Moppeter · 2 points · Posted at 14:40:00 on February 25, 2016 · (Permalink)
I know this will get buried because I am wayyyy to late but to multiply a two digit dumber by 11 just add them together and put that in the middle.
Example:
22 x 11 = 242 ////// 2 + 2 = 4 and put the 4 between the numbers.
ProjectSnipe · 2 points · Posted at 06:33:24 on March 6, 2016 · (Permalink)
5 = 7
AroundtheTownz · 7 points · Posted at 22:28:32 on February 13, 2016 · (Permalink)
ITT: People having no idea what's going on (me included).
[deleted] · 5 points · Posted at 00:16:15 on February 14, 2016 · (Permalink)*
[deleted]
jpdubbbs · 3 points · Posted at 02:26:53 on February 14, 2016 · (Permalink)
Or numberphile
[deleted] · 3 points · Posted at 02:51:45 on February 14, 2016 · (Permalink)
[deleted]
prmcd16 · 2 points · Posted at 03:05:30 on February 14, 2016 · (Permalink)
source? sounds interesting.
Waniou · 2 points · Posted at 06:05:50 on February 14, 2016 · (Permalink)
I think he's referring to how Maxwell used his four equations (That is, not all known physics equations) to demonstrate that light is an electromagnetic wave.
Personthingman2 · 2 points · Posted at 03:54:07 on February 14, 2016 · (Permalink)
This is a really sketchy statement for me. Can we get a source?
Waniou · 1 points · Posted at 06:07:01 on February 14, 2016 · (Permalink)
He's... almost right. I think he's referring to how Maxwell used his four equations to demonstrate that light is an electromagnetic field.
Waniou · 1 points · Posted at 06:05:20 on February 14, 2016 · (Permalink)
Err... not quite. I think what you're referring to is Maxwell's equations. That's not "all known physics equations", it's four specific equations that describe how electric and magnetic fields work. Two of these equations show that a changing electric field will generate a magnetic field, and a changing magnetic field will generate an electric field. Since generating a magnetic field is changing a magnetic field, this generates a new electric field, which generates a magnetic field and so on. For the most part, the new fields are progressively weaker until they become trivially weak and basically disappear. What Maxwell demonstrated that, if you have a wave moving at a specific speed, you could get a self sustaining electromagnetic wave. That is, a changing magnetic field that generates an electric field that's strong enough to create an identical magnetic field and it carries on, effectively forever. By plugging this into the four original equations, he got the speed of the wave and found it to be the speed of light, and this was some of the original evidence that light was an electromagnetic wave.
HKGxPython · 5 points · Posted at 03:04:29 on February 14, 2016 · (Permalink)
That even Graham's number, which is unfathomably large, is nothing compared to the weight of your mom.
[deleted] · 5 points · Posted at 06:10:09 on February 14, 2016 · (Permalink)
8008 spells boob
etpooms · 3 points · Posted at 21:29:31 on February 13, 2016 · (Permalink)
There are two diametrically opposite points on the Earth's equator where the temperatures are equal.
F-0X · 2 points · Posted at 22:06:42 on February 13, 2016 · (Permalink)
Borsuk-Ulam theorem
almightySapling · 2 points · Posted at 23:14:02 on February 13, 2016 · (Permalink)*
Go up a dimension and things get crazier: there is a pair of antipodal points on the earth's surface with identical temperature and humidity.
hijomaffections · 1 points · Posted at 05:31:42 on February 14, 2016 · (Permalink)
But not necessarily both at the same spot, if i understood the theorem properly, since those are those different continuous functions
almightySapling · 1 points · Posted at 05:33:14 on February 14, 2016 · (Permalink)*
Yes, at the same spot.
Edit: The Reason Why
The theorem says "any continuous map from the n-sphere to Euclidean n-space". "n-sphere" can be a little confusing, because n refers to the dimension of the surface of the sphere. So a 1-sphere is a circle, and a 2-sphere is the surface of a ball.
Temperature is a 1-dimensional value. As is Humidity. So taken separately, you have 2 different continuous functions from S2 to R1. I can simply define a new function f(p)=(T(p),H(p)) which is a continuous function from S2 to R2, so the theorem says there is a pair of points p and q on the surface of the earth where f(p)=f(q) and p=-q.
onairmastering · 4 points · Posted at 00:39:07 on February 14, 2016 · (Permalink)
ITT: People who need to read Malba Tahan's "The man who counted"
I read it as a kid, around 20 times and as an adult, pretty much the same amount. It is the sweetest Math tale.
Flufflepuffle42 · 4 points · Posted at 02:56:13 on February 14, 2016 · (Permalink)
The millionth number of PI is 0.
Flick1981 · 1 points · Posted at 05:39:07 on February 14, 2016 · (Permalink)
The billionth is 1
marpocky · 1 points · Posted at 11:02:48 on February 14, 2016 · (Permalink)
Well it had to be something
ArthurTheAstronaut · 3 points · Posted at 02:56:54 on February 14, 2016 · (Permalink)
There is an infinite amount of values between 0 and 1.
High school teacher said that.
My mind melted when I realized she was right.
dubbs505050 · 2 points · Posted at 02:59:38 on February 14, 2016 · (Permalink)
I told this to my 4th graders and they just went blank. I should probably teach high school instead.
ArthurTheAstronaut · 2 points · Posted at 03:17:55 on February 14, 2016 · (Permalink)
I wish my 4th grade teacher would have pointed this out to me! I feel jaded for having not been told that before high school :P
AutoBiological · 1 points · Posted at 02:59:26 on February 14, 2016 · (Permalink)
And not all infinite sets are the same size?
Hitokage_Tamashi · 3 points · Posted at 03:08:36 on February 14, 2016 · (Permalink)
More of an observation than anything, but 2 is the only number that you can add to itself, multiply by itself, and square by itself and still get the same result- 4
Felix_Tholomyes · 4 points · Posted at 03:18:15 on February 14, 2016 · (Permalink)
0 works as well.
Hitokage_Tamashi · 1 points · Posted at 03:20:38 on February 14, 2016 · (Permalink)
...Fuck. Uh.. Uh.. Uh.... Uhhh.. Two is uh... Uh.. The only number with uh... Substance that you can do that with! Yeah! That works!
'l'llseemyselfout
blakeh95 · 2 points · Posted at 05:31:41 on February 14, 2016 · (Permalink)
If you say raise to it's own power, then you would be correct. Furthermore, this holds true for the higher hyperoperations as well.
Jiggahawaiianpunch · 3 points · Posted at 03:28:19 on February 14, 2016 · (Permalink)
5318008 upside down
bucky_8 · 4 points · Posted at 11:36:22 on February 14, 2016 · (Permalink)
Typing 8008 on a calculator spells boob.
Euerfeldi · 5 points · Posted at 19:50:56 on February 13, 2016 · (Permalink)
In a room of just 23 people there’s a 50% chance that two people have the same birthday
Genderbent_Gilgamesh · 5 points · Posted at 20:09:25 on February 13, 2016 · (Permalink)
How?
You_Are_Blank · 8 points · Posted at 20:25:57 on February 13, 2016 · (Permalink)
If you have two people in a room, there's a 1/365 chance they share the same birthday. Pretty obvious.
Well, what if you have four people in a room? Turns out it's not 3/365, but actually about 1/61! Why? Well, now each person has about a 3/365 chance of sharing the birthday with someone else in the room, right? So you'd think it'd be three times more likely. But there are more possible pairs now, so the odds go up more.
With two people, there is only one possible pair. But with three people, there are 3 possible pairs. And with 4, there are 6 possible pairs. With 5 people, there are 10 possible pairs. With 6 people, 15 possible pairs. By the time we get to 23, there are 253 possible pairs of people, each with a 1/365 chance of sharing a birthday.
As you add more people, you not only increase the chances that a single individual person in the room shares a birthday with someone else in the room, but you also increase the number of chances by having more people.
WildxYak · 2 points · Posted at 21:10:02 on February 13, 2016 · (Permalink)*
This table can be helpful for some to help understand it.
kogasapls · 1 points · Posted at 09:05:38 on February 14, 2016 · (Permalink)
This explanation is incorrect. Your last line has the right idea; each new person increases the chances of every other person sharing a birthday with someone.
1 person having a unique birthday is certain: 365/365 A second person having a unique birthday is true on 364/365 days A third person having a unique birthday is true on 363/365 days etc.
The probability of an nth person having a unique birthday is (365 - n)/365 assuming (n-1) people have already been established with unique birthdays. To find the total probability of n people with unique birthdays, you find the chances of 1 unique birthday * the chances of a second * the chances of a third * ... * the chances of an nth:
(365 * 364 * 363 * ... * [365 - n]) / (365n)
That top number can also be expressed as a quotient of factorials
365 * 364 * 363 * ... * (365 - n) = 365! / (365 - n)!
Meaning the chances of n people having unique birthdays is
[365! / (365 - n)!] / 365n
or in its final form:
P(n) = 365! / [(365 - n)! * 365n]
The probability of at least 2 of n people having a birthday is 1 - P(n) because when it is NOT true that everyone has a unique birthday, then it is true that at least 2 people share a birthday.
1 - P(n) > 0.5 at n=23
The graph of this new function is slightly different from the one implied by your description of pairings and 1/365 chances.
Acemcbean · 5 points · Posted at 20:13:38 on February 13, 2016 · (Permalink)
It's relative to statistics and some applied mathematics. IIRC at 70 people the percentage is about 90%. Sorry for no sauce, I don't have any time currently, but hopefully another kind redditor can help out
kogasapls · 1 points · Posted at 08:59:50 on February 14, 2016 · (Permalink)
Yep, it's just past 99.9% with 70 people.
regdayrF · 1 points · Posted at 21:08:18 on February 13, 2016 · (Permalink)*
Assumption: Each day of the year is as likely to be a birtday as another day. Every birthday of the people in the room are independent to each other.
AC = No person has birthday on the same day
A = At least 2 persons have birthday on the same day
P(A) = 1 - P(AC ) = 1-(365!/(36523 *342!))
Small reminder: 365!/342! = 365 * 364 * ... * 343
( This is the amount of possibilities, that are out there for 23 different birthdays, now you just have to divide it by 36523, which is the amount of possibilities for the experiment. )
It follows the same principle as the possibility for one specific number on a dice to appear. P(B) = 1/6 --> P(BC ) = 1 - P(B) = 5/6. B being the event for one specific number to appear. BC being the event for this specific number not to appear. You have 6 numbers in total, and each number represents one possibilities. In this case 6 ~ 36523 and 5 ~ 365!/342!
user725 · 1 points · Posted at 01:01:16 on February 14, 2016 · (Permalink)
It helps if you look at is as 2 of them will have the same birthday, it's not just with your birthday.
LucifersBarrister · -17 points · Posted at 20:02:23 on February 13, 2016 · (Permalink)
False: Put 366 people in a room, each with a different birthday and there is 0% chance any of them have the same birthday.
MichaelOChE · 3 points · Posted at 20:16:46 on February 13, 2016 · (Permalink)
You're technically correct, but that doesn't disprove the 50% chance statement.
tillerman35 · 2 points · Posted at 13:20:27 on February 14, 2016 · (Permalink)
My son was seven or eight years old when he discovered this:
We were going over the "cheats" for divisibility (e.g. an integer is divisible by five if it ends in 0 or 5).
The "is divisible by three" heuristic was giving him trouble. Traditionally, you add up all the digits of an integer as if they were in the one's place, and if the resulting sum is divisible by three, then the original number was as well.
For example 9132 is divisible by 3 because 9+1+3+2 = 15, and 15 is divisible by 3.
When we showed him a few examples, he said "but you don't have to add them ALL up. Just add the ones that aren't already multiples of three." And then he did just that for each of the examples we'd been working with.
Same example: 9132 is divisible by 3 because 1 + 2 = 3, and 3 is obviously divisible by 3. I tried dozens of numbers, and it blew me away: it worked for every one.
I'd never seen that in any text book, and I couldn't find any reference to that method on the internet. So I found the proof for the traditional method and dicked around with it until I could show that, sure enough, you only have to add digits 1,4,7,2,5 and 8 (0+1, 3+1, 6+1, 3-1, 6-1, 9-1) to determine divisible-by-three.
I was completely freaked out. My pre-teen kid was able to intuitively grasp a mathematical fact that no person (as far as I could tell with the research material available to me at the time) had ever figured out.
nofaceniceface · 2 points · Posted at 16:10:07 on February 14, 2016 · (Permalink)
That is definitely great intuition for a 7/8 year old. Hopefully your proof gave you an intuitive sense for why this is true. For anyone else that is wondering:
When a value is divisible by 3 (this works for any other value) adding another value that is also divisible by 3 will yield a sum that is still divisible by 3.
Ex. 9 + 12 = 21. All these terms are divisible by 3.
Why is this relevant?
When considering an integer, you can separate the digits into two sets, those divisible by 3 ,set X = (0,3,6,9) and those that are not set Y= (1,2,4,5,7,8). If all the digits in set Y add up to a number divisible by 3, then adding any number of digits from set X would adhere to the principle stated above (adding two numbers divisible by 3). That is why one only needs to consider the digits from set Y.
Ex. Is 6319572628301 divisible by 3?
Splitting the digits into the two sets, we have: 6,3,9,6,3,0 1,5,7,2,2,8,1
Adding up the terms in the second set: 1+5+7+2+2+8+1 = 36
This is divisible by 3. Then, as all the terms, 6,3,9,6,3,0, are divisible by 3, the sum of the terms is divisible by 3 (the sum is 27), and adding that to 36 is 63, also divisible by 3. It was unnecessary to consider the terms: 6,3,9,6,3,0.
Hope this helps, and isn't too wordy.
gaussjordanbaby · 1 points · Posted at 15:03:14 on February 14, 2016 · (Permalink)
Not sure why you got the down vote. That's pretty smart for a 7/8 year old to notice.
[deleted] · 2 points · Posted at 19:22:18 on February 13, 2016 · (Permalink)
The golden ratio is replete throughout nature
yocum137 · 1 points · Posted at 01:53:06 on February 14, 2016 · (Permalink)
Not sure why you're getting down voted. Have an up vote.
Golden ratio is absolute beauty from ferns to shells to... EVERYTHING!
The Chicago Museum of Science and Industry has an entire exhibit on Numbers in Nature and it's fantastic!
http://www.msichicago.org/whats-here/exhibits/numbers-in-nature/
acatcus · 2 points · Posted at 03:54:46 on February 14, 2016 · (Permalink)
Nope. Read this: https://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm
yocum137 · 1 points · Posted at 14:48:27 on February 14, 2016 · (Permalink)
I stand corrected. More man made than natural. It is, as they say, pleasing to the eye though.
acatcus · 1 points · Posted at 23:12:40 on February 14, 2016 · (Permalink)
It's a mistake a lot of people, including me, fall for. It's a romantic notion. But if you study maths you find it's about structure and concepts, rather than magic properties of numbers. The whole golden ratio madness is not really meaningful, not to mention 99% of the logarithmic spirals claimed to be golden spirals in nature do not fit the ratio at all. It's a lot more meaningful and useful to study logarithmic spirals themselves and how they can be generated, rather than any specific ratio. Sure the golden ratio has many interesting properties, but it's not magic. Just interesting
gsuthi · 2 points · Posted at 21:26:30 on February 13, 2016 · (Permalink)
That one ∞ can be bigger than another (but don't shoot me, this is what I remember my maths teacher telling me about a couple years ago). It goes something like this:
So say you count from 1 onwards - 1, 2, 3, 4... etc. forever, that's an infinite amount of numbers.
Now do the same, but do it, and go up in 2s. So 2, 4, 6, 8 etc. You'll also be counting infinitely.
However, (and this is the slightly confusing bit for me) as much as they are both infinite, the second set of numbers contains half as many numbers as the first, making the first infinite bigger than the other.
EDIT: I had to look this up because I'm not great at explaining it, but here's a link - https://youtu.be/A-QoutHCu4o
ifarmpandas · 5 points · Posted at 21:59:20 on February 13, 2016 · (Permalink)
Your two examples are of the same class of infinity. You can easily show a 1 to 1 mapping between the 2 sets by multiplying the 1st set by 2 to get the 2nd set.
You can't find such a mapping between real numbers and integers though, so real numbers are in fact in a different class of infinity than integers.
gsuthi · 1 points · Posted at 22:12:09 on February 13, 2016 · (Permalink)
Ah right I see, I knew I messed something up, thank you!
Mage_of_Shadows · 1 points · Posted at 22:39:48 on February 13, 2016 · (Permalink)
You could just say all the numbers between 1 and 2 and all the numbers between 1 and 3
481x462 · 1 points · Posted at 22:49:09 on February 13, 2016 · (Permalink)
The two infinities you described are the same size, we call it countably infinite. As the source you linked says, if you can pair them off with no leftovers, then they're the same size. And if they can be mapped to the natural numbers, can be listed, then they are countably infinite, like in Hilbert's Hotel.
"Some infinities are bigger", the bigger infinity is uncountable, where there can be no system by which we could count the number of elements without missing any. Real numbers are uncountable, like your link shows any list of real numbers will be missing the specially constructed one. And similarly, these uncountable infinities are the same size if they can be mapped to each other, your link shows the real interval [0,1] mapped to [0,2], but can also be mapped to the entire real number line, and also to 2D space and more with Hilbert's curves.
yahtzeeshots · 2 points · Posted at 01:04:04 on February 14, 2016 · (Permalink)
I think I learned this on Reddit: So 238% of 62 is 62% of 238
Input any two numbers you like for 62 and 238 and it's still true.
Easy example:
200% of 10 = 20
10% of 200 = 20
somadIcanteven · 4 points · Posted at 03:13:18 on February 14, 2016 · (Permalink)
That's the commutativity (and associativity) of multiplication at work.
a% of b = (a / 100) * b = a * (1/100) * b
b% of a = (b / 100) * a = b * (1/100) * a
yahtzeeshots · 1 points · Posted at 07:33:26 on February 14, 2016 · (Permalink)
Well I know how it works but when I saw it written that way (how I wrote it) it kinda blew my mind
[deleted] · 2 points · Posted at 01:19:46 on February 14, 2016 · (Permalink)
One for the non-mathematical: there are an infinite amount of numbers between 2 and 3, and none of them are 4.
ehmatthes · 2 points · Posted at 03:38:01 on February 14, 2016 · (Permalink)
The formula for the force of gravity (in non-relativistic situations) is:
F = GmM/r2
In this equation, the number 2 is exact. It's not 2.01, or 1.99. It's not 2.00001 or 1.99999. As far as we have experimentally tested, the force of gravity is related to exactly the inverse square of the distance between two objects.
[deleted] · 2 points · Posted at 03:43:51 on February 14, 2016 · (Permalink)
[deleted]
BeBopBats · 1 points · Posted at 03:47:21 on February 14, 2016 · (Permalink)
Damn, that is cool. New party trick.
Karnatil · 1 points · Posted at 03:55:35 on February 14, 2016 · (Permalink)
Works for more than 2 digit numbers, too. Just add the first and second/second and third/third and fourth etc. digits, put them in the order you calculated between the first and last digit. Just remember to carry the tens.
For instance 11 x 11238654 becomes (1)2-3-5-11-14-11-9(4) which is 123625194.
cszlo · 1 points · Posted at 03:58:41 on February 14, 2016 · (Permalink)
11*99=1089 :(
I think it breaks after 90, but still very cool!
[deleted] · 2 points · Posted at 04:26:52 on February 14, 2016 · (Permalink)
It breaks any time the two digits add up to more than 9.
[deleted] · 2 points · Posted at 05:55:59 on February 14, 2016 · (Permalink)
5318008 upside down on a calculator spells BOOBIES.
TijuanaPoker · 2 points · Posted at 06:38:30 on February 14, 2016 · (Permalink)
15 + 1 in the chamber = you're dead.
Utming · 2 points · Posted at 07:05:46 on February 14, 2016 · (Permalink)
There are an infinite amount of numbers between 1 and 2, and an infinite number between 2 and 3... so between 1 and 3 there are infinite, but twice as many...
Birds_iView · 2 points · Posted at 08:12:31 on February 14, 2016 · (Permalink)
80085
TheAlias6 · 2 points · Posted at 11:24:08 on February 14, 2016 · (Permalink)
Infinity = -1/12
city_dweller · 0 points · Posted at 11:57:19 on February 14, 2016 · (Permalink)
Wrong. Sum to infinity is -1/12
dizzysexkitten · 2 points · Posted at 19:18:42 on February 13, 2016 · (Permalink)*
Is this mathematical enough?
A cubic yard of water weighs a ton
A cube of 14.2 inches of gold weighs a ton
Always thought that was amazing.
Also, how many quarts in a dozen, asked orally, stumps a lot of people, most of whom claim there aren't any.
Sheldon Cooper says 73 is the best number.
DanTheTerrible · 28 points · Posted at 19:50:46 on February 13, 2016 · (Permalink)
I think you have your units confused. A cubic meter of water weighs a metric ton. A cubic yard doesn't come out to anything even, its about .841 US tons.
[deleted] · 1 points · Posted at 15:20:37 on February 14, 2016 · (Permalink)
This is one of many reasons people like to use metric.
dizzysexkitten · -1 points · Posted at 19:54:30 on February 13, 2016 · (Permalink)
Sorry, I was never a mathlete. Sadly, I only watched from the stands, as the brave mathletes wrestled with the universe(s).
DanTheTerrible · 8 points · Posted at 19:57:48 on February 13, 2016 · (Permalink)
In my school system we had math olympics. Which I first competed in in high school, then later on in college served as a proctor. Which doesn't mean I have anything to brag about, it just lets me sound like an anal pedant on threads like this.
dizzysexkitten · 12 points · Posted at 20:01:24 on February 13, 2016 · (Permalink)
We did too. I played the left out position.
ArthurTheAstronaut · 1 points · Posted at 03:06:02 on February 14, 2016 · (Permalink)
Most underrated reddit comment ever.
patiofurnature · 12 points · Posted at 20:39:20 on February 13, 2016 · (Permalink)
In a dozen what? In a dozen quarts? 12. But the question doesn't tell you that, so you can't answer it. A quart is a unit of measure and a dozen is a number.
dizzysexkitten · -3 points · Posted at 20:59:49 on February 13, 2016 · (Permalink)
How many anything in a dozen?
patiofurnature · 6 points · Posted at 21:02:48 on February 13, 2016 · (Permalink)
12 units. But answering the question requires converting the units to quarts. So if you asked, "how many quarts in a dozen gallons?" the answer would be 48.
dizzysexkitten · -6 points · Posted at 21:09:57 on February 13, 2016 · (Permalink)
If I have 12 quarts. I actually don't know how many quarts I have. The more you know...thanks.
Duuhh_LightSwitch · 2 points · Posted at 21:47:51 on February 13, 2016 · (Permalink)
You said "how many quarts in a dozen". To you, the implied 'dozen quarts' seems obvious because you're asking the question. But you didn't specify.
How many quarts in a dozen quarts?
How many quarts in a dozen gallons?
How many quarts in a dozen bottles of beer?
Those all have different answers
dizzysexkitten · 0 points · Posted at 22:01:36 on February 13, 2016 · (Permalink)
I know, I know, fuck me, right?
orcscorper · 1 points · Posted at 05:31:47 on February 14, 2016 · (Permalink)
Username checks out.
patiofurnature · 3 points · Posted at 21:14:00 on February 13, 2016 · (Permalink)
You never said you had 12 quarts. You said you had 12. I don't understand how you can read my last comment and not understand your mistake, so I'll just let this end here.
chilly-wonka · 1 points · Posted at 22:01:34 on February 13, 2016 · (Permalink)
It works grammatically, because a lot of things are implied/assumed in English grammar. I'm better at this than you [are]. He dances like an elephant [dances]. How many quarts are in a dozen [quarts]?
Duuhh_LightSwitch · 2 points · Posted at 22:03:56 on February 13, 2016 · (Permalink)
Yes, it does work. But it leads to an ambiguous question
dizzysexkitten · 2 points · Posted at 22:21:12 on February 13, 2016 · (Permalink)*
Exactly, Sir Lancelot.
FatherStorm · 2 points · Posted at 03:14:45 on February 14, 2016 · (Permalink)
how many quarks are in a dozen eggs?
[deleted] · 1 points · Posted at 04:24:00 on February 14, 2016 · (Permalink)
But then there's also the not knowing quarts of what. How many quarts of milk are in a dozen quarts of cement?
chilly-wonka · 1 points · Posted at 05:01:08 on February 14, 2016 · (Permalink)
9.31
dizzysexkitten · -1 points · Posted at 22:20:27 on February 13, 2016 · (Permalink)*
I'm so sad. English is a nondeterministic grammar. Unlike a computer language which is not. Reality. The more you know...WHY are you slapping me?
o_shrub · 6 points · Posted at 19:27:13 on February 13, 2016 · (Permalink)
Maybe technically not mathematical, but the gold thing is astonishing. A 14" cube of gold weighing a ton? I figured you must have had it wrong. Nope, you're right....
WildxYak · 2 points · Posted at 21:08:10 on February 13, 2016 · (Permalink)
A litre of water weighs 1kg.
Petrol weighs about 0.75kg per litre.
dizzysexkitten · -1 points · Posted at 21:11:51 on February 13, 2016 · (Permalink)*
I like that too. But, are you Arab? Gold is much more impressive, to me, than Petrol. Though they are somewhat synonymous, I'll agree. Black gold, Texas tea. And tons beat the living dogsnot out of kg as far as impressive goes, dontcha think?
WildxYak · 1 points · Posted at 21:21:49 on February 13, 2016 · (Permalink)
An arab you say?! No.
Just I've found knowing those weights can be useful to most people. I guess knowing the weight of gold is probably mostly useful to, well, arabs.
dizzysexkitten · 1 points · Posted at 22:17:17 on February 13, 2016 · (Permalink)
lol. It's all monkey business.
tehftw · 2 points · Posted at 21:50:06 on February 13, 2016 · (Permalink)
Final proof that imperial system must be outlawed.
Ugsley · 1 points · Posted at 06:51:00 on February 14, 2016 · (Permalink)
Yes 73 is the best answer, because the answer to a question asking how many of ANYTHING in a dozen must always be 12.
Ugsley · 1 points · Posted at 06:51:02 on February 14, 2016 · (Permalink)
Yes 73 is the best answer, because the answer to a question asking how many of ANYTHING in a dozen must always be 12.
Riobhain · 0 points · Posted at 22:13:55 on February 13, 2016 · (Permalink)
There's a number for the number of numbers there are (Aleph-Null), and, because it is a number, you can do numbery things to it. As such, there is a number that is two times Aleph-Null (Aleph-One), which is exactly twice as large, even though both are infinitely large.
almightySapling · 22 points · Posted at 22:54:59 on February 13, 2016 · (Permalink)
Woooooah. This is way, way wrong.
Yes, the cardinal numbers are numbers. Yes, you can do arithmetic (numbery things) to them. But no, 2*aleph-null is not aleph-one.
In fact, due to the way cardinal arithemtic is defined, aleph-null*aleph-null = aleph-null.
No mathematician would ever say one infinite cardinal is "x times as big" as another. That's nonsense.
If you want to get "bigger" using only cardinals up to aleph-null and arithemtic, you have to use exponentiation. Of course, the problem now is even mathematicians don't agree how big 2aleph-null actually is. Aside from a few weird known restirctions, basically all we know is that it's bigger than aleph-null. It could be aleph-one. It could be aleph-two. It could be aleph-aleph-null.
MengerianMango · 3 points · Posted at 23:38:52 on February 13, 2016 · (Permalink)
Yep, I was gonna say this.
As a side note, you can do most normal mathy things with infinite ordinal numbers.
Riobhain · 1 points · Posted at 01:37:57 on February 14, 2016 · (Permalink)
Sorry. I'm a novice at mathematics (still in high school), and I read something similar to that on Wikipedia a few weeks ago -- I guess my memory contorted what I had read over time. I'd like to learn more about the cardinals, but there may be some math I'm missing out on. Do you know of a place where I could learn more about them?
almightySapling · 2 points · Posted at 03:20:19 on February 14, 2016 · (Permalink)
Honestly, if you truly want to learn about the cardinals, so that you have more than a tenuous grasp of "the rules" of arithmetic (because really, the arithmetic is only a tiny fraction of their utility), I would say wait until you've gone through calculus.
You can learn about them now, but their construction is extremely formal and rigorous, and it can be daunting for someone without a strong mathematical aptitude (it can be daunting for those with a strong aptitude). I would say start with a good intro to proofs book (personally recommend Transition to Advanced Mathematics), because you absolutely need the training and logical tools developed to make any headway. Once that's done, Hrbacek and Jech's "Introduction to Set Theory" is the where it's at.
[deleted] · 1 points · Posted at 16:59:55 on February 14, 2016 · (Permalink)
[deleted]
almightySapling · 1 points · Posted at 22:22:06 on February 14, 2016 · (Permalink)
Gentle is fine, and yes, a really motivated high schooler could probably teach themselves lots of things. But it's not so easy to dive right in when you lack the experience of manipulating proofs. There are very basic logical tools that many people don't pick up until Calculus, or even later, like what contraposition is, or how and why PMI works.
Terminatorneo · 1 points · Posted at 08:59:45 on February 14, 2016 · (Permalink)
Its like infinity multipled by 2 Lol
[deleted] · 2 points · Posted at 19:57:01 on February 13, 2016 · (Permalink)
[deleted]
ananori · 1 points · Posted at 22:16:15 on February 13, 2016 · (Permalink)
I got irrationally angry at this in 5th grade. Fucking bullshit.
datorangeguy · 1 points · Posted at 00:09:57 on February 14, 2016 · (Permalink)
Why? There are solutions that don't involve horizontal movements, I opened up ms paint and played around for 10 seconds at most in order to figure that out. Surely you must have figured those out.
phearsom_fysic · 3 points · Posted at 00:17:01 on February 14, 2016 · (Permalink)
From a recent (VSauce)[https://www.youtube.com/watch?v=ObiqJzfyACM] video:
You know if you rearrange a deck of cards, chances are you'll arrange it into an order that's never occurred before. Because, of course, there's 52! cards in a deck.
You know how big 52! is? Fucking huge.
So I've got two buddies; Carl and Erin. Now, Carl has in his hands a deck of cards. He really likes shuffling cards so he's going to do just that. Carl shuffles those cards so well that he rearranges them into a new order... every second. Every single second the cards have an entirely new arrangement.
Meanwhile, Erin is a bit of an adventurer so he starts by standing next to Carl on the equator. He then takes a single step forward... every billion years. Once Erin's circled the Earth (roughly 44million steps) he removes a single 0.5ml drop of water from the Pacific Ocean before walking around the equator again, one step every billion years. Now, when Erin has completely drained the Pacific Ocean, by removing a single drop every circumnavigation of the Earth, by taking a step every billion years... he places a single sheet of paper on the ground and refills the Pacific Ocean. He then continues his slow journey until the Pacific Ocean is empty once more, and then places a second sheet of paper on top of the first.
When this stack of paper reaches the fucking Sun... Carl is only a third of the way through shuffling every combination of cards.
tl;dr 52! is fucking huge
ItsUncleRick · 3 points · Posted at 01:17:39 on February 14, 2016 · (Permalink)
Man I don't understand a single thing in here
krazyfreak123 · 1 points · Posted at 05:45:37 on February 14, 2016 · (Permalink)
An opinion without 3.14 is just an onion
CarmakazieCthulhu · 2 points · Posted at 20:58:57 on February 13, 2016 · (Permalink)
That calculus 1 was the last math course I'd ever have to take the rest of my life
somadIcanteven · 2 points · Posted at 03:24:33 on February 14, 2016 · (Permalink)
Upvote for honesty.
TheHasselman · 2 points · Posted at 04:54:10 on February 14, 2016 · (Permalink)
Same here. Math made me sad.
mediumhydroncollider · 2 points · Posted at 21:43:59 on February 13, 2016 · (Permalink)
ITT polite people
TheMockingDead1 · 0 points · Posted at 22:24:05 on February 13, 2016 · (Permalink)
The smallest whole number to have the letter 'a' in its name is one hundred and one.
CommutatorUmmocrotat · 10 points · Posted at 00:47:34 on February 14, 2016 · (Permalink)
Or one thousand if you don't write the ands
Fake_Name_6 · 12 points · Posted at 01:03:31 on February 14, 2016 · (Permalink)
Technically "and" should only be used for a decimal place.
SpeaksToWeasels · 1 points · Posted at 03:14:43 on February 14, 2016 · (Permalink)
Relevant
avocadonumber · 1 points · Posted at 05:59:40 on February 14, 2016 · (Permalink)
Tell that to Spanish! All of their numbers: thirty and two, seventy and 4,
unhookingthestars · 2 points · Posted at 03:04:09 on February 14, 2016 · (Permalink)
Quatre.
LeoKhenir · 2 points · Posted at 01:03:01 on February 14, 2016 · (Permalink)
Whoa. I'm surely not the only one who read this and went "one two three four (...) eighty ninety hundred - he's right!"
The_Enemys · 2 points · Posted at 01:48:44 on February 14, 2016 · (Permalink)*
~I think you missed a few there~
EDIT: I'm an idiot
Xamberry · 3 points · Posted at 02:10:55 on February 14, 2016 · (Permalink)
Once you've had one to fifteen, you don't need each "eighty one, eighty two" etc anymore since you've already proven there is no A's in one to nine.
Chrenen · 1 points · Posted at 01:46:31 on February 14, 2016 · (Permalink)
Baker's Dozen?
[deleted] · 1 points · Posted at 14:49:32 on February 14, 2016 · (Permalink)
I think the name of that number is one hundred one. You wouldn't say ten and four when talking about fourteen, the and is a colloquially added filler word
ExtraCheesyPie · -2 points · Posted at 03:45:56 on February 14, 2016 · (Permalink)*
wut bout the # "aight"?
op is fucking dumb
tepori · 1 points · Posted at 21:52:48 on February 13, 2016 · (Permalink)
A number can be expressed in any base. For example, 126 in base 10 is 100 + 20 + 6 (multiples of powers of ten), or in base 2 is 64 + 32 + 16 + 8 + 4 + 2 (all powers of two). We all know this in this thread, this is not the interesting part yet... Observe that the required property is that places, when "full", must roll to the next higher place when incremented. In other words, working in bases are the simplest way to guarantee that when, say, 4 places of a base 10 number are maxed out, as in 9999, incrementing by 1 can be represented by a single value in the next place and zeroing out the rest: 10000. It turns out bases are not the only way to assign places. For instance, it so happens that 22! + 1! is one less than 3!. And: 55! + 44! + 33! + 22! + 11! is one less than 6!. This means that you can use factorial as a radix if you want, provided that the digit in each place is only allowed to go as high as the factorial associated with the place. So the way to count in this factorial radix is: factorial = conversion calculation = decimal 0 = 00! = 0 10 = 11! + 00! = 1 100 = 12! + 01! + 00! = 2 110 = 12! + 11! + 00! = 3 200 = 22! + 01! + 00! = 4 210 = 22! + 11! + 00! = 5 1000 = 13! + 02! + 01! + 0*0! = 6 1010 = … 1100 1110 1200 1210 2000 2010 2100 2110 2200 2210 3000 3010 3100 3110 3200 3210 10000 10010 … etc … Starting from the smallest place at the right and going left, instead of the 1s place, 10s place, 100s place (in base 10), there's the 0! place, the 1! place, the 2! place, the 3! place. The largest digit allowed in the 3! place is 3. The largest digit allowed in the 6! place is 6.
wsci · 1 points · Posted at 22:06:10 on February 13, 2016 · (Permalink)
When working in base n, the digital root of any multiple of n-1 will always be n-1. In base 5: 1 × 4 = 4 2 × 4 = 13; 1+3 = 4 12 × 4 = 103; 1+0+3 = 4 20413 × 4 = 133212; 1+3+3+2+1+2 = 22; 2+2 = 4 Changed wording for clarity
zsfy · 1 points · Posted at 22:10:13 on February 13, 2016 · (Permalink)
There are 62,000 miles of blood vessels in the human body – laid end to end they would circle the earth 2.5 times At over 2000 kilometers long, The Great Barrier Reef is the largest living structure on Earth A thimbleful of a neutron star would weigh over 100 million tons
AvatarCastiel · 1 points · Posted at 22:11:29 on February 13, 2016 · (Permalink)
If you take a bunch of consecutive nimbers and see how many times they can be divided evenly by 2 its makes a pattern within a pattern within a pattern continuously.
sfielbug · 1 points · Posted at 22:12:33 on February 13, 2016 · (Permalink)
The volume of a 6-inch cube equals the total of the volumes of a 5-inch cube, 4-inch cube, and a 3-inch cube.
[deleted] · 1 points · Posted at 22:24:41 on February 13, 2016 · (Permalink)
12345679 * 9 * X = XXXXXXXXX
X is a natural number from 1 to 9, but it has similar effects with other numbers.
SpoonsForSelfDefense · 1 points · Posted at 22:25:43 on February 13, 2016 · (Permalink)
back when I knew very little about math our teacher showed us Euler's identity: ei*pi + 1 = 0
Sellerofrice · 1 points · Posted at 22:29:20 on February 13, 2016 · (Permalink)
Euler's Equation (Identity): ei*pi + 1 = 0. Not only is this equation incredibly useful, especially in complex arithmetic, there is a kind of beauty to it as well. It includes many important numbers such as e, i, pi, the additive identity 0, and the multiplicative identity 0.
MrAcurite · 1 points · Posted at 22:29:52 on February 13, 2016 · (Permalink)
The fact that geometric constructions work
Charyou-Tree · 1 points · Posted at 22:42:42 on February 13, 2016 · (Permalink)
eπ*i +1=0
amandough · 1 points · Posted at 22:44:51 on February 13, 2016 · (Permalink)
For quadratic polynomials, we have a formula to find the zeroes. This is the quadratic formula.
For cubic polynomials, there is also a formula that will find the zeroes, but it is more complicated.
There is also a formula for quartic polynomials.
But there is cannot be a general formula that can solve quintic polynomials or polynomials of a higher degree. https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem
jplevene · 1 points · Posted at 22:45:27 on February 13, 2016 · (Permalink)
3 men go to a restaurant, the bill is $30 so they paid $10 each.
They then complain to the waiter saying it was too expensive so he speaks to the manager.
Manager says give them a $5 refund, so the waiter gets 5 x $1 bills from the cash register and keeps $2 for himself as they never left a tip and gives them $1 each refund.
They originally paid 3 x $10 = $30
They got a $1 refund each meaning they each paid $9 and the waiter kept $2.
3 x $9 = $27 + $2 = $29, where is the missing dollar.
[deleted] · 1 points · Posted at 23:45:37 on February 13, 2016 · (Permalink)
there's $35 in the system, not $30.
BOOSHACK360 · 1 points · Posted at 22:47:15 on February 13, 2016 · (Permalink)
24/24.3 is 0.98765432098765432...
Will someone please explain how this works and a similar example? This has been bothering me for quite some time.
[deleted] · 1 points · Posted at 23:48:00 on February 13, 2016 · (Permalink)
That's the same as 240/243. Any repeating decimal is going to be represented by a ratio of whole numbers A/B, so it just happens that 240 and 243 do the trick here.
Similarly, the pattern .123123123123... turns out to be 41/333.
doobyrocks · 1 points · Posted at 10:22:40 on February 14, 2016 · (Permalink)
Simplified, 80/81
10*8/9*9
Not sure where I'm going with this
[deleted] · 1 points · Posted at 14:46:42 on February 14, 2016 · (Permalink)
You can't simplify that fraction further, since 80 and 81 don't have any prime factors in common. But if you want the decimal representation, you can compute it by using long division.
Sarion56 · 1 points · Posted at 22:47:39 on February 13, 2016 · (Permalink)
There are as many whole numbers as there are positive whole numbers, but there are more real numbers between 1 and 2 than there are whole numbers.
Suminalixon · 1 points · Posted at 22:48:38 on February 13, 2016 · (Permalink)
Here is a trick that I learned to quickly multiply 11 by any two digit number. Add the two digits together and place the sum in the middle. Take 11x11 for example. 1+1=2, so the answer is 121.
11x12 = 132
11x13 = 143
11x35 = 385
If the sum is a two digit number, add the tens place of the sum to the hundreds place of the answer. Let's use 11x55 as an example. 5+5=10, so the answer is 605.
11x78 = 858
11x99 = 1089
lelouch_vi_brit · 1 points · Posted at 22:49:05 on February 13, 2016 · (Permalink)
Nine adds up to nine.
09 # 0+9 = 9
18 # 1+8 = 9
27 # 2+7 = 9
36 # 3+6 = 9
45 # 4+5 = 9
54 # 5+4 = 9
63 # 6+3 = 9
72 # 7+2 = 9
81 # 8+1 = 9
90 # 9+0 = 9
RedditLurker526507 · 1 points · Posted at 01:41:19 on February 14, 2016 · (Permalink)
Apparently any whole number you multiply by nine will do this. For example:
9x11=99, 9+9=18, 1+8=9
9x51=459, 4+5+9=18, 1+8=9
9x7289=65601, 6+5+6+0+1=18, 1+8=9
9x5864271=52778439, 5+2+7+7+8+4+3+9=45, 4+5=9
I've been playing with this on a calculator since I saw this thread and it always happens. I'm not very good with math, so if someone knows that this is wrong please say so.
edit: bad formatting.
orcscorper · 1 points · Posted at 05:45:56 on February 14, 2016 · (Permalink)
When you add nine to a number, you could say you are adding ten and subtracting one. In base-10, this means that every time you take one from the digit in the ones place, you add one to the digit in the tens place. It's trivial.
fennecdore · 1 points · Posted at 22:53:13 on February 13, 2016 · (Permalink)
i may be a little late for the party but here is a cool number : 142 857
142 857*2 = 285 714
142 857*3 = 428 571
142 857*4 = 571 428
142 857*5 = 714 285
142 857*6 = 857 142
Always the same digits but in a different order.
And 142 857*7 ? 999 999 ;)
Cody667 · 1 points · Posted at 23:43:40 on February 13, 2016 · (Permalink)
haha that's pretty cool, always in the order of 285714, just starting with a different one each time.
[deleted] · 1 points · Posted at 22:55:30 on February 13, 2016 · (Permalink)
There are more ways to arrange a deck of cards than there are atoms on earth
jaguar_mirror · 1 points · Posted at 22:58:54 on February 13, 2016 · (Permalink)
ei*pi = -1
plazzman · 1 points · Posted at 22:59:01 on February 13, 2016 · (Permalink)
This thread needs an NSFW tag. I'm getting all worked up here.
Twiggy02 · 1 points · Posted at 22:59:57 on February 13, 2016 · (Permalink)
0.9 recurring is equal to 1
yoguy2 · 1 points · Posted at 23:00:52 on February 13, 2016 · (Permalink)
I can't remember the maths, but if you google it, 0.9999999… is the same as 1.0.
ZeroCalamity · 1 points · Posted at 23:01:37 on February 13, 2016 · (Permalink)
The ratio between miles and kilometres is close to the ratio of numbers in the Fibonacci sequence. This means that 8 miles is almost equal to 13 kilometres. This is quite practical but you'll never need it.
elidefoe · 1 points · Posted at 23:03:55 on February 13, 2016 · (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 possible outcomes when shuffling a standard deck of cards.
thebush007 · 1 points · Posted at 23:04:30 on February 13, 2016 · (Permalink)
The fact that 0.9 (with the 9 repeating) does not equal 1, but at the same time does equal 1.
Consider: 1/9=0.1 (with the one repeating forever)
If this equation is multiplied (on both sides, of course) by 9:
1/9 x 9 = 0.1 (repeating 1) x 9
which, when simplified, equals:
1 = 0.9 (with the 9 repeating)
You might be confused, so here is the Wikipedia link
MpVpRb · 1 points · Posted at 23:07:41 on February 13, 2016 · (Permalink)
Euler's identity
https://en.wikipedia.org/wiki/Euler's_identity
DeathIceStorm · 1 points · Posted at 23:09:04 on February 13, 2016 · (Permalink)
1+1 = 2
lyds7 · 1 points · Posted at 23:11:50 on February 13, 2016 · (Permalink)
These are way over my head! I was happy with ... you can find out if a number is divisible by 3 by adding the digits together and if the answer is in the 3x tables it is!
RobB1987 · 1 points · Posted at 23:19:02 on February 13, 2016 · (Permalink)
A square can also be called: rectangle, parallelogram, rhombus, kite and quadrilateral.
almightySapling · 1 points · Posted at 23:19:34 on February 13, 2016 · (Permalink)
Background: there are multiple infinities. There are so many infinities, even, that none of the infinities is "infinite enough" to describe how many infinities there are.
Assuming the axiom of choice (most people do), we can order all the infinities. In particular, the "first infinity" is the size of the set of natural (counting) numbers. Many people believe the "second infinity" is the size of the set of real numbers.
So these infinities are ordered, and like computer scientists, they are indexed by 0 (the natural numbers are the "zeroth" infinity, instead of the "first").
The coolest part to me: there are infinities so big that they describe their own position in the ordering: that is to say, there is an infinite number k such that k is the "kth" infinity.
There are actually infinitely many infinities with this property.
Kiwi-kies · 1 points · Posted at 00:06:48 on February 14, 2016 · (Permalink)
So, infinity, infinity+1, infinity+2 etc :D
almightySapling · 2 points · Posted at 00:21:22 on February 14, 2016 · (Permalink)
While I see that you are joking, it is important it note that in my post, when I say "infinities" I am referring to infinite cardinal numbers.
We don't call any of these "infinity", because that would be weird: they are all infinite, none of them is "the" infinity.
However, for any particular infinite cardinal k, k+1 is not a cardinal number, it is an ordinal number with the same cardinality as k.
Further, neither of the infinite cardinals I mentioned in my post (aleph-null and aleph-one) have this property. Aleph-null is the "zeroth" infinite cardinal, not the "aleph-nullth" infinite cardinal, etc.
Jamjijangjong · 1 points · Posted at 23:19:52 on February 13, 2016 · (Permalink)
The banach tarski paradox
l-0_o-l · 1 points · Posted at 23:22:13 on February 13, 2016 · (Permalink)
.9999999 repeating is equal to 1. This isn't approximated, its actually exactly equal to 1.
1/3 = .333333
2/3 = .666666
3/3 = .999999 or 1
ThereOnceWasAMan · 1 points · Posted at 23:22:38 on February 13, 2016 · (Permalink)
There will always be at least one pair of antipodal points on earth that are at exactly the same temperature.
pinkfloyds · 1 points · Posted at 23:22:51 on February 13, 2016 · (Permalink)
Between any two real numbers there are an infinite number of irrational numbers. And between those same two real numbers there are an infinite number of rational numbers. But if you threw a dart at this number line, the likelihood that your dart will land on an irrational number is 100%
[deleted] · 1 points · Posted at 23:23:15 on February 13, 2016 · (Permalink)*
This reddit account has been removed.
georgeo · 1 points · Posted at 23:25:57 on February 13, 2016 · (Permalink)
the integer roots of 1 are evenly spaced on the circumference a unit radius circle on the complex plane and from that Euler's identity e{i \pi} + 1 = 0
drumjojo29 · 1 points · Posted at 23:26:36 on February 13, 2016 · (Permalink)
1 / 3 = 0.33333333333333333......
3 x 1/3 = 3/3 = 1
3 x 0.3333333333333333333333333...... = 0.999999999999
=> 0.999999999999..... = 1
Beastmonger · 1 points · Posted at 23:27:56 on February 13, 2016 · (Permalink)
.9999 repeating is exactly equal to 1
bugo1102 · 1 points · Posted at 23:28:19 on February 13, 2016 · (Permalink)
2+2=4
Captainl53 · 1 points · Posted at 23:28:36 on February 13, 2016 · (Permalink)
Zeno's Paradox- distance is infinite. Because to get from point A to point B, you have to go 1/2 the way, then 1/4, then 1/8, goes to infinity, and it turns out all motion is just an illusion.
shinypidgey · 1 points · Posted at 23:29:13 on February 13, 2016 · (Permalink)
i raised to the i power is a real number. ii ~0.208.
andysteakfries · 1 points · Posted at 23:30:54 on February 13, 2016 · (Permalink)
The difference in length of a smooth, arbitrary path and another path offset from the first by a distance, r, is 2×π×r.
TLDM · 1 points · Posted at 23:34:49 on February 13, 2016 · (Permalink)
ii is real. Proof:
Start with Euler's identity.
ei*pi = -1
Square root both sides:
ei*pi/2 = i
Do both sides to the power i:
ei*i*pi/2 = ii
e-pi/2 = ii.
Or alternatively, proof by WolframAlpha.
Crazy658 · 1 points · Posted at 23:35:31 on February 13, 2016 · (Permalink)
If you add up all the odd numbers, you get all the squares as you go.
1 = 12
+3 = 4 = 22
+5 = 9 = 32
+7 = 16 = 42
+9 = 25 = 52
+11 = 36 = 62
orcscorper · 1 points · Posted at 06:06:03 on February 14, 2016 · (Permalink)
You think that's cool, split the odd numbers in groups increasing by one each time, to get cubes. 1 = 1= 13 3 + 5 = 8 = 23 7 + 9 + 11 = 27 = 33
floorplanner · 1 points · Posted at 23:44:05 on February 13, 2016 · (Permalink)
9 is an interesting number. Multiply 9 by any number and the result, when added together, is divisible by 9.
Ex: 9x7=63 6+3=9
9x472=4248 4+2+4+8=18 1+8=9 18 is divisible by nine.
Try it yourself. It's fun!
nypvtt · 1 points · Posted at 23:44:45 on February 13, 2016 · (Permalink)
Einstein was good at it.
oldmanherbert22 · 1 points · Posted at 23:44:54 on February 13, 2016 · (Permalink)
1x1=2
Black_Dynamite66 · 1 points · Posted at 23:47:41 on February 13, 2016 · (Permalink)
I fucking suck at it
ChromeLynx · 1 points · Posted at 23:48:10 on February 13, 2016 · (Permalink)
You can determine whether a number is divisible by a power of 2 by the last 2log(power of 2 you're dividing by) numbers.
i.e. div by 2: last 2log(2) digit (-s) = last 1 digit
div by 4: Last 2log(4) digit (-s) = last 2 digits
div by 8: Last 3 digits
etcetera.
creek_slam_sit · 1 points · Posted at 23:51:14 on February 13, 2016 · (Permalink)
1000000000000066600000000000001 That's a prime number
Meowser01 · 1 points · Posted at 23:51:15 on February 13, 2016 · (Permalink)
I found this strange in middle school: 12345-54321+98765-56789=0
orcscorper · 1 points · Posted at 06:11:53 on February 14, 2016 · (Permalink)
I hope you stopped finding it strange. Look how the digits line up in the two added numbers. They all make tens. Same with the two subtracted numbers; all tens.
Meowser01 · 1 points · Posted at 20:15:59 on February 20, 2016 · (Permalink)
Hahaha, yeah, I definitely moved passed that. It was just a thing that blew my mind back then.
illdoitlaterokay · 1 points · Posted at 23:51:47 on February 13, 2016 · (Permalink)
You can find the multiplies for nine on your fingers.
X | | | | | | | | | = 9
| X | | | | | | | | =18
| | X | | | | | | | =27
Etc.
(assuming you have ten fingers)
violentwench · 1 points · Posted at 23:52:06 on February 13, 2016 · (Permalink)
1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
111111x111111=12345654321
1111111x1111111=1234567654321
11111111x11111111=123456787654321
111111111x111111111=12345678987654321
BeardySam · 1 points · Posted at 23:57:37 on February 13, 2016 · (Permalink)
The harmonic series diverges to infinity, unless you remove all the fractions with a nine in them, in which case it converges on about 23.
sulump5 · 1 points · Posted at 23:57:52 on February 13, 2016 · (Permalink)
Take any 3 or more digit number that isn't the same digits, then rearrange them. Subtract the lower value of that rearrangement from the higher value. Your answer will always be divisible by 9.
Example: 345. Rearrange that to 534. Since 345 is smaller than 534, you would do 534 - 345, which gives you 189. 189 is divisible by 9. Works everytime :)
weapongod10 · 1 points · Posted at 23:58:30 on February 13, 2016 · (Permalink)
i (square root of -1) to the i power is about 0.2. Crazy to this about
MyNameIsMasonAtwood · 1 points · Posted at 23:59:58 on February 13, 2016 · (Permalink)
Learned this from VSauce: 52! (52 factorial), aka the number of possible shufflings that a deck of cards can have is a really big number. Like REALLY big. It's extremely likely two card decks with true shufflings have never had the same order. If you truly shuffle a deck of cards it's overwhelmingly likely that's the first time it's ever been in that order. Here's an example of how big 52! is:
If you started a timer counting down by seconds from 52! then began to walk around the world one step at a time, with 1 billion years in between each step
then once you made it all the way around the world you took a drop of water our of the Pacific Ocean, and kept walking around the earth, stopping to take a drop of water every time you complete a trip around the Earth with one billion years between steps
then once you emptied the Pacific, you placed a piece of paper on the ground and refilled the ocean and by this whole process you made a stack of papers
by the time that stack reached the sun you would be 1/3000 of the way to 0 on your clock...
hadmeashindig · 1 points · Posted at 00:00:37 on February 14, 2016 · (Permalink)
If you take avogadros # and divide it by the golden ratio and multiply it by the derivative of force delta (dark matter fu / dark energy eu) then the girl you're desperately hitting on at the bar still won't suck your dick.
ekans812 · 1 points · Posted at 00:02:02 on February 14, 2016 · (Permalink)
140000/333 is 420.420 repeating
Arditwm · 1 points · Posted at 00:02:11 on February 14, 2016 · (Permalink)
If you assign a letter to the numbers in π (pi), so for example 1 will be a, 2 will be b and so on. You will have converted the sequence of numbers into a bunch of random letters. c.adaeibfecei.....
But since π in infinite and random, at some point those letters will make up words, sentences, and much more. If you (theoretically) search for long enough, you will find your life story in the digits of π, from start...to finish.
DaenerysTargaryen69 · 1 points · Posted at 00:02:39 on February 14, 2016 · (Permalink)
Take any number like 586 and count them. So it would be 5+8+6 = 19 do it again 1+9=10. 10 is not in the multiplication table of 3 so 586 can not be defined by 3.
Edit: sorry English is not my first language.
REB3LxSOUL · 1 points · Posted at 00:02:45 on February 14, 2016 · (Permalink)
The product of any single digit multiplied by nine has the 10's digit one less than the multiplied number with the one's digit 9 minus the ten's digit number.
Ex: 7*9=63 7-1=6 9-6=3
This always helped me get through the nines multiplication tables in grade school.
ITSBEPOBRO · 2 points · Posted at 00:11:15 on February 14, 2016 · (Permalink)
You could say the answer will be the multiplied number -1 and the answer must add up to 9
Ex: 7 - 1 = 6, 6 + 3 = 9 so the answer is 63
MashedPotatoesDick · 1 points · Posted at 00:03:10 on February 14, 2016 · (Permalink)
Multiplying two digit number by 11 is easy to do without calculators or working it out on paper.
Example (54): Add the 5 and 4 and insert it between the numbers. 54 is 5(5+4)4= 594
Example (67): Same as above, but since there is a remainder, it goes to the first digit. 67 is 6(6+7)7= 6 (11)7=717.
control_freek · 1 points · Posted at 00:04:07 on February 14, 2016 · (Permalink)
If you take any number two digits or more, rearrange the digits, and subtract them, the answer will always be divisible my nine. Also if you add all the digits of the new number, that new number will also be dividable by nine.
mike54076 · 1 points · Posted at 00:05:30 on February 14, 2016 · (Permalink)
ei*π+1=0 Euler's identity combines the concepts of imaginary numbers, irrational/rational numbers, and zero into one concise equation. It was named the most beautiful mathematical equation ever conceived.
strawkastle · 1 points · Posted at 00:05:31 on February 14, 2016 · (Permalink)
I'm going to die one day.
EebamXela · 1 points · Posted at 00:05:51 on February 14, 2016 · (Permalink)
The centers of a triangle all lie on a line. https://youtu.be/wVH4MS6v23U
[deleted] · 1 points · Posted at 00:07:17 on February 14, 2016 · (Permalink)
[deleted]
orcscorper · 2 points · Posted at 06:39:03 on February 14, 2016 · (Permalink)
Order of operations is unclear in sentence form. I came up with 2+3+5+7+11+13+17=58, and 58[2]=3364. Then I tried 4+9+25+49+121+169+289. Much better. On a side note, ((6+6+6)+(6+6+6))*(6+6+6)+(6+6+6)=666, and 1+2+3+...36=666.
bananafleet · 1 points · Posted at 00:08:09 on February 14, 2016 · (Permalink)
There is always at least one place one earth where the temperature is exactly equal to the temperature of the exact oppositie of that location
bacon__sandwich · 1 points · Posted at 00:09:31 on February 14, 2016 · (Permalink)
If you add 1/2 to 1/4, then add 1/8, 1/16, 1/32... It will eventually equal to 1
DoomsdayDog174 · 1 points · Posted at 00:10:08 on February 14, 2016 · (Permalink)
The answer to 9 * n is equal to (in the case of 1-10 anyway) 10 * n - n.
For example, if n = 6: 9 * (6) = 54; 10 * (6) = 60 - (6) = 54
orcscorper · 1 points · Posted at 06:45:16 on February 14, 2016 · (Permalink)
This not only works for every real number, it works if n=cookie. If you have 10 cookies and take away 1 cookie, you have 9 cookies. This is Sesame Street-level math, except they say C is for cookie.
DoomsdayDog174 · 1 points · Posted at 16:18:26 on February 14, 2016 · (Permalink)
No, I know that 10 - 1 = 9. I use what I said because I have trouble remembering multiples of numbers, not because I can't do simple subtraction.
SecondImpactDenier · 1 points · Posted at 00:10:47 on February 14, 2016 · (Permalink)
111,111,111x111,111,111=
12345678987654321
Technologic2 · 1 points · Posted at 00:12:37 on February 14, 2016 · (Permalink)
111111/9= 12345.67
madeofchemicals · 1 points · Posted at 00:14:02 on February 14, 2016 · (Permalink)
If you perfectly shuffle a deck of cards 8 times, it returns to the exact order it was originally.
MusicMagi · 1 points · Posted at 00:14:37 on February 14, 2016 · (Permalink)
All the pyramids in the share the same dimensions
bestofreddit_me · 1 points · Posted at 00:15:44 on February 14, 2016 · (Permalink)
Some infinite numbers are bigger than other infinite numbers...
http://www.scientificamerican.com/article/strange-but-true-infinity-comes-in-different-sizes/
jo_wil · 1 points · Posted at 00:15:48 on February 14, 2016 · (Permalink)
The derivative of the area of a circle (PI)(r)2 is the circumference of the circle 2(PI)(r) aka (PI)(d).
yugiyo · 1 points · Posted at 00:17:31 on February 14, 2016 · (Permalink)
.99999... is equal to 1.
https://en.wikipedia.org/wiki/0.999...
pretty_meta · 1 points · Posted at 00:18:07 on February 14, 2016 · (Permalink)
x2 + y2 = 4
y2 = 4 - x2
y = sqrt(4 - x2)
PI = integral from x = 0 to x = 2 of y = sqrt(4 - x2)
TriplePube · 1 points · Posted at 00:18:30 on February 14, 2016 · (Permalink)
Shuffle a deck of cards and you will most certainly get an order which no one else in the history of the world has gotten.
Polarized_Senses · 1 points · Posted at 00:20:11 on February 14, 2016 · (Permalink)
Fractions with repeating decimals are actually rational numbers which are exact values representing the fraction. There's no rounding required.
Ex.
1/3 = 0.333333333.....
10/3 = 3.33333333......
10/3-1/3 = 3.333333333......-0.3333333...... = 3
So the decimal representation of fractions is actually the exact value.
creamersrealm · 1 points · Posted at 00:23:01 on February 14, 2016 · (Permalink)
“The best number is 73…. 73 is the twenty-first prime number. Its mirror, 37, is the twelfth and its mirror, 21, is the product of multiplying (hang on to your hats) 7 and 3…. In binary, 73 is a palindrome: 1-0-0-1-0-0-1, which backwards is 1-0-0-1-0-0-1.”
GreyHexagon · 1 points · Posted at 00:43:18 on February 14, 2016 · (Permalink)
Illuminati confirmed
hotroddaveusa · 1 points · Posted at 00:23:51 on February 14, 2016 · (Permalink)
Pie are not squared. Pie are round. Cornbread are squared.
arvid_g · 1 points · Posted at 00:23:56 on February 14, 2016 · (Permalink)
The gogol and gogolplex are pretty cool numbers.
https://www.youtube.com/watch?v=5JOAoiX1LHA
sightlab · 1 points · Posted at 00:25:28 on February 14, 2016 · (Permalink)
Nine, nine, nine. Fantastic number nine. Times any number you can find, it all comes back to nine.
parla8ane123 · 1 points · Posted at 00:25:50 on February 14, 2016 · (Permalink)
That most people in Sweden have more than the average number of legs.
edwardhowrongtu · 1 points · Posted at 00:26:13 on February 14, 2016 · (Permalink)
Gabriel's Horn is a geometric figure that has an infinite surface area but a finite volume.
Wikipedia page for those interested: https://en.m.wikipedia.org/wiki/Gabriel%27s_Horn
ixfd64 · 1 points · Posted at 00:53:25 on February 14, 2016 · (Permalink)
You may also be interested in Koch's snowflake: https://en.wikipedia.org/wiki/Koch_snowflake
It's a curve of infinite length that encompasses a finite area.
M1cKle123 · 1 points · Posted at 00:26:29 on February 14, 2016 · (Permalink)
That you have the surface area of a tennis court in your lungs
AgentOrange96 · 1 points · Posted at 00:26:42 on February 14, 2016 · (Permalink)
-eiπ = 1
2112user · 1 points · Posted at 00:27:06 on February 14, 2016 · (Permalink)
6x8 is 48.
[deleted] · 1 points · Posted at 00:27:17 on February 14, 2016 · (Permalink)*
You can find the sine inverse of any value greater than one if you allow the solution be complex (includes i).
https://www.wolframalpha.com/input/?i=asin(2)
This goes for pretty much any function such that all functions in the complex region are unbounded, except for a constant function. It is known as Louiville's theorem and has some catches.
https://en.wikipedia.org/wiki/Liouville%27s_theorem_(complex_analysis)
EDIT: Added Wolfram Alpha as example.
rsslk · 1 points · Posted at 00:27:26 on February 14, 2016 · (Permalink)
ei(pi) = -1
Geocide_Ishna · 1 points · Posted at 00:27:41 on February 14, 2016 · (Permalink)
That a circle is has a infinite number of sides all with the length of 0
Thaufas · 1 points · Posted at 00:29:46 on February 14, 2016 · (Permalink)
Limit of (1 + 1/n)n as n->∞ = e = 2.7128...
boozin_ · 1 points · Posted at 00:34:10 on February 14, 2016 · (Permalink)
The kelvin and Rankine temperature scales are defined so that absolute zero is 0 kelvin (K) or 0 degrees Rankine (°R). The Celsius and Fahrenheit scales are defined so that absolute zero is −273.15 °C or −459.67 °F. At this stage the pressure of the particles is zero.
MasterKaen · 1 points · Posted at 00:34:47 on February 14, 2016 · (Permalink)
If you multiply a prime number by every prime number before it and then add one, you'll get a new prime number.
gaussjordanbaby · 1 points · Posted at 06:15:03 on February 14, 2016 · (Permalink)
This is false.
orcscorper · 1 points · Posted at 06:53:49 on February 14, 2016 · (Permalink)
Can you give an example of a prime number for which it is not true?
gaussjordanbaby · 1 points · Posted at 13:22:01 on February 14, 2016 · (Permalink)*
2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 is not prime, since 30031 = 59*509. This is the smallest counterexample. If this trick always did produce a new prime number, it wouldn't be such a big deal when the next largest prime number is discovered.
Icepick823 · 1 points · Posted at 00:35:45 on February 14, 2016 · (Permalink)
Graham's number is (was?) the largest number to be used in a proof. To express it basically required a new form of notation known as Knuth's up-arrow noation
ixfd64 · 1 points · Posted at 00:51:36 on February 14, 2016 · (Permalink)
Far larger numbers have since appeared in serious mathematics, such as TREE(3) and SCG(13).
legendariers · 1 points · Posted at 00:52:55 on February 14, 2016 · (Permalink)
I believe TREE(3) is the largest used.
ixfd64 · 1 points · Posted at 01:10:00 on February 14, 2016 · (Permalink)
SCG(13) is even larger: http://googology.wikia.com/wiki/Subcubic_graph_number
Friedman has defined theorems that imply even faster-growing functions, although he has not discussed any specific values.
sircolincollins · 1 points · Posted at 00:38:48 on February 14, 2016 · (Permalink)
That there's a theorem where the most likely case of a event is twice as likely as the second most like, three times more likely than the third, fourth for the fourth. This applies to almost all languages, colors in paintings, and many other scenarios.
cant_fit_the_dick · 1 points · Posted at 00:41:03 on February 14, 2016 · (Permalink)
Gabriel's horn - The function 1/x will have a definite volume but will have an infinite surface area.
in other words, if it were a cake, you could eat it, but not frost it.
TheQuestionableYarn · 1 points · Posted at 00:41:15 on February 14, 2016 · (Permalink)
25.80697580112788 is the root of all evil.
[deleted] · 1 points · Posted at 00:41:37 on February 14, 2016 · (Permalink)
You can fit every planet in between the Earth and the moon, excluding the newly discovered planets.
CommutatorUmmocrotat · 1 points · Posted at 00:42:06 on February 14, 2016 · (Permalink)
If you lay down a rope around the equator so that it is stretched taut, and then add 1 metre to its length, now if you pull the rope up from every point it will come up to a height of 16 cm above the ground. This is a property of all spheres and is irrespective of the radius
gaussjordanbaby · 1 points · Posted at 06:15:34 on February 14, 2016 · (Permalink)
This is a great one!
[deleted] · 1 points · Posted at 00:42:12 on February 14, 2016 · (Permalink)
9/11 = .8181818181... A is the 1st letter of the alphabet, and H is the 8th. So 9/11 = HAHAHAHA...
live52 · 1 points · Posted at 00:42:25 on February 14, 2016 · (Permalink)
The digits of the product of any number (not zero) and nine, will always add up to nine. Example: 9 X 101 = 909 > 9 + 0 + 9 = 18 > 1+8 = 9
artificialintegrity · 1 points · Posted at 00:42:35 on February 14, 2016 · (Permalink)
You can tell if a number is divisible by three by adding the numbers together and if that number is divisible by three then the first is also.
Example: 87462 / 3 = 29154.
8+7+4+6+2 = 27 which is 3x9.
Also 27 would be 2+7 which is 9 3x3
[deleted] · 1 points · Posted at 00:43:58 on February 14, 2016 · (Permalink)
Since this board doesn't do TeX, here's one that makes me very uncomfortable.
SmartAlec105 · 1 points · Posted at 00:44:22 on February 14, 2016 · (Permalink)
2+2=2*2=22 and so on for all higher operations.
Lokitheanus · 1 points · Posted at 00:44:51 on February 14, 2016 · (Permalink)
7 8 9
GreyHexagon · 1 points · Posted at 00:44:57 on February 14, 2016 · (Permalink)
Why the fuck am I looking at this? I'm dyscalculia I can't even understand the numbers. fml
Tahetal · 1 points · Posted at 00:47:42 on February 14, 2016 · (Permalink)
The smallest recordable amount of time is 13 attoseconds I believe
Scarce22 · 1 points · Posted at 00:50:24 on February 14, 2016 · (Permalink)
How to multiply 11 times any two digit number.
Bon_public · 1 points · Posted at 00:51:09 on February 14, 2016 · (Permalink)
(x-a)(x-b)(x-c)(x-d)...(x-z) = 0
jdoe5 · 1 points · Posted at 00:51:11 on February 14, 2016 · (Permalink)
An infinite amount of numbers can be added up to a finite sum
T3h_Cr33p3r · 1 points · Posted at 00:54:03 on February 14, 2016 · (Permalink)
let x = (sqrt(5)+1)/2
x+1 = x2
x-1 = x-1
[deleted] · 1 points · Posted at 00:54:56 on February 14, 2016 · (Permalink)
Fundamental theorem of calculus, of course! It's unbelievably useful.
poop9111 · 1 points · Posted at 00:56:59 on February 14, 2016 · (Permalink)
The integral of ex is ex.
a3wagner · 1 points · Posted at 06:19:54 on February 14, 2016 · (Permalink)
Depending on your perspective, this is also the definition of ex!
ctaie · 1 points · Posted at 00:57:12 on February 14, 2016 · (Permalink)
If you add all the digits up in a given number and their sum is divisible by three, then the original number is also divisible by three.
jmwbb · 1 points · Posted at 00:58:23 on February 14, 2016 · (Permalink)
There's quite a few!
There are infinitely many natural numbers, integers, rational numbers, real numbers... but these infinite are of different sizes. Natural numbers are "countably infinite", which is by definition; a set with as many things in it as their are natural numbers are countable. The reals on the other hand are uncountable, their size is called the cardinality of the continuum.
What's interesting is the integers and even the rationals are countable. The integers are countable because I can put them in a sequence like this: 0, 1, -1, 2, -2... and in this way I get one integer for every natural number.
The rationals are trickier, but they're all a/b for some integers a and b. So what I can do is make a 2d grid and then draw a spiraling line outward hitting every point I'm the grid, skipping over all the points that represent things like 2/4 and 3/9 since those can be reduced, and in this way I show a natural number exists for each rational.
But I can go further and look at the definable real numbers; numbers that can be defined. Let's pretend they're being defined in English, they'll actually be defined in first order logic or something but the principle is the same. I order all the definitions alphabetically and in this way I show that the definable numbers are countable. Therefore most real numbers can't actually be defined.
Pick 5 consecutive positive integers. Their product is divisible by 120, always.
Think of a number between 1 and 10.
It's 7, isn't it?
Fact: I will guess correctly at least some of the time probably
dangil · 1 points · Posted at 01:00:00 on February 14, 2016 · (Permalink)
epi*i = 1
pepintheshort · 1 points · Posted at 01:00:20 on February 14, 2016 · (Permalink)
10! (ten factorial) is the same as the number of seconds in six weeks.
Stove-pipe · 1 points · Posted at 01:00:26 on February 14, 2016 · (Permalink)
10/3=33,3 but 33,3=99,9. Every time you divide by 3 you lose 0,01
Choralone · 1 points · Posted at 01:03:35 on February 14, 2016 · (Permalink)
This is false.
10/3 isn't 33.3
It's 3.333333...
[deleted] · 1 points · Posted at 01:00:26 on February 14, 2016 · (Permalink)
0.9 repeated is 1.
poop9111 · 1 points · Posted at 01:00:34 on February 14, 2016 · (Permalink)
There is an infinite amount of real numbers from 0 to 1.
[deleted] · 1 points · Posted at 01:01:09 on February 14, 2016 · (Permalink)
12345679 x 9 = 111111111
12345679 x 8 = 98765432
thugasaurusrex0 · 1 points · Posted at 01:01:49 on February 14, 2016 · (Permalink)
So the Fibonacci sequence is cool but what's cooler is if you reduce the multi-digit numbers to a "single number representation" the pattern repeats endlessly. Basically its 1 1 2 3 5 8 13 21 34 55 89 144 233 etc. you take the multi digit numbers and add the digits together until you get a single digit number; so 13=4 21=3 34=7 etc. Now the pattern becomes 1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9 (and now repeats) 1 1 2 3 5 8 4 3 7.....etc.
ixfd64 · 1 points · Posted at 01:04:40 on February 14, 2016 · (Permalink)
You can use modular arithmetic to check for the divisibility of extremely large numbers, even those that are way beyond computing limits.
Windsong1024 · 1 points · Posted at 01:04:48 on February 14, 2016 · (Permalink)
12 = 1
112 = 121
1112 = 12321
11112 = 1234321
and so on of course
shapedude1 · 1 points · Posted at 01:05:21 on February 14, 2016 · (Permalink)
Gabriel's Horn is my favorite. There is a theoretical shape that has a finite volume and infinite surface area. That means a paint can in this shape could not hold enough paint to coat the interior of itself. Paradox!
ixfd64 · 1 points · Posted at 01:05:41 on February 14, 2016 · (Permalink)
You may also be interested in Koch's snowflake: https://en.wikipedia.org/wiki/Koch_snowflake
It's a curve of infinite length that encompasses a finite area.
blakflag · 1 points · Posted at 01:05:37 on February 14, 2016 · (Permalink)
The fascinating truth behind Euclid's Fifth Postulate. You see, Euclid had 5 axioms and 5 postulates which formed the basis of the study of geometry. The axioms and 4 of the postulates were really straight-forward. Stuff like "Two things each being equal to a third thing also must be equal".
But the Fifth Postulate was sort of, well, weird. From wikipedia:
This did not seem like something that couldnt be derived from the other basics. So for thousands of years, the best mathematicians tried to prove this fact from the other 5 axioms and 4 postulates. And they just couldn't do it.
Well, finally in the 19th century, people finally realized the truth that there WAS no inherent contradiction which could be reached by not assuming the fifth postulate was true. In other words, Non-Euclidean geometry was a real thing, and an internally consistent system.
So.. Euclid was either so brilliant that he intuitively knew that his system of geometry was just one of many others, or else he was just too embarrassed that he could not prove his fifth postulate from the others to ever give more commentary on the subject. Or a little of both.
falco_iii · 1 points · Posted at 01:07:26 on February 14, 2016 · (Permalink)
0 = 1 + epi*i
YONADAN · 1 points · Posted at 01:07:30 on February 14, 2016 · (Permalink)
Probably knowing binary.
Finite_Fractal · 1 points · Posted at 01:09:24 on February 14, 2016 · (Permalink)
I'd you look at only the odd entries in Pascal's triangle you will get sierpinski's triangle
ubergeek404 · 1 points · Posted at 01:09:43 on February 14, 2016 · (Permalink)
There are no 'floating point errors' (as in loss of precision), when using actual fractions, only when they are converted to decimals for binary ALU operations.
sweepyoface · 1 points · Posted at 01:12:13 on February 14, 2016 · (Permalink)
ITT: Numbers
The Zipf Mystery
zbromination · 1 points · Posted at 01:13:03 on February 14, 2016 · (Permalink)*
7! is equal to 7 * 8 * 9 *10
CommutatorUmmocrotat · 1 points · Posted at 01:13:55 on February 14, 2016 · (Permalink)
The derivative of area of a circle is its circumference.
The derivative of volume of a sphere is its surface area.
phonz1851 · 1 points · Posted at 01:14:43 on February 14, 2016 · (Permalink)
There are more irrational numbers than rational numbers in the real number system.
AReverieofEnvisage · 1 points · Posted at 01:15:11 on February 14, 2016 · (Permalink)*
Hmm, well, I always thought it interesting how you could get the answer in any multiplication of 9 by adding the two numbers together to get the answer.
It's hard to explain so
9x1=9
9x2=18 1+8=9
9x3=27 2+7=9
9x4=36 3+6=9
9x5=45 4+5=9
and so on. And it was also interesting that the answers would always add or subtract 1 as the multiplication got higher. 9
18
27
36
It was pretty cool to see a pattern in the number 9, but that really hasn't helped much, but you could also apply the same principle in learning your multiplication chart for any number with a little bit of work.
Durrandon · 1 points · Posted at 01:15:35 on February 14, 2016 · (Permalink)
Really weird fact: The Liouville numbers are, as a subset of the reals, measure 0 (i.e. "small," for some definition of small), and their complement (the set of everything that isn't them, in the reals) is meagre (i.e., 'small,' for a different definition of small).
So the reals can be divided into two sets, both of which are "small."
Colts_918 · 1 points · Posted at 01:15:45 on February 14, 2016 · (Permalink)
If a circle has a radius-Z then you can find the area as pizza (Pi x Z x Z= A)
super_leet_hacker · 1 points · Posted at 01:16:04 on February 14, 2016 · (Permalink)
1+3+3=7
Rocker78561 · 1 points · Posted at 01:16:09 on February 14, 2016 · (Permalink)
There is a cone known as Gabriel's horn that has a finite volume but infinite surface area. That means that it is possible to fill the cone with paint, but there isn't enough paint in the world to paint the inner walls of the horn.
seanrm92 · 1 points · Posted at 01:16:30 on February 14, 2016 · (Permalink)
That the sum of the infinite series of positive integers (1+2+3+4+etc.) equals -1/12.
Gingerfeld · 1 points · Posted at 01:17:16 on February 14, 2016 · (Permalink)
Anything involving quaternions. Shit's bonkers.
pantstickle · 1 points · Posted at 01:17:24 on February 14, 2016 · (Permalink)
Take any number >9. Rearrange the digits and subtract from the original and the answer will always be divisible by 9.
Example:
8457 - 4758 = 3699
3699 / 9 = 411
Neglected_Motorsport · 1 points · Posted at 01:17:49 on February 14, 2016 · (Permalink)
8008 looks like the word BOOB
mypolarbear · 1 points · Posted at 01:19:21 on February 14, 2016 · (Permalink)
.99 (repeating) = 1
Grocery-Storr · 1 points · Posted at 01:20:30 on February 14, 2016 · (Permalink)
Gabriel's Horn is what results when you revolve the function 1/x about the X-axis. What you'll find is that it has infinite surface area, but finite volume.
So imagine you have a paint can with infinitely thin walls. You can fill this thing all the way to the top, over flowing even. But when you dump out all the paint, you'll find that there's not enough paint in the universe to completely cover the inside.
IrishTechnician · 1 points · Posted at 01:21:27 on February 14, 2016 · (Permalink)
A bit late, but I love the fact that 1 is provably the same as 0.999 recurring.
9/9 = 0.999...
9/9 = 1
∴
1 = 0.999...
I couldn't work out how to put the recurring symbol over the top so '...' means recurring.
Fat7ace · 1 points · Posted at 01:22:19 on February 14, 2016 · (Permalink)
Day[9] on Graham's number
https://youtu.be/1N6cOC2P8fQ
ktisis · 1 points · Posted at 01:23:53 on February 14, 2016 · (Permalink)
987654312 / 123456789 = 8
red_sky33 · 1 points · Posted at 01:24:56 on February 14, 2016 · (Permalink)
eπ - π just happens to be really close to 20. No real reason other than it is.
ssbmhero · 1 points · Posted at 01:25:08 on February 14, 2016 · (Permalink)
Eiπ + 1 = 0
ProdigalEden · 1 points · Posted at 01:25:47 on February 14, 2016 · (Permalink)
9*2 is 18. First digit is -1 from the original number, second digit is the number needed to get 10 if added to the original number. Goes for any number 2-9
ChampionOfChaos · 1 points · Posted at 01:26:09 on February 14, 2016 · (Permalink)
The derivative of et is et......still boggles my mind when you truly understand intrinsically what it means
gambiter · 1 points · Posted at 01:26:11 on February 14, 2016 · (Permalink)
11111111/9 = 1234567.89
DarkAvenger12 · 1 points · Posted at 01:26:26 on February 14, 2016 · (Permalink)
Take the list of odd numbers 1,3,5,7,9, . . . Start with 0 and add the numbers in the list one at a time. At each step you have a perfect square. I wish I knew why this works.
To make my point more explicit:
0+1 = 1
1+3 = 4
4+5=9, etc.
orcscorper · 2 points · Posted at 07:14:33 on February 14, 2016 · (Permalink)*
Simple. To go from a 2x2 to a 3x3 square, add 2 along the top, 2 along the side, and 1 in the corner. 2+2+1=5. Add 3 and 3 along the top and side, and one in the corner. 3+3+1=7. This is best illustrated with Skittles or M&Ms.
[deleted] · 1 points · Posted at 01:27:00 on February 14, 2016 · (Permalink)
The number of combinations possible in a 52 card deck in seconds. Great visuals and ways to think about how fucking big 52! is.
maxtofunator · 1 points · Posted at 01:27:05 on February 14, 2016 · (Permalink)*
Its possible to have a triangle where the sum of the interior angles is either greater than or less than 180°
Jester_Thomas · 2 points · Posted at 01:28:27 on February 14, 2016 · (Permalink)
How?
brutalyak · 1 points · Posted at 01:30:44 on February 14, 2016 · (Permalink)
Using non-euclidian geometry. For example it is possible to draw a triangle with 3 90° angles on a sphere.
Jester_Thomas · 1 points · Posted at 01:41:06 on February 14, 2016 · (Permalink)
Ah. Makes sense.
maxtofunator · 1 points · Posted at 02:36:03 on February 14, 2016 · (Permalink)
Non-eucledian geometry is some weird abstract stuff. It has a lot to deal with how you define a line. On a plane or in a space like we are used to dealing with, lines are "straight" but if you look at the actual universe, most "lines" are actually curved space
infrequentaccismus · 1 points · Posted at 01:30:47 on February 14, 2016 · (Permalink)
How do you sum angels and what does that have to do with math?
maxtofunator · 1 points · Posted at 02:34:29 on February 14, 2016 · (Permalink)
My phone is great at autocorrecting. ..
wecl0me12 · 1 points · Posted at 01:29:17 on February 14, 2016 · (Permalink)
The first isomorphism theorem - let f:G->H be a group homomorphism, then G/kernel(f) ~ range(f)
butthackerz · 1 points · Posted at 01:29:27 on February 14, 2016 · (Permalink)
Duality between lines and points in projective geometry: any theorem still holds true if you replace if you make the following substitutions:
Duality in general appears a lot in mathematics. Duality between vectors and functionals in linear algebra. Duality between vertices and faces in combinatorial topology. Duality between conjugate complex numbers. Etcetera.
ravenmeister · 1 points · Posted at 01:29:40 on February 14, 2016 · (Permalink)
The relationship between all these constants is simply amazing
Tuxedo_Jackson · 1 points · Posted at 01:29:52 on February 14, 2016 · (Permalink)
Take the square of something and add the root number and the next number in sequence to get the square of the next number.
IE 4*4=16
16+4+5=25
25+5+6=36
Figured this pattern out on my own when I was younger. I was proud I did. Don't know who was the first person to do it tho. Can't imagine I was the first.
Calius1337 · 2 points · Posted at 01:49:55 on February 14, 2016 · (Permalink)
Sorry to burst your bubble, but that's literally the definition of one of the binomial formulae (a + b)2 = a2 + 2ab + b2
x2 + x + x + 1 = (x + 1)2
x2 + 2x + 1 = x2 + 2x + 1
q.e.d
Tuxedo_Jackson · 1 points · Posted at 05:35:29 on February 14, 2016 · (Permalink)
No worries. Good to know that it has an official title and formula attached to it tho. Never once thought it was something I came up with. Too many math geniuses came before me to have missed a pretty simple pattern.
[deleted] · 1 points · Posted at 01:30:02 on February 14, 2016 · (Permalink)
e ^ i . Pi = -1
SpareLiver · 1 points · Posted at 01:30:12 on February 14, 2016 · (Permalink)
If you choose a number completely at random (from the set of all real numbers) there is 0% chance that it will be a whole number. (I think it's actually rational number, not just whole, but not completely sure).
a3wagner · 2 points · Posted at 06:23:58 on February 14, 2016 · (Permalink)
Rational is also correct.
[deleted] · 1 points · Posted at 01:30:28 on February 14, 2016 · (Permalink)
When it comes to binary numeral system there are 10 types of people: the ones who get binary, and the ones who don't.
HumpyMagoo · 1 points · Posted at 01:30:29 on February 14, 2016 · (Permalink)
the square root of negative numbers are called imaginary numbers
LeeKinanus · 1 points · Posted at 01:30:31 on February 14, 2016 · (Permalink)
3 is a magic number
Mysta02 · 1 points · Posted at 01:31:37 on February 14, 2016 · (Permalink)
Multiplying any number by 11 is REALLY easy, even in your head.
Separate the digits, add each side-by-side sets of digits together (carrying if necessary), then delete each enclosed starting digit (not the end ones).
11x11. 1 2 1. 121.
11x111. 1 2
12 1. 1221.11x19. 2 0 9. 209.
Fun trick for the bar or with friends.
DarthKegger · 1 points · Posted at 01:34:11 on February 14, 2016 · (Permalink)
That 2 is the only even prime number
ixfd64 · 1 points · Posted at 01:42:56 on February 14, 2016 · (Permalink)
You could say it's also the oddest prime number.
orcscorper · 1 points · Posted at 07:22:39 on February 14, 2016 · (Permalink)
That's language, not math. "Even" in this context means "divisible by two". I made up the word "threeven", and defined it as "divisible by three". Three is the only threeven prime there is.
lotekjeromuco · 1 points · Posted at 01:35:33 on February 14, 2016 · (Permalink)
When I would take calculator and count, multiple or divide numbers I see by their diagonal, width or lenght I would get some funny numbers. And, uhm, yeah Fibonacci.
cronos844 · 1 points · Posted at 01:35:50 on February 14, 2016 · (Permalink)
The incompleteness theorems. Math is semantically incomplete, meaning there is some proposition that is a paradox of math.
Kobmoney43 · 1 points · Posted at 01:35:56 on February 14, 2016 · (Permalink)
The golden ratio is literally everywhere in nature. It's the building block for earth
amatava · 1 points · Posted at 01:36:03 on February 14, 2016 · (Permalink)
I once heard that no electron can spin at the same rate of speed and temperature as any other electron, meaning anything that affects one informs all electrons in the Universe.
Any know if that's true?
akustix · 1 points · Posted at 01:36:13 on February 14, 2016 · (Permalink)
ei*pi + 1 = 0
The relationship between the five most important numbers all summed up in one tidy expression.
Loshermanos · 1 points · Posted at 01:36:28 on February 14, 2016 · (Permalink)
If you take any multi-digit number and add all its individual digits up, adding together the digits of any sums with 2+ digits in any order you choose, adding all digits together until you get down to one single digit sum, it will always be the same number. Doesn't matter which ones you add in which order, will always end up as the same single digit. Example:
13579
9+7=16 1+6=7 7+5=12 12+3=15 15+1=16 1+6=7
Mix it up in any way you want, adding the two digits of a sum or not, and it will always be 7.
orcscorper · 1 points · Posted at 07:32:25 on February 14, 2016 · (Permalink)
This is the basis behind the ancient pseudoscience of numerology. What you did is called "casting out the nines". You see how you added 9+7 and the 9 disappeared? The 1+3+5 went the same way.
TheOboeMan · 1 points · Posted at 01:37:17 on February 14, 2016 · (Permalink)
Because it is spherical and not a flat plane, any triangle drawn on the surface of the earth has more than 180 degrees as the sum of its angles.
MrLKK · 1 points · Posted at 01:37:35 on February 14, 2016 · (Permalink)
Gabriel's Horn blew my mind in Calc II. If you take f(x) = 1/x and create a concave funnel like thing (or a horn) by rotating that graph over the x-axis from x=0 to x = infinity you create an object (Gabriel's Horn) that has an infinite surface area, but a finite volume.
UniversalFarrago · 1 points · Posted at 01:40:44 on February 14, 2016 · (Permalink)
wut
MrLKK · 1 points · Posted at 01:53:20 on February 14, 2016 · (Permalink)
With calculus you can make a horn-like 3D object that extends to infinity with an infinite surface area and finite volume. You can fill it with paint, but you'll never have enough paint to paint the outside
UniversalFarrago · 1 points · Posted at 02:14:18 on February 14, 2016 · (Permalink)
Oh, I see. Sort of. It's basically infinitely tall? Like, super narrow, I'd guess?
MrLKK · 1 points · Posted at 02:58:32 on February 14, 2016 · (Permalink)
Yeah, it's on its side, but it's the same idea. It's kinda shaped like a bugle
mces97 · 1 points · Posted at 01:37:41 on February 14, 2016 · (Permalink)
I don't know if all this is true, but when I was taking physics in college my professor was talking about the Pythagorean theorem. A squared + B squared = C squared. So here's the thing. The square root of 2 is an irrational number, but if you have two sides of a right triangle equal to 1 (whatever unit), then the hypotenuse has a definite length. He said the guy who figured that out was burnt at the stake.
gaussjordanbaby · 1 points · Posted at 06:19:08 on February 14, 2016 · (Permalink)
I often heard he was thrown off a ship.
RedHexmaster · 1 points · Posted at 01:38:21 on February 14, 2016 · (Permalink)
80085 on a calculator spells "boobs" and 530411351 spells "I sell hoes"
mikemcgu · 1 points · Posted at 07:07:48 on February 14, 2016 · (Permalink)
Upside down of course.
dap03 · 1 points · Posted at 01:38:32 on February 14, 2016 · (Permalink)
3 to the 3rd power plus 4 to the 4th power plus 3 to the 3rd power plus five to the fifth power equals 3435. So 3×3×3+4×4×4×4+3×3×3+5×5×5×5×5=3435
maxdoss · 1 points · Posted at 01:38:59 on February 14, 2016 · (Permalink)
If you graph y = abs(X) - squareroot(1 - X2) and y = abs(X) + squareroot(1 - X2), you make a heart.
EGOiST91 · 1 points · Posted at 01:39:00 on February 14, 2016 · (Permalink)
A factorial (denoted by "!") is evaluated as n! = (n)(n-1)(n-2)...(1). So for example 5! = (5)(4)(3)(2)(1) = 120. Factorials are often applied in probability to describe combinations and choices, hence, you pretty much only see n! when n is some integer. However, as it turns out you can take factorials of fractions as well.
(1/2)! = sqrt(pi)/2
This is a result of the gamma function, which is an integral that generalizes factorials for any real number n.
[deleted] · 1 points · Posted at 01:39:12 on February 14, 2016 · (Permalink)
If you take 1/x where x>=1 and rotate it in three dimensional space about the x-axis the resulting surface has infinite surface area but finite volume. That is to say you could fill it with a finite amount of paint, but you could never have enough paint to cover its exterior. This surface is known as the Gabriel's Horn or Torricelli's trumpet.
Whorrox · 1 points · Posted at 01:39:17 on February 14, 2016 · (Permalink)
y = 1 / sqrt (- abs(x)) is hard to graph...
Riobhain · 1 points · Posted at 01:39:23 on February 14, 2016 · (Permalink)
There's a formula called Tupper's self-referential formula ( https://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula ) that graphs itself when plotted.
[deleted] · 1 points · Posted at 01:39:38 on February 14, 2016 · (Permalink)
111,111,1112 = 12,345,678,987,654,321
Jimmyjangles85 · 1 points · Posted at 01:39:42 on February 14, 2016 · (Permalink)
2+2=Potato
jkSam · 1 points · Posted at 01:39:52 on February 14, 2016 · (Permalink)
12345679 x 82 = 888888888 12345679 x 73, 64, 54 and so on also works. Also works if flipped (28, 37)
Pegguins · 1 points · Posted at 01:40:05 on February 14, 2016 · (Permalink)
Hmm, the one I use most often is the general magic that fourrier transformations make. I don't like it though.
MiG-25 · 1 points · Posted at 01:40:11 on February 14, 2016 · (Permalink)
A Gabriel's Horn, or cornucopica, has infinite surface area but finite volume. Just went over this in calc.
fred1674 · 1 points · Posted at 01:40:23 on February 14, 2016 · (Permalink)*
1 * 1=1
11 * 11=121
111 * 111=12321
1111 * 1111=1234321
11111 * 11111=123454321
111111 * 111111=12345654321
1111111 * 1111111=1234567654321
11111111 * 11111111=123456787654321
111111111 * 111111111=12345678987654321
it's not that amazing, but i did like doing it on my calculator
1CosMcCray · 1 points · Posted at 01:41:16 on February 14, 2016 · (Permalink)
Kepler's 3rd Law of Planetary Motion: Period squared = Distance cubed
Ammastaro · 1 points · Posted at 01:42:35 on February 14, 2016 · (Permalink)
There is a number, called Graham's number that can't be defined in any terms of writing the digits, as even if every single digit was an atom, there aren't enough atoms in the universe to encompass it. The number is so large that it must be written using series and special notation. To give some reference, if you took the earth as it stands, ground it up into sand, took that sand and then expanded them each to the size of the universe, then took those universes and completely filled them with lead, and took the weight of all of those universes, the weight in pounds would be less than Graham's number by a significant amount.
Comalol · 1 points · Posted at 01:42:46 on February 14, 2016 · (Permalink)
My area code (563) is one of three known Wilson primes under 20 billion. The other two are 5 and 13.
BritishAristocracy · 1 points · Posted at 01:43:21 on February 14, 2016 · (Permalink)
.999 repeating = 1
1/9 = 0.1111... 2/9 = 0.2222... ... ... 9/9 (1) = 0.9999...
[deleted] · 1 points · Posted at 01:43:23 on February 14, 2016 · (Permalink)
0.999... = 1
crumards2 · 1 points · Posted at 01:43:58 on February 14, 2016 · (Permalink)
1 x 1 = 2
[deleted] · 1 points · Posted at 01:44:01 on February 14, 2016 · (Permalink)
One in every five people is born in china
Ammastaro · 1 points · Posted at 01:44:53 on February 14, 2016 · (Permalink)
1/998,001 yields every single combination of three digit numbers (.000001002003004...) but not 998, (.000 001 002... 996 997 999) then repeats at 000
_nullpointer · 1 points · Posted at 01:45:15 on February 14, 2016 · (Permalink)
To multiply any single digit and 9, hold up all 10 fingers and then put down the finger you want to multiply with 9. The fingers still standing to the left is the tens position, fingers to the right in singles position.
Really only useful in 2nd grade or so, but that one has stuck with me.
ceraith · 1 points · Posted at 01:45:24 on February 14, 2016 · (Permalink)
You can create 2 identical spheres from one sphere that is also identical to the 2 new spheres
GaloisGroupie3474 · 1 points · Posted at 01:45:50 on February 14, 2016 · (Permalink)
If you take a wire in the shape of a cycloid, place two beads anywhere on its length, and release them simultaneously, they will reach the bottom at the same time.
supersonic-turtle · 1 points · Posted at 01:45:59 on February 14, 2016 · (Permalink)
thousands have died being subjected to malaria experiments... millions reap the benefits
DuapDuap · 1 points · Posted at 01:46:39 on February 14, 2016 · (Permalink)
The average human does not have two legs.
mpatel00 · 1 points · Posted at 01:47:06 on February 14, 2016 · (Permalink)
That when rolling 10 dice the probability of rolling 6666666666 is the same as rolling 1234561234 or 1526451634
smerkwithskizzle · 1 points · Posted at 01:48:06 on February 14, 2016 · (Permalink)
All those mc esher things
Darkstar_98 · 1 points · Posted at 01:48:53 on February 14, 2016 · (Permalink)*
That the space between each square(you have to include 0 squared and 1 squared) goes up by odds. 0+1=1 1+3=4 4+5=9 9+7=16 16+9=25 And so on
Edit: Reddit doesn't like carrot exponents
bigfoot1825 · 1 points · Posted at 01:49:29 on February 14, 2016 · (Permalink)
111,111,111 x 111,111,11 = 12,345,678,987,654,321
Mikeismyike · 1 points · Posted at 01:49:36 on February 14, 2016 · (Permalink)
I can receipt pi to the 200th digit for no apparently reason.
hubife13 · 1 points · Posted at 01:50:05 on February 14, 2016 · (Permalink)
[ei(pi)] + 1 = 0 seriously what the shit
edit: formatting doesn't work. gave up.
voltism · 1 points · Posted at 01:50:35 on February 14, 2016 · (Permalink)
The individual digits of 9 times or divided by most numbers adds to 9
MiserableLurker · 1 points · Posted at 01:50:43 on February 14, 2016 · (Permalink)
Nice try, kid trying to cheat on homework!
Mr_Skeleton · 1 points · Posted at 01:51:29 on February 14, 2016 · (Permalink)
Maybe someone could answer a question for me. Why does BEDMAS work? Like what are the logical steps to it? I mean i know what it is but I still don't really get why that's the proper way to do an equation.
OverlordLork · 1 points · Posted at 04:46:47 on February 14, 2016 · (Permalink)
It's not some kind of mathematical fact, it's just how we write our equations. 2 + 5 * 3 is ambiguous, so we DEFINE it to mean 2 + (5 * 3). We could just as easily use BEASMD or any other ordering, we'd just have to write some of our equations a little differently.
It's like how the symbol "4" doesn't objectively mean the fourth number, it's just how we choose to represent that concept.
HylianPeacock · 1 points · Posted at 01:51:44 on February 14, 2016 · (Permalink)
The number 1 actually has 2 values. 1 divided by 3 =.333 repeating .333 repeating multiplied by 3 = .999 repeating therefore the number 1 simultaneously has the value of 1 and .999 repeating.
loozid · 1 points · Posted at 08:22:32 on February 14, 2016 · (Permalink)
wat
soxdye9 · 1 points · Posted at 01:52:03 on February 14, 2016 · (Permalink)
Kind of late to the thread but the number 6174 is very unique in that when ever you take any 4 digit number (i.e. 1254) and arrange the number from high to low (5421) then subtract the numbers from low to high (1245), you'll get some number then repeat the pattern with the new number (this case 4176), which then you get (7641-1467=6174). You will always end the pattern at the number 6174. This only works when one of the four numbers is different from the rest (1111 doesn't work but 1110 does.)
gaussjordanbaby · 1 points · Posted at 06:20:11 on February 14, 2016 · (Permalink)
Great one!
TheDarkitect · 1 points · Posted at 01:52:26 on February 14, 2016 · (Permalink)
There are as many elements between 0 and 1 as there are in R.
And [0,1] is included in R.
Infinity is an incredible concept.
chasingthemoon23 · 1 points · Posted at 01:52:40 on February 14, 2016 · (Permalink)
Any number that is divisible by 3, the sum of its digits will by divisible by 3. This is true with 9. If the number is also even, it is divisible by 6. Base 10 system.
astro_max · 1 points · Posted at 01:52:50 on February 14, 2016 · (Permalink)
Three irrational numbers magically transform into an rational number: ei*pi=-1
cd943t · 1 points · Posted at 01:53:48 on February 14, 2016 · (Permalink)
The sin of 666° is equal to the golden ratio divided by -2.
vodkasoup · 1 points · Posted at 01:53:49 on February 14, 2016 · (Permalink)
Because pi is infinitely long, your entire life - your birth, death, and everything in between - is encoded within it.
Somewhere in its infinity of digits there is a perfect image of the first thing you ever saw, and the last thing you will ever see.
OrangeNova · 1 points · Posted at 01:53:58 on February 14, 2016 · (Permalink)
Graham's Number!
At least explained by this man.
https://www.youtube.com/watch?v=1N6cOC2P8fQ
redute343 · 1 points · Posted at 01:54:07 on February 14, 2016 · (Permalink)
0.99 to the power of infinity = 1
gindc · 1 points · Posted at 15:23:34 on February 14, 2016 · (Permalink)
0.99 to the power of infinity = 0
callingallkids · 1 points · Posted at 01:54:09 on February 14, 2016 · (Permalink)
1+1=1
Dreuh2001 · 1 points · Posted at 01:54:57 on February 14, 2016 · (Permalink)
Take any number and add up it's digits. If the sum is divisible by 3 then so is the original number.
4281 4+2+8+1=15/3=5 (check) 4281/3=1427 (confirmed)
LegatePanda · 1 points · Posted at 01:55:14 on February 14, 2016 · (Permalink)
Charles Babbage designed the first computer in the work. The Difference Engine was the first mechanical calculator, And it could tabulate polynomial functions.
Petrichorest · 1 points · Posted at 01:55:41 on February 14, 2016 · (Permalink)
25.8069758011 is the root of all evil.
25.8069758011 squared = 666
FoolishChemist · 1 points · Posted at 01:56:36 on February 14, 2016 · (Permalink)
102 + 112 + 122 = 132 + 142
markd315 · 1 points · Posted at 01:57:02 on February 14, 2016 · (Permalink)
Euler's identitiy!
Wellhowboutdat · 1 points · Posted at 01:57:17 on February 14, 2016 · (Permalink)
Ive saved this thread to re-read each time I get a bit cocky. Reddit has some smart mofos in here.
d33pwint3r · 1 points · Posted at 01:57:28 on February 14, 2016 · (Permalink)
I did the calculations on this once (can't remember if I used googol or googolplex) but if stored as .doc you would need a pile of 64-gigabyte microsd cards the size of 180 million~ pyramids of Giza to store the number. I lost the calculations during a computer reset, wish I could say for certain which it was
baseacegoku · 1 points · Posted at 01:57:28 on February 14, 2016 · (Permalink)
That Euler discovered or invented so many mathematical formulas and equations that they had to start naming them after the second person to discover them so that they all weren't named after Euler.
_Purple_Tie_Dye_ · 1 points · Posted at 01:57:58 on February 14, 2016 · (Permalink)
Gabriel's Horn can be filled with paint but cannot be painted.
A revolution of a curve about its axis. (Don't recall the equation off the top of my head)
nanostorm · 1 points · Posted at 01:57:59 on February 14, 2016 · (Permalink)
pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 .......
13thmurder · 1 points · Posted at 01:58:11 on February 14, 2016 · (Permalink)
2+2=4
But also...
2x2=4
ProfessorMisanthrope · 1 points · Posted at 01:58:27 on February 14, 2016 · (Permalink)
If you cut a ball into a finite number of parts (at least five), and reassemble it in a different way by only translating and rotating the pieces, you will end up with two balls. The Banach–Tarski paradox.
https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox?wprov=sfti1
(I can't find the relevant xkcd)
Braxo · 1 points · Posted at 01:59:25 on February 14, 2016 · (Permalink)
Mine is somewhat weird - but take a standard calculator with the layout of:
So, following the left to right pattern and in reverse:
Then, the top to bottom pattern and in reverse:
Then, take the top-left diagonal pattern and in reverse:
Then, take the bottom-left diagonal pattern and in reverse:
Just a silly coincidence I suppose.
kingofthefeminists · 1 points · Posted at 01:59:26 on February 14, 2016 · (Permalink)
ei*pi+1=0
MyPornographyAccount · 1 points · Posted at 01:59:32 on February 14, 2016 · (Permalink)
For every prime number greater than or equal to 5, one less than its square is divisible by 24.
Short proof:
Say x is prime. In the sequence x-1, x, x+1, at least one of those numbers must be divisible by 3. It can't be x, because otherwise x wouldn't be prime. Additionally, we know that one of x-1 and x+1 is divible by 2 and the other is divisible by 4, because every other consecutive even number is divisible by 4 and those are two consecutive even numbers, because x must be odd for it to be prime.
So that means (x-1)(x+1) must be divisible by 2 x 3 x 4, which is 24, since factors of the multicants are also factors of the product.
(x-1)(x+1) = x2 - x + x -1 = x2 -1, which is 1 less than the square of x, which as we said at the start is any prime number greater than or equal to 5.
QED
adesimo1 · 1 points · Posted at 01:59:39 on February 14, 2016 · (Permalink)
A little late to the party, but does Simpson's Paradox count?
Here's one of my favorite examples:
David Justice had a higher batting average than Derek Jeter in both 1995 and 1996, but when you combine both seasons Jeter's batting average is much higher. In this instance it's mostly due to the very small sample size for Jeter in 1995, and small sample for Justice in 1996.
AH_MLP · 1 points · Posted at 01:59:59 on February 14, 2016 · (Permalink)
111,111,111 squared =
12345678987654321
hardbrain · 1 points · Posted at 01:59:59 on February 14, 2016 · (Permalink)
π% of 1337 = 42
Airth · 1 points · Posted at 02:00:16 on February 14, 2016 · (Permalink)
Multiplication by 11. If it's two digits, you can just add the two digits and put the result in the middle. tho, you have to carry over when its greater than 10. Example: 25 x 11 : 2 + 5 = 7, 275.
djkimothy · 1 points · Posted at 02:00:20 on February 14, 2016 · (Permalink)
1 = 0.9...
don_truss_tahoe · 1 points · Posted at 02:01:25 on February 14, 2016 · (Permalink)
The Black-Scholes asset pricing model from finance and economics becomes the heat equation from physics when you set interest rates to zero.
CougarBen · 1 points · Posted at 02:01:28 on February 14, 2016 · (Permalink)
.9999 repeating = 1
TaedW · 1 points · Posted at 02:02:32 on February 14, 2016 · (Permalink)
There are (almost exactly) pi seconds in a nano-century.
Hounmlayn · 1 points · Posted at 02:03:07 on February 14, 2016 · (Permalink)
Most videos from numberphile are the coolest facts I know
workiswork2563 · 1 points · Posted at 02:03:15 on February 14, 2016 · (Permalink)
When you shuffle playing cards it is most likely the first time that any deck EVER has been ordered that way. And it will continue to be a unique order for billions and billions and billions of years from now.
Now, go make some history!
More info: http://qi.com/infocloud/playing-cards
FreakinSweet86 · 1 points · Posted at 02:03:28 on February 14, 2016 · (Permalink)
Ive always been fascinated with Fibonacci Numbers. For those unfamiliar, you start at zero, then count to one. At this point you add the two together to get 0+1=1. Now add the new number to the previous, 1+1=2, then 2+1=3 and so on. It should look like this:
0, 1, 1, 2, 3, 5, 8, 13, 21.......
Interestingly enough, these sequences can also be found in nature. Fascinating stuff!
flangepaddle · 1 points · Posted at 02:03:46 on February 14, 2016 · (Permalink)
0.9 recurring = 1
OwnUbyCake · 1 points · Posted at 02:04:43 on February 14, 2016 · (Permalink)
Current secure encryption for things like your banking information or any time that you use your credit card online uses 2 extremely large prime numbers (In the billions or trillions or bigger) to form a key that are then multiplied together into something called a semi-prime. That semi-prime is then the public key that you use to encrypt your credit card information when buying something or your username and password when logging in somewhere. Because it is so difficult to discover the exact 2 prime numbers that created the semi-prime it is completely safe to send your information online using this encryption. (As long as you don't have a virus or anything on your computer)
To put how difficult it is to guess the 2 numbers that created the semi-prime, it would take all of the computers in the world longer than the length of the current age of the universe to crack the code. Its cool because something that we use every day is just math.
[deleted] · 1 points · Posted at 02:04:54 on February 14, 2016 · (Permalink)
2 + 2 = 4
2 x 2 = 4
C0m3b4cK1d · 1 points · Posted at 02:05:34 on February 14, 2016 · (Permalink)*
the persistence of the ratio phi in nature
so fucking cool
Often this fact is abused in nutcase documentaries you can find on youtube. But overlook this and it's still amazing. Seriously, tomorrow go outside and stare really close at the center of a flower. Mindblowing.
dark2400 · 1 points · Posted at 02:05:37 on February 14, 2016 · (Permalink)
5138008 is the best number on a calculator.
loozid · 1 points · Posted at 08:23:30 on February 14, 2016 · (Permalink)
if you can't spell...
B170755 · 1 points · Posted at 02:05:39 on February 14, 2016 · (Permalink)
1+1=2
SELEKTOR_ · 1 points · Posted at 02:05:44 on February 14, 2016 · (Permalink)
"It's the same in every country" - Cady
Xor_Boole · 1 points · Posted at 02:06:13 on February 14, 2016 · (Permalink)
Projective space is like space where you can get to infinity.
Think of it like a sphere. If you start at the center, you can go in a straight line to the boundary, and if you try to go further, you end up starting to go back to where you started... you went in a circle while going in a straight line.. Moreover, when you get to the boundary, you're on two opposite points of the sphere's boundary... at the same time.
Formally, real projective space RPn is Sn/~, where v ~ -v on the boundary, and Sn is the n-dimensional sphere (well, ball, it's a solid).
More interestingly, when n = 1, we have the one-dimensional version, the projective line, which is just a line with the ends glued together: a circle! Also, the space of rotation in 3D, known as SO3, looks exactly like RP3!
Source: I study mathematics.
ceazah · 1 points · Posted at 02:06:37 on February 14, 2016 · (Permalink)
80,085 spells boobs on a calculator
pclack · 1 points · Posted at 02:07:23 on February 14, 2016 · (Permalink)
ei pi = -1
Otherwise known as eulers formula. I just think it's cool that an identity containing the most famous irrational numbers is equal to something so simple as -1.
rhgla · 1 points · Posted at 02:07:32 on February 14, 2016 · (Permalink)
That I sucked at math in school and excel at my job, which is heavily based upon a requirement to be skilled at math.
NotSoSuperNerd · 1 points · Posted at 02:08:39 on February 14, 2016 · (Permalink)
I find it interesting what is actually not known by mathematicians. For example, nobody knows if every even number >2 can be written as the sum of two primes, and yet nobody has found a counterexample. Also, do you know the popular claim that Shakespeare's plays are encoded in the digits of pi? That hasn't been proven either.
parvicus · 1 points · Posted at 02:08:52 on February 14, 2016 · (Permalink)
If the difference in the balance of your till is divisible by 9 you transposed a number:
[DEFINITION of 'Transposition Error' A simple error of data entry. Transposition errors occur when two digits that are either individual or part of a larger sequence of numbers are reversed (transposed) when posting a transaction. Although this error is small and unintentional, it can result in huge financial losses or errors in some instances.
BREAKING DOWN 'Transposition Error' When two adjacent numbers are transposed, the resulting mathematical error will always be divisible by 9 (e.g. (72-27)/9 = 5). Bank tellers can use this rule to quickly find their errors in many cases. Transposition errors also occur in accounting firms, brokerages and all other areas of finance.](http://www.investopedia.com/terms/t/transposition-error.asp#ixzz406Vx8xwx )
TurrPhennirPhan · 1 points · Posted at 02:08:55 on February 14, 2016 · (Permalink)
5=7
KeltronX · 1 points · Posted at 02:09:19 on February 14, 2016 · (Permalink)
To convert from meters per second to miles per hour, multiply by the square root of five.
flyyyyyyyyy · 1 points · Posted at 02:09:44 on February 14, 2016 · (Permalink)
use the fibonacci sequence to convert miles to kilometers.
fibonacci sequence is just starting from 1 and the previous two numbers added together:
5 miles is about equal to 8 km,
55 km is about equal to 34 miles,
etc
[deleted] · 1 points · Posted at 02:10:11 on February 14, 2016 · (Permalink)
5/7 = 10/10
WraithTanker · 1 points · Posted at 02:10:26 on February 14, 2016 · (Permalink)
arabic numbers was written such the number has that many angles. 1-1 angle 2-2 angles 3-3 angles ....
orcscorper · 1 points · Posted at 08:01:59 on February 14, 2016 · (Permalink)
True for 1-4. 5 was a circle below a line, later opened on one side and attached to the line, left in to distinguish it from a circle above the line, which meant 10. 6 was a circle (representing a hand) with one finger up for 5+1.t 9 was 10 with one finger down to subtract 1. The circle with three fingers up morphed into the modern 8, and the circle disappeared from the 7, probably to distinguish it from 5 and 6.
CHKNFWIEDWICE · 1 points · Posted at 02:10:33 on February 14, 2016 · (Permalink)
1+1=11
DishwasherTwig · 1 points · Posted at 02:11:04 on February 14, 2016 · (Permalink)
Graham's number is famously the largest number that is used in a serious mathematical proof. It is so large that if you were to write each digit in one planck volume, the smallest volume physically possible, you wouldn't be able to fit it within the observable universe. Not only that, but jumping off of /u/PlasmicDynamite's comment, you still couldn't fit it in the observable universe even if you attempted to write it using tetrations. And if you're thinking that means that means that it's larger than the number of Planck volumes, you're wrong. It means that the number has over 4 x 1085 digits. If the scale of the universe is unfathomable to you, Graham's number is sure to be as well.
And moreover, since its discovery, it has actually been dethroned as the largest useful number in mathematics a few times.
7firewire · 1 points · Posted at 02:11:33 on February 14, 2016 · (Permalink)
Ok step away from the calculations
wadss · 1 points · Posted at 02:11:36 on February 14, 2016 · (Permalink)
a number is divisible by 3 if the sum of all its digits is also divisible by 3. 102 is because 1+0+2=3, likewise 123456 also is.
ghroat · 1 points · Posted at 02:11:36 on February 14, 2016 · (Permalink)
111111111*111111111=12345678987654321
Brayzure · 1 points · Posted at 02:11:40 on February 14, 2016 · (Permalink)
Maybe not coolest, but one I find interesting.
e (i pi) = -1
PacmanNemesis · 1 points · Posted at 02:11:42 on February 14, 2016 · (Permalink)
60% of the time it works every time.
[deleted] · 1 points · Posted at 02:12:02 on February 14, 2016 · (Permalink)
ITT: People who became mathematicians after watching vsauce.
satan_loves_us · 1 points · Posted at 02:12:33 on February 14, 2016 · (Permalink)
80085 spells boobs on a calculator.
Sciencetor2 · 1 points · Posted at 02:12:42 on February 14, 2016 · (Permalink)
That there is a magic way to prove that arbitrarily large numbers are prime without factoring them https://www.youtube.com/watch?v=lEvXcTYqtKU
jedi-son · 1 points · Posted at 02:13:02 on February 14, 2016 · (Permalink)
There's different sizes to infinity and it's relatively easy to prove and see. I wont outline the proof now because I'm in a cab and my girlfriend is pissed I'm on my phone but check out cantor's snake or google countable /uncountable infinity. Very cool and powerful concept that actually comes up a lot.
BeastofLoquacity · 1 points · Posted at 02:13:14 on February 14, 2016 · (Permalink)
Every multiple of 9 from 1 to 10 has digits that add up to 9. 9 = 9 1 + 8 = 9 2 + 7 = 9 Etc.
PJDubsen · 1 points · Posted at 02:13:22 on February 14, 2016 · (Permalink)
How about .999999 repeated == 1
1/3 = .333333...
1/3 * 3 = 1
.333333... * 3 = .99999...
eldeeder · 1 points · Posted at 02:13:30 on February 14, 2016 · (Permalink)
52! or 52 Factorial illustrated. https://youtu.be/ObiqJzfyACM?t=14m7s Explains it very well.
Basically, in the history of human kind, a deck of cards has never been shuffled the same way twice. If all the possibilities were seconds, you could stand at the equator, and wait ONE BILLION years to take ONE step. Then wait another BILLION. Keep doing this, until you've gotten all the way around the globe. Then remove 1 drop of water from the ocean. Now, start over again. By the time the pacific ocean is dry, you haven't even made a dent in the number. The video explains it so much better, but you'll never look at a deck of cards the same way again.
[deleted] · 1 points · Posted at 02:13:33 on February 14, 2016 · (Permalink)
1+1= windows
Llamanog · 1 points · Posted at 02:14:06 on February 14, 2016 · (Permalink)
1 + 1 = 3
this_is_your_dad · 1 points · Posted at 02:14:07 on February 14, 2016 · (Permalink)
Adding two odd numbers makes an even number, according to my youngest child.
Hypersmith · 1 points · Posted at 02:14:15 on February 14, 2016 · (Permalink)
When launching an object away from another object, the theoretical distance of the gravitational field is infinity. However, you can launch it far enough for it not to be attracted any longer. That distance is infinity, and yet by the definition of infinity, still infinitely far away from infinity.
alicethedeadone · 1 points · Posted at 02:14:37 on February 14, 2016 · (Permalink)
Eight and eight fell on the floor Picked 'em up, it was sixty-four.
BOOM! You're welcome.
arista81 · 1 points · Posted at 02:14:49 on February 14, 2016 · (Permalink)
Any integer to the 5th power has the same last digit as the original number.
[deleted] · 1 points · Posted at 02:14:56 on February 14, 2016 · (Permalink)
I would like to post my answer as a video, because all the mathematical facts I know are thanks to Square One and the Children's Television Workshop. <3
"The story you're about to see is a fib, but it's short."
https://www.youtube.com/watch?v=HJD-GeSJ-oY
(Actually it's 50 gorram minutes of math melodrama but James Earl Jones appears at minute 3 and it just gets better from there.)
surfkaboom · 1 points · Posted at 02:15:06 on February 14, 2016 · (Permalink)
Counting multiples of 9 on your hands
flyyyyyyyyy · 1 points · Posted at 02:15:21 on February 14, 2016 · (Permalink)
PI*e/PHI * 1000 = 5,277.84 = almost exactly the number of feet in a mile (5280)
dunno whether that's the original definition or just a coincidence
orcscorper · 1 points · Posted at 08:09:27 on February 14, 2016 · (Permalink)
More sciency than mathish, but a light-nanosecond is almost exactly one foot. And they say the Imperial system is arbitrary and silly.
flyyyyyyyyy · 1 points · Posted at 15:24:33 on February 14, 2016 · (Permalink)*
4322 is within 0.2% of the speed of light in a vacuum in miles per second (432Hz is crown chakra resonance)
and it's the 8th octave of the solar plexus chakra resonance (729Hz)
i'd love to find a list of all these imperial system 'coincidences' - and hand it to engineering students ;)
chateaublue32 · 1 points · Posted at 02:15:40 on February 14, 2016 · (Permalink)
You can measure pizza.
TP3NG · 1 points · Posted at 02:16:05 on February 14, 2016 · (Permalink)
1 + 2 + 3 + 4 + 5 + 6 ... = -1/12
Sum of all positive integers is NEGATIVE 1 over 12. Blew my mind.
Here's a simplified proof: https://www.youtube.com/watch?v=w-I6XTVZXww
And a more mathy proof: https://www.youtube.com/watch?v=E-d9mgo8FGk
Bearacolypse · 1 points · Posted at 02:16:07 on February 14, 2016 · (Permalink)
The Birthday problem if you have 23 people in a room there is a 50% chance that someone will share the same birthday.
Slaytanist · 1 points · Posted at 02:16:22 on February 14, 2016 · (Permalink)
4004067.5 x 2 = 8008135
7steak7 · 1 points · Posted at 02:16:28 on February 14, 2016 · (Permalink)
8000 + 8 = BOOB
fpw1 · 1 points · Posted at 02:16:41 on February 14, 2016 · (Permalink)
i is imaginary.
ii is about 0.21. It's not even complex. It's real, and it's about a fifth.
spicyG95 · 1 points · Posted at 02:16:41 on February 14, 2016 · (Permalink)
A number squared is always only 1 more than if you multiply the number before and after. For example 72 =49 and 6*8=48
DOUG_UNFUNNY · 1 points · Posted at 02:16:48 on February 14, 2016 · (Permalink)
5318008 upside down spells BOOBIES
its_a_rock_fact · 1 points · Posted at 02:16:53 on February 14, 2016 · (Permalink)
Can't believe this isn't here already. If you take i to be the imaginary unit sqrt(-1), then ii ~= 0.20788, a totally real number.
Star-spangled-Banner · 1 points · Posted at 02:17:12 on February 14, 2016 · (Permalink)
ei·π = -1
stupornatural · 1 points · Posted at 02:17:15 on February 14, 2016 · (Permalink)
Rule of 72
The rule of 72 is a shortcut to estimate the number of years required to double your money at a given annual rate of return. The rule states that you divide the rate, expressed as a percentage, into 72
TripleThreat1212 · 1 points · Posted at 02:17:28 on February 14, 2016 · (Permalink)
The sum of a positive numbers from 1 to infinity is -1/4.
[deleted] · 1 points · Posted at 02:17:56 on February 14, 2016 · (Permalink)*
Gabriel's Horn is a geometric shape with finite volume but infinite surface area. If you wanted to paint the horn, you could paint the inside with a finite amount of paint, but no matter what, all the paint in the world wouldn't be enough to paint the outside.
Ipsoka · 1 points · Posted at 02:18:15 on February 14, 2016 · (Permalink)
That 1+2+3+4+5+6+... = - 1/2
dyfx · 1 points · Posted at 02:18:18 on February 14, 2016 · (Permalink)
When sending messages, if each letter has over a 50% chance of being received correctly, then there is way to encode the messages before sending so that the receiver can decode the messages with basically 100% accuracy AND the encoded message is very short. Shannon's Theorem
thenudedentist · 1 points · Posted at 02:18:29 on February 14, 2016 · (Permalink)
Every next square can be found in order of increasing odd numbers added to the previous square.. Hard to explain in words but 12 is 1, 22 is 4 which is 1+3, 32 is 9 which is 4+5, 44 is 16 which is 9+7... I think thats pretty cool
GrimwoodCT · 1 points · Posted at 02:28:26 on February 14, 2016 · (Permalink)
This pattern works even as you proceed into cubes and beyond power progression. Here is the example for cubes. Fourth (and later) progressions require use of lesser powers broken down similarly.
43=64 53=125 125-64=61 (52)+(42)+(4*5)=61
63=216 73=343 343-216=127 (62)+(72)+(6*7)=127
dsahai · 1 points · Posted at 02:18:38 on February 14, 2016 · (Permalink)
Well given that it's valentine's day and what not, type this into Google: sqrt(cos(x))cos(300x)+sqrt(abs(x))-0.7)(4-x*x)0.01, sqrt(6-x2), -sqrt(6-x2) from -4.5 to 4.5
st8ofinfinity · 1 points · Posted at 02:18:53 on February 14, 2016 · (Permalink)
The Amplituhedron
https://en.m.wikipedia.org/wiki/Amplituhedron
bigflanders · 1 points · Posted at 02:20:10 on February 14, 2016 · (Permalink)
You can spell boobs on a calculator
mikredditor · 1 points · Posted at 02:20:11 on February 14, 2016 · (Permalink)
That if you fold a piece of paper in half 117 times, that it is thicker than the observable universe.
theduckspants · 1 points · Posted at 02:20:29 on February 14, 2016 · (Permalink)
12345679 * 9 = 111111111
12345679 *18= 222222222
12345679 *27= 333333333
and so on
ajax2k9 · 1 points · Posted at 02:20:32 on February 14, 2016 · (Permalink)
The summation of 2n-1 from 1 to n is n*n
thePurpleAvenger · 1 points · Posted at 02:20:32 on February 14, 2016 · (Permalink)
The limit of the volume of a d-dimensional unit box as d goes to infinity is 1. The limit of the volume of a d-dimensional unit ball as d goes to infinity is 0 though.
ajax2k9 · 1 points · Posted at 02:21:21 on February 14, 2016 · (Permalink)
Also that if you add a number's digits and that sum is divisible by 3, the number itself is divisible by 3
superblobby · 1 points · Posted at 02:21:27 on February 14, 2016 · (Permalink)
111,111,111 x 111,111,111 = 123,456,789,876,543,210
iluvgrannysmith · 2 points · Posted at 03:09:10 on February 14, 2016 · (Permalink)
There is no 0 at the end :P
DavesWorkRedditName · 1 points · Posted at 02:21:32 on February 14, 2016 · (Permalink)
I'm not even high but reading this post makes me feel like I'm a [10]
PJBthefirst · 1 points · Posted at 02:21:34 on February 14, 2016 · (Permalink)*
If you want to drive a car with square wheels smoothly on a road, the road must have bumps.
The shapes of these bumps are Catenaries, the same curve seen on hanging power lines. https://en.wikipedia.org/wiki/Catenary
kitch2495 · 1 points · Posted at 02:22:18 on February 14, 2016 · (Permalink)
You have six dots, with three in one row and three in the other. If you try to draw a line from each dot and connect it to all others (so each dot has three lines coming from it), it's impossible to do so without any line intersecting the other. This is provable with Euler's Graph Theory
dash-dash-hyphen · 1 points · Posted at 02:22:37 on February 14, 2016 · (Permalink)
1 = 0.99999999999...
Let x = 0.999999...
Then 10x = 9.9999.....
So 10x - 1x would be
9x = 9 or x = 1
steampoweredbacon · 1 points · Posted at 02:22:41 on February 14, 2016 · (Permalink)*
That every triangle on this Poincaré disk has an angle sum of zero.
Edit: Also, there exists an infinite amount of triangles within the disk.
[deleted] · 1 points · Posted at 02:22:52 on February 14, 2016 · (Permalink)*
[deleted]
iluvgrannysmith · 2 points · Posted at 03:06:41 on February 14, 2016 · (Permalink)
Keep going, if a number is divisible by nine, it's digits summed together will be divisible by nine. Similarly, if a number is divisible by 3, it's digits are divisible by 3. Give it a try:) 123 is divisible by 3. 567 is divisible by 9.
[deleted] · 1 points · Posted at 02:23:14 on February 14, 2016 · (Permalink)
Here's something to think about: Every time you shuffle a deck of cards, you make history.
Shuffle a deck of cards once per second. Every billion years, take one step. Every time you walk around the world, take a sip from the ocean. Everytime you drain the ocean, put a single piece of paper on the ground. Once the stack of paper touches the Sun, you have only done 1/3000 of the shuffles the deck could have.
(I think that's correct. Someone please correct me if I messed that up)
Xorondras · 1 points · Posted at 02:23:40 on February 14, 2016 · (Permalink)
The Ulam Spiral is quite cool.
UlrichZauber · 1 points · Posted at 02:23:41 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Graham%27s_number
Graham's number, an integer so large that, using any conventional notation, it cannot be expressed in this universe. Because it's just too big.
And it has a name because some guy actually needed it to do a proof!
RyanR1991 · 2 points · Posted at 02:38:26 on February 14, 2016 · (Permalink)
A few years ago, I had him as a professor at University of California, San Diego in a Computer Science class. He was awesome!
He casually slid in that there was a number named after him, and I thought he was joking that there coincidentally was a number that shared his last name. I looked it up later; I was wrong.
Nicapopulus · 1 points · Posted at 02:23:42 on February 14, 2016 · (Permalink)
The sum of the numbers of any multiple of 9 will be 9, or 18..etc.
Example 9*9=81 ->8+1=9
9*375=3375 -> 3+3+7+5=18
KaBar42 · 1 points · Posted at 02:23:44 on February 14, 2016 · (Permalink)
There is not enough space in the known universe to write a googolplex and it would take billions of years to write.
It would take so long, the amount of time it would take is longer than the amount of time the Universe has existed…
A googol is presumed to be larger than the amount of atoms in the Observable Universe.
gwf · 1 points · Posted at 02:24:09 on February 14, 2016 · (Permalink)
Stirling's formula, an approximation for factorials of large numbers, is one of my favorites:
n! ~ sqrt(2 pi n) * nn * e-n
Mr_Tank · 1 points · Posted at 02:24:16 on February 14, 2016 · (Permalink)
That every possible sequence of numbers is contained in Pi.
If you convert that to text this means that every answer to any conceivable question is contained in that number.
This also means that every persons life, alive, dead or to be born, is also contained in Pi.
It's just bind boggling how much knowledge is contained in Pi.
Destiny_and_pie · 1 points · Posted at 02:24:38 on February 14, 2016 · (Permalink)
Their are more combinations for a deck of cards then seconds in the universe
TransitJohn · 1 points · Posted at 02:24:42 on February 14, 2016 · (Permalink)
The sum of an infinite number of numbers is a finite number.
Felix_Tholomyes · 1 points · Posted at 02:53:05 on February 14, 2016 · (Permalink)
That obviously depends on which numbers you are summing, it does not hold for all numbers.
CubularRS · 1 points · Posted at 02:24:49 on February 14, 2016 · (Permalink)
1/998001 equals 0.001002003... so on and so forth through 999, where it repeats again.
quesadyllan · 1 points · Posted at 02:24:54 on February 14, 2016 · (Permalink)
eix = cosx + isinx. Don't know what it is about Euler's formula, but seeing how these completely unrelated functions come together like this for the first time in my diff eq class made me realize how awesome math is
InaudiableHorse · 1 points · Posted at 02:24:56 on February 14, 2016 · (Permalink)
None because I'm not nerd!!!!
pwuille · 1 points · Posted at 02:25:10 on February 14, 2016 · (Permalink)
The polynomial x/1! + (x+y)(x+y+1)/2! + (x+y+z)(x+y+z+1)(x+y+z+2)/3! + ... is a bijection between vectors of natural numbers and natural numbers.
theLiftedMind · 1 points · Posted at 02:25:11 on February 14, 2016 · (Permalink)
If you take the distance from the mouth of a winding river to its tail, the ratio of that distance against a straight line from mouth to tail is approximately 3.14
Anders_A · 1 points · Posted at 02:26:48 on February 14, 2016 · (Permalink)
ei𝜋 = -1
It's amazingly cool.
Yes, I know about Euler's formula and why this is, but it's still almost like magic :).
SpecificityBitch · 1 points · Posted at 02:26:50 on February 14, 2016 · (Permalink)
Integral is the area under the curve or the function and derivative is just the slope of the function.
GreenAce92 · 1 points · Posted at 02:27:19 on February 14, 2016 · (Permalink)
Was pythagoras killed on a beach while drawing triangles?
iluvgrannysmith · 1 points · Posted at 03:01:34 on February 14, 2016 · (Permalink)
Pythagoreas was net necessarily a person. He was worshiped by a cult called the pythagoreans. They attributed much work to him, evidence of his actual existence is questionable.
GreenAce92 · 2 points · Posted at 03:34:31 on February 14, 2016 · (Permalink)
Awe really? I remember being told about the beach scene, some soldier or something killed him while he was drawing tribgles on a beach. Well there goes one of my "old person rambling speech no young child wants to hear"
gaussjordanbaby · 1 points · Posted at 06:24:58 on February 14, 2016 · (Permalink)
You're almost certainly thinking of Archimedes.
GreenAce92 · 1 points · Posted at 16:40:27 on February 14, 2016 · (Permalink)
I'll have to read up on him then and see
Sersanc18 · 1 points · Posted at 02:28:18 on February 14, 2016 · (Permalink)*
It is possible to roll out a piece of dough such that it has a finite volume, but infinite surface area (gabriels horn).
It is possible to cut a soccer ball into small pieces, and rearrange them so that the end product is two soccerballs of the same size as the one which you started with (tarskis paradox)
The first is approachable (understandable, really) if you are familiar with some calculus. The second has to do with complex set theory and topology
Duo34 · 1 points · Posted at 02:28:55 on February 14, 2016 · (Permalink)
It is possible to prove that a solution to a problem exists, and prove we will never know what it is.
Videojoe2000 · 1 points · Posted at 02:28:57 on February 14, 2016 · (Permalink)
That if you say the quadratic formula to the jack in the box beat it works perfectly. X equals negative b plus or minus the square root b squared minus 4 ac all over 2 a
GreenAce92 · 1 points · Posted at 02:29:05 on February 14, 2016 · (Permalink)
The Gabrielle's horn thing with volume and surface area
SooyoungSone · 1 points · Posted at 02:29:20 on February 14, 2016 · (Permalink)
1+1=2
PaulsRedditUsername · 1 points · Posted at 02:30:03 on February 14, 2016 · (Permalink)
2+2=5 for very large values of 2
Azozel · 1 points · Posted at 02:30:04 on February 14, 2016 · (Permalink)
Infinity + 1 is still Infinity
Infinity - 1 is still infinity
Infinity - Infinity is still Infinity.
therealjerseytom · 1 points · Posted at 02:30:59 on February 14, 2016 · (Permalink)
Wish I could remember the expression.. maybe it was 1/x2.. something where if you were to spin it into a horn-like shape it would hold a finite volume but have infinite surface area (or vice versa).
Ninja_of_Physics · 1 points · Posted at 02:31:15 on February 14, 2016 · (Permalink)
The area under the curve of 1/x from x=1 to x= infinity gives you an infinite area. If you take that area and wrap it around the x-axis the volume is pi.
I_will_draw_boobs · 1 points · Posted at 02:32:18 on February 14, 2016 · (Permalink)
Zenos paradox. Love it.
Torque-A · 1 points · Posted at 02:32:58 on February 14, 2016 · (Permalink)
epi - pi = 19.999...
HugeTittyBanger · 1 points · Posted at 02:33:19 on February 14, 2016 · (Permalink)
The square root of 69 is 8.30662386292
Supersnazz · 1 points · Posted at 02:33:54 on February 14, 2016 · (Permalink)
Any circle anywhere in the world (or universe) will have two opposite points with the same temperature.
KatharticHymen · 1 points · Posted at 02:34:01 on February 14, 2016 · (Permalink)
5=7
quicksilver991 · 1 points · Posted at 02:34:08 on February 14, 2016 · (Permalink)
Interuniversal teichmuller theory has practical applications.
GabRreL · 1 points · Posted at 02:34:25 on February 14, 2016 · (Permalink)
you can multiply by 5 dividing by 2 then multiplying by 10.
5 * 1860 = (1860/2) * 10 = 930 * 10 = 9300
_u_s_e_r_n_a_m_e · 1 points · Posted at 02:34:44 on February 14, 2016 · (Permalink)
11 times any 2-digit number (xy) equals the tens digit (x) followed by the sum of the the tens digit and the units digit (x+y) followed by the units digit (y).
e.g. 11 x 13 = 1 (1+3) 3...143.
Gets a little trickier when the sum of x+y is a 2-digit number...you just have to carry the "1" to the tens digit (x).
e.g. 11 x 57 = 5 (5+7) 7...627.
Supersnazz · 1 points · Posted at 02:34:58 on February 14, 2016 · (Permalink)
Most numbers are bigger than Graham's number. In fact nearly all are.
lebronianmotion · 1 points · Posted at 02:35:04 on February 14, 2016 · (Permalink)
ii is a real number: e-pi/2
PhilyEagles · 1 points · Posted at 02:35:09 on February 14, 2016 · (Permalink)
The infinite number of decimals is greater than the infinite amount of whole numbers.
darkforestzero · 1 points · Posted at 02:35:11 on February 14, 2016 · (Permalink)
When you are the age your parent was when you are born, it's the first and last time they will be exactly twice your age
jimmym007 · 1 points · Posted at 02:35:21 on February 14, 2016 · (Permalink)
I'm a little late for this, but it has to be the mathematical probabilty of shuffling the same deck as anyone else (in the same order) in the history of mankind. Meaning each time you shuffle a deck of 52 cards, it's most likely the first time in history this deck in this order has been shuffled.
The number of possibilities is 52!, which is 52 factorial, meaning 52x51x50x49x48... All the way to 1. This number is astronomical.
To illustrate how big it is, imagine this:
If every star in our galaxy has a trillion planets, and each planets had a trillion people living on them, and every single of them had a trillion deck of cards. If Somehow, they could all shuffle each pack a thousand times a SECOND, and that since the big bang, just today we would start seeing the same combinations twice.
This fact is just mind boggling to me.
awesome528 · 1 points · Posted at 02:35:34 on February 14, 2016 · (Permalink)
Numbers are different because there are other numbers in between them. Ex In between 1 and 2 is 1.1, 1.5, 1.6860, etc.
But there is nothing in between
1.99999999..... repeating and 2
So technically they are the same number.
naricstar · 1 points · Posted at 02:36:19 on February 14, 2016 · (Permalink)
57
talllankybastard · 1 points · Posted at 02:36:53 on February 14, 2016 · (Permalink)
73 is the 21st prime number. It's mirror, 37, is the 12th, and it's mirror, 21, is the product of multiplying 7 and 3. In binary, 73 is a palindrome, 1001001. Backwards thats 1001001, exactly the same.
slshGAHH · 1 points · Posted at 02:37:12 on February 14, 2016 · (Permalink)*
If you're a party of two or more people, then there exist at least two people with the same number of friends. Assuming that if Amy is friends with Brad then Brad is friends with Amy.
wasabimatrix22 · 1 points · Posted at 02:37:13 on February 14, 2016 · (Permalink)
This video on how to theoretically turn a sphere inside out really messed with my head! Very well done though, it was interesting and entertaining to watch, even if I didn't fully understand it.
TheGreat_Danton · 1 points · Posted at 02:37:42 on February 14, 2016 · (Permalink)
you can take apart a solid sphere in only 4 pieces, and using only rigid movements and rotations in 3-d space, you can rearrange them in to 2 spheres identical to the original.
according to math, you can create matter.
this the banack-tarski theorem and relies on the axiom of choice.
fatman_fil · 1 points · Posted at 02:38:03 on February 14, 2016 · (Permalink)
12345679*8=98765432
gildme_11 · 1 points · Posted at 02:38:08 on February 14, 2016 · (Permalink)
ITT: spheres and circles have cool maths.
ImAGringo · 1 points · Posted at 02:38:16 on February 14, 2016 · (Permalink)
A simple trick I always used when multiplying a double digit number with 11 is to use the first digit of the double digit number as the begging digit of the answer, second digit of the answer was both digits added together, and the last digit of the answer being the last digit of the orignial double digit number.
Example:
11*24=264
2 (2+4) 4 = 264
OneForMany · 1 points · Posted at 02:38:31 on February 14, 2016 · (Permalink)
6+9×6+9=69
ihackedthisaccount · 1 points · Posted at 02:39:00 on February 14, 2016 · (Permalink)
12345679 x 9 = 111111111
iluvgrannysmith · 1 points · Posted at 02:46:06 on February 14, 2016 · (Permalink)
112 = 121; 1112 = 12321; 11112= 1234321; ... 1111111112= 12345678987654321
Do it on paper, I'd be surprised if a calculator stored the digits
exucsd · 1 points · Posted at 02:39:32 on February 14, 2016 · (Permalink)
The value of a log is the power to which the base must be raised to equal the argument.
Felix_Tholomyes · 1 points · Posted at 02:47:24 on February 14, 2016 · (Permalink)
That's just the definition of a logarithm, was that really the coolest mathematical fact you could think of?
exucsd · 1 points · Posted at 02:48:15 on February 14, 2016 · (Permalink)
I have it memorized.
TheGreat_Danton · 1 points · Posted at 02:39:49 on February 14, 2016 · (Permalink)
if you add up 1/n with n to infinity, you get infinity. but if you add up 1/(n2) you get (pi2 )/6
rhouse1983 · 1 points · Posted at 02:39:54 on February 14, 2016 · (Permalink)
If you square each number sequentially, the difference grows sequentially by odd numbers. 1² is 1. 2² is 4. 3² is 9. 4²=16, 5²=25, 6²=36. So 1² (1) and 2² (4), is a difference of 3. Then the next (2² and 3²) is a difference of 5. 3² (9) and 4² (16) is a difference of seven. 4 (16) and 5 (25) is 9. And each growth of odd number is also made by adding the original number. Hope this makes sense. Try larger numbers for more mind bogglingness.
iluvgrannysmith · 1 points · Posted at 02:44:09 on February 14, 2016 · (Permalink)
The ones place is a palindrome. Also, the tens place goes up by 1 more each time you pass a nine. As in, it goes up by 0 each increment until 9, then it goes up by 1s until 49, then it goes up by 2s until 169, ect...
ScreamWithMe · 1 points · Posted at 02:41:17 on February 14, 2016 · (Permalink)
To find the half of any fraction, merely double the bottom number. Half of 1/4 is 1/8. Half of 8/16 is 8/32, etc.
[deleted] · 1 points · Posted at 02:41:18 on February 14, 2016 · (Permalink)
God this thread makes me feel stupid
[deleted] · 1 points · Posted at 02:41:23 on February 14, 2016 · (Permalink)
The mathematical object termed "Gabriel's Horn" is an object that has an infinite surface area and finite volume. The shape can be created by ploting y = 1/x for x >= 1. Revolve this curve about the x-axis and the swept path creates the 3-d object. Interestingly enough, you create a shape that mathematically has infinite surface area yet finite volume. In terms of trying to paint such an object, you would theoretically never be able to paint the outside of the object, however you could fill it up with paint.
TimeisaLie · 1 points · Posted at 02:41:47 on February 14, 2016 · (Permalink)
I started reading some of these but I got a headache and apparently having auditory hallucinations and an errant twitching of my left hand.
alternate_account_en · 1 points · Posted at 02:41:55 on February 14, 2016 · (Permalink)
The sum of the odd numbers is the squares:
1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 Etc
Not hard to prove but I still get a kick out of it.
idontreadfineprint · 1 points · Posted at 02:42:24 on February 14, 2016 · (Permalink)
Leaned this in my days as a teller:
When counting your box if you have a difference that's divisible by 9 then you most likely transposed a number during your audit.
TheGreat_Danton · 1 points · Posted at 02:42:30 on February 14, 2016 · (Permalink)
the cult of Euclid killed the man that proved the square root of two is irrational. meaning there are no two integers x,y: x/y = sqrt(2)
TwoTonTub · 1 points · Posted at 02:42:39 on February 14, 2016 · (Permalink)
If you watched static on a 42" TV @ 30 fps, and each pixel was a star in the universe. It would take 11,000 earth lifetimes or 50,000,000,000,000 years sitting in front of the TV to see every star.
[deleted] · 1 points · Posted at 02:43:39 on February 14, 2016 · (Permalink)
Not so much a fact as a musing, but combination locks should be called permutation locks.
If they truly were combination locks, then a lock that is opened by 30-17-23 would also open with 30-17-23, 17-30-23, 17-23-30, 23-30-17, and 23-17-30.
frubjoppa234 · 1 points · Posted at 02:43:40 on February 14, 2016 · (Permalink)
There are 360 unique combinations of the letters in the word circle.
pulseout · 1 points · Posted at 02:43:43 on February 14, 2016 · (Permalink)
7 x 13 = 28
Nettius2 · 1 points · Posted at 02:43:58 on February 14, 2016 · (Permalink)
Take three circles with three different radii. Taking two at a time, look at their outer tangent lines. The intersection of each pair of outer tangent lines forms a point. There are three such points (one for each pair of circles). Those points are colinear.
VelociJupiter · 1 points · Posted at 02:44:48 on February 14, 2016 · (Permalink)
12345679 x 3 = 37037037 12345679 x 6 = 74074074 12345679 x 9 = 111111111 ... basically 12345679 times any number that's a multiple of 3 creates a pattern.
TheGreat_Danton · 1 points · Posted at 02:44:59 on February 14, 2016 · (Permalink)
the greatest common divisor of any two numbers is the smallest linear combination of the numbers. linear combination meaning ax + by = c. example 16 and 12. 16(1) + 12(-1) = 4. the greatest common divisor of 12 and 16 is 4. this true for any two numbers.
vassah · 1 points · Posted at 02:45:36 on February 14, 2016 · (Permalink)
The Borsuk-Ulam theorem is a cool one to think about. Any continuous way of setting a sphere of any given dimension into Euclidean space of the same dimension must assign two antipodal points the same place in Euclidean space. If you think about this in terms of temperature on the Earth, or any two continuously varying real quantities on the Earth's surface, you'll see that there have to be two opposite points having the same value, etc.
SquidJeans · 1 points · Posted at 02:46:00 on February 14, 2016 · (Permalink)
If you tear a sheet of paper in half, stack the halves on top of each other and repeat 50 times, the height theoretically would reach the sun.
SuicidalNoob · 1 points · Posted at 02:46:22 on February 14, 2016 · (Permalink)
I can recite pi to the hundredth place
Israe12 · 1 points · Posted at 02:46:30 on February 14, 2016 · (Permalink)
1/(1-x-x2 ) = 1+x+2x2 +3x3 +5x4 +8x6 +... If you let x= 1/10, you get 100/89. This explains why this works. By choosing x = 1/100, you get 10000/9899. In general, if you take x=1/10n, you get the Fibonacci's spaced out farther and farther.
aerohk · 1 points · Posted at 02:46:35 on February 14, 2016 · (Permalink)
The answer to life the universe and everything is 42.
nmdaniels · 1 points · Posted at 02:46:43 on February 14, 2016 · (Permalink)
The existence of undecidability, incompleteness of arithmetic, and the uncomputability of Kolmogorov complexity.
BooRoxAlot · 1 points · Posted at 02:46:56 on February 14, 2016 · (Permalink)
That if I can explain my answer using gumdrops and nonsensical diagrams, I pass.
apert · 1 points · Posted at 02:47:11 on February 14, 2016 · (Permalink)
You can calculate the number pi with some accuracy by dropping a needle on ruled paper.
DingJones · 1 points · Posted at 02:47:16 on February 14, 2016 · (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.
slopecarver · 1 points · Posted at 02:47:39 on February 14, 2016 · (Permalink)
The largest number in existence exists solely for fulfilling the purpose of being the largest number in existence.
brutalyak · 1 points · Posted at 02:49:12 on February 14, 2016 · (Permalink)
There is no largest number.
slopecarver · 1 points · Posted at 02:55:20 on February 14, 2016 · (Permalink)
Infinity isn't an answer.
brutalyak · 1 points · Posted at 02:58:39 on February 14, 2016 · (Permalink)
That is true, infinity is not a number, but there is still no largest number.
devildocjames · 1 points · Posted at 02:48:00 on February 14, 2016 · (Permalink)
E = mc 2
JonathanWarner · 1 points · Posted at 02:48:04 on February 14, 2016 · (Permalink)
The average deviation from the mean measured by "d" in any data set is 0. The sum of all x's minus the averages is 0. For ALL datasets.
Great nerd party trick.
Pretty stupid once you figure out why though.
EricTheEmu · 1 points · Posted at 02:48:18 on February 14, 2016 · (Permalink)
Not super cool, but useful. The Fibonacci sequence provides an approximate conversion from kilometers to miles.
3 miles is about 5 kilometers. 5 miles is about 8 kilometers. 8 miles is about 13 kilometers. 13 miles is about 21 kilometers. etc.
TheGreat_Danton · 1 points · Posted at 02:48:35 on February 14, 2016 · (Permalink)
the number of counting numbers (1, 2, 3...) is equal to the number of integers (...-2, -1, 0, 1, 2...) is equal to the number of rational numbers. (...-1/1, 0, 1/1...). but the set of real numbers is bigger than all of them.
[deleted] · 1 points · Posted at 02:48:42 on February 14, 2016 · (Permalink)
ITT: Many people MUCH smarter than I am.
Montgomery233 · 1 points · Posted at 02:48:57 on February 14, 2016 · (Permalink)
good
sawowner · 1 points · Posted at 02:49:12 on February 14, 2016 · (Permalink)
Using calculus, you can create a hypothetical 3d shape with a finite volume but infinite surface area.
iregret · 1 points · Posted at 02:49:24 on February 14, 2016 · (Permalink)
Numbers don't actually exist. Matter of fact, math doesn't exist. You can't show me a number. You can't show me a triangle. You can only show me a representation. Math is an absolute truth.
Je7pax · 1 points · Posted at 02:51:11 on February 14, 2016 · (Permalink)
I learned this in middle school.
Large multiplied by 11 can be easily figured out by doing this:
34 * 11 * Take the 34 and split it into 3 and 4 * Add them together and you put the sum in the middle, the 3 in the front and the 4 as the last number * 3+4 = 7 * 374
If the sum of the two numbers is above 10 (IE: 85 * 11) you do the following
11 * 85 * 8 + 5 = 13 * Take the 1 and add it to the 8 * 935
sorry I'm not very good at explaining math
Atheist_Simon_Haddad · 1 points · Posted at 02:51:23 on February 14, 2016 · (Permalink)
the sum of any two consecutive triangular numbers is a square number
or
any square number can be expressed as the sum of two consecutive triangular numbers
aMAYESingNATHAN · 1 points · Posted at 02:51:29 on February 14, 2016 · (Permalink)
If you take the graph of 1/x for x>=1, then rotate the curve 360 degrees around the x axis, the shape produced has an infinite surface area but a finite volume.
It's called Gabriel's Horn and I find it pretty interesting.
nodejs787 · 1 points · Posted at 02:51:50 on February 14, 2016 · (Permalink)
Take any number > 10, say for example 47. Add the 4 + 7 = 11. Now take away 11 from 47. 47 - 11 = 36 Add the result 3 + 6 and you will always get 9.
It works on any number.
583 5 + 8 + 3 = 16 583 - 16 = 567 5 + 6 + 7 = 18 1 + 8 = 9 <----- Always ends with 9.
psyki · 1 points · Posted at 02:52:12 on February 14, 2016 · (Permalink)
12345679x8=98765432
Jabez89 · 1 points · Posted at 02:52:38 on February 14, 2016 · (Permalink)
3 4 5 rule
GamingWithBilly · 1 points · Posted at 02:53:02 on February 14, 2016 · (Permalink)
Women are the squareroot of Evil.
gangrenecactus · 1 points · Posted at 02:53:37 on February 14, 2016 · (Permalink)
Gödels incompleteness theorems
https://en.m.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
ray_zhor · 1 points · Posted at 02:53:47 on February 14, 2016 · (Permalink)
take any number, count the number of letters it takes to spell that number. repeat with the count being your new number. eventually, every number will become 4. 16 = sixteen, 7 letters 7 = seven, 5 letters 5 = five, 4 letters 4 = four, 4 letters
kianoosh34 · 1 points · Posted at 02:53:51 on February 14, 2016 · (Permalink)
111,111,111 x 111,111,111 = 12345678987654321
PoisonMind · 1 points · Posted at 02:53:58 on February 14, 2016 · (Permalink)
Benford's Law. There is an uneven frequency distribution of leading digits in most sets of natural data. It's a useful tool for identifying naively fabricated data.
LetMeFinishWoman · 1 points · Posted at 02:55:58 on February 14, 2016 · (Permalink)
ei*pi + 1= 0
Like what
battering-ram · 1 points · Posted at 02:56:02 on February 14, 2016 · (Permalink)
If you write out pi to two decimal places, backwards it spells “pie”.
https://img.buzzfeed.com/buzzfeed-static/static/2014-06/25/12/enhanced/webdr07/enhanced-17542-1403712086-18.jpg
reallyloveadventures · 1 points · Posted at 02:56:03 on February 14, 2016 · (Permalink)
Something I realized one day while on a train is that when increasing the base of a squared exponent by one, the next value is the sum of the previous base and the next base added to the previous exponential value. For example: 12=1, 22=4, 1+2+1=4. 42=16, 52=25, 4+5+16=25. IDK if i explained this well but this just is something i realized one day and it's helped me with odd exponents. IDK if the principle or anything similar applies to any exponent power above the squared power.
ROTCHunter · 1 points · Posted at 02:56:36 on February 14, 2016 · (Permalink)
The largest number you can make with only three numbers is 999
NanchoMan · 1 points · Posted at 02:56:43 on February 14, 2016 · (Permalink)
I think this is the coolest one I know.
Take the graph 1/x2 and separate the whole thing into 2 parts. Every thing from 0 to 1, and everything from 1 to infinity.
If you shade in the area under that graph between 0 and 1, it will be an infinitely large space
If you shade the area under the graph from 1 to infinity, it will have an area of 1 unit2
ExpertSaladTosser · 1 points · Posted at 02:56:55 on February 14, 2016 · (Permalink)
If a number added up equals a number divisible by 3 it is in itself divisible by 3...
Start with 729 for example: 729 7+2+9 = 18 729÷3=243 243 = 9 243÷3=81 Breaks down all the way to 1... 730 7+3=10 730÷3= 243.3.... number is not divisible by 3.
This is the only thing I remember from middle school.
Shigjetar · 1 points · Posted at 02:57:27 on February 14, 2016 · (Permalink)
Mathematically, you can turn a sphere inside out.
Pdubs2_0 · 1 points · Posted at 08:23:26 on February 14, 2016 · (Permalink)
https://youtu.be/-6g3ZcmjJ7k
Bouffant_Joe · 1 points · Posted at 02:57:38 on February 14, 2016 · (Permalink)
I always liked sin 0 = sqrt(0)/2, sin pi/6 = sqrt(1)/2, sin pi/4 = sqrt(2)/2, sin pi/3 = sqrt(3)/2, sin pi/2 = sqrt(4)/2
prmcd16 · 1 points · Posted at 02:58:25 on February 14, 2016 · (Permalink)*
I've always (since I learned about it) been a fan of the Euler identity for relating three things that a lot of people probably don't fully understand to each other and giving a result that every preschooler can count to. (If you don't feel like clicking the link, TL;DC: the Euler identity states that ei*pi+1=0)
Edit: another favorite is that there only need to be 23 people in a room for there to be a >50% probability that two of them share a birthday.
hilarymeggin · 1 points · Posted at 02:59:05 on February 14, 2016 · (Permalink)
All maps are 4- colorable. Meaning, you can color any mandala in any hipster adult coloring book using only the crayons Pomegranate, Sandstone, Cirrhosis and Labrador, and not have any Pomegranate sections touching each other.
Wampxz · 1 points · Posted at 02:59:13 on February 14, 2016 · (Permalink)
a little interesting thing i found myself while doing a math homework is that √(x . 4x) = 2x
Example: √(2 . 8) = 4 , √(128 . 512) = 256
I really can't think of any practical use for it in any case, nor is it mind blowing, but i find it quite neat
Uhdoyle · 1 points · Posted at 02:59:37 on February 14, 2016 · (Permalink)
That whole "sum of all natural numbers = -1/12" thing. Blew my mind. I think it's still broken.
gaussjordanbaby · 1 points · Posted at 03:00:06 on February 14, 2016 · (Permalink)
A group of students attend a frat party. At the door, someone takes all of their hats. The hat-taker becomes drunk by the end of the night, and randomly hands out hats to the group members. What is the probability that no person in the group receives their own hat back?
As the size of the group grows, that probability approaches 1/e.
SpaceHooker · 1 points · Posted at 03:00:14 on February 14, 2016 · (Permalink)
69
punkkapoika · 1 points · Posted at 03:00:30 on February 14, 2016 · (Permalink)
Imagine any closed path, say trip from Finland to Spain to Turkey and back, take any measure that changes seamlessly, say temperature, choose any point on the path and check the measure. It's guaranteed that somewhere down the line there will be an other point with that exact measure, if the point you chose wasn't the highest or lowest peak of the measure
VSG28 · 1 points · Posted at 03:00:37 on February 14, 2016 · (Permalink)
There's an actual song with the lyrics "sin2 theta + cos2 theta = 1"
Athrul · 1 points · Posted at 03:00:42 on February 14, 2016 · (Permalink)
2+2=5
crewserbattle · 1 points · Posted at 03:00:55 on February 14, 2016 · (Permalink)
I just went down a rabbit hole with klein bottles, a 3 dimensional representation of a 4 dimensional object
[deleted] · 1 points · Posted at 03:01:35 on February 14, 2016 · (Permalink)
A bunch of cool facts about 37:
it is 73 backwards
it is the 12th prime number, and 73 is the 21st prime number
KetchupLA · 1 points · Posted at 03:01:52 on February 14, 2016 · (Permalink)
You can always square root the addition of consecutive odd integers.
1+3 = 4
1+3+5 = 9
1+3+5+7= 16
1+3+5+7+9= 25
...so on
joshnoble07 · 1 points · Posted at 03:02:07 on February 14, 2016 · (Permalink)
The difference between any number squared and the next number squared is the next odd number sequentially.
I.e. 12 is 1, 22 is 4. The difference is three.32 is 9. The difference is 5. 42 is 16. The difference is 7 etc.
battering-ram · 1 points · Posted at 03:02:19 on February 14, 2016 · (Permalink)
The Fibonacci sequence is completely encoded in 1/89
1/89 ~= 0.01123595505
0.01
0.001
0.0002
0.00003
0.000005
0.0000008
0.00000013
0.000000021
0.0000000034
etc.
Here is a proof: library.thinkquest.org/27890/applications3p.html
[deleted] · 1 points · Posted at 03:03:39 on February 14, 2016 · (Permalink)
12345679 x 8= 98765432
eirealbarevolution · 1 points · Posted at 03:04:00 on February 14, 2016 · (Permalink)
That whole 6174 thing. That thing is pretty cool.
MikeyNg · 1 points · Posted at 03:05:01 on February 14, 2016 · (Permalink)
(3+4)3 = 343 As far as I know, that's the only combination that's like that.
(A+B)C = ABC (written out, not their product)
InfieldTriple · 1 points · Posted at 03:05:10 on February 14, 2016 · (Permalink)
ei*pi+1=0
i_floop_the_pig · 1 points · Posted at 03:05:20 on February 14, 2016 · (Permalink)
Four is the only number whose has the same amount of letters in its name as its corresponding number value
lurgi · 1 points · Posted at 03:05:21 on February 14, 2016 · (Permalink)
Between any two irrational numbers there is a rational number. Between any two rational numbers there is an irrational number. Yet there are more irrational numbers than rational numbers.
1up_for_life · 1 points · Posted at 03:05:49 on February 14, 2016 · (Permalink)*
...9999.9999... = 0
"proof"
everyone knows .9999... = 1
let's look at ...9999.
let x = ...9999.
then 10x = ...9990.
10x - x = ...9990. - ...9999.
9x = -9
x = -1
so:
...9999.9999... = ...9999. + .9999... = -1 + 1 = 0
Gravity_Bot · 1 points · Posted at 03:06:14 on February 14, 2016 · (Permalink)
When adding all of the digits to the power of themselves for the number 3435, the sum is the number itself, 3435.
(3 to the power of 3=27)+(4 to the power of 4=256)+(3 to the power of 3=27)+(5 to the power of 5=3125) =3435
matt_panaro · 1 points · Posted at 03:06:20 on February 14, 2016 · (Permalink)
Kempner series
z4St0romShad0w · 1 points · Posted at 03:06:43 on February 14, 2016 · (Permalink)
1 + 1 = 3 or 4 or 5 or 11 1male + 1female = WHAT EVER! We spin on a spiral baby!
_Commander · 1 points · Posted at 03:07:26 on February 14, 2016 · (Permalink)
how to invert a sphere
upinflamezzz · 1 points · Posted at 03:07:43 on February 14, 2016 · (Permalink)
the opposite of b plus or minus the square root of b squared - 4ac divided by 2a. Quadratic formula
Th3BlackLotus · 1 points · Posted at 03:07:46 on February 14, 2016 · (Permalink)
-40F and -40C are the same temperature. Now that's 'cool'...
[deleted] · 1 points · Posted at 03:07:48 on February 14, 2016 · (Permalink)
Put a map of your city on the ground. There is guaranteed to be a point on the map which directly overlaps its corresponding point on the ground.
AutoBiological · 1 points · Posted at 03:08:05 on February 14, 2016 · (Permalink)
Euclid's fifth postulate made math much more interesting, but even though he knew something was different about it, it took many more years to get nonstandard everything.
Sl33pW4lker · 1 points · Posted at 03:08:10 on February 14, 2016 · (Permalink)
Some infinities are bigger than others. Or the fact that theoretically you can split an object into 6 equal parts, combine them into two separate objects, both the exact same size as the original
shennanigram · 1 points · Posted at 03:09:19 on February 14, 2016 · (Permalink)*
A photon is beyond time. If you were to magically see from a photons perspective, the moment you departed the sun and the moment you hit Neil degrade Tyron's face would be the same moment without any time passing.
ohsnaplookatthis · 1 points · Posted at 03:09:45 on February 14, 2016 · (Permalink)
every breath you take you have a chance of about 80% to inhale one of the air molecules that ceasar had in his last breath.
LeftbrainLeft · 1 points · Posted at 03:10:19 on February 14, 2016 · (Permalink)
"The square root of 69 is 8-something" -Aubrey graham
[deleted] · 1 points · Posted at 03:10:59 on February 14, 2016 · (Permalink)
ei pi = - 1
koghrun · 1 points · Posted at 03:10:59 on February 14, 2016 · (Permalink)
Some friends and I discovered this in high school. For any triangle inscribed in a circle the number of degrees of any angle is equal to half the number of degrees along the circle between the two other points.
For triangle ABC inscribed in a circle: the number of degrees of angle A is equal to half the number of degrees along the circle between B and C.
AthiestCowboy · 1 points · Posted at 03:11:00 on February 14, 2016 · (Permalink)
Euler's identity. E to the (pi*i) +1 =0.
On mobile otherwise would do the proper syntax. But basically 5 universal constants independently discovered are all related. Some extrapolate this as the god theorom as it just is too perfect. Certainly gives credit to the "universal theory of everything" in mathematics which is the holy grail today.
https://en.m.wikipedia.org/wiki/Euler%27s_identity
tehfurrydj · 1 points · Posted at 03:11:10 on February 14, 2016 · (Permalink)
The original mathematical proof for 1+1=2 is over 100 pages long
merryjester · 1 points · Posted at 03:11:36 on February 14, 2016 · (Permalink)
It was never surprising to me that there are an infinite number of prime numbers... But what IS interesting to me is that there are an infinite number of "prime pairs" - cases where n and n+2 are both prime.
Isuhydro · 1 points · Posted at 03:12:22 on February 14, 2016 · (Permalink)
I don't understand math enough to find any of these interesting... Or I drank too much tonight.
danielthornton · 1 points · Posted at 03:12:26 on February 14, 2016 · (Permalink)
A straight line is synonymous with a circle that has an infinite circumference.
yeolddiver · 1 points · Posted at 03:13:28 on February 14, 2016 · (Permalink)
1+1= a window
mobius_stripe · 1 points · Posted at 03:13:33 on February 14, 2016 · (Permalink)
https://en.wikipedia.org/wiki/Carleson%27s_theorem
Fourier wanted to prove this, but they didn't even have the terminology to describe what Carleson proved.
For non-math people, here is what it says. Take pretty much any function. Anything you could think of really. Then there it can be represented as an infinite series. If you throw a dart at the number line, the probability that the series converges at the point you hit is precisely 1. However, there are still points for which the series does not converge. But how could the dart not hit those? Take a course in measure theory.
DUCKISBLUE · 1 points · Posted at 03:14:37 on February 14, 2016 · (Permalink)
Euler's Identity. It says the e to the power of (i*pi) equals -1. A number raised to the power of an imaginary numbed is somehow a real number. Blows my mind.
SnappingEmu · 1 points · Posted at 03:15:18 on February 14, 2016 · (Permalink)
If you shuffle a deck of cards ten times it's probable that you have ordered the cards in a way that has never been done before... 52! Is a very large number.
StackerPentecost · 1 points · Posted at 03:15:40 on February 14, 2016 · (Permalink)
Graham's Number is so large that if you wrote it down, it would have more digits than there are atoms in the universe.
Kraft_Punk · 1 points · Posted at 03:15:54 on February 14, 2016 · (Permalink)
In my math textbook, I came across the problem ABCD * 4 = DCBA. This problem intrigued me and a few hours later I constructed a formula to find all the possible 4 digit reversible numbers.
A = all natural numbers, 1<=A<=9 D = 10-A B = A-1 C = D-1
ABCD*(D/A) = DCBA
Probably not that great but I thought it was interesting.
ashuk203 · 1 points · Posted at 03:16:19 on February 14, 2016 · (Permalink)
If you had a one in a million chance of winning a lottery ticket, and you bought a million lottery tickets. The probability that you have won is just 63.2%.
[deleted] · 1 points · Posted at 03:16:29 on February 14, 2016 · (Permalink)
1246 + 11876 doesn't always equal 13002
brutalyak · 1 points · Posted at 03:16:29 on February 14, 2016 · (Permalink)
That every time this is posted someone posts the "fact" that 1+2+3+4+5...=-1/12
GuttersnipeTV · 1 points · Posted at 03:16:34 on February 14, 2016 · (Permalink)
I wish I was high on potanus.
Stamboolie · 1 points · Posted at 03:16:35 on February 14, 2016 · (Permalink)
TIL - there are so many math nerds on reddit
oldirishpig · 1 points · Posted at 03:16:41 on February 14, 2016 · (Permalink)
That I will never ever have to take Calculus again.
aerodyna · 1 points · Posted at 03:16:47 on February 14, 2016 · (Permalink)
The hairy ball theorem... There's always a storm somewhere on earth.
[deleted] · 1 points · Posted at 03:17:10 on February 14, 2016 · (Permalink)
[deleted]
lank3y · 1 points · Posted at 03:46:33 on February 14, 2016 · (Permalink)
wrong.
The number ( 9 / 11 ) is non-zero. Simply using it as the base raised to a large exponent will NEVER result in zero.
An approxiamate answer is :
This is because ( 9/11 )420 can be calculated on any home computer running linux thus :
Now raise that to the exponent 69 and you get your result :
Trivial with logarithms.
Here .. see a Wolfram Alpha result with a few digits : https://www.wolframalpha.com/input/?i=%28+%289%2F11%29^420+%29+^+69
machotoast · 1 points · Posted at 03:18:08 on February 14, 2016 · (Permalink)
58008 on a calculator turned upside down
ChaosWolf1982 · 1 points · Posted at 03:18:18 on February 14, 2016 · (Permalink)
2 is the only number which has the same result when either doubled or squared.
2+2=4
2x2=4
evohans · 1 points · Posted at 03:18:20 on February 14, 2016 · (Permalink)
The circumference if a large pringle can is the same length as its height.
irrelevant8 · 1 points · Posted at 03:19:11 on February 14, 2016 · (Permalink)
6.0429639023813999128 is the highest number you can get too on a calculator, just 9.999999999E99, found it on my schools scientific calculators in middle school.
lank3y · 1 points · Posted at 03:34:47 on February 14, 2016 · (Permalink)
You just need a better calculator. Try a HP calculator that uses RPN and the upper limits are much much higher.
irrelevant8 · 1 points · Posted at 03:52:57 on February 14, 2016 · (Permalink)
Well, now my mathematical skills really are unredeemable.
acolyte_to_jippity · 1 points · Posted at 03:19:22 on February 14, 2016 · (Permalink)
Math exists. We aren't really creating anything "new". Not since we came up with imaginary numbers. Since that point, we've just been discovering properties of numbers. All the complicated, calculus and weird theorms and shit? That's just...there. Its part of numbers.
one, two, three, four, five... Everything is already there, we're just discovering it.
EnglishThor · 1 points · Posted at 03:22:46 on February 14, 2016 · (Permalink)
I don't even think we made anything new with imaginary numbers either. The way we write them is new I guess, but they exist in nature. Like for AC current you need a system like imaginary numbers to represent the phase of the current
acolyte_to_jippity · 1 points · Posted at 03:42:27 on February 14, 2016 · (Permalink)
is AC current naturally occurring?
EnglishThor · 1 points · Posted at 09:21:53 on February 14, 2016 · (Permalink)
Waves that act in the same way as AC current are, that was just the easiest to understand example in everyday life I could think of
CornCobKnows · 1 points · Posted at 03:19:22 on February 14, 2016 · (Permalink)
My teacher in high school showed us a really cool trick when you're multiplying two numbers together. For instance take 99×99. 99 is 1 away from 100, so 1+1 is 2. 100 - 2 = 98. Then 1 × 1 = 1, or 01. So 99 × 99 = 9801.
I think it works all the way down to 51 and there's a way to do the numbers below that but I can't quite remember
[deleted] · 1 points · Posted at 03:19:31 on February 14, 2016 · (Permalink)
Ask me for the statistics of the likelyhood of an event happening in the future.
CHTCB · 1 points · Posted at 03:20:51 on February 14, 2016 · (Permalink)
when will i get laid?
[deleted] · 1 points · Posted at 03:22:34 on February 14, 2016 · (Permalink)
It has to be the likelyhood of an event happening. It can't pinpoint a date but if you ask, "will I get laid over a certain time period" I can give you the likelyhood of it happening over that period of time.
CHTCB · 1 points · Posted at 03:34:14 on February 14, 2016 · (Permalink)
will i get laid tomorrow?
[deleted] · 1 points · Posted at 03:51:19 on February 14, 2016 · (Permalink)
There's a 50% chance you get laid tomorrow
lank3y · 1 points · Posted at 03:33:50 on February 14, 2016 · (Permalink)
soon.
However expressed in geological time the entire history of mankind is a blink in time. So "soon" is really relative.
sjryan · 1 points · Posted at 03:19:45 on February 14, 2016 · (Permalink)
There are hierarchies of infinity. For example, suppose that the universe is infinite and one out of every trillion atoms is the element gold. Then the number of atoms in the universe is infinite, then so is the number of gold atoms.
Likewise, suppose that we presume that one out of a hundred planets in the universe is earthlike, and that one out of a hundred of those planets has intelligent life. In an infinite universe, we might initially think there's infinite room because there are infinite planets. But the ratio works out to one hundred planets for every intelligent species. Draw the interstellar boundaries carefully, or there will be a lot of territorial wars.
For every n integer, there are an infinite number of rational numbers between n and n+1. Yet there are also an infinite number of integers! So we could say that there isn't just an infinity of rational numbers, there's an infinity of infinity of rational numbers.
crashsuit · 1 points · Posted at 03:20:29 on February 14, 2016 · (Permalink)
e^(pi*i)=-1
FogleMonster · 1 points · Posted at 03:20:53 on February 14, 2016 · (Permalink)
The infinite sum...
4 * ( 1 - 1/3 + 1/5 - 1/7 + 1/9 ... )
Equals pi.
I don't see how you can get pi from that.
lank3y · 1 points · Posted at 03:32:44 on February 14, 2016 · (Permalink)
Expansion of a taylor polynomial. You can look it up.
FogleMonster · 1 points · Posted at 03:39:37 on February 14, 2016 · (Permalink)
I know it's a taylor series, I just don't have any intuitive understanding of how this equates to pi.
lank3y · 2 points · Posted at 04:01:15 on February 14, 2016 · (Permalink)
Let me be less of a jerk here if I can. You know that a taylor series can be a fairly good approxiamation to a function at a given value x. Let's say that we want a taylor approxiamation to tan(x) or even the inverse function arctan(x). If we both agree that arctan(1) = 0.7853981633974483096... then what we have here is arctan(1) = pi/4. Now just miltiply by four and you get pi. Consider that angles are calculated in radians around a cirlce and that a circle is a full 2 x pi radians. Then pi/2 would be the same as 90 degrees and pi/4 would be the same as 45 degrees. Visualize a right angle triangle inside a circle and it gets real clear real fast that the tangent of that angle is just 1. Anyways, a taylor polynomial expression with infinite terms will be just exactly what you posted. Multiply by four and you get pi. Easy?
lank3y · 1 points · Posted at 03:50:43 on February 14, 2016 · (Permalink)
https://www.math.hmc.edu/funfacts/ffiles/30001.1-3.shtml
taedrin · 1 points · Posted at 03:21:14 on February 14, 2016 · (Permalink)
The maximum number of moves needed to solve ANY (legal) configuration of the Rubik's Cube is 20. This is called "God's Number". This fact was not discovered until 2010.
swaggler · 1 points · Posted at 03:21:31 on February 14, 2016 · (Permalink)
The act of expressing a computer program and proving a proposition under intutionistic logic, are the same activity.
tiredeyes2 · 1 points · Posted at 03:22:32 on February 14, 2016 · (Permalink)*
"Irrational numbers" do not have an exact value: they have an endless set of digits to the right of the decimal point.
Pi, approximately 3.14159 ... Is irrational, and so is "e", which appears very often in mathematics; its value is about 2.718 ... (the three dots mean "and so on").
i is often the symbol for the square root of -1; it's called an "imaginary" number because in elementary algebra, negative numbers can't have square roots.
So: three numbers with apparently no common features. But there is an equation called "Euler's identity" which says that
Read aloud, this says "e raised to the power of i times pi equals -1".
I was astonished when I first read this, and more so when I could prove it mathematically.
Felix_Tholomyes · 1 points · Posted at 03:27:53 on February 14, 2016 · (Permalink)
Just because a number has an endless amount of decimals doesn't mean it hasn't got an exact value (whatever that's supposed to mean). Pi, e, sqrt(2), etc. do have exact values. As do rational numbers with endless decimal expansions such as 1/3.
lank3y · 1 points · Posted at 03:31:47 on February 14, 2016 · (Permalink)
pi expressed in base pi is 1.
EmancipatedByLimits · 1 points · Posted at 03:23:18 on February 14, 2016 · (Permalink)
;)
QHeiNein · 1 points · Posted at 03:24:14 on February 14, 2016 · (Permalink)
My birthdy represented by 4 numbers divided by 2 is my sisters birthday. My birthday is April 3rd 1996 so 4396, and my sisters is February 1st 1998 which is 2198
IfTheseTreesCouldTal · 1 points · Posted at 03:24:24 on February 14, 2016 · (Permalink)
In terms of rating 5/7 = 5/10
[deleted] · 1 points · Posted at 03:24:39 on February 14, 2016 · (Permalink)
[deleted]
lank3y · 1 points · Posted at 03:30:15 on February 14, 2016 · (Permalink)
prove it .. however you need to post a youtube video of you doing the recital .. no need for much in the video but you do need to recite the digits in a video. Also, yes, that is geeky and cool. In my world it is.
IandIreckon · 1 points · Posted at 03:24:45 on February 14, 2016 · (Permalink)
Multiplication tables x9
09 18 27 36 45 54 63 72 81 90
I suck at math, I'll show myself out.
Toastification · 1 points · Posted at 03:25:30 on February 14, 2016 · (Permalink)
To help with multiplying single digits by nine, put up all ten of your fingers and put which number you're multiplying by nine. The remaining fingers on the left are your tens and the remaining on the right are your ones.
Pretty much nothing compared to everyone else's, but it blew my mind in third grade.
SpecialSnoflake · 1 points · Posted at 03:25:39 on February 14, 2016 · (Permalink)
I don't know if anyone already said this one, but I couldn't find it:
You can multiply
15 x 15,
25 x 25,
35 x 35
and so forth quickly. Any double digit number that ends in 5 by itself quickly by taking the first digit multiplying it by itself plus one and putting 25 on the end. For example:
45 x 45
4 x 5 = 20
Tack 25 on the end is 2025
45 x 45 = 2025.
Another example to solidify:
85 x 85
8 x 9 = 72
85 x 85 = 7225
Works for 15 multiplied by itself up to 95. This one is easy to teach to kids and gets them excited about learning their multiplication facts.
LizardsOfTheToast · 1 points · Posted at 03:34:24 on February 14, 2016 · (Permalink)
It doesn't even stop at 95. It even works up to 1005 and further. It just works for the square of any number that ends in 5.
AYO_VINNY · 1 points · Posted at 03:25:42 on February 14, 2016 · (Permalink)
133 mod(33) = 1
233 mod(33) = 2
333 mod(33) = 3
works all the way to 3233
murdill36 · 1 points · Posted at 03:26:15 on February 14, 2016 · (Permalink)
2+2=5
SolsKing · 1 points · Posted at 03:26:27 on February 14, 2016 · (Permalink)
1 + 1 = 2
sswitch404 · 1 points · Posted at 03:27:48 on February 14, 2016 · (Permalink)
I'm a little late to the party, but if you had a circle the size of the observable universe, and you wanted to compute its circumference with an accuracy equal to the size of a proton, the number of digits of pi that you'd need is only 43.
Either mathematicians are totally crazy for trying to find more and more digits of pi, or they're planning ahead for a time when the survival of humanity will depend on the ability to construct extremely large, accurate circles.
[deleted] · 1 points · Posted at 03:27:49 on February 14, 2016 · (Permalink)
I fell like the internet is the only place math can be "cool".
atlas3121 · 1 points · Posted at 03:28:31 on February 14, 2016 · (Permalink)
I am nowhere near smart enough to appreciate this thread.
Its_Magic_ · 1 points · Posted at 03:29:18 on February 14, 2016 · (Permalink)
The shoelace formula. You can find the area of any simple polygon if you know the coordinates of all the vertices: https://en.wikipedia.org/wiki/Shoelace_formula
DanielSank · 1 points · Posted at 03:29:55 on February 14, 2016 · (Permalink)
exp(i pi) + 1 = 0
The pythagorean theorem works for arbitrary dimensional objects. Suppose I have n-dimensional space, and in that space I make a k-dimensional parallelogram. If I project that parallelogram onto one of the k-dimensional coordinate planes i n-dimensional space, that projection has a k-dimensional area. If you sum the squares of all of the k-dimensional areas of these k-dimensional projections and then take the square root, you get the k-dimensional area of the original parallelogram.
If a differential forms is closed, meaning its derivative is zero, then it must be exact, meaning that it is the derivative of some other differential form. However, this is only true on a space with no holes. If you poke a single hole in space, then there is one equivalence class of forms which is closed but not exact. This form is essentially the electric field of a point charge.
CapnSweg · 1 points · Posted at 03:30:40 on February 14, 2016 · (Permalink)
There are more ways to shuffle a (52 count) deck of cards than there is ATOMS THAT MAKE UP THE PLANET EARTH.
furman82 · 1 points · Posted at 03:31:01 on February 14, 2016 · (Permalink)
The sum of all natural numbers (1 + 2 + 3 + 4 + ...) equals -1/12.
NoticedGenie66 · 1 points · Posted at 03:31:21 on February 14, 2016 · (Permalink)
[Meta] this whole thread is making my head hurt
[deleted] · 1 points · Posted at 03:31:24 on February 14, 2016 · (Permalink)
The most efficient base for expressing numbers is 3 (actually, you need at least e numbers, since e is about 2.7..., you need to round up to 3). And Donald Knuth has written balanced ternary "the prettiest number system of all".
Wudaokau · 1 points · Posted at 03:31:36 on February 14, 2016 · (Permalink)
Me+U=Us
Nipsmagee · 1 points · Posted at 03:32:02 on February 14, 2016 · (Permalink)
8=D
RoadKillManiac · 1 points · Posted at 03:32:29 on February 14, 2016 · (Permalink)
According to string theory, the sum of all positive integers = -1/12
lazyeyejack · 1 points · Posted at 03:33:17 on February 14, 2016 · (Permalink)
lets add you and me then let us multiply then subtract your mother and law and divide the kids between us=DISFUNCTIONAL
chozar · 1 points · Posted at 03:33:21 on February 14, 2016 · (Permalink)
I always liked that 1 = .9999...
One is equal to point nine repeating. They're not just so close to where they don't matter, they're the same number.
Gnarok518 · 1 points · Posted at 03:33:24 on February 14, 2016 · (Permalink)
If you swap the digits of any two digit number, the difference between the original number and the swapped number will always be divisible by 9.
staytaytay · 1 points · Posted at 03:33:43 on February 14, 2016 · (Permalink)
Hexaflexagons.
Weird little paper curiosity that you can make in 2 minutes and play with for hours.
DarthBoBo · 1 points · Posted at 03:33:58 on February 14, 2016 · (Permalink)
A real number is a factor of 3 if the sum of its digits is also factor of three.
Take 123 as an example;
1+2+3 = 6 6 = 3×2
123 = 3×41
BenKatz88 · 1 points · Posted at 03:34:11 on February 14, 2016 · (Permalink)
I cannot confirm this, but I know I've read it from more than a couple sources, but it may (or may not) be true that the number "Googol" (a 10100) is SO large that there's not even estimated to be a googol atoms in the ENTIRE universe. I think the estimate is somewhere around 1067 atoms; but, I'm sure I'm off by a few orders of magnitude....
koleslaw · 1 points · Posted at 03:35:15 on February 14, 2016 · (Permalink)
Eleven Plus Two is an anagram of One Plus Twelve, and they both equal thirteen.
[deleted] · 1 points · Posted at 03:35:17 on February 14, 2016 · (Permalink)
[deleted]
kerry63 · 1 points · Posted at 03:45:12 on February 14, 2016 · (Permalink)
I learned this in 5th grade, but with a slightly different approach. I was taught to take 25 x 25 and raise one of the numbers to a 3 and cross multiply. So 3 x 2 = 6 and then add 25 since it was the same numbers.
If you wanted to multiply 25 x 35 you would raise the higher of the two. So it would be 4 x 2 and since the two were different you would add 75. Therefore 25 x 35 would be 875.
HolyRamenEmperor · 1 points · Posted at 03:35:41 on February 14, 2016 · (Permalink)
2 × 3 = 3 × 2
jeffl97 · 1 points · Posted at 03:36:50 on February 14, 2016 · (Permalink)
One time I was just messing around with numbers and I found out this interesting thing with 9's. For instance
9 X 8 = 72.
If you put a 9 after the number you're multiplying by, and then subtract it from the addition of 9 to that same number you'll get the right answer. Ie: 89 - 17 = 72.
100 X 9 = 900 or 1009 - 109 = 900 12 X 9 = 108 or 129 - 21 = 108. 145 X 9 = 1305 or 1459 - 154 = 1305 etc.
[deleted] · 1 points · Posted at 03:37:20 on February 14, 2016 · (Permalink)
I like the way cones can be sliced up to reveal hyperbolas, parabolas, circles, ellipses, lines, or a single point.
stalkythefish · 1 points · Posted at 03:37:24 on February 14, 2016 · (Permalink)
The digits of multiples of 9 always add up to 9.
KingCabbage · 1 points · Posted at 03:37:37 on February 14, 2016 · (Permalink)
That reading cool English maths facts is difficult when you were thaught maths in a different language (Dutch in my case).
onacloverifalive · 1 points · Posted at 03:37:44 on February 14, 2016 · (Permalink)
When I was in the 8th grade I noticed that consecutive squares equal the sum of consecutive odd integers. It's simple but somehow surprisingly impressive.
0+1=1 1+3=4 4+5=9 9+7=16 16+9=25 25+11=36...
bigedthebad · 1 points · Posted at 03:38:09 on February 14, 2016 · (Permalink)
The coolest math fact is that math never changes, it's one of the few things you can count on as a constant.
Coolmikefromcanada · 1 points · Posted at 03:38:12 on February 14, 2016 · (Permalink)*
0.999999=1
how you may ask well simpy
1/9=0.111111
(1/9)9=(0.111111)9
therefor
9/9=0.999999
or
1=0.999999
destroted · 1 points · Posted at 03:38:38 on February 14, 2016 · (Permalink)
For any multiple of 5, if you divide the multiplier by 2 and move the decimal over one spot you get the answer (eg: 275 = ?, 27/2=13.5, so 275=135)
MindlessZ · 1 points · Posted at 03:39:02 on February 14, 2016 · (Permalink)
1 = 0.999... That'll never stop blowing my mind. They're not just close, they're equal
Fire2box · 1 points · Posted at 03:39:16 on February 14, 2016 · (Permalink)
That Morty and Summer are pieces of shit.
ParanoidAltoid · 1 points · Posted at 03:39:29 on February 14, 2016 · (Permalink)
The number 1/81 (or 3-4) is 0.123456790 repeating.
What I want to know is what happened to the 8.
bucky46 · 1 points · Posted at 03:39:51 on February 14, 2016 · (Permalink)
If 1 = 0 then donald trump = a banana
odawgyeetdaddy · 1 points · Posted at 03:40:28 on February 14, 2016 · (Permalink)
Due to the Infinite Probability Theorem, you can put in laundry into your dryer and there is a chance that it will come out perfectly folded. Though there's a 100% chance my mom folds it if it doesn't.
call_me_danal · 1 points · Posted at 03:40:29 on February 14, 2016 · (Permalink)
0! (read as zero factorial) is equal to 1
TheShadowBox · 1 points · Posted at 03:40:37 on February 14, 2016 · (Permalink)
There are an infinite number of prime numbers.
It blows my mind thinking there are unfathomably large numbers that are only divisible by 1 and itself.
GoCubsGo2016 · 2 points · Posted at 03:42:46 on February 14, 2016 · (Permalink)
I absolutely hate this fact solely because every theory math class goes over this proof. I probably saw it 5 or 6 times in undergrad
Vortico · 1 points · Posted at 07:33:06 on February 14, 2016 · (Permalink)
Here's a topological proof of the infinitude of primes that might bring more fun to the fact.
https://primes.utm.edu/notes/proofs/infinite/topproof.html
yomerol · 1 points · Posted at 03:42:01 on February 14, 2016 · (Permalink)
The sum of N odd numbers is equal to the square of N, for N >= 1 1 = 12 1 + 3 = 22 1 + 3 + 5 = 32 ... sum(1,N) = N2
Karnatil · 1 points · Posted at 03:43:22 on February 14, 2016 · (Permalink)
Multiplication by 11. For a two digit number, add the two digits and stick it in the middle.
So for 43 x 11: 4+3=7, 437
62 x 11: 6+2=8, 682
84 x 11: 8+4 =12. The tens digit carries over into the next column, giving us 924
You can take this on to higher digit numbers, too. Triple digit multiplied by 11, add the left and middle, the right and middle, and stick those numbers between the first and last digit.
123 x 11: 1+2=3, 2+3=5, therefore 1353
438 x 11: 4+3=7, 3+8=11 (tens carry over), therefore 4818
You can actually keep going - with a number of any size, just add the first and second, the second and third, etc. etc., then put those digits in the order you calculated them between the first and last digits.
45132 x 11 = 496452
Try it yourself!
ColtonKB55 · 1 points · Posted at 03:43:39 on February 14, 2016 · (Permalink)
Gabriel's Horn. Basically, if you take the improper integral from 1 to infinity of the graph of 1/x and rotate it about the x-axis, you get a shape with an infinite surface area but a finite volume.
4Sken · 1 points · Posted at 03:44:17 on February 14, 2016 · (Permalink)
(753+951)-852=852 Also works backwards; (159+357)-258=258
HookDragger · 1 points · Posted at 03:44:28 on February 14, 2016 · (Permalink)
The number of permutations possible in a randomly shuffled deck of cards means that there are more permutations than stars in the galaxy.
But if you perfectly shuffle a deck of cards 8 times it's back in its original order
[deleted] · 1 points · Posted at 03:45:25 on February 14, 2016 · (Permalink)
My birthday is on 2pi day. 3.14*2=6.28=June 28th
bigdon199 · 2 points · Posted at 04:00:52 on February 14, 2016 · (Permalink)
that's tau day http://tauday.com/
tiddyspreenkels · 1 points · Posted at 03:45:45 on February 14, 2016 · (Permalink)
Seven ate nine.
findles · 1 points · Posted at 03:46:06 on February 14, 2016 · (Permalink)
ei*pi+1=0
professortweeter · 1 points · Posted at 03:47:28 on February 14, 2016 · (Permalink)
Here's a fun one that you've probably heard before, but never seen a simple explanation for. There are an infinite number of infinities that are all different sizes.
To be formal, there are really an infinite number of infinite sets, which all have different cardinality. If you're unfamiliar, cardinality is just the word we use to describe how many elements are in a set, like {banana, apple, pear} is composed of the elements: banana and apple and pear. We say that set has cardinality 3. Now here's the fun part. There are naturally sets with infinite cardinality. Like the natural numbers, N. N is {1,2,3,4...so on}. We say N is countably infinite. Sets larger than N are not countably infinite. This generally comes across as weird, cause intuition tells us that infinity is infinity right. Well the most interesting parts of math are where intuition fails and the truth has to be hunted down.
Enter the power set denoted P (S) where S is a set. The power set returns the set of all subsets of S. A subset is exactly what it sounds like, it's a set made up only of elements in S. For finite sets it goes like this.
S={1,2,3}
P (S)={(1,2,3), (1,2), (1,3), (2,3), (1), (2),(3), and the empty set, which has no elements}
Now the power set has a neat property for set S, P (S) will have greater cardinality than S. And that's all she wrote. The dominoes are starting to fall like a house of cards, checkmate. Take the set N, we've discussed it, it has infinite cardinality. P (N) has greater cardinality than N. P (P (N))has even greater cardinality than that. Every time you apply the power set to your infinite set, the result has greater cardinality and is still infinite. And from here we have an infinite set of different infinities.
Edit: brevity
silent_engineer · 1 points · Posted at 03:48:32 on February 14, 2016 · (Permalink)
now if I could only get a grip on my human math.....
IamFinis · 1 points · Posted at 03:49:18 on February 14, 2016 · (Permalink)
epi*i + 1 = 0
5 of the most important mathematical numbers in a balanced equation.
wsdmskr · 1 points · Posted at 03:50:57 on February 14, 2016 · (Permalink)
You can multiply 6x6 up to 10x10 using your fingers.
Misaniovent · 1 points · Posted at 03:51:19 on February 14, 2016 · (Permalink)
0.7734 upside down on a calculator spells "hello."
Fatchance82 · 1 points · Posted at 03:51:29 on February 14, 2016 · (Permalink)
folding a piece of 42 times gets you to the moon. 103 times becomes as wide as the universe.
goofy91 · 1 points · Posted at 03:51:57 on February 14, 2016 · (Permalink)*
Graham's number is a number so large that its ordinary digital representation cannot be contained in the observable universe (assuming that each digit occupies one Planck volume, i.e. the smallest measurable space). Also, its last rightmost decimal digit is 7.
(more info on Wikipedia)
Other cool facts:
its 500 rightmost decimal digits are known;
it was published in the 1980 Guinness Book of World Records;
it is so large that cannot be expressed using power towers of the form abcd... ;
it can be described using Knuth's up-arrow notation.
Fatchance82 · 1 points · Posted at 03:52:24 on February 14, 2016 · (Permalink)
folding a piece of paper 42 times gets you to the moon. 103 times becomes as wide as the universe.
cszlo · -1 points · Posted at 03:53:58 on February 14, 2016 · (Permalink)
This doesn't make sense.
LukesFather2011 · 1 points · Posted at 04:08:38 on February 14, 2016 · (Permalink)
http://www.iflscience.com/space/fold-piece-paper-half-103-times-and-it-will-be-thick-universe
cszlo · 1 points · Posted at 05:02:18 on February 14, 2016 · (Permalink)
But I thought the universe is constantly expanding at an ever increasing rate? :/ the moon part I have no problem with.
Watched the video in the link and it says observable universe, so in that sense i understand :)
Corneg · 1 points · Posted at 03:52:27 on February 14, 2016 · (Permalink)
To find out if any number is divisible by 3, add the digits together and if that number is divisible by 3, the original number is too.
Example: 66434567 > 6 + 7 + 4 + 3 + 4 + 5 + 6 + 7 = 42. 42 is divisible by 3 so 66434567 will be too.
meatb4ll · 1 points · Posted at 03:52:32 on February 14, 2016 · (Permalink)
You can do algebra with geometry. In fact, you're probably great at math if you look at it geometrically.
[deleted] · 1 points · Posted at 03:52:49 on February 14, 2016 · (Permalink)
Romans didn't believe in Zero
Splinter1591 · 1 points · Posted at 03:53:14 on February 14, 2016 · (Permalink)
How much lucky numbers have in common with prime numbers
https://en.m.wikipedia.org/wiki/Lucky_number
tabasaur · 1 points · Posted at 03:53:17 on February 14, 2016 · (Permalink)
My head hurts
MSgtGunny · 1 points · Posted at 03:53:19 on February 14, 2016 · (Permalink)
The sum of odd numbers gives you the list of perfect squares.
1= 1
+3=4
+5=9
+7=16
Etc
remi19 · 1 points · Posted at 03:53:54 on February 14, 2016 · (Permalink)
"contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck's constant). Scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of Planck’s constant may be, will all come up with 137, because it is a pure number. Lederman recalled that Richard Feynman had even suggested that all physicists put a sign in their offices with the number 137 to remind them of just how much they don’t know.
snaky69 · 1 points · Posted at 03:53:55 on February 14, 2016 · (Permalink)
The Möbius strip and Klein bottles come to mind.
Bombay66 · 1 points · Posted at 03:54:14 on February 14, 2016 · (Permalink)
All double digit multiples of nine add up to nine except 99. 18, 27, 36, 45, 54, 63, 72, 81, 90.
Squeetums · 1 points · Posted at 04:56:22 on February 14, 2016 · (Permalink)
Actually 99 works if you add both of the 9 + 9 digits together. 9 + 9 = 18. 1 + 8 = 9
byronigoe · 1 points · Posted at 03:54:34 on February 14, 2016 · (Permalink)
41 is the beginning of a long sequence of prime numbers, where you add consecutive even numbers. 41, 43, 47, 53, 61, 71, 83, ... and many more are all prime. I think the chain is broken around 650.
meodd8 · 1 points · Posted at 03:54:34 on February 14, 2016 · (Permalink)
Infinity of an imaginary number actually has a real value.
Vortico · 1 points · Posted at 07:23:47 on February 14, 2016 · (Permalink)
What?
ryan_503 · 1 points · Posted at 03:54:45 on February 14, 2016 · (Permalink)
The 3-4-5 triangle
iamtheben999 · 1 points · Posted at 03:55:16 on February 14, 2016 · (Permalink)
The Collatz Conjecture
Pick a number, any number!
If the number is odd, multiply it by 3 and add 1.
If it is even, divide it by two.
Repeat the two steps enough times, and any number can be reduced to 1.
cormac596 · 1 points · Posted at 03:56:10 on February 14, 2016 · (Permalink)
If you curcumscribe (draw a circle around, touching the corners of, but not intersecting) a perfect hexagon, the radius of the circle is the side length of the hexagon.
RichCovs · 1 points · Posted at 03:56:24 on February 14, 2016 · (Permalink)
To teach your kids their 9 times tables:
Hold your hands up in front of you and whatever you're multiplying 9 by, put that finger down and you have your answer.
E.g 9x3, you put down your 3rd finger from the left, so you now have 2 fingers on the left, and 7 fingers on the right, so those are your digits, 2 and 7 - 27.
Errmagrrd · 1 points · Posted at 03:57:25 on February 14, 2016 · (Permalink)
The derivative of ex is ex.
desmosabie · 1 points · Posted at 03:57:30 on February 14, 2016 · (Permalink)
I'm going to reverse your question on you. You tell me the mathmatical fact. ~ Three people check into a motel. The manager says that will be $30. Each person hands over $10 and the manager tells them they have room 123 for the night. They go to their room and about an hour later the manager says "damn the rooms are $25 tonight". He calles in the bellboy and gives him $5 to return to the people in room 123. On the way the bellboy thinks to himself "$5 is near impossible to divide amongst 3 people so I will keep $2 and give them each $1." That's what he does and the people thank him. "Thanks" Now each person paid $9, for a total of $27 and the bellboy has $2 for a total of $29 but they paid $30. So where is the missing $1 ?
georgefnix · 1 points · Posted at 04:11:22 on February 14, 2016 · (Permalink)
What extra dollar? They certainly paid 27, but the owner only has 25 and the bellboy has 2.
desmosabie · 1 points · Posted at 04:20:10 on February 14, 2016 · (Permalink)
OK, here is the coolest mathematical fact I know of. If you counted one dollar every second for a $1 million it would take you roughly 11 days. Doable. If you did that with $1 billion it would take you roughly 37 years. Nopeble.
Squeetums · 1 points · Posted at 04:54:04 on February 14, 2016 · (Permalink)
Well they still payed ~9.33 cents, assuming that the bell boy took the two dollars evenly from each of the people. Otherwise, i cant explain it.
Squeetums · 1 points · Posted at 04:54:05 on February 14, 2016 · (Permalink)
Well they still payed ~9.33 cents, assuming that the bell boy took the two dollars evenly from each of the people. Otherwise, i cant explain it.
[deleted] · 1 points · Posted at 03:57:33 on February 14, 2016 · (Permalink)
I'm not smart enough to grasp anything anyone's typing here, except maybe the one about the cowlick on the tennis ball.
iTSEu · 1 points · Posted at 03:57:41 on February 14, 2016 · (Permalink)
Did my math prof post this???
pnvv · 1 points · Posted at 03:58:12 on February 14, 2016 · (Permalink)
XKCD = 24 + 11 + 3 + 4 = 42
A nerd I am.
The_ThirdFang · 1 points · Posted at 03:58:21 on February 14, 2016 · (Permalink)
373 is prime god.
3 - 7 - 3 are each prime numbers.
37 - 73 are prime numbers
3+3+7=13 a prime number
Pretty cool if you ask me
LukesFather2011 · 1 points · Posted at 04:01:30 on February 14, 2016 · (Permalink)
Is it pretty cool?
The_ThirdFang · 1 points · Posted at 04:53:42 on February 14, 2016 · (Permalink)
A little
ahhhellashit · 1 points · Posted at 03:58:52 on February 14, 2016 · (Permalink)
6 is afraid of 7.
shitbadger · 1 points · Posted at 04:02:24 on February 14, 2016 · (Permalink)
why?
ahhhellashit · 2 points · Posted at 04:58:47 on February 14, 2016 · (Permalink)
cuz 7 ate 9... Me
dscab00se · 1 points · Posted at 04:13:45 on February 14, 2016 · (Permalink)
this is the correct answer
juggalofr33k · 1 points · Posted at 03:59:48 on February 14, 2016 · (Permalink)
The fact I dont care about math, yet I'm a good mathematician?
shitbadger · 1 points · Posted at 04:00:05 on February 14, 2016 · (Permalink)
A pyramid based on Pi varies by only 0.1% from the Great Pyramid’s estimated dimensions.
http://www.goldennumber.net/phi-pi-great-pyramid-egypt/
Moufang_Loop · 1 points · Posted at 04:00:15 on February 14, 2016 · (Permalink)
There's no such thing as a "knot" in four dimensional space. That is, no matter how you arrange loop of string in four dimensional space, it can be untied completely by pulling on it. However, there is a way to "knot" a sphere in four dimensional space.
Vortico · 1 points · Posted at 07:07:58 on February 14, 2016 · (Permalink)
For those interested, a 2-knot is an embedding of S2 into R4 (or S4 ), and their behavior is even more eccentric than classical knots, which are themselves surprisingly difficult to classify.
CrushHazard · 1 points · Posted at 04:00:49 on February 14, 2016 · (Permalink)
Lots of number theory on here, which is very cool, but if we think of cool as extremely counterintuitive, I am always reminded of the woefully incorrect statement that is repeated by intelligent but mathematically disinclined individuals: "you can't prove a negative."
That idea of course has no basis in fact. Any statement can be thought of as a negative of its own negative (for example "2+2 equals 4" can be thought of as "2+2 doesn't not equal 4", but that's just to demonstrate that there is nothing uniquely special about a "negative").
I understand that by "proving a negative", most people mean "proving that something does not exist." That is admittedly hard, because one must consider all the possible ways that something can exist and disprove each one of them. Sometimes the mathematics works out so that such a thing is possible.
More interestingly, one of the most significant cases of "proving a negative" in mathematics is the proof that while a polynomial of the 2nd, 3rd and 4th degree can be solved in a deterministic way, polynomials of 5th degree or more cannot be solved. This was proved by Evariste Galois. Furthermore and far more interestingly, it was based on writings that he developed throughout his 20-year lifetime, the last of which were written late at night on the 30th of May 1832, the night before he was to die in a duel over a woman. Part of his last writings was a plea that his works were extremely significant and should be reviewed by famous mathematicians of the time.
Of course, he was right, and the branch of mathematics that he invented (all by the age of 20 mind you) is one of the few that is still studied to this day.
subito_lucres · 1 points · Posted at 04:01:04 on February 14, 2016 · (Permalink)
ei*pi +1 = 0
dicroce · 1 points · Posted at 04:01:21 on February 14, 2016 · (Permalink)
The sum of all positive integers is -1/12. Popular Videos - Natural number & Mathematical proof: https://www.youtube.com/playlist?list=PLXkqIzYHy9Y1_oAcIZddpRoZTCy3XjD0e
elhaupto · 1 points · Posted at 04:01:22 on February 14, 2016 · (Permalink)
Every even integer is the sum of two prime numbers. Nobody has ever written a proof for this.
So 4 = 1 +3
6 = 1 + 5
22 = 11 + 11
46 = 41+ 5
hashymika · 1 points · Posted at 04:01:24 on February 14, 2016 · (Permalink)
So how many of these have you done /u/Jeff_Dujon
Linard · 1 points · Posted at 04:01:26 on February 14, 2016 · (Permalink)
You can force any combination of numbers into a repeating never ending decimal by doing the following:
<numbers you choose to repeat> / <a number only consisting of 9's the same length as your chosen numbers>
Example:
13564/99999 = 0.13564135641356413564....
If you divide through a 9er number with more digits, each extra 9 adds a 0 between your chosen numbers before repeating:
Example:
123/9999 = 0.01230123012301230123....
The only exception where you can't do this is when your chosen number only consists of 9's like 999/999 because that obviously is 1.
What you can do however is add here another 9 like 999/9999 and you get like with the above example 0.09990999099909990999....
Chessrocks · 1 points · Posted at 04:02:13 on February 14, 2016 · (Permalink)
Shannon's number. Mind blowing
MrManslaughter · 1 points · Posted at 04:02:49 on February 14, 2016 · (Permalink)
Your head physically can not store enough information in your head to process graham's number (the largest number ever used in a proof). This is because a black hole the size of your head can't even store that much information.
Children_Of_Fish · 1 points · Posted at 04:03:07 on February 14, 2016 · (Permalink)
There's a law which states that in the numerical representation of many things such as the constants of nature, lengths of rivers, heights of buildings or even tax returns, the leading digit is more likely to be a small number. Benford's Law.
politichan · 1 points · Posted at 04:03:23 on February 14, 2016 · (Permalink)
y=mx+b... I'm not good at math.
zouppp · 1 points · Posted at 04:03:27 on February 14, 2016 · (Permalink)
1+2+3+4+5+6+7+8+9+10+9+8+7+6+5+4+3+2+1=100
brickmack · 1 points · Posted at 04:03:29 on February 14, 2016 · (Permalink)
Not really a fact, but relevant because Valentines Day. Put r=a(1-cos(theta)) into a graphing calculator (in polar mode). Hand that calculator to your crush/SO/whatever. You're welcome.
Also, there are functions like the Weierstrass function that are continuous everywhere, but differentiable nowhere. Because fuck logic
SPQC · 1 points · Posted at 04:03:33 on February 14, 2016 · (Permalink)
All the numbers from 1 to 100 add up to 5050.
dittbub · 1 points · Posted at 04:03:43 on February 14, 2016 · (Permalink)
0.999... Is exactly equal to 1
mallad · 1 points · Posted at 04:03:51 on February 14, 2016 · (Permalink)
In English, four is the magic number.
If you spell out any number and count the number of letters in it, then continue that pattern until the number doesn't change, you always land on four.
For example, ten is 3 letters. Three is 5 letters. Five is 4 letters. Four is 4 letters because four is the magic number.
It's a fun little game to play with people who don't know it - tell them to name any number, then count the letters in your head and tell them the results. IE - "ten is three, three is five, five is four and four's the magic number" and then have them try another number until they figure out the rule.
schodrum · 1 points · Posted at 04:04:27 on February 14, 2016 · (Permalink)
If you add 1234567890+1234567890 and keep pressing equals on the calculator, you get 11,111,111,010 22,222,222,020 33,333,333,030 44,444,444,040 55,555,555,050 66,666,666,060 77,777,777,070 88,888,888,080 99,999,999,090 eventually
I just thought it was cool when 5th grade self found that out by myself.
Sinkaix · 1 points · Posted at 04:04:36 on February 14, 2016 · (Permalink)
ei*pi +1 = 0, also known as euler's identity. https://en.wikipedia.org/wiki/Euler%27s_identity
Johnie4usc · 1 points · Posted at 04:04:43 on February 14, 2016 · (Permalink)
I have a cool one (to me) but I'm late so no one will see it lol
ginganinja900 · 1 points · Posted at 04:04:43 on February 14, 2016 · (Permalink)
How 0.999999 = 1 0.99999 = X 9.99999 = 10X 9.00000 = 9X 1.00000 = X
[deleted] · 1 points · Posted at 04:04:48 on February 14, 2016 · (Permalink)
Every compact orientable 2-manifold (surface) of genus (# of holes in surface) g>=1 is homeomorphic (can be deformed into) the connected sum of g tori.
*connected sum: http://www-history.mcs.st-and.ac.uk/~john/MT4521/Diagrams/x25-1.gif
chaoism · 1 points · Posted at 04:04:58 on February 14, 2016 · (Permalink)
that we have this value 'e'
how about the fact that we can fit every single number on a plane into a unit circle? I find that one really cool too
rebelgirlpa · 1 points · Posted at 04:05:21 on February 14, 2016 · (Permalink)
Hey I'm just proud of the fact that I can pronounce Pythagorean Theorem, let alone what the hell it is...
Legend_Zector · 1 points · Posted at 04:05:23 on February 14, 2016 · (Permalink)
i3 = -i
∛i = -i
[deleted] · 1 points · Posted at 04:06:02 on February 14, 2016 · (Permalink)
3* 0,33 = 1
won
[deleted] · 1 points · Posted at 04:06:14 on February 14, 2016 · (Permalink)
ei*pi=-1
For real.
em3am · 1 points · Posted at 04:06:17 on February 14, 2016 · (Permalink)
If we try and communicate with extra-terrestrial aliens by using umber systems, are we prepared if their number system is based on e. It is the basis of many, many, many natural phenomena?
hzepplin · 1 points · Posted at 04:06:18 on February 14, 2016 · (Permalink)
You have 23 random people in a room. More than 50% of the time, two of them will share a birth date (month and day, not year) 70 people in a room? 99.9% chance that at least two of them share a birthdate.
JonathanLi · 1 points · Posted at 04:06:23 on February 14, 2016 · (Permalink)
16/64 = 1/4 because you cancel out the 6's
[deleted] · 1 points · Posted at 04:06:28 on February 14, 2016 · (Permalink)
The actual origin of 666 and 616.
futureformerteacher · 1 points · Posted at 04:07:28 on February 14, 2016 · (Permalink)
0! is 1.
datadamage · 1 points · Posted at 04:08:11 on February 14, 2016 · (Permalink)
1+ 2 +3 + .... + N + .... + 3 + 2 + 1 = N2 for any N.
flare2000x · 1 points · Posted at 04:08:38 on February 14, 2016 · (Permalink)
eiπ + 1 = 0
Bongo9911 · 1 points · Posted at 04:09:18 on February 14, 2016 · (Permalink)
28 is equal to the sum of its divisors / 2
SharkFart86 · 1 points · Posted at 04:09:26 on February 14, 2016 · (Permalink)
If someone gave Jesus Christ $1000 every 15 minutes from the day he was born until today, he still wouldn't have as much money as Bill Gates. $1000 x 4 x 24 x 365.25 x 2016 = $70.6B. Bill Gates net worth = $79.2B
Loyheta · 1 points · Posted at 04:09:49 on February 14, 2016 · (Permalink)
1/9 = .11111 2/9= . 22222 3 /9= . 333333 .... 9/9= . 999999
mlpiceking · 1 points · Posted at 04:35:28 on February 14, 2016 · (Permalink)
ummm... 9/9= 1
Loyheta · 1 points · Posted at 04:41:29 on February 14, 2016 · (Permalink)
.999... And 1 are the same number
https://en.m.wikipedia.org/wiki/0.999...
Gerryisswag · 1 points · Posted at 04:09:51 on February 14, 2016 · (Permalink)
1+1=2
momo8969 · 1 points · Posted at 04:10:02 on February 14, 2016 · (Permalink)
There are more stars in the universe then grains off sand on earth....yet in one grain of sand there are more atoms then stars in all the universe.
grandaddy7 · 1 points · Posted at 04:10:24 on February 14, 2016 · (Permalink)*
A square number plus the square root plus the square root plus 1 equals the next square number. I have no idea how else to explain it. I was just sitting in geometry freshman year in High School and figured out the pattern. I've never read this pattern or seen it anywhere so its kind of fun figuring this stuff out on your own.
22 = 4
2+3+4 = 9
32 = 9
3+4 = 7
9+7 = 16
42 = 16
Another example maybe easier to understand?
62 = 36
6+7+36 = 49
72 = 49
I guess the equation would be X2 + 2X+1 = (X + 1)2
ginkomortus · 2 points · Posted at 04:22:39 on February 14, 2016 · (Permalink)
Imagine square numbers as actually squares on a grid. So, 4 is this:
and 9 looks like this:
As you can see, to go from 4 to 9, you have to add 5 square units. Two on the side and three on the bottom, or some combination thereof. Imagine going from 9 to 16, and you'll see you need to add 4 on one side and 5 on the other.
Opheltes · 1 points · Posted at 04:10:29 on February 14, 2016 · (Permalink)
There have to be an infinite number of prime numbers. Why?
Because if there were a finite number of them, you could multiple them all together, add 1, and get a new prime number that wasn't part of the original count.
Here is the ELI5 comment where I first saw this and it exploded my brain. (Props to /u/Chel_of_the_sea)
SatchBoogie1 · 1 points · Posted at 04:10:44 on February 14, 2016 · (Permalink)
1 is still the loneliest number.
not-so-funhaus · 1 points · Posted at 04:11:13 on February 14, 2016 · (Permalink)
You can find 8% of 200 by finding 200% of 8, 16. Credit: some stupid imgur post I saw and completely forgot about.
puterdood · 1 points · Posted at 04:11:19 on February 14, 2016 · (Permalink)
There is a proof of the infinitude of primes that goes something like:
pi/4 = (3/4)(5/4)(7/8)(11/12)(13/12)(17/16)(19/20)... etc where the numerators of the product are prime numbers and the denominators are the nearest multiple of 4 to the numerator. It equals exactly pi/4, which is kind of interesting.
duckrabb1t · 1 points · Posted at 04:11:24 on February 14, 2016 · (Permalink)
Any sufficiently strong formal system (e.g., arithmetic) is incomplete, if it is consistent. Basically, Godel proved that there are some mathematical truths which are unproveable.
LeonardSmallsJr · 1 points · Posted at 04:11:51 on February 14, 2016 · (Permalink)
There exists a continuous function from zero to one [f(0)=0 and f(1)=1] where the slope at every point is flat.
/cantor function
Millacol88 · 1 points · Posted at 04:11:53 on February 14, 2016 · (Permalink)
Conditionally convergent infinite series (series which converge when the terms alternate in sign, but are divergent when each term is made positive) can have the order of summation rearranged so that they are equal to any number.
e.g. the series 1 + 1/2 + 1/3 + 1/4 + ... is divergent.
The series 1 - 1/2 + 1/3 - 1/4 + ... converges to log(2) = 0.693... However if we rearrange the exact same set of numbers:
1 - 1/2 -1/4 + 1/3 - 1/6 -1/8 + 1/5 - 1/10 -1/12 +...
But we can group together the first two numbers out of each group of 3:
= 1 - 1/2 -1/4 + 1/3 - 1/6 -1/8 + 1/5 - 1/10 - 1/12 +...
= 1/2 -1/4 + 1/6 -1/8 + 1/10 - 1/12 +...
= 1/2*(1 - 1/2 + 1/3 -1/4 + 1/5 - 1/6 +...)
= log(2)/2
Half the sum of the first ordering (!)
[deleted] · 1 points · Posted at 04:11:54 on February 14, 2016 · (Permalink)
69=6*9+6+9 mind blowing. I know.
yourdadswife · 1 points · Posted at 04:12:11 on February 14, 2016 · (Permalink)
You can do the nines table on your hands.
Hold up ten fingers. For 2 * 9 put down your second finger from the left. You're left with 1 finger up on the left and 8 fingers up on the right (18).
5 x 9 up down your fifth finger from the left. You're left with 4 on the left side and 5 on the right (45).
FowD9 · 1 points · Posted at 04:12:44 on February 14, 2016 · (Permalink)*
a googol is already a pretty hard to understand large number: 10100 that's 1 followed by 100 zeros.
A googolplex is almost incomprehensible with how big it actually is: 10googol or 1010100. that's 1 followed by a googol zeros
just to attempt to put it into perspective, if the universe were 1010100 meters long there would be EXACT clones of you.
to further explain this, say in a 1x1 meter cube, there is a finite number of possibilities in which particles (electrons/protons) can be arranged. and while you might think that the number of combinations particles can be arranged in a 1x1 meter cube is almost uncomprehensible. there will be so many instances of that 1x1 meter cube in a googolplex meter long universe, that there will be multiple EXACT copies of that 1x1 meter cube.
so, if you're standing in that 10x10 meter cube, with particles aligned in a specific way that make you, you. A googolplex meter universe is so large, that there will be multiple copies of you in that universe
another example on just how ridiculously large this number is, if you were to take every single particle (electrons/protons, smaller than atoms, it's what atoms are made of) in the observable universe and use those particles to each represent a zero. you wouldn't have enough zeros to write out the number for googolplex (1010100 )
/edit here... i remember seeing this video a while ago, a great explanation on just how big a googolplex is https://www.youtube.com/watch?v=8GEebx72-qs
ReverendUncle · 1 points · Posted at 04:12:54 on February 14, 2016 · (Permalink)
The average person has one testicle and one ovary.
ScimitarLover · 1 points · Posted at 04:16:47 on February 14, 2016 · (Permalink)
FUCK YOU! I HAVE TWO GODAMMIT!
jez2718 · 1 points · Posted at 04:13:31 on February 14, 2016 · (Permalink)
There is a function from the real numbers to the real numbers for which the image of any interval is the real line.
The Devil's staircase is a continuous function which is almost everywhere constant, but is 0 at 0 and rises to 1 at 1.
[deleted] · 1 points · Posted at 04:13:32 on February 14, 2016 · (Permalink)
[deleted]
ScimitarLover · 1 points · Posted at 04:15:37 on February 14, 2016 · (Permalink)
1.109191656751434135751453127676923139848631257623458765932478426874635246325476315851693764257608974325463526421976409602587480470856297127817061758626146182720815487536519460381468136497635473676
KevinsPhallus · 1 points · Posted at 04:14:44 on February 14, 2016 · (Permalink)
One of mine is that 10/81 is 0.123456790123456790..... which can be written as 1/10 + 2/102 + 3/103 ... + 8/108 .... + n/10n most people assume that the 8/108 term isn't part of the sequence because there is no 8 in 10/81 but this is just the 1 carried over from the 10/10n is 10/1010 = 1/109 which can be easily added to 9/109 to make 10/109 = 1/108 which adds to 8/108 making it 9/108
0.1234567
0.00000008
0.000000009
0.0000000010
0.00000000011
which makes the digit 8 not appear in the decimal despite being in the squence
Sorry for shit format don't often post but nothing like some maths to get me going
ZummerzetZider · 1 points · Posted at 04:14:48 on February 14, 2016 · (Permalink)
e ^ (pi i) = -1
InvalidUser_Name · 1 points · Posted at 04:15:23 on February 14, 2016 · (Permalink)
Some actor thinks 1 x 1 = 2.
QCA_Tommy · 1 points · Posted at 04:15:27 on February 14, 2016 · (Permalink)
If you need to multiply any double-digit by 11, just add those two numbers together and stick the middle number in the middle... So, 11 x XY = X(X+Y)Y; or 11 x 23 = 253!
stripesonfire · 1 points · Posted at 04:16:24 on February 14, 2016 · (Permalink)
.999999999...=1
twerkinwithcoffee · 1 points · Posted at 04:16:39 on February 14, 2016 · (Permalink)
The sum of ALL positive integers equals -1/12. There is a great numberphile video on this and it's absolute none sense but apparently mathematically accurate.
choochoosaresafe · 1 points · Posted at 04:16:50 on February 14, 2016 · (Permalink)
Something about adding the numerical order of the words math toequal the number 42...
Douglas Adams 4 life.
poopyheadthrowaway · 1 points · Posted at 04:17:25 on February 14, 2016 · (Permalink)
The golden ratio is a good approximation of the conversion factor between miles and kilometers. This makes the Fibonacci sequence also a good approximation when converting between miles and kilometers (e.g., 8 miles is approximately 13 kilometers).
MrMi10s · 1 points · Posted at 04:17:42 on February 14, 2016 · (Permalink)
This is going to get buried but it's super useful.
If you want to divide a number by 5, first multiply it by 2 and then divide it by 10.
For example we have 37.
37x2=74 74÷10=7.4
7.4 × 5 = 35
Posta92 · 1 points · Posted at 04:18:09 on February 14, 2016 · (Permalink)
In a room of just 23 people there’s a 50-50 chance of two people having the same birthday.
orcscorper · 1 points · Posted at 04:19:02 on February 14, 2016 · (Permalink)
I found a cool pattern linking Pascal's and Euler's triangles, and exponents. I hadn't even heard of Euler's Triangle when I found it. First, overlay Pascal's Triangle with Euler's Triangle, rotated 60° with the peak resting on the second column (the consecutive integers). Multiply each number in Euler's by the corresponding number in Pascal's. Add the numbers in Euler's rows. Example: place the top 1 (Euler) over 5 (Pascal). The next row (11) covers (10 15). Multiply by 1, add them to get 25. Two consecutive triangle numbers make a square; not the cool part. The next row (1 4 1) covers (10 20 35). Multiply to get 10+80+35, or 125. Likewise, (1 11 11 1) over (5 15 35 70) yields 5+165+385+70, or 625. It worked with every number I tried, but I have no idea how to prove that it's always true.
Joseon194 · 1 points · Posted at 04:19:48 on February 14, 2016 · (Permalink)
mom+dad+sex=you
[deleted] · 1 points · Posted at 04:20:18 on February 14, 2016 · (Permalink)
This is more of a science fact than a math fact, but there are over 80 trillion possible DNA combinations as a result of two human gametes creating a fertilized egg.
That's what my genetics professor at ASU said anyway.
AqUaNtUmEpIc · 1 points · Posted at 04:20:31 on February 14, 2016 · (Permalink)
Graham's number is too big to grasp and would cause your head to collapse into a black hole
AresIII · 1 points · Posted at 04:21:40 on February 14, 2016 · (Permalink)
The Golden Ratio
The Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form, it looks like this:
a/b = (a+b)/a = 1.6180339887498948420 …
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
_Prisoner_24601_ · 1 points · Posted at 04:22:18 on February 14, 2016 · (Permalink)
12,345,679 x 8 = 987,654,32
oddlycurious1 · 1 points · Posted at 04:23:15 on February 14, 2016 · (Permalink)
That Russell and Whithead spent the time and effort to create a mathematical proof that 1 + 1 = 2 (around 300 pages or so)
DocFail · 1 points · Posted at 04:24:01 on February 14, 2016 · (Permalink)
i
ostensibly_derived · 1 points · Posted at 04:24:10 on February 14, 2016 · (Permalink)
You can prove mathematically that given infinite time, a drunk ant is guaranteed to visit the same Cartesian coordinates (X, Y) more than once, but a drunk bird is not guaranteed to hit the same coordinates (X, Y, Z) more than once.
Futurist110 · 1 points · Posted at 04:24:26 on February 14, 2016 · (Permalink)
While I don't know if this counts for this, here goes:
https://en.wikipedia.org/wiki/Monty_Hall_problem
"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?"
The answer to this question is that Yes, it certainly is to my advantage to switch my choice. :)
Indeed, nearly 1,000 people with PhDs got the answer to this question/problem wrong. :(
timecronus · 1 points · Posted at 04:25:53 on February 14, 2016 · (Permalink)
everything from 9 * 1 to 9 * 10 the product adds to eachother is equal to 9.
For example, 9 * 9 = 81, 8 + 1 = 9. 9 * 4 = 36, 3 + 6 = 9.
trickICR · 1 points · Posted at 04:26:03 on February 14, 2016 · (Permalink)
The average person has less than 2 arms
SuddenInclination · 1 points · Posted at 04:26:11 on February 14, 2016 · (Permalink)
Any whole number that that is evenly divisble by 3, when reversed, is still evenly divisible by 3.
Don't know what principle it is, who first figured it out, or what it's good for. All I know is that I figured it out one day when I looked at the thermostate at work and had a bit of an apple to the head moment.
I believe it also applies to the number 9.
If anyone knows about this, or if I'm actually totally wrong, comment please.
4011 · 1 points · Posted at 04:32:50 on February 14, 2016 · (Permalink)
Any time the sum of digits in a number add up to 3, it will be divisible by 3. So that means that 234, 342, 432, etc. will all be divisible by 3. And if the number is even, it's also divisible by 6.
galaxiekat · 1 points · Posted at 04:26:51 on February 14, 2016 · (Permalink)
for any natural number, a, (a+i)/(a-i), when rationalized and simplified, the numerator and denominators will generate a pythagorean triple.
for example:
(3+i)/(3-1)
(3+1)(3+i)/(3-i)(3+1)
(9+6i+i2 )/(9-i2 )
(9-6i-1)/(9 +1)
(8-6i)/(10)
(4-3i)/5
3, 4, and 5 are a pythagorean triple.
imTinyRick_ · 1 points · Posted at 04:26:57 on February 14, 2016 · (Permalink)
TIL Math still isn't cool.
Razor1834 · 1 points · Posted at 04:27:07 on February 14, 2016 · (Permalink)
The sum of the digits of all multiples of 9 add up to 9 or one of its multiples (which in turn add up to 9). It's possible to know if a number is evenly divisible by 9 by adding the digits up (and then adding the digits of the sum up) and seeing if you get 9.
Goldilocks420 · 1 points · Posted at 04:27:26 on February 14, 2016 · (Permalink)
0.999... recurring equals one.
amanager · 1 points · Posted at 04:27:58 on February 14, 2016 · (Permalink)
9 × anything always reduces numerically back to 9.
9×2=18 (1+8=9) 9×3=27 (2+7=9) 9×65=585(5+8+5=18 [1+8=9])
9 is an amazing number.
DangerDamage · 1 points · Posted at 04:28:16 on February 14, 2016 · (Permalink)
.9999999999999999999999999999999999999999999999 repeating is equal to one.
SOADLT · 1 points · Posted at 04:28:53 on February 14, 2016 · (Permalink)
6 * 9 + 6 + 9 = 69
BirdBlind · 1 points · Posted at 04:29:53 on February 14, 2016 · (Permalink)
To add up all the numbers from 1 to 100, just multiply 100 * 101 and divide by 2. This works for any finite amount of numbers from 1 to n.
Amazing how powerful math can be.
pocketsquarehampster · 1 points · Posted at 04:30:00 on February 14, 2016 · (Permalink)
I'm too drunk to understand this thread right now
pmwws · 1 points · Posted at 04:30:18 on February 14, 2016 · (Permalink)
It is possible to invert a sphere without creases, but not a circle.
miniature_light · 1 points · Posted at 04:30:37 on February 14, 2016 · (Permalink)
https://en.m.wikipedia.org/wiki/Collatz_conjecture
[deleted] · 1 points · Posted at 04:30:38 on February 14, 2016 · (Permalink)
A father dies leaving instructions that his 17 camels are to be split up between his 3 sons as follows -
Failing to think of a way of carrying out their father's wishes, they decided to seek help. So they sent a message across the desert to their uncle, who though poor was considered to be wise.
A month later, up rode their uncle on his grotty old camel. After he'd had a rest and something to eat, they explained their problem to him.
"Tell you what", he said, "I'll lend you my camel, then you'll have 18, and you should be able to divide them up without difficulty."
So the eldest son chose his 9 camels from the flock, the middle son chose his 6 camels, and the youngest son chose his 2 camels. Uncle then got back on his camel (which no-one had chosen because it was old and grotty) and rode back home across the desert (no doubt muttering to himself about the failings of the younger generation).
Dathouen · 1 points · Posted at 04:30:39 on February 14, 2016 · (Permalink)
Repeated addition is multiplication.
Repeated multiplication is exponentiation.
Repeated exponentiation is tetration.
Repeated tetration is penetration.
Repeated penetration is sexation.
kingdowngoat · 1 points · Posted at 04:30:54 on February 14, 2016 · (Permalink)
If you have siblings, there is one day when your ages added together equal the age of your mother.
On that day you are each as old as your mother was when she gave birth to the other.
IAMAwerewolfAMA · 1 points · Posted at 04:31:19 on February 14, 2016 · (Permalink)
I will never need to know it for anything I ever do in real life, and yet for some reason I'm required to take algebra (which I loathe and can't do) for my degree! Yay! Such a cool math fact.
Vortico · 2 points · Posted at 06:56:41 on February 14, 2016 · (Permalink)
I am a mathematician but empathize with you. I was required to take a few literature, philosophy, psychology, history, and economics classes in college, and while they were fun at times, I feel my time could have better been spent on courses directly related to my specialization.
MisterJose · 1 points · Posted at 04:31:33 on February 14, 2016 · (Permalink)
e is the natural growth rate of things: ~ 2.71828 It's fundamental in chemistry, finance, statistics, you name it. It's part of how the world works.
i is equivalent to √-1, the fundamental imaginary number. A place holder you could say, for a thing that doesn't exist along the standard real number line.
π = 3.14159... You know, pi. Everyone likes pi. Has to do with circles and stuff.
Three numbers fundamental to our core understanding, two irrational, one imaginary, seemingly unrelated and from three different branches of math. Except that...
eiπ = -1
Whoa.
romxza · 1 points · Posted at 04:38:40 on February 14, 2016 · (Permalink)
Allow me to nitpick lol. That is a common misconception... e isn't the "natural growth rate of things". ekx is how we write growth rates when the growth rate is proportional to the current value, i.e. "exponential growth". But k here can stand for any rational number, so in effect the growth is ax for some rational number a. Using base e as a base of the exponent is just convenient because the constant of proportionality in the growth rate of ex is precisely one.
MisterJose · 1 points · Posted at 04:51:14 on February 14, 2016 · (Permalink)
Yeah, I had a big paragraph about e, but cut it down for proportion.
boxxa · 1 points · Posted at 04:32:15 on February 14, 2016 · (Permalink)
The usefulness of prime numbers has always been interesting
KnowledgeGreaterThan · 1 points · Posted at 04:32:37 on February 14, 2016 · (Permalink)
Math actually stands for:
Mental abuse to humans
jdylopa · 1 points · Posted at 04:32:38 on February 14, 2016 · (Permalink)
I'm very late to the party, so not many people will see this, but here goes:
Not all "infinities" are equal, but there are the same amount of integers (whole numbers both positive and negative) as there are natural numbers (whole numbers starting at 0 or 1 depending on the book). This goes for a lot of things (for instance, the set of all integers also has the same amount of numbers as the set of all even numbers, or the set of all rational numbers...infinite cardinality can be a weird thing).
[deleted] · 1 points · Posted at 04:33:23 on February 14, 2016 · (Permalink)
The 9 times table trick, it's pretty hard to explain 9x1=9 9x2=18 9-1=8 add the 1 to the 10 digit 9*3= 27 8-1=7 add the 1 to the 2 and you get 3
Yeah it's hard to explain.
bukkakepriestess · 1 points · Posted at 04:33:44 on February 14, 2016 · (Permalink)
one of the fundamental "proofs" in quantum field theory, you can show that the sum of all positive integers (1+2+3+4+5...) is -1/12. It's insane: https://www.youtube.com/watch?v=w-I6XTVZXww
omegasavant · 1 points · Posted at 04:36:10 on February 14, 2016 · (Permalink)
There are two-sided shapes, which are called lunes, and it's surprisingly straightforward to make them. You just can't do it on a flat plane.
OnlyMath · 1 points · Posted at 04:36:13 on February 14, 2016 · (Permalink)
The number sets we know today were created on the basis of an empty set. Such as: Let 0 denote the empty set then: 1 = {0} 2 = {{0},0} and so on. Our numbers were created from nothing, much like everything else we know and love.
HyperMidgit · 1 points · Posted at 04:38:11 on February 14, 2016 · (Permalink)
9+10=21
trobing · 1 points · Posted at 04:38:43 on February 14, 2016 · (Permalink)
The digits of all multiples of 9 adds up to 9.
9 x 3 = 27 (2+7=9) 9 x 6 = 54 (5+4=9) 9 x 131 = 1179 (1+1+7+9=18; 1+8=9) etc.
crgsmith1234 · 1 points · Posted at 04:39:09 on February 14, 2016 · (Permalink)
If you put this < and this 3 together you make a heart <3
darealpipe · 1 points · Posted at 04:39:11 on February 14, 2016 · (Permalink)
Mine is a bit of a word problem. This is a mathematical equation that proves that girls are evil. Several variables in this equation. G=Girls T=Time M=Money E=Evil Girls require time and money. G= T×M Everyone knows time is money T=M G= M×M or M2 Money is the root of all Evil M= square root (E) Square both sides. M2 = E If G=M2 Then G=E Girls must be evil.
Rick0r · 1 points · Posted at 04:39:46 on February 14, 2016 · (Permalink)
I have an above average number of arms.
elfliner · 1 points · Posted at 04:40:56 on February 14, 2016 · (Permalink)
as numbers guy and, coincidentally, an accountant, bookkeeper is the only word with 3 consecutive duplicate letters. Not very "mathematical" but it might help you out in jeopardy.
ythl · 1 points · Posted at 04:41:09 on February 14, 2016 · (Permalink)
One of the consequences of the second law of thermodynamics is that a certain amount of energy is necessary to represent information. To record a single bit by changing the state of a system requires an amount of energy no less than kT, where T is the absolute temperature of the system and k is the Boltzman constant. (Stick with me; the physics lesson is almost over.)
Given that k = 1.38×10-16 erg/°Kelvin, and that the ambient temperature of the universe is 3.2°Kelvin, an ideal computer running at 3.2°K would consume 4.4×10-16 ergs every time it set or cleared a bit. To run a computer any colder than the cosmic background radiation would require extra energy to run a heat pump.
Now, the annual energy output of our sun is about 1.21×1041 ergs. This is enough to power about 2.7×1056 single bit changes on our ideal computer; enough state changes to put a 187-bit counter through all its values. If we built a Dyson sphere around the sun and captured all its energy for 32 years, without any loss, we could power a computer to count up to 2192. Of course, it wouldn't have the energy left over to perform any useful calculations with this counter.
But that's just one star, and a measly one at that. A typical supernova releases something like 1051 ergs. (About a hundred times as much energy would be released in the form of neutrinos, but let them go for now.) If all of this energy could be channeled into a single orgy of computation, a 219-bit counter could be cycled through all of its states.
These numbers have nothing to do with the technology of the devices; they are the maximums that thermodynamics will allow. And they strongly imply that brute-force attacks against 256-bit keys will be infeasible until computers are built from something other than matter and occupy something other than space.
source
source2
toxicity187 · 1 points · Posted at 04:41:19 on February 14, 2016 · (Permalink)
2+2=4
mudskipper3000 · 1 points · Posted at 04:41:37 on February 14, 2016 · (Permalink)
ei*pi + 1 = 0
dmr83457 · 1 points · Posted at 04:41:50 on February 14, 2016 · (Permalink)
1 = .9 repeating
Isturma · 1 points · Posted at 04:42:01 on February 14, 2016 · (Permalink)
I owe Day [9] for teaching me this exists, but I've learned more about it since then - Graham's number. It's the largest possible number to a simple theorem, but it's so impossibly large that it has more digits than there are stars in the observable universe.
GrandMaster621 · 1 points · Posted at 04:42:18 on February 14, 2016 · (Permalink)
That there are infinite number of primes.
The proof is ridiculously easy, even if the statement is true, I find it very hard to wrap my head around this simple fact. There are infinite number of primes, no matter how many of them you find, you will keep finding them
Danteska · 1 points · Posted at 04:42:31 on February 14, 2016 · (Permalink)
A little bit late to the party I guess, but will post it anyway.
And so on. Was shown this in Belgium when I was a kid. Doesn't have a practical use probably, but still cool thing to play with IMO :)
Also, don't know why do you have to skip 8, but if you try to play around with that number, you'll sometimes get a mess like this:
has all the numbers from 0 to 9, except 4.
again, has all the numbers from 0 to 9, except the 8. The order is quite nice, too :)
sexapotamus · 1 points · Posted at 04:42:41 on February 14, 2016 · (Permalink)
I just want to say that my math teacher girlfriend is basically orgasming as I read every single one of these.
MageTank · 1 points · Posted at 04:42:43 on February 14, 2016 · (Permalink)
Integral z-squared dz From 1 to the cube root of 3 Times the cosine Of three pi over 9 Equals log of the cube root of e.
[deleted] · 1 points · Posted at 04:42:49 on February 14, 2016 · (Permalink)
Not entirely math but time moves slower closer to mass.
IE. 2 Twins. One goes to live on a mountain and the other goes to live at sea level, the one on the mountain would age faster.
Nicepotato · 1 points · Posted at 05:37:19 on February 14, 2016 · (Permalink)
Why ?
[deleted] · 1 points · Posted at 15:01:17 on February 14, 2016 · (Permalink)
Simply put, gravity and mass slow down time. If you want a deeper explanation read " A brief history of time by Stephen Hawking"
Z_Coop · 1 points · Posted at 04:42:50 on February 14, 2016 · (Permalink)
Waayyy late to the party, but I haven't seen someone mention this one yet.
If you sum the digits of any number, and that sum is divisible by 3, the larger, original number is too.
Eg. "183492"
1+8+3+4+9+2 = 27
2+7 = 9
9 is divisible by 3, so 183492 is too! (It equals 61164 for those playing along at home)
Or:
183490 1+8+3+4+9+0 = 25 2+5 = 7
7 isn't divisible by 3, so neither is 183490. (Makes sense, only 2 less than the other example.)
This works for any integer.
JK_NC · 1 points · Posted at 04:42:56 on February 14, 2016 · (Permalink)
If you add the individual numbers in any multiple of 9, it always equals 9.
9x3= 27. 2+7=9.
9x11=99. 9+9=18. 1+8=9
Andykbrown · 1 points · Posted at 04:42:56 on February 14, 2016 · (Permalink)
2 simple facts:
Everything multiplied by 9 adds up to 9. 9(9)=81 8+1=9, this works no matter how high you go. 9(3393)= 30537 3+5+3+7=18 1+8=9
Also the numbers between squared number increase like so
1(1)=1 2(2)=4 3(3)=9 4(4)=16 the difference between these numbers is 1 then 3 then 5 then 7 and so on, this will always increase in this pattern.
InverseCascade · 1 points · Posted at 04:43:11 on February 14, 2016 · (Permalink)
There are different sizes of infinity and some are bigger than others.
Nicepotato · 1 points · Posted at 05:34:59 on February 14, 2016 · (Permalink)
How so ?
InverseCascade · 1 points · Posted at 05:40:39 on February 14, 2016 · (Permalink)*
The smallest infinity is the set of whole numbers going upwards forever. It's called accountable infinity. The set of all real numbers (the number line) is bigger than that. You can make even larger infinities by combining infinite sets in a certain way. It's called a power set. All of this was first discovered by Cantor. He went insane after discovering it because mathematicians during his time didn't accept it, even though he had solid proof of what he was saying. There is a way of determining the relative size of different sets (finite or infinite). You can say that two sets are the same size if you can make a 1 to 1 correspondence between all the elements of the two sets and there are none left over. One is larger than the other if there are some elements left over in the larger set after you have accounted for all the elements in the smaller set.
Shiroi_Kage · 1 points · Posted at 04:43:39 on February 14, 2016 · (Permalink)
0.99 repeating is equal to 1.
MrMeow251 · 1 points · Posted at 04:43:40 on February 14, 2016 · (Permalink)
0!=1
glberns · 1 points · Posted at 04:44:14 on February 14, 2016 · (Permalink)
The Four Color Theorem. If you wish to color a map so no two contiguous regions have the same color, you'll only need 4 colors.
FrustratedInterested · 1 points · Posted at 04:45:31 on February 14, 2016 · (Permalink)
There are so many different permutations (orderings) a 52 card playing deck that a) it's extremely unlikely that a sufficiently shuffled deck has ever resulted in the same one in human history and b) they out number the stars in the observable universe.
fuzzycuffs · 1 points · Posted at 04:45:41 on February 14, 2016 · (Permalink)*
The Steiner Probability Theorem:
He was nominated for a Fields Medal for his work in probability theory.
luckytopher · 1 points · Posted at 04:46:40 on February 14, 2016 · (Permalink)
11 times any 2-digit number is the first digit of the 2-digit, then the sum of the 2 digits, then the second digit of the 2-digit.
Such as: 11 x 45 = 4 (first), 9 (4+5), and 5 (second) -> 495.
[deleted] · 1 points · Posted at 04:46:52 on February 14, 2016 · (Permalink)
[deleted]
Vortico · 1 points · Posted at 06:44:02 on February 14, 2016 · (Permalink)
An element is either in the set or it isn't. There's no time dependence.
darkenhand · 1 points · Posted at 04:47:53 on February 14, 2016 · (Permalink)
Reason why 2=1 and why it's not.
loozid · 1 points · Posted at 08:32:33 on February 14, 2016 · (Permalink)
reason why 3=4 and it's not! HAHAHA!
Pikpik07 · 1 points · Posted at 04:48:01 on February 14, 2016 · (Permalink)
10000/9801 = 1.01020304050607080910111213... And so on. I believe these are called "designer decimals".
KazumaDuy · 1 points · Posted at 04:48:09 on February 14, 2016 · (Permalink)
There are about 370 ways to price the Pythagorean Theorem
papi617 · 1 points · Posted at 04:48:26 on February 14, 2016 · (Permalink)
12=1
112 =121
1112 =12321
11112 =1234321
...
1111111112 =12345678987654321
Snoochey · 1 points · Posted at 04:48:27 on February 14, 2016 · (Permalink)
Not the coolest but pretty neat. The 9 times tables are pretty easy to remember. If you're wondering if your answer is right, just add up the answer's digits and if you get 9 or a number divisible by 9 then you're probably on the right track.
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)
...
9 x 37 = 333 (3 + 3 + 3 = 9)
...
9 x 237 = 2,133 (2 + 1 + 3 + 3 = 9)
...
9 x 3586 = 32,274 (3 + 2 + 2 + 7 + 4 = 18; 18 is divisible by 9)
Nine is also pretty cool when dividing!
9 / 9 = 1
8 / 9 = 0.8888_
7 / 9 = 0.7777_
6 / 9 = 0.6666_
I'm sure you see what I'm getting at.
Here's one more cool "9 fact". If you multiply anything by a number which each digit is 9 the answer is very simple.
9 x 999 = 8991 (9 x 9 = 81, add the 2 remaining 9s in the middle of the 81)
7 x 999,999 = 6,999,993 (7 x 9 = 63, add the 5 remaining 9s in the middle of the 63)
4 x 999,999,999,999,999 = 3,999,999,999,999,996 (4 x 9 = 36, add the 14 remaining 9s in the middle of the 36)
I believe that part only works until 10 though. For instance:
21 x 9,999 = 209,979 (21 x 9 = 189; same procedure doesn't work)
Dirty-Freakin-Dan · 1 points · Posted at 04:49:11 on February 14, 2016 · (Permalink)
I was able to replicate this illusion with some java code.
The cool part is that I used a sine function to get the balls moving in a smooth back and fourth motion.
Then for each new ball I added, I incremented the starting position and angle by equal amounts (30 degrees).
It just sort of fell into place and made a circle. I love working with sine to see all the ways it can be used with circles
[deleted] · 1 points · Posted at 14:43:57 on February 14, 2016 · (Permalink)
Would love to see the code for that.
Dirty-Freakin-Dan · 1 points · Posted at 17:39:42 on February 14, 2016 · (Permalink)
You can find it here
If you want to run it, you'll need to download textpad and use that. Version 8 should be able to compile and run java code as soon as you install it.
Make sure both files are saved in the same location
[deleted] · 1 points · Posted at 14:43:59 on February 14, 2016 · (Permalink)
Would love to see the code for that.
[deleted] · 1 points · Posted at 04:50:02 on February 14, 2016 · (Permalink)
The Fibonacci Series can be used to roughly convert between kilometers and miles
1, 1, 2, 3, 5, 8, 13...
1 mile = 2 kilometers
2 miles = 3 kilometers
3 miles = 5 kilometers
5 miles = 8 kilometers
8 miles = 13 kilometers...
Brocktoon_in_a_jar · 1 points · Posted at 04:50:15 on February 14, 2016 · (Permalink)
congruent parts of congruent triangles are congruent
Brocktoon_in_a_jar · 1 points · Posted at 04:50:15 on February 14, 2016 · (Permalink)
congruent parts of congruent triangles are congruent
eskuvai · 1 points · Posted at 04:50:35 on February 14, 2016 · (Permalink)
There are shapes with finite area and infinite perimeter
BurtaciousD · 1 points · Posted at 04:51:22 on February 14, 2016 · (Permalink)
I always thought it was interesting that pi is calculated to such extreme precision as the infinite sum (from n=0) of 4*(-1)n /(2n+1). Learned it in AP Calc, still fascinated by it. Also, makes integration and summation a whole lot easier than if we didn't have a pi constant.
immortalalphoenix · 1 points · Posted at 04:51:31 on February 14, 2016 · (Permalink)
1+1+1x0=2
tylerbird · 1 points · Posted at 04:52:03 on February 14, 2016 · (Permalink)
I'm horrible at explaining but:
If you double a number and add one to it. Then add that number to the original numbers square, you get the square of the next number.
Example: let's say you wanna know the square of 26. 25x2= 50. 50+1=51. 51+525=576.
So I think it would be (x-1)2+(2x-1)=x2. I haven't taken math in a while, but I remember that fact.
Djperkoff · 1 points · Posted at 04:52:37 on February 14, 2016 · (Permalink)
1111x1111=1234321 and so on.
Dissessence · 1 points · Posted at 04:52:44 on February 14, 2016 · (Permalink)
0.9999(repeating) = 1 And not just through rounding
9/9 = 1
1/9 = 0.1111(repeating)
(9)(0.1111(repeating)) = 0.9999(repeating) = 9/9 = 1
AllTheMegahertz · 1 points · Posted at 04:52:55 on February 14, 2016 · (Permalink)
Most numbers have the digit '3' in it.
ThumperTriple · 1 points · Posted at 04:52:56 on February 14, 2016 · (Permalink)
epi*i + 1 = 0
Pretty mind boggling.
[deleted] · 1 points · Posted at 04:53:34 on February 14, 2016 · (Permalink)
There is no largest number expressible in nine words because it would be smaller than the largest number expressible in nine words plus one.
ksiyoto · 1 points · Posted at 04:53:39 on February 14, 2016 · (Permalink)
If you have two fractions with different denominators, and you want to find a fraction in between the two, you can just add the numerators together and the denominators together.
Example: 5/7 and 64/73---> 69/80 would be in between those two.
aerovistae · 1 points · Posted at 04:53:42 on February 14, 2016 · (Permalink)
I discovered this
http://math.stackexchange.com/questions/1338059/why-are-there-palindromic-subsequences-at-random-among-this-sequence
[deleted] · 1 points · Posted at 04:53:52 on February 14, 2016 · (Permalink)
Zipfs law
luckytopher · 1 points · Posted at 04:54:40 on February 14, 2016 · (Permalink)
The integral of ex is equal to the function of un.
ginkomortus · 1 points · Posted at 05:11:27 on February 14, 2016 · (Permalink)
Hell yeah it is.
[deleted] · 1 points · Posted at 04:55:41 on February 14, 2016 · (Permalink)
Stretching a thin piece of iron until it breaks will cause it to break at a 45 degree angle.
KDizzleTheBigSizzle · 1 points · Posted at 04:56:01 on February 14, 2016 · (Permalink)
I'm pretty late so I bet this will get buried, but I think it's cool how the different between subsequent perfect squares can be modeled by the equation 3+2n.
For example, diff of 1 and 4 is 3
4 and 9 is 5
9 and 16 is 7
And so on and so forth... Idk maybe that a widely known thing but it's just something I realized awhile back
ayyyyytacobell · 1 points · Posted at 04:56:29 on February 14, 2016 · (Permalink)
The derivative of ex = ex. I don't feel like typing out the proof for it because I'm on mobile (also why the formatting is weird) but it's super cool that the derivative, which observes the slope of a functuon, is itself. So, if you were to map out the change in the slope of it, you would just graph it again. This blew my mind when I first learned it.
turkeypants · 1 points · Posted at 04:56:49 on February 14, 2016 · (Permalink)
Once you get your math credits out of the way in college, YOU NEVER HAVE TO TAKE MATH AGAIN FOR THE REST OF YOUR LIFE. It's glorious!
TheFAPnetwork · 1 points · Posted at 04:57:54 on February 14, 2016 · (Permalink)
11:15, restate my assumptions: 1. Mathematics is the language of nature. 2. Everything around us can be represented and understood through numbers. 3. If you graph these numbers, patterns emerge. Therefore: There are patterns everywhere in nature.
Midas_Warchest · 1 points · Posted at 04:58:59 on February 14, 2016 · (Permalink)
Russian hand method to multiply 9 by [1-9]. Put out your hands so you see all 10 fingers. To multiply 9 by 2 put down your ring finger on your left hand (basically count from the left counting each finger as 1 spot). To the left of the ring finger is one finger so the 10's place is one. To the right of the downed finger are eight fingers to the 1's place is 8. 9 * 2 = 18. For 9 x 7 put out your hands and count your fingers from the left until you reach the 7th one (the right index finger). Put that finger down. To the left of the downed finger are 6 fingers so the 10's spot is 6. To the right of the downed finger are 3 fingers so the 1's spot is 3. 9 * 7 = 63.
hyperbolicuniverse · 1 points · Posted at 04:59:23 on February 14, 2016 · (Permalink)
0! =1! for no reason other than convention.
Vortico · 1 points · Posted at 06:35:51 on February 14, 2016 · (Permalink)
Well, it's a natural extension of repeated multiplication of the first n whole numbers. 1 is the multiplicative identity, so an empty product should definitely be 1 by convention. This makes computing binomials and stuff a lot cleaner.
hyperbolicuniverse · 1 points · Posted at 14:48:49 on February 14, 2016 · (Permalink)
Yes. I understand the necessity. It just always bugged me that it it holds up for convenience.
saltlife72 · 1 points · Posted at 05:01:35 on February 14, 2016 · (Permalink)
I'm not sure if this counts as math but there's a common misconception that cycling anything that can only yield 2 possible answers an even number of times will always result in a 50/50 draw, when in reality there's just as much of a chance for the results to be 100/0 or 60/40 as for the latter.
An extraordinarily large amount of people I ask about this seem to think that statistics such as those are set in stone.
crusoe · 1 points · Posted at 05:36:11 on February 14, 2016 · (Permalink)
Right. But the chance ifa sequence diverging more and more from average as it co tinues becomes less and likely. Regression to the mean.
saltlife72 · 1 points · Posted at 10:05:35 on February 14, 2016 · (Permalink)
True. But no matter how you look at it, flipping a coin 10 times doesn't guarantee 5 heads and 5 tails. Then again, statistics rarely guarantee anything.
Thenidhogg · 1 points · Posted at 05:01:37 on February 14, 2016 · (Permalink)
Some infinite sequences are larger than others.
Vortico · 1 points · Posted at 06:31:44 on February 14, 2016 · (Permalink)
What do you mean? There are transfinite sequences, but when you hear the word "sequences" you usually mean a countably long list, which are all the same size.
Thenidhogg · 1 points · Posted at 14:28:26 on February 14, 2016 · (Permalink)
I mean that an infinite sequence of whole numbers will be larger than an infinite sequence of odd numbers, but theyre still both infinite
Vortico · 1 points · Posted at 18:43:39 on February 14, 2016 · (Permalink)
The two sequences you gave are actually the same size since there is a bijection between the whole numbers and odd numbers. To me, this is perhaps more bizarre than infinite sequences having different sizes.
Thenidhogg · 1 points · Posted at 20:01:38 on February 14, 2016 · (Permalink)
1,2,3,4,5... 1,3,5,7,9...
Both infinite, but one is larger
That's all i got, I do philosophy, not math.
Vortico · 1 points · Posted at 20:29:08 on February 14, 2016 · (Permalink)
You can only put a finite number of elements between your first ellipsis. Otherwise, since all elements in a sequence have an index, what index would the second 1 be? (It must be an integer.) Since there is a one-to-one association between the elements in a sequence and their index, all sequences have the same number of elements as the set of positive integers.
Thenidhogg · 1 points · Posted at 21:51:16 on February 14, 2016 · (Permalink)
Well done, but i wasn't talking about punctuation
Vortico · 1 points · Posted at 00:17:45 on February 15, 2016 · (Permalink)
I wasn't either. You've given a sequence that you claim to be larger than the sequence of positive integers, by stating that there are an infinite number of elements, and then 1, 3, 5, etc. You can't do that as explained above, so your sequence is ill-defined.
Yosepmcsilky · 1 points · Posted at 05:02:10 on February 14, 2016 · (Permalink)
Math is an example of mankinds ability to create perfection
MT_Flesch · 1 points · Posted at 05:11:25 on February 14, 2016 · (Permalink)
math is mankind's ability to observe and define perfection. perfection already exists
Yosepmcsilky · 2 points · Posted at 05:17:23 on February 14, 2016 · (Permalink)
Perfection in the way of mathematics does not occur in nature, right angles, perfect circles, all examples of things that do not occur naturally
[deleted] · 1 points · Posted at 05:02:29 on February 14, 2016 · (Permalink)
You can rearrange the digits of any number divisible by three into combination and the result is divisible by 3.
153 ... 531 .... 513.
13419 ..... 91431 .... 31149 .... 11439 all divisible by 3
BrawlinStalin · 1 points · Posted at 05:03:44 on February 14, 2016 · (Permalink)
ei π = 1
nardawg66 · 1 points · Posted at 05:05:09 on February 14, 2016 · (Permalink)
ei*π +1 = 0
[deleted] · 1 points · Posted at 05:07:30 on February 14, 2016 · (Permalink)
The Banach-Tarski Paradox.
Simply put: given any object, you can take something out of that object, and still have the original with something left over. Vsauce did a really cool video on it a while back.
crusoe · 1 points · Posted at 05:34:40 on February 14, 2016 · (Permalink)
This only works for infinitely fine sets. Real matter is made of atoms so you can't use this to duplicate matter...
KillMeNow35 · 1 points · Posted at 05:07:39 on February 14, 2016 · (Permalink)
69 is still 69 when viewed upside down. Not math but still numbers.
rolledupdollabill · 1 points · Posted at 05:08:00 on February 14, 2016 · (Permalink)
if you sum all the numbers to 10 you get 55
if you sum all the numbers to 100 you get 5050
if you sum all the numbers to 1000 you get 500500
if you sum all the numbers to 10000 you get 50005000
every time you add a zero add a zero :)
matadata · 1 points · Posted at 05:08:13 on February 14, 2016 · (Permalink)*
Everything travels through space-time at the speed of c (299 792 458 m/s), yet quantum mechanics allows 2 particles to instantly react to each other from any distance.
Thebacklash · 1 points · Posted at 05:08:44 on February 14, 2016 · (Permalink)
I remember hearing you experience something that is "One in a million" type experience once every 3 months on average.
_Psyki · 1 points · Posted at 05:09:31 on February 14, 2016 · (Permalink)
Fermat's Last Theorem, one of the most famous problems in maths that took hundreds of years to solve, was one of many scribblings in a textbook by French Mathematician Pierre de Fermat. He proposed his theorem not long before he died, along with a line to the effect of "I have a wonderful proof, but I do not have enough space to write it down". I like to think that he never even thought that he had proven his conjecture and was just an early troll.
10028ar · 1 points · Posted at 05:09:42 on February 14, 2016 · (Permalink)
122=144 212=441
132=169 312=961
Discovered this myself.
RippyTheGator · 1 points · Posted at 05:10:09 on February 14, 2016 · (Permalink)
Using maxwells equations to extrapolate the speed of light has always got me. First time I saw the derivation I was pretty mind blown.
fb3playhouse · 1 points · Posted at 05:10:22 on February 14, 2016 · (Permalink)
Multiplying nines on my hands :) http://m.wikihow.com/Remember-the-9's-in-Multiplication-Using-Your-Hands
Cri5pyM1lk · 1 points · Posted at 05:10:40 on February 14, 2016 · (Permalink)
111111111 x 111111111 = 12345678987654321
SnapKreckelPop · 1 points · Posted at 05:10:51 on February 14, 2016 · (Permalink)
that any two digit number equals 9.
ex.: 69.. 6+9=15.. 1+5=6.. 15-6=9. or 77. 7+7=14.. 1+4=5.. 14-5=9.
Pure Magic.
kajorge · 1 points · Posted at 05:11:06 on February 14, 2016 · (Permalink)
Here's one I learned recently:
Take a number, say 6, and find both its square and its cube and concatenate them (put them together). So we have 62 = 36, 63 = 216 so our result is 36216. This number has one 1, one 2, one 3, and two 6's.
How many numbers are there that when you do this operation, your result has all the numbers 0 through 9 repeated only once?
The answer is only one! It's 69.
iflylikewilma · 1 points · Posted at 05:11:26 on February 14, 2016 · (Permalink)
Multiples of 9, when added together, make 9. Example: 81(8+1) 72(7+2) 36(3+6)... You might be thinking"what about triple digits?", well... 108(1+0+8) 144(1+4+4) 126(1+2+6)... And so on. Pretty cool! Is there a name for this kind of phenomenon?
escherbach · 1 points · Posted at 05:12:36 on February 14, 2016 · (Permalink)
spelling of parallel is easy to remember if you use 112 = 121
_Psyki · 1 points · Posted at 05:13:04 on February 14, 2016 · (Permalink)
Even if we were to write each digit down on a single (separate) atom, there still would not be enough atoms in the universe to write down a googolplex.
TheHumanGuitarman · 1 points · Posted at 05:13:17 on February 14, 2016 · (Permalink)
Benford's law. Naturally occurring numbers are more likely to begin with smaller digits than larger digits. For example, if you were to measure the length of a random river, there would be about a 30% chance the leading digit of your measurement would be a 1, and less than a 5% chance that it would be a 9. However, in order for the law to work numbers must be from some type of distribution that crosses many orders of magnitude (1,10,100,1000, etc.), so people's height in feet or meters wouldn't work, but height in millimeters would. Additionally, the numbers cant be normally distributed, such as IQ scores. (normal distributions have a symmetric bell shaped curve, in which the peak is equal to the median, mode, and average.) And this law is also used as evidence for fraudulent behavior.
https://en.wikipedia.org/wiki/Benford%27s_law
rbaltimore · 1 points · Posted at 14:12:57 on February 14, 2016 · (Permalink)
Do you have any examples where this was successfully used to detect a fraud of some sort?
TheHumanGuitarman · 2 points · Posted at 23:44:32 on February 15, 2016 · (Permalink)
this article talks about one particular case
https://utica.edu/academic/institutes/ecii/publications/articles/BA3731B0-E34E-D616-13423E6271970395.pdf
rbaltimore · 2 points · Posted at 13:27:38 on February 16, 2016 · (Permalink)
Thanks! That was a surprisingly interesting read!
Arlyn_Aquos · 1 points · Posted at 05:13:18 on February 14, 2016 · (Permalink)
Any multiple of 9 (18, 27, 32, ect.) when added to itself to 1 digit always equals 9.
9x19=171 ~ 1+7+1=9
9x9834=88506 ~ 8+8+5+0+6=9
Always help me see if a number was divisible by 9 or 3
ExploitedToast · 1 points · Posted at 05:13:24 on February 14, 2016 · (Permalink)
Figured this one out when I was bored in High School Algebra: ((X+1)2)-(X2)= X+(X+1)
Example: the difference between four squared and five squared is 4+5
blue_no_red_ahhhhhhh · 1 points · Posted at 05:13:30 on February 14, 2016 · (Permalink)
4 out of five dentists prefer Dentine.
drazerclaw · 1 points · Posted at 05:14:08 on February 14, 2016 · (Permalink)
ei*pi= -1
geosquirrel1 · 1 points · Posted at 05:14:54 on February 14, 2016 · (Permalink)
Zeno's paradox. Basically says that, if you were to half the distance between you and a wall in front of you an infinite amount of times, you'd never reach the wall, thanks to numbers being infinite. The wiki article explains it much more eloquently.
KyaniteArcher · 1 points · Posted at 05:15:10 on February 14, 2016 · (Permalink)
12345679 X 54 = 666,666,666
I just blew your mind.
ekazu129 · 1 points · Posted at 05:15:11 on February 14, 2016 · (Permalink)
Nothing especially cool but something I noticed, any number divisible by 9 that doesn't have more than one digit as 9, the digits will add up to 9.
This pattern remains unbroken until 99, which of course adds up to thirty bazillion.
Tw_raZ · 1 points · Posted at 05:15:35 on February 14, 2016 · (Permalink)
rad(2) is the approximate ratio for scaling things on paper. Eg. 8.5"/11" is ~1:rad(2)
Vortico · 2 points · Posted at 06:20:14 on February 14, 2016 · (Permalink)
The relationship between A4 and A3 paper sizes (more common outside the US) has the exact ratio of sqrt(2). https://en.wikipedia.org/wiki/File:A_size_illustration2.svg
tasty-fish-bits · 1 points · Posted at 05:15:48 on February 14, 2016 · (Permalink)
ej*pi = -1.
Blows my mind every single time I do the derivation / expansion.
princessbynature · 1 points · Posted at 05:16:42 on February 14, 2016 · (Permalink)
Some infinities are bigger than other infinities. There are an infinite infinities also.
pound30 · 1 points · Posted at 05:16:56 on February 14, 2016 · (Permalink)
I must not be that smart but I guess multiplying 11 by any double digits you add the double digits and put it in the middle. If its over 10 you carry the one.
ex: 11 x 23 = 253
crusoe · 2 points · Posted at 05:30:44 on February 14, 2016 · (Permalink)
Not if they are parallel. Or in 3 dimensions. Now if you mean non euclidean space, then in spaces with positive curvature even parallel lines will cross.
pound30 · 1 points · Posted at 05:38:44 on February 14, 2016 · (Permalink)
Well I was going to bring that up but I thought it could be somewhat confusing.
Apostropherad · 1 points · Posted at 05:17:48 on February 14, 2016 · (Permalink)
In the 9 times table if you write it out as follows the numbers on either side of the answers runs consecutively from top to bottom and back up again 0-9 then 0-9 again 9x1= 09 9x2= 18 9x3= 27 9x4= 36 9x5= 45 9x6= 54 9x7= 63 9x8= 72 9x9= 83 9x10=90
I only learnt this the other day.
00squirrel · 1 points · Posted at 05:18:01 on February 14, 2016 · (Permalink)
Gabriel's Horn. A true mathematical paradox--structure with infinite surface area and finite volume--and something those with only a basic understanding of calculus and understand. https://en.wikipedia.org/wiki/Gabriel%27s_Horn
rbaltimore · 1 points · Posted at 14:10:15 on February 14, 2016 · (Permalink)
TIL that I've forgotten most of the calculus I learned in high school.
KellanM · 1 points · Posted at 05:19:11 on February 14, 2016 · (Permalink)
Ziph's law... You will thank me later when you look it up.
Supersnoop25 · 1 points · Posted at 05:20:09 on February 14, 2016 · (Permalink)
.99 repeating is equal to 1... 1/3 is .33reapting and 1/3 times 3 is 1 so .33 repeating times 3 is 1
Latholan · 1 points · Posted at 05:21:00 on February 14, 2016 · (Permalink)
There are shapes other than circles which have a constant width. One example is the curvilinear triangle.
http://www.cut-the-knot.org/do_you_know/cwidth.shtml
Strangely this shape could be used to drill a nearly square hole.
ThePharros · 1 points · Posted at 05:24:17 on February 14, 2016 · (Permalink)
This may be more physics-based than mathematical, but I've found it pretty interesting that nature itself will use the hyperbolic cosine function to naturally minimize the gravitational potential energy. These are called catenaries and can be seen by resting a string that is fixed at both ends. It can also be seen if you take two rings dipped into bubble soap, put them together, then slowly pull them away as the soap film creates the hyperbolic cosine. :)
Tera_GX · 1 points · Posted at 05:24:59 on February 14, 2016 · (Permalink)
The basic multiplication table for 9 inverses itself halfway through. As in 18 (9×2) is reverse of 81 (9×9). It also increments the first digit by +1 and the second digit by -1. So easy to understand nines.
9×1= 09
9×2= 18
9×3= 27
9×4= 36
9×5= 45
9×6= 54
9×7= 63
9×8= 72
9×9= 81
9×10=90
escherbach · 1 points · Posted at 05:26:36 on February 14, 2016 · (Permalink)
You can make two balls from one just by rotations and translations
https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Apps4Life · 1 points · Posted at 05:27:44 on February 14, 2016 · (Permalink)
If you multiply 'e' by itself imaginary-pi times, the answer is -1
midknightdragon · 1 points · Posted at 05:28:16 on February 14, 2016 · (Permalink)
Almost all numbers contain the digit 3.
Also if you take a mobius strip(a 1d shape) and combine it with another you get a klien bottle which is a 4d shape.
Vortico · 1 points · Posted at 06:13:39 on February 14, 2016 · (Permalink)
A Klein bottle is a 2D surface, since it is the topological product of a Mobius strip and a line segment, which are both 1D.
midknightdragon · 1 points · Posted at 07:48:08 on February 14, 2016 · (Permalink)
But it can only exist in 4d space.
Vortico · 1 points · Posted at 07:51:25 on February 14, 2016 · (Permalink)
Right, 4 is the lowest dimension in which an embedding exists.
HCPwny · 1 points · Posted at 05:29:07 on February 14, 2016 · (Permalink)
If you take an infinite number of numbers, and then remove all of the even numbers, you would still have an infinite number of numbers.
It's why the idea of infinite universes is so overstated. Just because an infinite number of universes could potentially exist, not every possible variation necessarily has to exist.
freakmad · 1 points · Posted at 05:29:15 on February 14, 2016 · (Permalink)
I found the Euler's identity pretty cool: ei π = -1.
Lunchboxzez1229 · 1 points · Posted at 05:29:20 on February 14, 2016 · (Permalink)
Gabriel's Horn: it has infinite surface area, but finite volume.
Volume
Surface Area
MericanCheese · 1 points · Posted at 05:30:02 on February 14, 2016 · (Permalink)
89% of statistics are made up on the spot.
[deleted] · 1 points · Posted at 05:30:26 on February 14, 2016 · (Permalink)
That 6 is afraid of 7 because 7 8 9
greenmeat3 · 2 points · Posted at 06:00:32 on February 14, 2016 · (Permalink)
And because 7 is a registered 6 offender.
Benjo_ · 1 points · Posted at 05:30:45 on February 14, 2016 · (Permalink)
If you differentiate the volume of a sphere formula you get the surface area formula. Similarly, if you differentiate the area of the circle formula you get the circumference formula
Vortico · 1 points · Posted at 06:10:27 on February 14, 2016 · (Permalink)
You can also integrate sqrt(1 - A(z)2) from -1 to 1 where A(z) is the area of a circle to get the volume of a sphere. Continue doing this with A(z) being the "n-volume" of the previous step to get the volume of an n-sphere.
Raffix · 1 points · Posted at 05:31:30 on February 14, 2016 · (Permalink)*
Find any 4 consecutive integers. Multiply the smallest with the biggest and you'll always get the multiple of the other two minus 2.
4 * 7 = (5 * 6) - 2
9 * 12 = (10 * 11) - 2
2865 * 2868 = (2866 * 2867) - 2
This works with ANY 4 consecutive integers even the biggest integers you can think of or with negative integers, even with zero (-2, -1, 0, 1 -> [-2 * 1] = [-1 * 0] - 2). This little trick helped me remember that 6 * 9 = 54 and 7 * 8 = 56 which I always confused in my multiple tables as a kid.
SuperSocrates · 1 points · Posted at 05:31:40 on February 14, 2016 · (Permalink)
There exist at least two people in Paris (or any city with over ~1 million people people) that have exactly the same number of hairs on their head.
Vortico · 1 points · Posted at 06:06:22 on February 14, 2016 · (Permalink)
I love this one. It's kinda like the pigeonhole principal but with an assumption that most people have less than 1 million hairs on their head.
Cajunbot · 1 points · Posted at 05:32:00 on February 14, 2016 · (Permalink)
Here's one: 111,111×111,111 =12,345,654,321
buckeyebearcat · 1 points · Posted at 05:32:05 on February 14, 2016 · (Permalink)
you can have a line with a length of one with a point on that line that divides the line segment into two parts and the ratio of the smaller part to bigger part is equal to ratio smaller part to both parts added together. Meet PHi http://www.goldennumber.net/
Paradoxou · 1 points · Posted at 05:33:33 on February 14, 2016 · (Permalink)*
If you add all the 'unique' romans numbers except for 1000 (M) it equals 666.
I(1) + V(5) + X(10) + L(50) + C(100) + D(500) = 666
zerohootz · 1 points · Posted at 05:34:05 on February 14, 2016 · (Permalink)
Every number you add the letters to will always end back at 4.
Exp: 10 is 3, 3 is 5, and 5 is 4. And 4 is the magic number
[deleted] · 1 points · Posted at 05:34:10 on February 14, 2016 · (Permalink)
I don't know why I expected to understand any of these fine(I'm guessing) examples..
ZinMan · 1 points · Posted at 05:34:38 on February 14, 2016 · (Permalink)
3-4-5 all right triangles
iluvgrannysmith · 1 points · Posted at 05:57:16 on February 14, 2016 · (Permalink)
5-12-13. There are infinirelt many special triangles. These are the two most prominent on standardized tests though
ZinMan · 2 points · Posted at 19:27:29 on February 14, 2016 · (Permalink)
right triangles, two sides 3, 4 the hypotenuse is always 5.
iluvgrannysmith · 1 points · Posted at 20:38:49 on February 14, 2016 · (Permalink)
Yeah, if you have a triangle whose sides are in the ratio 5-12-13, then it will also be a right triangle:). Also, 7, 24, 25
CaresLessEveryday · 1 points · Posted at 05:35:56 on February 14, 2016 · (Permalink)
That mathematicians can simply say "but if we simply do this, like this instead" or " if we cheat a bit" to explain/prove theories and no one will call them out on that bullshit. This happens in mathematics too often and people are hailed as a genius when they do. If you can't prove or disprove a mathematical equation without changing the equation to get the answer you want, you didn't prove shit.
iluvgrannysmith · 1 points · Posted at 05:55:06 on February 14, 2016 · (Permalink)
Sounds like you had a teacher that did some magic
Autarch_Kade · 1 points · Posted at 05:36:49 on February 14, 2016 · (Permalink)
5/7 is perfect
ADSRelease · 1 points · Posted at 05:37:00 on February 14, 2016 · (Permalink)
There are cooler ones, but I always loved the simplicity of how anything over equal digits of 9s is just 0.(the number, repeating).
6/9=0.6666...
54/99=0.54545454...
743/999=0.743743743743...
Viddog4 · 1 points · Posted at 05:37:40 on February 14, 2016 · (Permalink)
If you add every number together you get infinity!
Vortico · 1 points · Posted at 06:01:47 on February 14, 2016 · (Permalink)
Well, this is at least more accurate than the people saying that the natural numbers sum to -1/12.
overconvergent · 1 points · Posted at 06:02:02 on February 14, 2016 · (Permalink)*
Edit: I can't read.
Viddog4 · 1 points · Posted at 06:09:10 on February 14, 2016 · (Permalink)
There are an infinite amount of numbers, so why not?
overconvergent · 1 points · Posted at 06:10:56 on February 14, 2016 · (Permalink)
lol ignore me... I was responding to all the -1/12 folks and didn't even make it to the end of your sentence...
GuyNamedWhatever · 1 points · Posted at 05:38:26 on February 14, 2016 · (Permalink)
Tupper's self-referential formula. Basically its a function that writes itself once graphed. It's k units high on the y-axis, which represents a 543 digit number.
waymorbetter · 1 points · Posted at 05:39:03 on February 14, 2016 · (Permalink)
That I will never enjoy nor have a knack for maths
best-commenter · 1 points · Posted at 05:40:38 on February 14, 2016 · (Permalink)
Russell’s paradox is a set of all things that exclude themselves.
An “everything” bagel is such a paradox.
A bagel cannot have everything on it. The bagel can have all the cream cheese, tomatoes, burnt tires, flowers, broken glass, Schrodinger’s Cat, oil fires, Miss Universe, the concept of hope, Whitey Bulger, and on and on until everything definable in the universe but it cannot also be on itself.
gotsanity · 1 points · Posted at 05:41:38 on February 14, 2016 · (Permalink)
That I really suck at math compared to all of these people
Iron1Man · 1 points · Posted at 05:43:24 on February 14, 2016 · (Permalink)
There is more than one kind of infinity.
Kindofaniceguy · 1 points · Posted at 05:43:37 on February 14, 2016 · (Permalink)
A gogholplex is such a high number, that it is physically impossible to represent it outside of scientific notation.
GroundhogExpert · 1 points · Posted at 05:43:43 on February 14, 2016 · (Permalink)
Science, as an exploration, has a destructive nature. New science will replace and disprove previous science. Mathematics is eternal and purely additive. If it's ever mathematically true, it's always true.
LastStar007 · 1 points · Posted at 05:44:36 on February 14, 2016 · (Permalink)
This
OneWhoDoesNotSimply · 1 points · Posted at 05:45:51 on February 14, 2016 · (Permalink)
This squaring trick just kinda popped in my head a couple years ago.
So, say you know one square (in this example I'll use 12) but you don't know the square above it (in this case 13). So, to figure it out with addition we take 122 (144) add 12 (our original number) then 13 (our next number) which'll give us 169. Which just so happens to be 132 .
And, this of course can be done in a sequence. 169 + 13 +14 = 196 = 142 196 + 14 + 15 = 225 = 15 2 225 + 15 + 16 = 256 = 162 Etc.
Manta209 · 1 points · Posted at 05:49:27 on February 14, 2016 · (Permalink)
If you add up the digits of the number that's being multiplied by 11 and stick it in the middle of said numbers, you'll get the answer. Examples: 11x23 2+3=5 So... 11x23= 253
11x53 5+3=8 11x53=583
Neelshah0123 · 1 points · Posted at 05:50:03 on February 14, 2016 · (Permalink)
The sum from n = 1 to infinity of 1/(n2) where n are the natural numbers is equal to pi2 /6.
https://en.wikipedia.org/wiki/Basel_problem
blocker45 · 1 points · Posted at 05:50:05 on February 14, 2016 · (Permalink)
If an equilateral triangle has an area of 1, its height is the fourth root of 3.
Fail_Pedant · 1 points · Posted at 05:50:36 on February 14, 2016 · (Permalink)
https://m.xkcd.com/179/
So much beauty in that equation
elkazay · 1 points · Posted at 05:53:28 on February 14, 2016 · (Permalink)
9-2 = 0.0123456789 or something like that
eric_ja · 1 points · Posted at 05:54:13 on February 14, 2016 · (Permalink)
Not only can we make up a number, i, and define it to be a square root of -1, we need not stop there. We can actually create any number of additional square roots of -1, that are not i or -i. And we need not stop there, either, we can actually create any number of square roots of positive 1, besides 1 and -1. And the resulting algebra, a Clifford algebra is not only sane, but it is actually useful for geometry and physics.
RebeccaAlexander · 1 points · Posted at 05:54:13 on February 14, 2016 · (Permalink)
Among all shapes with the same area circle has the shortest perimeter
NidfridLeoman · 1 points · Posted at 05:54:27 on February 14, 2016 · (Permalink)
The letters in the word circle can be arranged in exactly 360 distinct ways.
egalroc · 1 points · Posted at 05:55:02 on February 14, 2016 · (Permalink)
I am in the center of the universe.
RobDaGinger · 1 points · Posted at 05:55:25 on February 14, 2016 · (Permalink)
The Dragon Curve
Siganid · 1 points · Posted at 05:56:37 on February 14, 2016 · (Permalink)
That mathematics is such an unnecessary thing I can go entire weeks without needing it.
[deleted] · 1 points · Posted at 05:57:06 on February 14, 2016 · (Permalink)
10 / 3 = 3.3~
3.3~ x 3 = 9.9~
Where'd the .1~ go? Shrug.
water_bottle_goggles · 1 points · Posted at 06:05:12 on February 14, 2016 · (Permalink)
Hehehehe nice try :-)
Since 0.999~ = 1
9.9~ = 9 + 0.999~ = 9 + 1 = 10
There is your .1~
TheKinkMaster · 1 points · Posted at 05:57:14 on February 14, 2016 · (Permalink)
I am not a mathematical person, so almost everything in this thread looks like it is in another language.
AmericanBigDog · 1 points · Posted at 05:57:22 on February 14, 2016 · (Permalink)
I think Gabriel's Horn paradox is pretty cool. I would describe it to y'all but that would take a while and Wikipedia does a way better job. So here is the link https://en.wikipedia.org/wiki/Gabriel%27s_Horn . TLDR It is a Theoretical shape that has infinite surface area and a finite volume.
alxnewman · 1 points · Posted at 05:57:28 on February 14, 2016 · (Permalink)
ITT: lay persons trying to understand math over their head ._.
eddmario · 1 points · Posted at 05:58:10 on February 14, 2016 · (Permalink)
The writers of Futurama created a brand new math formula
Turtlebelt · 1 points · Posted at 05:58:37 on February 14, 2016 · (Permalink)
The volume of a hypersphere of diameter n approaches zero as the dimensionality of the sphere approaches infinity.
The volume of a hypercube of width n approaches infinity as the dimensionality of the cube approaches infinity.
This means that if you embed a hypersphere of dimension n inside a hypercube of the same dimension, as you increase the size of n the sphere takes up less and less volume within the cube. The limit of this is an infinite dimension representation where the sphere takes up no room inside the infinitely voluminous cube while having a diameter the same size as the width of the cube.
lintamacar · 1 points · Posted at 05:59:59 on February 14, 2016 · (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
MkLease · 1 points · Posted at 06:00:18 on February 14, 2016 · (Permalink)
You can sing the quadratic formula to the tune of pop goes the weasel
thrylkyl · 1 points · Posted at 09:16:43 on February 14, 2016 · (Permalink)
Do you live in West Michigan?
MkLease · 1 points · Posted at 19:39:29 on February 14, 2016 · (Permalink)
Minnesota actually
mattmaster68 · 1 points · Posted at 06:01:02 on February 14, 2016 · (Permalink)
The square root of 69 is 8 something
yhsanave · 1 points · Posted at 06:04:24 on February 14, 2016 · (Permalink)
Math is the Illuminati https://youtu.be/DfnBW6HvNwM
Sofa__King__Cool · 1 points · Posted at 06:04:32 on February 14, 2016 · (Permalink)
If you add a number and the sum is divisible by 3, then the original number is also divisible by 3. Ex. The sum of the numbers in 1476 are 18. Since 18 is divisible by 3 than so is 1476. 1476/3=491
timeslider · 1 points · Posted at 06:04:52 on February 14, 2016 · (Permalink)
Take any number, lets call it x! :D
x mod 9 = the sum of the digits in x and if x > 10, then those digits added together until x is < 10.
Unless is comes out to zero then the digits add to 9.
Example:
429 MOD 9 = 6 because 4 + 2 + 9 = 15 and 1 + 5 = 6 111 MOD 9 = 3
81 MOD 9 = 0 but the sum is 9
77 MOD 9 = 5 because 7 + 7 = 14 and 1 + 4 = 5
You can round a decimal number to halves, thirds, etc using this formula.
round(x*n)/n
Example:
Let x be 4.3 and we want to round to the nearest 3rd so n = 3.
xn = 4.3(3) = 12.9
We round this like we normally do and get 13
Then we divide by 3 and get 4.3333...
This may seem trivial but if you needed to round to the nearest 16th or something crazy, it makes it a lot easier.
If you use a slight different formula, you can round to the nearest whole number.
round(x/n)*n
Say we wanted to round to the nearest 5th whole number.
Let x = 23.43
n = 5
x/n = 4.686
rounding we get 5
5 * n = 5 * 5 = 25
So 23.43 rounded to the nearest 5 whole number is 25.
I found this most useful for snapping objects to a grid when programming my puzzle game.
Agent_Cookie · 1 points · Posted at 06:05:07 on February 14, 2016 · (Permalink)
0 / 0 can equal anything and everything.
hhuerta · 1 points · Posted at 06:05:28 on February 14, 2016 · (Permalink)
1+1=2 (maybe)
LickedAss420 · 1 points · Posted at 06:06:37 on February 14, 2016 · (Permalink)
MATHEMATICAL!!
jose_conseco · 1 points · Posted at 06:06:39 on February 14, 2016 · (Permalink)
Tautochrone curve.
ToastieCoastie · 1 points · Posted at 06:07:00 on February 14, 2016 · (Permalink)
There's a lot of complex and seemingly unnecessary math required for making the teeth of gears and sprockets.
SLtQKWznKm · 1 points · Posted at 06:07:41 on February 14, 2016 · (Permalink)
0.5 = 1-1+1-1+1-1+1-1+1...
-1/12 = 1+2+3+4+5+6+7+...
DiDalt · 1 points · Posted at 06:07:51 on February 14, 2016 · (Permalink)
99 x 99 = 9801
theMystk · 1 points · Posted at 06:08:04 on February 14, 2016 · (Permalink)*
Fibonacci Sequence to convert km to miles; helped immensely as an American living in Asia
edit: removed redundancies
yarzospatzflute · 1 points · Posted at 06:08:07 on February 14, 2016 · (Permalink)
0.777777... = 7/9
0.67676767... = 67/99
0.567567567... = 567/999
If all the digits to the right of the decimal are repeat, the equivalent fraction is those digits over the same number of 9s.
But there is also a pattern when not all the digits are repeating:
0.123123123... = 123/999 (following the above pattern) 0.123232323... = 122/990 0.123333333... = 111/900
To get the numerator for 0.123232323..., take the digits prior to the point where the repetition begins (in this case, 123) and subtract from it the digits that AREN'T repeating: 123 - 1 = 122.
The denominator will have the same number of digits (3 in this case); the number of 9s will be equal to the number of repeating digits, followed by zeros. In this case, 2 digits are repeating, so two 9s followed by a zero: 990.
Recognizing this pattern helps you quickly figure out that, for example, 0.1234555555... = 11111/90000.
Glenmordor · 1 points · Posted at 06:10:12 on February 14, 2016 · (Permalink)
If you have the sum of all natural numbers to infinity, it is equal to negative 1 over 12. You are only adding positive numbers and end up with a negative.
Kinzuko · 1 points · Posted at 06:10:12 on February 14, 2016 · (Permalink)
You can draw a triangle on a sphere with nothing but right angles.
Edit: after looking through the other responses I feel really dumb x.x
Too_Meta_69 · 1 points · Posted at 06:10:26 on February 14, 2016 · (Permalink)
Fractals, such as the coast line of Britain, have non-integer dimension.
Bonus: If a complex function is once differentiable, it is infinitely differnetiable.
ChipsMakeAMeal · 1 points · Posted at 06:11:22 on February 14, 2016 · (Permalink)
Nothing from nothing leaves nothing.
roseffin · 1 points · Posted at 06:11:44 on February 14, 2016 · (Permalink)
I'm downvoting every post with -1/12 in it. /s
arakys · 1 points · Posted at 06:13:18 on February 14, 2016 · (Permalink)
The sum of all positive integers is -1/12
Explained here
Viking_Lordbeast · 1 points · Posted at 06:13:27 on February 14, 2016 · (Permalink)
ITT: Every Numberphile or Vsauce video topic ever made.
alola78 · 1 points · Posted at 06:13:48 on February 14, 2016 · (Permalink)
111111111 * 111111111=12345678987654321
kkell806 · 1 points · Posted at 06:14:01 on February 14, 2016 · (Permalink)
Tupper's Self-Referential Formula.
https://youtu.be/_s5RFgd59ao
Xiphias_ · 1 points · Posted at 06:15:03 on February 14, 2016 · (Permalink)
Probably waaay late to the party, but the number 6174 has a very interesting property. If you take any 4 digit number where at least 2 non-equal digits, and then rearrange the digits into two numbers, one as big as it can be and one as small as it can be, and then take that difference you get a new 4 digit number. Repeat this process and you'll always end up with 6174 in less than 8 iterations.
Example: 2534. Biggest: 5432, Smallest: 2345. Difference: 5432-2345 = 3087. And repeat no more than 7 times.
Oh and when you have 6174 you're "stuck" since: 7641-1467=6174
This is known as "Kaprekar's constant"
noslenkwah · 1 points · Posted at 06:15:15 on February 14, 2016 · (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
This is not a joke. Dead serious.
[deleted] · 1 points · Posted at 06:15:52 on February 14, 2016 · (Permalink)
If you fold a sheet of paper in half and then that paper in half... and repeated 50 or so more times. The thickness of the paper would reach the moon.
RaoulZDuke · 1 points · Posted at 06:16:24 on February 14, 2016 · (Permalink)
8675309 is prime.
Reverserer · 1 points · Posted at 06:19:37 on February 14, 2016 · (Permalink)
Jenny
Screwnames21 · 1 points · Posted at 06:16:29 on February 14, 2016 · (Permalink)
Simple one, but there's an infinite number of numbers, and in-between numbers(decimals) there's also an infinite number of numbers.
adalab · 1 points · Posted at 06:17:28 on February 14, 2016 · (Permalink)
Doing my 9 times tables on my fingers. I still use it lol.
i_forget_again · 1 points · Posted at 06:17:44 on February 14, 2016 · (Permalink)
Pie r squared is a triangle.
mushrooms_suck · 1 points · Posted at 06:19:16 on February 14, 2016 · (Permalink)
Maybe a pretty well known one but if you want to know a number's square and you know the previous number's square you can add those two numbers together plus the previous square and find the next one.
Example:
You want to find 262
You know that 252 = 625
Add (26+25) + 625 = 676 = 262
I was just sitting in math class one day and it worked every time.
lucien15937 · 1 points · Posted at 06:19:40 on February 14, 2016 · (Permalink)
e ^ (i * pi) + 1 = 0
WR810 · 1 points · Posted at 06:19:52 on February 14, 2016 · (Permalink)
If all the single digits of a number equal a multiple of three, the number is divisible my three without a remainder.
ChaotosTheDark · 1 points · Posted at 06:21:16 on February 14, 2016 · (Permalink)
You can never see the actual edge of an image on a mirrored sphere. A sphere is a 3D representation of an exponential function so the visual 'edge' of the image is just infinitesimal refraction.
jm6492 · 1 points · Posted at 06:22:58 on February 14, 2016 · (Permalink)*
The sum of the natural numbers is -1/12!
https://www.youtube.com/watch?v=w-I6XTVZXww
ParadiseSold · 1 points · Posted at 06:24:26 on February 14, 2016 · (Permalink)
1112 equals 12321. 11112 equals 1234321. 1111111112 equals 12345678987654321.
invalid_usr · 1 points · Posted at 06:24:59 on February 14, 2016 · (Permalink)
I read through a bunch here and didn't find this one.
Using the fibonacci sequence to (roughly) convert miles per hour to kilometers per hour - and vice versa.
The fibonacci sequence is when you take 0 and 1 and add them to get 1. Then take the previous number and add it to the next number.
0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21.
so you end up with a string of numbers like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233
3 miles per hour is 5 km/h, 21mph is 34km/h
Take it a step further. If you wanted to calculate 100mph. It isn't in the sequence BUT you can add existing numbers in the sequence to get 100 and take the numbers next to those - add them up and you get km/h.
So 3+8+89 = 100. The numbers next to those numbers can be added up.
5+13+144 = 162 km/h (100 mphis actually 160KM/h but its close enough.
If you can remember that string of fibonacci sequence, you can do rather quick and get a rough equivalent between the two numbers.
The fibonacci sequence is pretty interesting in of itself and can do a number of things I'm sure I don't know about.
TheNarwhalrus · 1 points · Posted at 06:25:14 on February 14, 2016 · (Permalink)
Jesus Christ.... I thought I was bad at math and after skimming this thread, I KNOW I'm bad at math...
Leporad · 1 points · Posted at 06:26:30 on February 14, 2016 · (Permalink)
You can take one sphere, break it into pieces (5 minimum) and rearrange the pieces to make two identical spheres (the same size as the original).
timpinen · 1 points · Posted at 06:27:46 on February 14, 2016 · (Permalink)
One cool thing I like to share is that there are more irrational numbers between 0 and 1 than there are rational numbers across the whole number line. There are some subtleties about it, but pretty cool none the less
EnkiiMuto · 1 points · Posted at 06:28:11 on February 14, 2016 · (Permalink)
Extremely disappointed the top comment isn't an Absolute Zero-related formula.
funnystuff97 · 1 points · Posted at 06:28:33 on February 14, 2016 · (Permalink)
1 - 1 + 1 - 1 + 1 - 1... = 1/2.
Confused? Numberphile, yo.
carcinoma_kid · 1 points · Posted at 06:29:40 on February 14, 2016 · (Permalink)
Every even number can be expressed as the sum of two primes. There's not really a reason for this but it holds true in every example anyone has ever tested.
KarenPolley · 1 points · Posted at 06:30:12 on February 14, 2016 · (Permalink)
''The guy that proved the existence of irrational numbers was murdered for his finding.''
[deleted] · 1 points · Posted at 06:30:49 on February 14, 2016 · (Permalink)
This thread makes me feel so fucking stupid
ptht3 · 1 points · Posted at 06:30:53 on February 14, 2016 · (Permalink)
I may be a sap, but I find a lot of the group classification theory really cute: https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups
ballerlakers24 · 1 points · Posted at 06:31:29 on February 14, 2016 · (Permalink)
4 Color Theorem with map of the world
Basically, any map can be colored with 4 colors such that locations that share borders don't have the same color
thepopcornwizard · 1 points · Posted at 06:32:48 on February 14, 2016 · (Permalink)
The sum of all natural numbers (1 + 2 + 3 + 4 ... to infinity) is -(1/12)
Source: https://www.youtube.com/watch?v=w-I6XTVZXww
TomatoJoe11 · 1 points · Posted at 06:33:15 on February 14, 2016 · (Permalink)
ei*pi-1=0
fanalin · 1 points · Posted at 08:19:20 on February 14, 2016 · (Permalink)
It's ei*pi+1 = 0 (Euler's identity) Easy to remember by thinking about the unit circle. exipi follows along the unit circle with increasing x, and x=0 and x=2 you are at the 1 (e2ipi=1). For x=1, you have eipi = -1.
tresbizarre · 1 points · Posted at 06:33:40 on February 14, 2016 · (Permalink)
Starting with the 15 trillionth digit of Pi there is a circle shape encoded in zeros and ones.
djf1982 · 1 points · Posted at 06:36:32 on February 14, 2016 · (Permalink)
It'll certainly be in there somewhere......
Along with every number sequence possible.
cbr777 · 1 points · Posted at 06:34:11 on February 14, 2016 · (Permalink)
The fact that 0.(9) = 1.
Call_HoH_SiS · 1 points · Posted at 06:37:40 on February 14, 2016 · (Permalink)
If you think of any two-digit number (eg, 43), add the two numbers that make it up (eg, 4+3=7) and then subtract it from the number you originally had (eg, 43-7=36), you'll get a multiple of 9.
Georgeygerbil · 1 points · Posted at 06:39:24 on February 14, 2016 · (Permalink)
I had a teacher do a proof that proved that 0.99 repeating was exactly equal to 1.
Growing up I always had this assumption that it was an infinitely small step away from 1 while never truly being 1.
j0hnk50 · 1 points · Posted at 06:39:25 on February 14, 2016 · (Permalink)
to find half of any fraction simply double the denominator. quick! what is half of 7/16?
mag0802 · 1 points · Posted at 06:39:43 on February 14, 2016 · (Permalink)
The number of possible digits between 0 and 1 and 1-Infiniti are not the same. The number of digits between 0-1 is more - a term referred to as aleph infiniti.
muzau · 1 points · Posted at 06:39:44 on February 14, 2016 · (Permalink)
Given that x is equal to four,
x1 is a line 4 units long, one dimension. x2 (x squared) is a square, each edge 4 units long. two dimensions. x3 (x cubed) is a cube, each edge also measuring 4 units long. three dimensions.
So what happens at x4? or x100. Just the idea that math allows for these crazy unfathomable constructs to exist s mind blowing.
0ne_Winged_Angel · 1 points · Posted at 06:40:31 on February 14, 2016 · (Permalink)
114 is the only square number in the Fibonacci Sequence (excluding 02 = 0 and 12 = 1), and it's the 12th number in the sequence.
tjpoe · 1 points · Posted at 06:40:58 on February 14, 2016 · (Permalink)
That due to the nature of the random and infinite length of Pi, every number you'll ever see will be in in there. Your phone number, your social security number, your birthday and your death date.
OneCircleSquared · 1 points · Posted at 06:41:20 on February 14, 2016 · (Permalink)
Given that the basic trigonometric functions sin(x) and cos(x) have derivatives that are cyclical in nature, computing their large-numbered derivatives is trivial.
Given f(x) = sin(x), then:
So, every nth derivative is equal to the (n-4)th derivative, with the exception of the first 3.
Stated more generally, fn (x) = fn%4 (x).
For example, the 16,000,001st derivative of sin(x) is cos(x), because 16,000,001 % 4 = 1, so we look at the first derivative.
This makes chain rule / integration by parts much easier if you have a large derivative.
isaidit_imeantit · 1 points · Posted at 06:42:48 on February 14, 2016 · (Permalink)
Fact: Math doesn't lie!
Hallorannn · 1 points · Posted at 06:44:04 on February 14, 2016 · (Permalink)
e; it is its own curve. A single finite number is its own curve.
imregrettingthis · 1 points · Posted at 06:44:16 on February 14, 2016 · (Permalink)
There are different size sets of infinite numbers.
Edit: for instance there is an infinite amount of possible numbers between 1 and 2 but there there is a bigger infinite number set between 1 and 3 etc etc.
Commander_Prime · 1 points · Posted at 06:44:45 on February 14, 2016 · (Permalink)
My face is about to fucking implode reading through these responses
geofurb · 1 points · Posted at 06:45:01 on February 14, 2016 · (Permalink)
Draw a line from 0 to 1 along the x-axis. Move each point up in the y-direction by the distance it is from the origin. You should now have a line segment from (0,0) to (1,1) along y = x
It's longer. Calculus is weird, man.
Phileap · 1 points · Posted at 06:45:09 on February 14, 2016 · (Permalink)
I forgot what it is called, but imagine you stand in front of a wall. Say you are a meter in front of it. You walk half a distance, and then half of that distance, and half of that distance and so on. You will never touch the wall.
[deleted] · 1 points · Posted at 06:45:18 on February 14, 2016 · (Permalink)
You can paint a neverending fence with less then 1 liter of paint.
MyUshanka · 1 points · Posted at 06:46:21 on February 14, 2016 · (Permalink)
The last four digits of my home number (3928) minus my mom's cell (0281) plus my dad's cell (2713) equals my sister's cell (6360).
[deleted] · 1 points · Posted at 06:47:23 on February 14, 2016 · (Permalink)*
The golden ratio (aka φ) (~ 1.618034) is embedded within itself in so many ways. Here's the most head-scratching example of this that I happened upon:
Take the Fibonacci sequence. As the sequence goes up, the difference between two successive numbers approaches the golden ratio.
So, if you took a Fibonacci number, then multiplied it by the golden ratio, you'd get an approximation of the next Fibonacci number. (For example, 610 and 987 are two consecutive Fib numbers. And (610 * φ) = ~987.0007331. Pretty good guess!).
But this approximation method starts off pretty bad. (1 * φ) = ~1.618034, which is not that close to 1. Let's skip up a few levels. (3 * φ) = ~4.854102. Hm, good guess, but the correct answer was 5.
The error gets slimmer and slimmer as the sequence goes up. So let's now look at how big the error is for every step.
And so on...
Now here's the kicker. What do you get when you add up all those error numbers in the third column?
1.61803398874989... !!
I studied the golden ratio for two years (albeit in high school) and still don't understand how it can be hidden so deeply within itself.
EDIT: Formatting
[deleted] · 1 points · Posted at 06:47:35 on February 14, 2016 · (Permalink)
ITT: Really interesting shit I cannot dispute or truly understand. I need to maths more
pnut88 · 1 points · Posted at 06:48:49 on February 14, 2016 · (Permalink)
2+2=4. Yea I know, I'm fucking stupid.
northrupthebandgeek · 1 points · Posted at 06:49:50 on February 14, 2016 · (Permalink)
Jenny's phone number - 8675309 - is a prime number.
letitgoelsa · 1 points · Posted at 06:51:57 on February 14, 2016 · (Permalink)
1 = 0.999999999999999999999999999999999999...
sugar-independant · 1 points · Posted at 06:52:51 on February 14, 2016 · (Permalink)
If you dehydrate a potato with 99% water down to 98%, its total mass reduces to 50%.
horrorshowmalchick · 1 points · Posted at 06:53:17 on February 14, 2016 · (Permalink)
-1=eπi
Zax1989 · 1 points · Posted at 06:55:49 on February 14, 2016 · (Permalink)
A goof plus a gaff equals a laugh.
hozzleton · 1 points · Posted at 06:56:36 on February 14, 2016 · (Permalink)
dividing 0 will give your calculator a hemorrhage
illustribox · 1 points · Posted at 06:57:27 on February 14, 2016 · (Permalink)
Not a "fact" as of yet, but a substantial number of mathematicians have dedicated their careers to the proof of Goldbach's Conjecture, which has been shown to hold up to 4x1018. Extremely simple statement:
Every even integer greater than 2 can be expressed as the sum of two primes.
Wilreadit · 1 points · Posted at 06:57:40 on February 14, 2016 · (Permalink)
I never knew there were so many math geeks on Reddit.
Suihaki · 1 points · Posted at 06:58:30 on February 14, 2016 · (Permalink)
You can do your 9s multiplication tables using fingers really easily. Hold all 10 fingers out in front of you
9x2 -- put left ring finger down -- 1 finger on the left, 8 on the right of the finger placed down -- looks like 18
9x3 -- put left middle finger down -- 2 fingers on left, 7 on right-- looks like 27
Can do it all the way through 10. That's how I learnt them easily in grade school.
Merediv · 1 points · Posted at 06:58:31 on February 14, 2016 · (Permalink)
You can create a theoretical cone that has finite volume but infinite surface area.
idga_chuck · 1 points · Posted at 06:58:32 on February 14, 2016 · (Permalink)
What a good thread for those drunk men with bashful bladder trying to piss before heading to bed. Thanks!
Ollieislame · 1 points · Posted at 06:59:59 on February 14, 2016 · (Permalink)
1+1=window
KalasLas · 1 points · Posted at 07:00:44 on February 14, 2016 · (Permalink)
That adding together all positive integers will yield the sum -1/12. https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
mashek · 1 points · Posted at 07:00:46 on February 14, 2016 · (Permalink)
late to the party and couldn't find it itt - my favourite is that the sum of all natural numbers is... -1/12
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
Jonashaglund · 1 points · Posted at 07:00:46 on February 14, 2016 · (Permalink)
In a room filled with 57 people, the probability of two sharing the same birthday is over 99%.
EndsInATangent · 1 points · Posted at 07:01:17 on February 14, 2016 · (Permalink)
If your parents are 30 when they have you then once you are 15 you are a 3rd of their age and once you are 30 you are half of their age.
properstranger · 1 points · Posted at 07:01:50 on February 14, 2016 · (Permalink)
.999999999 (ad infinitum) is actually equal to 1. Here's the proof.
My high school math teacher showed me this. If someone would care to explain I'm all ears.
callmesally1989 · 1 points · Posted at 07:19:48 on February 14, 2016 · (Permalink)
rounding? not entirely sure
properstranger · 1 points · Posted at 07:21:14 on February 14, 2016 · (Permalink)
It's not rounding, that proof shows that .99999999999 is actually equal to 1.
The proof makes sense, yet I know logically that .999 obviously doesn't actually equal 1. So if anyone has any ideas I'd love to hear them.
rafaelement · 1 points · Posted at 08:51:01 on February 14, 2016 · (Permalink)
then is .19999999... equal to .2?
[deleted] · 1 points · Posted at 07:02:54 on February 14, 2016 · (Permalink)
I know my calculus.
It says you plus me equals us.
callmesally1989 · 1 points · Posted at 07:18:04 on February 14, 2016 · (Permalink)
you're very lonely indeed...
[deleted] · 1 points · Posted at 08:02:29 on February 14, 2016 · (Permalink)
No, not really. It's a reference to a silly mtv bit band spoof, 2ge+her. If anyone sees that comment who remembers that, they'll get a good chuckle.
Tenspeedhero · 1 points · Posted at 07:03:23 on February 14, 2016 · (Permalink)
1 is the loneliest number
marianas_anal_trench · 1 points · Posted at 07:03:39 on February 14, 2016 · (Permalink)
d + b = dickbutt
maahhkus · 1 points · Posted at 07:04:55 on February 14, 2016 · (Permalink)
5318008
Kreizhn · 1 points · Posted at 07:05:29 on February 14, 2016 · (Permalink)
Probably too late, and also probably only of interest to real nerds, but the following nerd sniped myself and my colleagues the other day.
If A is any nxn matrix, there exists a homogeneous degree (n-1) polynomial p_A such that p_A(A) = exp(A). In fact, for any analytic function, such a polynomial exists.
Proof: Do it for diagonalizable using Lagrange interpolation. Use density of diagonalizable in (nxn)-matrices to extend in general. Only problem comes in that the Lagrange polynomial fails for eigenvalues of non-unit multiplicity. The fix is effectively L'Hopital's rule, though to show that this is still analytic, some work needs to be done. Form an n! cover of the (nxn)-matrices {A,lambda1,...,lambda_n} and argue from there.
ACyclistsRant · 1 points · Posted at 07:06:59 on February 14, 2016 · (Permalink)
The derivative graph of sine ...is cosine
Perverteshwar · 1 points · Posted at 07:07:14 on February 14, 2016 · (Permalink)
The ratio of the circumference and diameter of every circle is constant and equal to π
Kreizhn · 1 points · Posted at 07:07:48 on February 14, 2016 · (Permalink)
Or another just ridiculous mind-blowing fact. The projective dimension of C[x,y,z] is 2 if CH, and 3 if not-CH.
FatGordon · 1 points · Posted at 07:09:26 on February 14, 2016 · (Permalink)
Social numbers
mrwhibbley · 1 points · Posted at 07:36:17 on February 14, 2016 · (Permalink)
watched the numberphile video on that and didn't see the importance.
FatGordon · 1 points · Posted at 09:16:11 on February 14, 2016 · (Permalink)
I thought they were cool, thread asked for cool maths things, try dave gormans stand up about it.
https://youtu.be/EM46_5Yd5II
mrwhibbley · 1 points · Posted at 11:34:55 on February 14, 2016 · (Permalink)
Its not that they aren't cool. I just didn't get it. I watched the video a couple days ago. Can you explain it again?
metaasmo · 1 points · Posted at 07:10:51 on February 14, 2016 · (Permalink)
You can't eat Pi.
NotObviouslyARobot · 1 points · Posted at 07:11:35 on February 14, 2016 · (Permalink)
Numbers are a special language that we have developed in order to better understand and communicate the characteristics of our reality.
ILOVEHACKEYSACK · 1 points · Posted at 07:12:31 on February 14, 2016 · (Permalink)
I can't understand any of this! As cool as it may sound lol
BigOldCar · 1 points · Posted at 07:13:00 on February 14, 2016 · (Permalink)
I can multiply by nines on my fingers.
No, it's not "projective dimensions" or "derivative graphs of sine" or whatever, but hey--I'm not a math guy and I need to count on my fingers.
DON'T JUDGE ME!
I'M NOT ASHAMED!
udo2000 · 1 points · Posted at 07:14:21 on February 14, 2016 · (Permalink)
If you multiply number 3367 by 33 you get 111111. Add 33 to 33 and multiply 3367 by 66 and you get 222222. +33 (99) will get you 333333 and so on...
K1ngPCH · 1 points · Posted at 07:15:16 on February 14, 2016 · (Permalink)
If you shuffle a deck of cards, there's a really good chance that that combination has never existed before.
mrwhibbley · 1 points · Posted at 07:35:20 on February 14, 2016 · (Permalink)
I was a magician for 15 years. Shuffled cards 5 times for each trick, three card tricks per show. that's 15 shuffles per show, averaged 4 shows per week, or 60 shuffles. That means I have shuffled decks 46,800 times and I haven't even included that hundreds of thousands of times during practicing. And I haven't even come close to .001% of all the combinations.
Camdenfalcon · 1 points · Posted at 07:16:33 on February 14, 2016 · (Permalink)
I've had sex with 0 people
YoungHeartsAmerica · 1 points · Posted at 07:17:24 on February 14, 2016 · (Permalink)
https://m.youtube.com/watch?v=2QamU4-8NUw
2 plus 2 is 4
Henry_J · 1 points · Posted at 07:18:00 on February 14, 2016 · (Permalink)
The answer to the ultimate question of life, the universe, and everything is 42.
Only math I'll ever need.
Slim_Maldinaldo · 1 points · Posted at 07:18:10 on February 14, 2016 · (Permalink)
Feeling a little late to the party, but the magical multiplication of 11 is my favorite! 11 multiplied by any two digit number NR is equal to NFR where F = N(digit) +R(digit). For example (1132=352, because N=3 and R=2 so F=N+R or F=3+2 there for 1132=352 because NFR= 3 5 2). That was harder to explain than expected.
[deleted] · 1 points · Posted at 07:18:34 on February 14, 2016 · (Permalink)
When you divide an integer 'm' by another integer 'n', the maximum number of unique decimal places after which the pattern repeats itself is n-1. For example, 1/11 is 0.090909... so the pattern repeats itself after every 2 digits and 1/7 = 0.1428571428.. which repeats itself after 6 digits. So 1/555 would have a maximum of 554 decimal places after which the sequence would repeat.
swampfoxsc · 1 points · Posted at 07:18:56 on February 14, 2016 · (Permalink)
That 7 ate 9!
MagicOfFriendship · 1 points · Posted at 07:19:42 on February 14, 2016 · (Permalink)
12345679*9 = 11111111
[deleted] · 1 points · Posted at 07:19:54 on February 14, 2016 · (Permalink)
[deleted]
Suicidal_Ghost · 1 points · Posted at 07:24:52 on February 14, 2016 · (Permalink)
456 x 11?
rusk00ta · 1 points · Posted at 07:44:03 on February 14, 2016 · (Permalink)
Deleted my comment because I didn't explain that part well enough.
This video explains it pretty well.
AnthonySlips · 1 points · Posted at 07:20:07 on February 14, 2016 · (Permalink)
.9999... Is actually equal to 1.
Think about it.
.333... = 1/3
.333... × 3 = 3/3 = 1 =.999...
mrwhibbley · 1 points · Posted at 07:31:24 on February 14, 2016 · (Permalink)
that is because at some point the .333 rounds up. .3333 x 3 = .9999 =/= 1.
AnthonySlips · 1 points · Posted at 08:12:15 on February 14, 2016 · (Permalink)
Nah dawg.
x = 0.9...
10x = 9.9...
10x - x = 9.9... - x
10x - x = 9.9... - 0.9... (because x = 0.9...)
9x = 9
x = 1
therefore x = 1 and x = 0.9...
Theres many variations of this proof.
mrarain · 1 points · Posted at 07:20:40 on February 14, 2016 · (Permalink)
the Unless you get a jump second. That doesn't happen all the time however
imnutslol · 1 points · Posted at 07:20:41 on February 14, 2016 · (Permalink)
"Theoretically the sum of an entire human experience can be quantified in an algorithm. What we consider the soul is actually a direct reflection of an amalgamation of any and all available experiences, which could supposedly be quantified, assuming our experiences produce a certain brain reaction. These reactions could be mapped, copied, and made into modules."
RevengeSprints · 1 points · Posted at 07:21:37 on February 14, 2016 · (Permalink)
If your legs are 10 degrees apart. Your dick is the cross product of your legs.
https://fish1964.wordpress.com/2013/08/02/the-cross-product-of-your-legs-is-your-penis/
My_3rd_Account_Evah · 1 points · Posted at 07:22:01 on February 14, 2016 · (Permalink)
That Pythagoras originally studied the mathematics of music. He invented the notation system that is used in the western contries today.
gustaf182 · 1 points · Posted at 07:22:11 on February 14, 2016 · (Permalink)
I like to think of prime numbers as the periodic table of integers. All integers (excluding -1, 0, 1) are composed of prime numbers. Which also in itself proves that there are infinite prime numbers which is also very cool!
Rivetture · 1 points · Posted at 07:22:35 on February 14, 2016 · (Permalink)
.999999 repeating forever = 1
mrwhibbley · 1 points · Posted at 07:29:58 on February 14, 2016 · (Permalink)
I understand what they mean, but I still disagree. if you extend 0.99999999 for 999,999,999,9999999999999999999 then it is still less than 1. but then that is not infinite. 1 = 1. 0.999 forever is still every so infinitesimally slightly less than one.
Rivetture · 1 points · Posted at 07:34:20 on February 14, 2016 · (Permalink)
Give me a number between .99(repeating forever) and 1, u can't, which means it's the same number. Also .99999999999 divided by 3 = .333333333333333, and 1 divided by 3 =.333333333, plus 3/3 =1 and .99999999(RF)
ChargerEcon · 1 points · Posted at 07:36:35 on February 14, 2016 · (Permalink)
Please don't start this argument again...
mrwhibbley · 1 points · Posted at 11:35:28 on February 14, 2016 · (Permalink)
I am just poking the bear. :)
Elbows · 1 points · Posted at 07:24:27 on February 14, 2016 · (Permalink)
IF you take any number and swap the numbers around front to back and subtract them the result is divisible by 3. Ex. 973 - 379 = 594 / 3 = 198
[deleted] · 1 points · Posted at 08:17:55 on February 14, 2016 · (Permalink)
Even better, if you take one number and rearrange the digits as you like, and subtract the two numbers, the result is always divisible by 9.
Example 65327 - 25763 = 39564 = 9 * 4396.
camnasty91 · 1 points · Posted at 07:24:32 on February 14, 2016 · (Permalink)
A guy named George Dantzig, solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman. Learned about this in a math class in college, most impressive thing iv heard about math.
therajahbrooke · 1 points · Posted at 07:25:01 on February 14, 2016 · (Permalink)
The number zero had to be invented.
deh707 · 1 points · Posted at 07:27:17 on February 14, 2016 · (Permalink)*
You can figure out 9 x 0-10 (nine times zero through ten) with the 10 fingers on your hands.
Imagine looking at both of your hands (palms facing you, unclenched), then think of each finger in this manner:
Left thumb = 1
Left index = 2
Left middle = 3
Left ring = 4
Left pinky = 5
Right pinky = 6
Right ring = 7
Right middle = 8
Right index = 9
Right thumb = 10
For example; for 9 x 4, clench your left ring finger (4), and count how many fingers remain on the left side (3), then count how many remain on the right side (6).
You have 36 as the answer to 9 x 4.
Shelverman · 1 points · Posted at 07:28:30 on February 14, 2016 · (Permalink)
Fascinating.
abaddamn · 1 points · Posted at 07:29:57 on February 14, 2016 · (Permalink)
Fermat's theorem.
RanzhaVEmodrach · 1 points · Posted at 07:31:40 on February 14, 2016 · (Permalink)
The sum from k=0 to infinity of ((n-1)k * (n choose k)) = nn.
This works for all natural numbers (whole numbers) n bigger than 1.
This is an application of the binomial theorem, but I intuited it while solving a combinatorics problem and have been unable to prove it independently of the binomial theorem.
And it's FUCKING COOL.
Watch:
22 = (10 * 2C0) + (11 * 2C1) + (12 * 2C2) = 1 + 2 + 1 = 4.
And again:
1010 = (90 * 10C0) + (91 * 10C1) + (92 + 10C2) + (93 + 10C3) + (94 + 10C4) + (95 + 10C5) + (96 + 10C6) + (97 + 10C7) + (98 + 10C8) + (99 + 10C9) + (910 + 10C10)
= 1 + 90 + 3645 + 87480 + 1377810 + 14880348 + 111602610 + 573956280 + 1937102445 + 3874204890 + 3486784401 = 10000000000.
Blows me away every time.
octavio2895 · 1 points · Posted at 07:33:38 on February 14, 2016 · (Permalink)
You can describe most functions (as long as they have a finite number of discontinuities) with a sum of infinite different sines and cosines. You can describe 1/x (a function that jumps from -infinite to +infinite) with a sum to infinity of sines and cosines.
Beefsoda · 1 points · Posted at 07:34:01 on February 14, 2016 · (Permalink)
An infinite sequence can be exhausted in a finite amount of time using supertasks
brhodewalt · 1 points · Posted at 07:36:29 on February 14, 2016 · (Permalink)
Test for divisibilty by 7:
Remove final digit, and double it. Subtract that number from remaining digits.
If the difference is a multiple of seven, original number was also.
Forgot-My-Name_again · 1 points · Posted at 07:37:39 on February 14, 2016 · (Permalink)
ii is a purely real number
SourShoes674 · 1 points · Posted at 07:38:13 on February 14, 2016 · (Permalink)
BEDMAS is all I know
notjosh3 · 1 points · Posted at 07:38:42 on February 14, 2016 · (Permalink)
Even though a number cannot be divided by zero, 0! = 1
Knever · 1 points · Posted at 07:38:45 on February 14, 2016 · (Permalink)
No counting space beyond Earth, humans currently inhabit roughly 0.0000000000000000000015% of the observable universe.
neotropic9 · 1 points · Posted at 07:39:13 on February 14, 2016 · (Permalink)
There are an equal number of rational numbers as integers, but there are more real numbers.
[deleted] · 1 points · Posted at 07:39:32 on February 14, 2016 · (Permalink)
0.99 recurring is equal to 1
seantme · 1 points · Posted at 07:39:36 on February 14, 2016 · (Permalink)
If you condense binary numbers there's a "secret" reoccurring pattern to infinity--an underlying "code" of the universe. 1 2 4 8 16 (7) 1+6 32 (5) 3+2 64 (1) 6+4=10 1+0 128 (2) 1+2+8=11 1+1 256 (4) 512 (8) 1024 (7) 2048 (5) 4096 (1) 8192 (2) 16,384 (4) 32,768 (8) 3+2+7+6+8=26 2+6 65,536 (7)
the code is 124875
zenist69 · 1 points · Posted at 07:40:00 on February 14, 2016 · (Permalink)
1 + 1 = 2
rossco96 · 1 points · Posted at 07:42:33 on February 14, 2016 · (Permalink)
Starting from 0 add each consecutive odd number, 1,3, 5 etc. These will give you the square of numbers, 12=1(0+1), 22=4(1+3), 32=9(4+5) and so on, I think
[deleted] · 1 points · Posted at 07:42:51 on February 14, 2016 · (Permalink)
Both the sun and the moon appear to be identical in size when observed from earth, despite being drastically different sizes, distances, and orientations to the planet.
infiniteartifacts · 1 points · Posted at 07:43:02 on February 14, 2016 · (Permalink)
8008135 (boobies)
omniarcan · 1 points · Posted at 07:43:32 on February 14, 2016 · (Permalink)*
Putting this here in case anyone reads it. It's a fact I like to throw to my friends more because I took the time to figure it out (and haven't seen it elsewhere, though it's not exactly easy to google, so if somebody could point me to anywhere else it's discussed that'd be awesome.) It's not exactly useful in any way I've found, so that also makes sense.
The difference between (n) and (n+1) is, obviously enough, 1.
The difference between the difference between (n)2 and (n+1)2 is 2, (22 - 12 = 3, 32 - 22 = 5, 42 - 32 = 7; 7 - 5 = 5 - 3 = 2) something that's pretty common knowledge, I'd expect.
The difference between the difference between the difference between (n)3 and (n+1)3 is 6, (23 - 13 = 7, 33 - 23 = 19, 43 - 33 = 37, 53 - 43 = 61; 19 - 7 = 12 37 - 19 = 18, 61 - 37=24; 24 - 18 = 18 - 12 = 6).
The difference between the difference between the difference between the difference between (n)4 and (n+1)4 is 24, (24 - 14 = 15, 34 - 24 = 65, 44 - 34 = 175, 54 - 44 = 369, 64 - 54 = 671; 65 - 15 = 50, 175 - 65 = 110, 369 - 175 = 194; 671 - 369 = 302; 110 - 50 = 60, 194 - 110 = 84, 302 - 194 = 108; 108 - 84 = 84 - 60 = 24.)
This sequence continues at least out through n5 and n6, though I'm obviously not showing those here as the amount of operations required to demonstrate it grows rather quickly, to give the sequence n!. This is also limited by other factors (like needing to stick to the counting numbers; as one might expect involving the negatives in sequences revolving around exponents leads to a bad time.)
Also I apologize deeply for formatting, I'm not at all used to putting up equations on reddit.
[deleted] · 1 points · Posted at 08:12:42 on February 14, 2016 · (Permalink)
This is true in general, i.e., if you take k times the differences between k-th powers, you always get a constant. And this constant is k! (k factorial), that is 1 * 2 * 3 * 4 .... * k.
This can be useful in this sense. Imagine you have a series of numbers 10, 29, 72, 151, 278, 465, 724, 1067, 1506, 2053 and you want to know if they come from a polynomial.
Well, clearly they can always come from a polynomial because given n points there is always a polynomial of degree at most n-1 that pass through those points. However one is usually interested in low degree polynomials.
So you take differences. In this case, if you take differences 3 times you obtain 12,12,12,12,12,... this tells us two things, first that this come from a cubic polynomial, the second is that the leading coefficient, the coefficient of x3 is equal to 12 / 3! = 12 / 6 = 2. So our polynomial starts with 2 * x3. Now we can subtract 2 * 13, 2 * 23 , 3 * 33, ... from our list of numbers and we are left with 8, 13, 18, 23, 28, 33, 38, 43,.. we take differences one time and we get constant 5. So we know that these numbers come from a polynomial of degree 1, with coefficient 5/1! = 5. So our polynomial starts with 2 * x3 + 5 * x and taking this away from our list of numbers we are left with a list of 3's. So we have obtained that our original list of numbers can be obtained with the formula 2 * x3 + 5 * x + 3.
omniarcan · 1 points · Posted at 09:00:24 on February 14, 2016 · (Permalink)
The first bit is essentially what I spent that entire post getting at, but the application is really cool-thanks for sharing it.
schnoibie · 1 points · Posted at 07:43:32 on February 14, 2016 · (Permalink)
0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999... infinitely repeating, is equal to 1.
gaybuttlickler · 1 points · Posted at 07:45:33 on February 14, 2016 · (Permalink)
Take 259 x (Your Age Here) x 39
scoobydoobiedoodoo · 1 points · Posted at 07:45:56 on February 14, 2016 · (Permalink)
Does this count? I think it's cool that division by zero is still undefined.
anotheranotherother · 1 points · Posted at 07:47:27 on February 14, 2016 · (Permalink)
I've hit load more comments a few times and still haven't seen this.
The number 41 is awesome. 41 is prime. Add 2 and you get 43, also prime. Add 4 to that and you get 47, also prime. Add 6 to that and you get 53, also prime. This sequence continues for 41 intervals.
A neat gif representation
Ninja edit : Oh and the final number, that 41st prime, is the number 421. Starts in 4, ends in 1, and the intervals increase by 2 each time.
bbrundage07 · 1 points · Posted at 07:47:33 on February 14, 2016 · (Permalink)
111x111=12321 1111x1111=1234321
RollerJesus · 1 points · Posted at 07:48:11 on February 14, 2016 · (Permalink)
7.2 - 1.2 = 6
7.2 / 1.2 = 6
I don't know of any other numbers that subtract and divide to the same value except 4 and 2.
-TurntUp- · 1 points · Posted at 07:49:40 on February 14, 2016 · (Permalink)*
Ok. This is just simple elementary math, but still pretty cool & helpful to kids. The sum of the numbers in the results of the 9 times table, from x2 through x9, always total 9. Additonally (teehee), the first digit in the results is always one less than the multiplier. So:
9x2=18 ... 1+8=9 9x3=27 ... 2+7=9 9x4=36 ... 3+6=9 And so on and so forth
Well, it does work for 9x1 too, but who needs that lol?
I was taught this in school as a child. I thought everyone was. But everyone I ever told this too had never heard of it. My kids thought it was magic. Needless to say, I have always had to think waaay less while multiplying by 9. Chee!
CarpeCyprinidae · 1 points · Posted at 08:03:03 on February 14, 2016 · (Permalink)
I just multiply the number by ten then subtract it once. Quicker
-TurntUp- · 1 points · Posted at 08:06:22 on February 14, 2016 · (Permalink)
Interesting. Can you elaborate?
CarpeCyprinidae · 2 points · Posted at 08:29:01 on February 14, 2016 · (Permalink)*
2x9 =(2x10)-2. (18)
57x9 = (57x10)-57 (513)
Multiplying by ten is really easy then subtracting one number isn't hard.
I use this method for multiplying by eight, too. Just subtract twice..
laxlife5 · 1 points · Posted at 07:49:52 on February 14, 2016 · (Permalink)
I remembered my 9 times table first by learning that the tens count up and the ones count down up to 9×10.
09 18 27 36 45 54 63 72 81 90
blackhotchilipepper · 1 points · Posted at 07:51:30 on February 14, 2016 · (Permalink)
123456789 * 8 = 987654312 Just 9 short of 987654321
dirkbirkin · 1 points · Posted at 07:51:41 on February 14, 2016 · (Permalink)
An object can have an infinite perimeter, yet a finite volume.
epsilon526 · 1 points · Posted at 07:53:51 on February 14, 2016 · (Permalink)
i raised to the power of i is about .205
tigerInAnENet · 1 points · Posted at 07:54:00 on February 14, 2016 · (Permalink)
There are always two points opposite each other on the equator that are the exact same temperature. This is because of the intermediate value theorem.
eremylto · 1 points · Posted at 07:55:37 on February 14, 2016 · (Permalink)
Algebra and functions is what is used to do trasmission calculus. So, you are using internet and phone because of math.
lokirmccloud · 1 points · Posted at 07:56:12 on February 14, 2016 · (Permalink)
In a room of 23 people, there is a 50% chance that 2 people will share the same birthday date.
In a room of 75 people, there is a 99.9% chance that 2 people will share the same birthday date.
HermioneD4nger · 1 points · Posted at 08:01:45 on February 14, 2016 · (Permalink)*
d/dx(ex)= ex
(The derivative of ex is ex)
6panlid · 1 points · Posted at 08:01:54 on February 14, 2016 · (Permalink)
One idiot can fuck up countless lives.
peazey · 1 points · Posted at 15:53:55 on February 14, 2016 · (Permalink)
Or, more properly, countably infinite lives.
TumblrTheFish · 1 points · Posted at 08:02:31 on February 14, 2016 · (Permalink)
If you assume that temperatures are continuous (which you should due to the way that temperature diffuses) then you can mathematically prove that there exists a point on the earth where if you drilled a hole from it, through the earth's core and out the other side (a straight line), the temperature on both sides is the same.
puntti · 1 points · Posted at 08:03:10 on February 14, 2016 · (Permalink)
There are so many ways to arange a deck of cards (52!), that every time you scramble the deck, the cards almost certanly go into an order never seen before by any man.
Here's a video about this (and other card stuff): https://youtu.be/ObiqJzfyACM
urgle55 · 1 points · Posted at 08:03:22 on February 14, 2016 · (Permalink)
If you add 1 + 1/2 + 1/3 + 1/4... you get infinity. But if you leave out every number with a 9 in it, the result converges.
[deleted] · 1 points · Posted at 08:03:40 on February 14, 2016 · (Permalink)
You can tell if a number is divisible by 3 if the sum of the number's digits is divisible by 3.
RyanRiot · 1 points · Posted at 08:04:59 on February 14, 2016 · (Permalink)
0.9999... = 1
[deleted] · 1 points · Posted at 08:05:09 on February 14, 2016 · (Permalink)
Locally increasing functions are increasing! It is a fact that seems trivial but is surprisingly deep.
turboyabby · 1 points · Posted at 08:05:10 on February 14, 2016 · (Permalink)
Forty is the only number whose letters are in alphabetical order.
ohnoitsgodzilla · 1 points · Posted at 08:06:46 on February 14, 2016 · (Permalink)
The Staircase Paradox is fun to think about.
[deleted] · 1 points · Posted at 08:07:21 on February 14, 2016 · (Permalink)
0.99999repeating = 1
pinkminitriceratops · 1 points · Posted at 08:07:25 on February 14, 2016 · (Permalink)
You can cut a taurus into two interlocking möbius strips. This is best done with a bagel, although it's a bit hard to spread the cream cheese.
PepeRohnie · 1 points · Posted at 08:07:27 on February 14, 2016 · (Permalink)
0.999999 repetend is exactly 1
Indie_Dev · 1 points · Posted at 08:08:45 on February 14, 2016 · (Permalink)*
That the infinite sequence 1 + 2 + 3 + 4 + 5 + ... = -1/12.
It's a proven fact and also used in many areas of physics, where it works flawlessly.
[deleted] · 1 points · Posted at 08:09:33 on February 14, 2016 · (Permalink)
Not only does 11+2=12+1, but the phrase 'Eleven Plus Two' can be rearranged into 'Twelve plus one'
Da_Wuff_Princess · 1 points · Posted at 08:09:48 on February 14, 2016 · (Permalink)
I always thought it was cool that 11x11=121 so separating the 1s and putting the sum in the middle. 11x12=132 11x13=143 11x45=495 this only works until the sum is greater than 9, but when I realised this as a kid I knew God was maths. also the old 9xsibgle digit numbers is 1 less than said number with however much is left until 9 next to it. e.g. 9x4=36 3+6=9
I realise everyone knows this, but maybe someone doesn't? Also I suck at math and can't wrap my mind around most of these. :<
JulyBurnsRed34 · 1 points · Posted at 08:10:07 on February 14, 2016 · (Permalink)
The sum of all numbers up to infinite is -1/12
Flippedfoot · 1 points · Posted at 08:10:24 on February 14, 2016 · (Permalink)
Guide to seeing if a number can be factored by most numbers 1-10
1- everything 2- even numbers 3- add the individual digits of the number until you get 3,6 or 9 4- half the number will be even 5- units digit will be 0 or 5 6 - even amd the trick of 3s works 7 - I don't know of a trick but if you do please share 8 - half of a half will be even 9- add the individual digits of the number until you get 9 10 - the units digit is 0
Some/all of these are common knowledge, but I didn't learn all of them at first.
Toover · 1 points · Posted at 08:12:15 on February 14, 2016 · (Permalink)
Godel's incompleteness theorems
In few words: whatever the axioms you choose, your theory cannot be complete: there will always be something improvable.
In fewer words: there is no theory of everything.
And if you take a set of theories to cover everything, they will be inconsistent with one another.
colorem · 1 points · Posted at 08:13:18 on February 14, 2016 · (Permalink)
Benford's Law, lower numbers are disproportionately more likely to appear in the first digit of numbers. This is often used to catch
https://en.wikipedia.org/wiki/Benford%27s_law
bionikspoon · 1 points · Posted at 08:14:10 on February 14, 2016 · (Permalink)
When a 4 legged table is wobbely on a flat surface, you can fix the wobble by rotating it up to quarter turn. This is proven mathematically.
Fix a Wobbly Table (with Math)
GUNTMUFFIN · 1 points · Posted at 08:14:40 on February 14, 2016 · (Permalink)
(The sum of 1+2+3+.....+Infinity)=-1/12
The_Pudge · 1 points · Posted at 08:15:40 on February 14, 2016 · (Permalink)
33 + 44 + 33 + 55 = 3435
RPmatrix · 1 points · Posted at 08:16:05 on February 14, 2016 · (Permalink)*
Nine has weird mathematical powers
i.e. The sum of the numbers of any whole number that ends in 9 and multiplied by nine will add up to 9 (i think!)
e.g.
9x9=81 ... 8+1=9
9x314=2826 ... 2+8+2+6=18=1+8=9
Make one of the numbers over 1000 and it will equal 2
and so forth
maxradness · 1 points · Posted at 08:16:10 on February 14, 2016 · (Permalink)
I understand none of this. Doesn't matter.
VR_And_Sex · 1 points · Posted at 08:18:04 on February 14, 2016 · (Permalink)
The sum of factors of 9 add up to 9. I don't know when this doesn't work as I'm lazy and don't want to do math.
9x2= 18 (1+8=9) 9x3= 27 (2+7=9)
Thought this was a break through when I was in first grade.
ralphierocket · 1 points · Posted at 08:18:05 on February 14, 2016 · (Permalink)
You can relate three of the arguably most important mathematical constants by the expression:
epi*i = -1, or
epi*i + 1 = 0
WeAreGlidingNow · 1 points · Posted at 08:19:43 on February 14, 2016 · (Permalink)
Question: How many numbers have the number 3 within them (e.g.: 437)?
Answer: All of them.
OK, some explanation. Obviously, some numbers do not contain a 3, such as 10 and 20. But if examine all the numbers up to 3644, you'll see that 40% of them do, in fact, contain a 3. By the time you get to 40,000, about half of the numbers will contain a 3. Before you get to four billion, 70% of the numbers will contain a 3.
The ratio does not increase smoothly. It dips and zig-zags, but grows steadily.
For the mathematically inclined, the ratio of numbers less than N that contain a 3 is something like:
0.297793 * ln(ln(N)) - 0.215225
Not an exact formula, but holds almost true into the hundreds of trillions. The point is that the ratio increases forever, albeit slowly. Eventually, all numbers contain a 3.
zzalec · 1 points · Posted at 08:20:12 on February 14, 2016 · (Permalink)
Pascal's Triangle
Biobak_ · 1 points · Posted at 08:21:24 on February 14, 2016 · (Permalink)
5=7
dylsexic_man · 1 points · Posted at 08:21:31 on February 14, 2016 · (Permalink)
99.999999999999...% is equal to 100%
foilcurtain · 1 points · Posted at 08:21:44 on February 14, 2016 · (Permalink)
Late to the party, but here's my less interesting more weird fact:
Add up any digits of a multiple of 9, and you'll get a multiple of 9.
27 or 2 + 7 = 9
135... = 9
297... = 18
and so on. There's definitely some incredibly simple connection I'm missing here, though. edit: formatting
Yragary · 1 points · Posted at 08:22:29 on February 14, 2016 · (Permalink)
Another ex) .272727.....=.272727....../.999999.....= .27/.99=27/99=3/11
This can be done since .9999999......=1 and both can be proven using the sum of an infinite series.
NapalmCheese · 1 points · Posted at 08:22:45 on February 14, 2016 · (Permalink)
That there are infinite infinities, each one larger than the previous.
BeLoWZeRo427 · 1 points · Posted at 08:23:38 on February 14, 2016 · (Permalink)
That 6 was afraid of 7, cause 7 ate 9...
MeraxesSnow · 1 points · Posted at 08:24:24 on February 14, 2016 · (Permalink)
http://imgur.com/RibeelQ
Sry I had to do that.
aizaz09 · 1 points · Posted at 08:25:27 on February 14, 2016 · (Permalink)
The Fibonacci sequence is completely encoded in 1/89
1/89 ~= 0.01123595505
0.01
0.001
0.0002
0.00003
0.000005
0.0000008
0.00000013
0.000000021
0.0000000034 etc. Here is a proof: library.thinkquest.org/27890/applications3p.html
EDIT: Yeah! Highest rated comment about Fibonacci. Algebraic!
EDIT: No longer highest rated. Is sad day. Such is life.
spunknugget · 1 points · Posted at 08:26:08 on February 14, 2016 · (Permalink)
That if you type in 58008 and flip it upside down it spells something awesome.
[deleted] · 1 points · Posted at 08:26:39 on February 14, 2016 · (Permalink)
The zipfs law, 80-20 rule will always hold.
Oleing · 1 points · Posted at 08:26:56 on February 14, 2016 · (Permalink)
According to my grade 12 math teacher the quadratic equation and bringing your calculus book to a party will get you the most women. That fact has stuck with my ever since then.
dodedede16 · 1 points · Posted at 08:28:55 on February 14, 2016 · (Permalink)
Multiplying numbers by 11:
For two digit numbers: To find the answer, separate the two digits, then take the sum of the two digits and insert it in between. Take 43x11 for example. 4_3, 4+3 = 7, so 43x11 = 437 If you have to carry, say for example 48x11, then do 4_8, 4+8= 12, then put the 2 in the middle and carry the 1, so 48x11 = 528
For digits greater than 2 digits, the process is similar. Take 324x11 for example. 3_ _ 4, then do 3+2 = 5, and 2+4 = 6. Thus 324x11 = 3564 Take 4317x11 as another example. 4_ _ _ 7, 4+3 = 7, 3+1 = 4, 1+7 = 8, thus 4317x11 = 47487.
MojaveMilkman · 1 points · Posted at 08:29:24 on February 14, 2016 · (Permalink)
I don't know what the fuck anyone in this thread is talking about.
BromeotheBard · 1 points · Posted at 08:30:44 on February 14, 2016 · (Permalink)
7 ate 9
WhompWump · 1 points · Posted at 08:33:02 on February 14, 2016 · (Permalink)
a closed set can also be open
me239 · 1 points · Posted at 08:33:37 on February 14, 2016 · (Permalink)
Babylonian method of finding square roots. You can accurately find square roots after just a few iterations. https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
nxsky · 1 points · Posted at 08:33:50 on February 14, 2016 · (Permalink)*
There are many cool things but only one that I use regularly. It involves tan, cos and sin as well as angles 30, 45, 60 and 90 degrees (although I don't use it for 90).
Draw an equilateral triangle of side length 2 and cut in half (use either side). You're left with sides 2, 1 and sqrt3. Angles 30, 60 and 90.
Draw a right angle triangle sides 1, 1 and sqrt2. You then have angles 45 and 90.
All you're left with is SOH CAH TOA.
Also, fractals: https://youtu.be/gruJ0S3TTtI http://m.intmath.com/complex-numbers/fractals.php
In short, it's complex numbers iterated on a computer program to fully generate images. Trees, islands, rocks and so on.
Aslam_Shad · 1 points · Posted at 08:35:02 on February 14, 2016 · (Permalink)
kind of an interesting analogy for government in a way.
Taytethegreat · 1 points · Posted at 08:36:16 on February 14, 2016 · (Permalink)
Start at the 762nd digit of pi the number 9 repeats six times. So you could recite all the numbers until the nines and say " and so on" to imply that pi was rational.
ShakaUVM · 1 points · Posted at 08:37:39 on February 14, 2016 · (Permalink)
We can determine that a number is very probably prime without having the faintest idea what the actual factors are.
Fermat's Little Theorem
Bongoots · 1 points · Posted at 08:37:42 on February 14, 2016 · (Permalink)
The Ancestor Paradox - where you calculate the number of your ancestors in each generation of your family tree. Two parents. Four grandparents. Eight great-grandparents. Etcetera. Keep going back about say 800 years and you have 4 billion ancestors in a single generation of your family tree. Another generation, 8 billion. Another generation, 16 billion. And that's just roughly 850 years ago.
Let alone that most of your ancestors even at this point will only be from one geographic area (say the United Kingdom, or at least just Western Europe, for example). Add in things like the Black Death that wiped out a third of Europe's population in the 1340s. There are a lot of bottlenecks involved.
Inbreeding!
BajaBlu · 1 points · Posted at 08:38:07 on February 14, 2016 · (Permalink)
That 58008 upside down reads BOOBS.
Jdrawer · 1 points · Posted at 08:38:09 on February 14, 2016 · (Permalink)
The fact that 1! = 0! and the simple proof that proves it.
Also, the German word for "factorial" is the same for "faculty."
CarpeCyprinidae · 1 points · Posted at 08:42:08 on February 14, 2016 · (Permalink)
Makes sense. Faculty also means ability in English and factors are about the ability to evenly divide
captainp42 · 1 points · Posted at 08:39:24 on February 14, 2016 · (Permalink)
123456789 x 2 = 246913578 (same digits, rearranged)
246913578 x 2 = 439827156
439827156 x 2 = 987654312
987654312 x 2 = 1975308624 (same trend, add the "0")
1975308624 x 2 = 3950617248
rubberseatbelt · 1 points · Posted at 08:39:27 on February 14, 2016 · (Permalink)
Geometry question: If a dot is infinitely small and a line is infinitely thin, if you were to look a the start of the line in the 3rd dimension (looking down the length of the line from the end), it would be a dot, right? However, since a dot is infinitely smll, would that mean that the 3rd dimension is infinitely small, too?
zmacker34 · 1 points · Posted at 08:40:31 on February 14, 2016 · (Permalink)
"It's a stormy day on the sea off the coast of Greece" - I see what he did there
earlobe7 · 1 points · Posted at 08:42:53 on February 14, 2016 · (Permalink)
ei*pi = -1
In my opinion, some of the most beautiful mathematics lies in the complex domain.
wolfendale · 1 points · Posted at 08:43:40 on February 14, 2016 · (Permalink)*
According to the Riemann Zeta Function, the sum of all integers is -1/12.
https://en.wikipedia.org/wiki/Riemann_zeta_function
Smokey_Circles · 1 points · Posted at 08:44:05 on February 14, 2016 · (Permalink)
Einstein used Pythagoras to prove/demonstrate (not sure tbh) time is relative to the observer's speed
Bombagal · 1 points · Posted at 08:44:18 on February 14, 2016 · (Permalink)
1+1-1+1-1....... (repeat forever)
has 3 solutions: 1, 0 and 0.5
marpro15 · 1 points · Posted at 08:44:22 on February 14, 2016 · (Permalink)
If you want to know a number squared, like 13, and you know the previous or the next squared number, say we do know 12 squared, then you can add the sum of the two numbers (12+13) to the square of the lower number (144), which gives you the higher number squared (169)
tlowson1 · 1 points · Posted at 08:44:29 on February 14, 2016 · (Permalink)
2 minus 3 equals negative fun!
Thanks Troy McClure!
TheSupernatural · 1 points · Posted at 08:47:10 on February 14, 2016 · (Permalink)
Graham's number is incomprehensibly big.
There aren't enough atoms in the universe to write it fully down.
Yea... big.
ace2ey · 1 points · Posted at 09:51:30 on February 14, 2016 · (Permalink)
And yet we know it ends in a 7.
soapwagon · 1 points · Posted at 08:47:58 on February 14, 2016 · (Permalink)
Don't know if this came up yet but:
26 is the only number between a squared (25 = 52) and a cubic (27 = 33) value!
iAMmincho · 1 points · Posted at 08:48:45 on February 14, 2016 · (Permalink)
epi*i = -1 I still have no idea why.
Orange_Ash · 1 points · Posted at 09:01:55 on February 14, 2016 · (Permalink)
Look at the Wikipedia for Euler's identity
IWBTS · 1 points · Posted at 08:50:35 on February 14, 2016 · (Permalink)
2 + 2 = 🐠
[deleted] · 1 points · Posted at 08:54:00 on February 14, 2016 · (Permalink)
ex is its own derivative.
[deleted] · 1 points · Posted at 08:54:52 on February 14, 2016 · (Permalink)
To within half a percent pi seconds is a nano-century.
Procerus · 1 points · Posted at 08:55:33 on February 14, 2016 · (Permalink)
8675309 is prime.
DeusUper · 1 points · Posted at 08:57:17 on February 14, 2016 · (Permalink)
It is possible to check if a number can be divided by three of you simply add all the individual digits and divide them by three. I.e. 4317 = 4 + 3 + 1 + 7 = 15. 15 can be divided by 3 and thus can 4317.
Amazingly this works on every iteration (15 = 1 + 5 = 6)
Terminatorneo · 1 points · Posted at 08:58:07 on February 14, 2016 · (Permalink)
Anything divided by zero is not defined . Zero is like a joker in the pack of cards . Depends on the user how to get the most out of it . Zero is indeed like our universe : very little is known to us .
Appare · 1 points · Posted at 08:58:14 on February 14, 2016 · (Permalink)
I probably spent a total of 20 hours working on this week's physics homework. The highest grade I can get on it is an 87.5%.
Not a cool fact, but I'm bitter.
[deleted] · 1 points · Posted at 08:58:29 on February 14, 2016 · (Permalink)
1 + 0 = 1
1 + 1 = 2
11 + 1 = 12 ... 1 + 2 = 3
2457 + 1 = 2458 ... 2 + 4 + 5 + 8 = 19 ... 1 + 9 = 10 ... 1 + 0 = 1
2458 + 1 = 2459 ... 2 + 4 + 5 + 9 = 20 ... 2 + 0 = 2
2459 + 1 = 2460 ... 2 + 4 + 6 + 0 = 12 ... 1 + 2 = 3
2460 + 1 = 2461 ... 2 + 4 + 6 + 1 = 13 ... 1 + 3 = 4
5679 + 1 = 5680 ... 5 + 6 + 8 + 0 = 19 ... 1 + 9 = 10 ... 1 + 0 = 1
5680 + 1 = 5681 ... 5 + 6 + 8 + 1 = 20 ... 2 + 0 = 2
How does this work?
folen · 1 points · Posted at 08:59:27 on February 14, 2016 · (Permalink)
that math has it limits (where it becomes wrong)
newtfloss · 1 points · Posted at 09:00:24 on February 14, 2016 · (Permalink)
Two Plus Two Is Four!
Rvnscrft · 1 points · Posted at 09:00:40 on February 14, 2016 · (Permalink)
A circle with an infinite circumference is a straight line
LeonTanis · 1 points · Posted at 09:01:14 on February 14, 2016 · (Permalink)
1+2+3+4+5+6... = -1/12 https://youtu.be/w-I6XTVZXww
TtotheItotheM · 1 points · Posted at 09:01:16 on February 14, 2016 · (Permalink)
5318008
tnh88 · 1 points · Posted at 09:02:41 on February 14, 2016 · (Permalink)
12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
and so on.
Jasonwfranks · 1 points · Posted at 09:04:19 on February 14, 2016 · (Permalink)
Only 49 perfect numbers have been discovered (https://en.m.wikipedia.org/wiki/Perfect_number), but it is still unknown whether there are an infinite number. Also, all 49 are even, and it is still unproven whether there exists an odd perfect number.
Thisisdom · 1 points · Posted at 09:04:23 on February 14, 2016 · (Permalink)
The sum of all natural numbers, 1 + 2 + 3 + 4 + ... = - 1/12
Steph4869 · 1 points · Posted at 09:06:37 on February 14, 2016 · (Permalink)
ii is a real number :O
ohmanitsjose · 1 points · Posted at 09:07:04 on February 14, 2016 · (Permalink)
789 :D
[deleted] · 1 points · Posted at 09:09:51 on February 14, 2016 · (Permalink)
Every even integer (greater than 4) is the sum of two (unique?) prime numbers.
Cool_babes · 1 points · Posted at 09:15:31 on February 14, 2016 · (Permalink)
I never picked up that "irrational" means "cannot be a ratio".
gingerly_said · 1 points · Posted at 09:15:32 on February 14, 2016 · (Permalink)
8008135
Kukadin · 1 points · Posted at 09:15:33 on February 14, 2016 · (Permalink)
2 is more than 3
op135 · 1 points · Posted at 09:15:36 on February 14, 2016 · (Permalink)
1/2 + 1/4 + 1/8 + 1/16....through infinity, is equal to 1.
Jnr_Guru · 1 points · Posted at 09:15:50 on February 14, 2016 · (Permalink)
1 + 1 = window
Fredvdp · 1 points · Posted at 09:17:59 on February 14, 2016 · (Permalink)
The following is not definitely a fact, but it certainly applies to many numbers.
Take any integer above zero. If it's even, divide by two. If it's uneven, multiply by 3 and add one. If you keep repeating this, you will eventually reach 1.
e.g. 7 - 22 - 11 - 34 - 16 - 8 - 4 - 2 - 1
This has not been proven, so if you can find a number to which this doesn't apply, mathematicians will start writing about you.
https://en.wikipedia.org/wiki/Collatz_conjecture
dpawsit · 1 points · Posted at 09:18:05 on February 14, 2016 · (Permalink)
The summation of all natural numbers (0-->Infinity) is -1/12
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
AnEchoOfBetterTimes · 1 points · Posted at 09:18:07 on February 14, 2016 · (Permalink)
1+2+3...=-1/12
Das_Mojo · 1 points · Posted at 09:18:08 on February 14, 2016 · (Permalink)
You're all wrong. The coolest mathematical fact is that Madonna had 69 booties. That was 2 2 2 many 51 guys x8 them that left her 55378008
juventinosochi · 1 points · Posted at 09:18:18 on February 14, 2016 · (Permalink)
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946 etc.
ideaman21 · 2 points · Posted at 00:54:03 on February 15, 2016 · (Permalink)
I LOVE Fibonacci numbers
ataby · 1 points · Posted at 09:19:06 on February 14, 2016 · (Permalink)
There are always two antipodal (diametrically opposite) places on Earth with the same weather (temperature and pressure). Also known as the [Bursok-Ulam Theorem].(https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem)
MrWedge18 · 1 points · Posted at 09:19:06 on February 14, 2016 · (Permalink)
The sum of all the natural numbers (1 + 2 + 3 + 4 + ...) is equal to -1/12.
cyaul8er · 1 points · Posted at 09:20:17 on February 14, 2016 · (Permalink)
one of my favorite involves dividing numbers by 9. if 1/9 is 0.11111111... and 2/9 is 0.2222222... and 3/9 is 0.3333333... and so forth, shouldn't 9/9 be 0.9999999, and not 1?
Tehbeefer · 1 points · Posted at 09:43:09 on February 14, 2016 · (Permalink)
You may already know this, but 0.9999.... = 1 exactly.
1=3/3=1/3+1/3+1/3=0.333....+0.333...+0.333.....
cyaul8er · 1 points · Posted at 19:36:05 on February 14, 2016 · (Permalink)
but if the decimals were repeating indefinitely, you'd always be 0.000000...........1 off!
Tehbeefer · 2 points · Posted at 15:00:02 on February 15, 2016 · (Permalink)*
Another explanation:
First, let x =0.999...
10x = 9.999...
10x-x = 9.999... - x
9x = 9
x = 1
GratefulGrape · 1 points · Posted at 09:22:12 on February 14, 2016 · (Permalink)
123456789x9=11111111101
123456789x18=22222222202
123456789x27=33333333303
All the way to
123456789x81=99999999909
AreThereAnyCoolNames · 1 points · Posted at 09:23:18 on February 14, 2016 · (Permalink)
π = 3
Juggale · 1 points · Posted at 09:23:20 on February 14, 2016 · (Permalink)
Boring but 111,111,111 x 111,111,111 = 12345678987654321
AnEchoOfBetterTimes · 1 points · Posted at 09:24:21 on February 14, 2016 · (Permalink)
1 + 1 + 1 ... = -1/2
1 + 2 + 3 ... = -1/12
1 + 4 + 9 ... = 0
water_pipes · 1 points · Posted at 09:24:35 on February 14, 2016 · (Permalink)
Time cube
chemicaldecay · 1 points · Posted at 09:26:23 on February 14, 2016 · (Permalink)
42.
original_lunokhod · 1 points · Posted at 09:26:44 on February 14, 2016 · (Permalink)*
On a calculator... subtract sequential even numbers combined from sequential odd numbers combined.
13 - 2 = 11
135 - 24 = 111
1357 - 246 = 1111
13579 - 2468 = 11111
likes_limp_penis · 1 points · Posted at 09:26:47 on February 14, 2016 · (Permalink)
1+2+3+...= -1/12 https://www.youtube.com/watch?v=w-I6XTVZXww&feature=youtu.be
trebell · 2 points · Posted at 09:58:54 on February 14, 2016 · (Permalink)
Interesting video.
TriRight · 1 points · Posted at 09:26:55 on February 14, 2016 · (Permalink)
The square root of -69 is i8.something
pei_cube · 1 points · Posted at 09:27:50 on February 14, 2016 · (Permalink)
On mobile and don't know how to ctrl+f so I hope this isn't already mention but the sum of all positive integers is -1/12 and that's not a typo
Again mobile but here is full link http://m.youtube.com/watch?v=w-I6XTVZXww
It is proven through more advanced methods but it is absolutely true
Nenor · 1 points · Posted at 09:30:04 on February 14, 2016 · (Permalink)
From an infinity of integers, only one is situated between a square and a cube.
spudtatoe · 1 points · Posted at 09:30:10 on February 14, 2016 · (Permalink)
I ate and I ate till I was sick on the floor. Eight eights are sixty four.
HateGrassStains · 1 points · Posted at 09:30:51 on February 14, 2016 · (Permalink)
That if you add all positive integers from 1 to infinity, you end up with the answer -1/12. Just let that soak in for a bit. Adding positive numbers only to get a negative fraction.
Here you go
trxnny · 1 points · Posted at 09:31:14 on February 14, 2016 · (Permalink)
5/7 == 100%
Rossage99 · 1 points · Posted at 09:32:06 on February 14, 2016 · (Permalink)
A dozen, a gross and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
= 9 squared and not a bit more
speeddealer420 · 1 points · Posted at 09:32:48 on February 14, 2016 · (Permalink)
That it's possible to create two things, let's say spheres out of one. It was in a Vsauce video I forgot which.
JX3D97 · 1 points · Posted at 09:33:42 on February 14, 2016 · (Permalink)
that any form of math above elementary level somehow shuts my brain off until exposure to said math is eliminated
6ilchrist · 1 points · Posted at 09:37:03 on February 14, 2016 · (Permalink)
I guess I would say that the derivative of the sine function is the cosine function. That is, the slope of the tangent line to the sine curve is the same as the value of the cosine function.
That or the derivative of ex is... ex. It's the only function where that is true.
Can you tell that I'm taking calculus again and we just got to derivatives?
[deleted] · 1 points · Posted at 09:37:17 on February 14, 2016 · (Permalink)
There are the same number of points in the entire set of real numbers as there are between 0 and 1
Jcstodds · 1 points · Posted at 09:37:28 on February 14, 2016 · (Permalink)
6 + 9 + (6 x 9) =
NuclearNoodle · 1 points · Posted at 09:38:17 on February 14, 2016 · (Permalink)
All primes can be sorted into 2 categories 4n+1 and 4n-1. Any of the p ≡ 1 (mod 4) types (which is technical way of saying 4n+1) can be written as the sum of two primes but the 4n-1 can't.
For example 3*4 +1 = 13 = 32 + 22
hesohi · 1 points · Posted at 09:38:31 on February 14, 2016 · (Permalink)
Florence Nightingale was the first person to use statistics for anything other than gambling. She wasn't the first to suggest that hospitals should be clean, but she was the first to be successful in arguing it by using numbers. She also created the prequel to the pie chart.
guntygoo · 1 points · Posted at 09:38:41 on February 14, 2016 · (Permalink)
https://www.youtube.com/watch?v=w-I6XTVZXww
guntygoo · 1 points · Posted at 09:39:14 on February 14, 2016 · (Permalink)
the sum of ALL numbers (to infinity) = 1/12
TekStarUK · 1 points · Posted at 09:38:57 on February 14, 2016 · (Permalink)
Less of a fact but more knowing how big the number 52! (52 factorial) is. Watch Vsauce's video about it if you are interested
darkmega31 · 1 points · Posted at 09:39:12 on February 14, 2016 · (Permalink)
Something i learned and not as fancy as some of these answer:
Assume there is 3 doors, behind 2 of them are empty and 1 has a goat. Your goal is to pick the door that has a goat behind it. After you picked a door, the the host (or someone) will reveal one of the the remaining 2 doors that happened to be empty and ask you if you want to switch your decision. Question now is: what will be your chance of getting the door that has the the goat if you choose to switch door?
Most people will think they have 50% (one out of 2 doors). However, it was proven that they will have in fact 2/3 chance of picking the door that has the the goat after switch. There is a name for this paradox but I don't remember, on mobile currently
Also, most of the people who read my comment would most likely ignore the the fact that the word "the" always appear twice side by side
ideaman21 · 2 points · Posted at 09:47:11 on February 14, 2016 · (Permalink)
"what will be your chance of getting the door that has the the goat if you choose to switch door?"
You skipped one............................^
CarpeCyprinidae · 1 points · Posted at 10:09:33 on February 14, 2016 · (Permalink)
While mathematically true this (the monty hall problem) isn't reflected in the outcome of repeated experiment as the probability of a door being correct was set WHILE there were still three doors. It's clever mathematic bullshit.
Minority8 · 1 points · Posted at 09:39:51 on February 14, 2016 · (Permalink)
1+2+3+4+5+... = -1/12
Also, this is used in physics (string theory)
Good explanation: https://www.youtube.com/watch?v=w-I6XTVZXww
SchrodingersTabby · 1 points · Posted at 09:40:47 on February 14, 2016 · (Permalink)
Graham's Number is a really big number.
The entropy of a black hole the size of your head carries less information then it would take to write out Graham's Number. So if you tried to write out Graham's Number in your head it would eventually have so much information that it would collapse in on itself to form a black hole.
Here's a video explaining Graham's Number.
Grug16 · 1 points · Posted at 09:41:24 on February 14, 2016 · (Permalink)
1/3 = 0.3333333...
2/3 = 0.6666666...
1/3 + 2/3 = 1.
0.3333333... + 0.6666666... = .9999999...
.9999999... = 1;
[deleted] · 1 points · Posted at 09:43:36 on February 14, 2016 · (Permalink)
Maybe not the most complicated or anything, but one of my favorites, which is weird al inspired is:
"My pancreas attracts every other pancreas in the universe, with a force, proportional, to the product of their masses, and inversely proportional, to the distance between them." also know as: F = G((m1*m2)/D2) (forgive me if it's off, hard to format it into reddit) Which is the formula for gravity.
Okhlahoma_Beat-Down · 1 points · Posted at 09:46:13 on February 14, 2016 · (Permalink)
111,111,111 x 111,111,111 = 12345678987654321
xiape · 1 points · Posted at 09:47:43 on February 14, 2016 · (Permalink)
If you have a complex function with a derivative everywhere, it must have infinitely many derivatives everywhere (entire), and must go off to infinity (unless it's completely flat)
areyouproudofmemom · 1 points · Posted at 09:47:54 on February 14, 2016 · (Permalink)
If you calculate the powers of 11 from 1 until 4 it follows pascals triangle exactly, and then weirdly breaks this pattern.
HjeBrruhhhhhhhhy · 1 points · Posted at 09:48:26 on February 14, 2016 · (Permalink)
Y=mx+b...
[deleted] · 1 points · Posted at 09:48:45 on February 14, 2016 · (Permalink)
Fairly common, but: 1+2+3+4+5+...+(infinity) = ? Should tend to infinity, right?
Nope. 1+2+3+4+5+...+(infinity) = -1/12 HWAT?
For a little bit of intuition and an explanation (courtesy of Numberphile): https://www.youtube.com/watch?v=w-I6XTVZXww
octar1ne · 1 points · Posted at 09:48:58 on February 14, 2016 · (Permalink)
12345679x9=111111111
GaiusRosal · 1 points · Posted at 09:49:05 on February 14, 2016 · (Permalink)
It is possible to cut a sphere into several pieces, and then to reassemble those pieces without stretching into two identical balls w/ the same dimensions as the original.
Cptn_McAwesome · 1 points · Posted at 09:49:41 on February 14, 2016 · (Permalink)
I feel dumb.
[deleted] · 1 points · Posted at 09:49:44 on February 14, 2016 · (Permalink)
Natural logarithms and ex The derivative of ex is ex... That's fucked up
Jca1 · 1 points · Posted at 09:51:12 on February 14, 2016 · (Permalink)
There are the same amount of natural numbers, real numbers, and complex numbers, despite the fact that real numbers contain all the natural numbers and more, and complex numbers contain all the real numbers and more
PizzaGoinOut · 1 points · Posted at 10:20:26 on February 14, 2016 · (Permalink)
This is not true, the cardinality of the reals and the complex numbers is greater than that of the natural numbers
turkishcat · 1 points · Posted at 09:51:44 on February 14, 2016 · (Permalink)
I personally think that quadratic reciprocity is one of the coolest things in mathematics; basically, if you have two primes p, q, the problems of whether or not p is a perfect square modulo q and whether q is a perfect square modulo p are related in an beautiful, symmetric way.
smithmf · 1 points · Posted at 09:52:26 on February 14, 2016 · (Permalink)
That maths works in nature too. If you measure a river as the crow flies from its source to the sea and multiply that distance by pi, you get roughly the distance of it from source to sea including all its meandering corners. This is, apparently, especially true in S. America for some reason.
theeggroaster · 1 points · Posted at 09:54:47 on February 14, 2016 · (Permalink)
The differential of the volume of a sphere = the surface area of that sphere. Also differentiating the surface area of a circle will = the radius. First time I heard this my mind blew.
[deleted] · 1 points · Posted at 09:55:29 on February 14, 2016 · (Permalink)
Pi can be worked out as 4*(1-1/3+1/5-1/7+1/9-...) ad infinitum. When people work out Pi in their heads this is how they do it
I_Raptus · 1 points · Posted at 10:08:12 on February 14, 2016 · (Permalink)
How do you work out 1/7 in your head?
[deleted] · 1 points · Posted at 10:14:12 on February 14, 2016 · (Permalink)
It's rational which means it repeats:
1/7 = 0.142857142857142857...
I_Raptus · 1 points · Posted at 10:20:24 on February 14, 2016 · (Permalink)
Ah okay fair enough. It's still non-trivial mental arithmetic.
[deleted] · 1 points · Posted at 20:05:15 on February 14, 2016 · (Permalink)
Depends on your definition of trivial...
I could work it out in my head and I'm far from being a savant. The trick is knowing: 100/7 = 14 r 2 200/7 = 28 r 4 400/7 =57 r 1
Then you get a loop. Works with 13 too: 100/13 = 7 r 9 900/13 = 69 r 3 300/13 = 23 r 1
This gives 1/13 = 0.076923076923...
All rational numbers will reach that loop
mcmlxiv · 1 points · Posted at 09:56:54 on February 14, 2016 · (Permalink)
ITT: I know nothing about mathematics.
tom3131Y · 1 points · Posted at 09:57:23 on February 14, 2016 · (Permalink)
The sum of the natural numbers is -1/12.
scw55 · 1 points · Posted at 09:59:30 on February 14, 2016 · (Permalink)
Probability is very interesting when applied to MMORPGs (loot drops, probability of combat effects etc.).
bancherul · 1 points · Posted at 10:00:22 on February 14, 2016 · (Permalink)
0.(9)=1
MrMarakuma · 1 points · Posted at 10:03:33 on February 14, 2016 · (Permalink)
I always liked the model of information and probability mathematics delivers. A friend once told me this little riddle with the caption "Mathematics is witchcraft":
A woman tells you she has two children, one of them is a girl. What is the likelihood of said woman having two daughters? By looking through all the possible combinations of two children she can have ((boy,boy);(girl,boy);(boy,girl);(girl,girl)) and excluding (boy,boy) we can verify that the likelihood amounts to 1/3.
Now the woman tells you she has two children, one of which is a girl, and said girl is born on a monday. The probability of her having two female children now rises to 13/27. Whilst the information on which day the girl was born seems arbitrary and not at all related to our question, it still alters our model a lot. Intuition: By stating that the girl was born on a monday, she becomes more fixed. Think about what would happen if the woman told you she had two children, with the older one being a girl. Now the probability for two girls would be 50%.
ninja edit: paragraphs
Popey456963 · 1 points · Posted at 10:06:02 on February 14, 2016 · (Permalink)
Some infinities are larger than other infinities.
PonkyBreaksYourPC · 1 points · Posted at 10:06:08 on February 14, 2016 · (Permalink)
1 + 1 = Window
pjokkidudels · 1 points · Posted at 10:06:30 on February 14, 2016 · (Permalink)
The sum of all positive numbers is -1/12
reign-storm · 1 points · Posted at 10:06:56 on February 14, 2016 · (Permalink)
You can mathematically "prove" that .99999999999 is equal to 1
ecco311 · 1 points · Posted at 10:08:59 on February 14, 2016 · (Permalink)
so 99999999999=100000000000 ?
no
reign-storm · 1 points · Posted at 10:50:16 on February 14, 2016 · (Permalink)
I guess I should have said .999999999999 repeating
ecco311 · 1 points · Posted at 11:31:40 on February 14, 2016 · (Permalink)
thought so
jfffj · 1 points · Posted at 10:08:48 on February 14, 2016 · (Permalink)
Exactly 100% of the infinite series of integers contain the digit 3.
Also: There are an infinite number of integers that do not contain the digit 3.
http://threes.com/percentage-of-integers-containing-digit-3/
Inifinity is weird.
[deleted] · 1 points · Posted at 10:08:56 on February 14, 2016 · (Permalink)
[deleted]
2-Scoopz · 1 points · Posted at 10:30:07 on February 14, 2016 · (Permalink)
one hundred and one.........eat a dick
I_Raptus · 1 points · Posted at 10:10:19 on February 14, 2016 · (Permalink)
The fact that it's the language of Nature and that we can understand it and hence Nature through it.
CarpeCyprinidae · 1 points · Posted at 10:15:14 on February 14, 2016 · (Permalink)
It really should still be called Natural Philosophy. Far better and more apt name.
House_Badger · 1 points · Posted at 10:10:55 on February 14, 2016 · (Permalink)
When you multiply 9 times 1,2,3,4,or 5 the numbers reverse if you multiply them by 6,7,8,9 and 10.
01x9=09 90=10x9 2x9=18 81=9x9 3x9=27 72=8x9 4x9=36 63=7x9 5x9=45 54=6x9
These numbers multiplied by 9 are not exclusive to multiplications of 10 or less but the formula stays pretty much the same. To go into it would involve me typing from or oratating from something other than a smart phone.
timndime · 1 points · Posted at 10:11:00 on February 14, 2016 · (Permalink)
we got some real math nerds in here, haha, I like it!
iambrezrealian · 1 points · Posted at 10:12:04 on February 14, 2016 · (Permalink)
This will probably get buried, but it's a part of mathematics relating to step theory problems.
Let's say some dot can move to the left one unit and right one unit, and it chooses either direction with the same probability (50% chance of the left and 50% of the right), is there a theoretical guarantee that if the dot leaves it's initial point (even if after almost an infinite number of moves), that it'll return to where it starts eventually?
The answer is yes.
Now, assume there is a flat plane of points. So the dot can now move up, down, left, and right, all with equal probability again. Is the dot theoretically guaranteed to return to its starting point?
Yes it is.
Now, assume this dot is in a 3-dimensional space, where it can move left, right, up, down, above, and below itself, all with equal probability. Is the dot theoretically guaranteed to at some point return to its starting point?
No it is not!
It's pretty interesting if you're someone who takes interest in probability/statistics, or math in general!
fenrisulfr94 · 1 points · Posted at 10:12:27 on February 14, 2016 · (Permalink)
Anything to the power of 0 is 1.
[deleted] · 1 points · Posted at 10:12:28 on February 14, 2016 · (Permalink)
a0 =1. This is extremely mindblowing
CharredLunchbox · 1 points · Posted at 10:12:51 on February 14, 2016 · (Permalink)
Clicks to learn something new Oh goes back to watching cartoons
zhl · 1 points · Posted at 10:12:59 on February 14, 2016 · (Permalink)
Prime numbers and their properties. Also big numbers like G64 or TREE(3).
Falonefal · 1 points · Posted at 10:15:26 on February 14, 2016 · (Permalink)
https://www.youtube.com/watch?v=1N6cOC2P8fQ
this would be it :)
crazy_chimps · 1 points · Posted at 10:16:02 on February 14, 2016 · (Permalink)
When multiplying two-digit numbers by 11, add the digits of the "non-11" together and put the result of that in the middle of the two.
Example: 11*27 -> 2+7 = 9 -> 297.
With three-digit numbers, add the 1st and 2nd digits together and then the 2nd and 3rd digits together. Replace the 2nd digit in the three-digit number with the two numbers you got from adding the 1st and 2nd digit and the 2nd and 3rd digit.
Example: 11*234 -> 2+3 = 5 -> 3+4 = 7 -> 2574
I hope that was clear enough.
SolarLiner · 1 points · Posted at 10:16:43 on February 14, 2016 · (Permalink)
1+2+3+4+5...=-1/12
Guguskis · 1 points · Posted at 10:16:52 on February 14, 2016 · (Permalink)
I know that by how many ones you square, the number goes up till the amount of ones and them comes down like pyramid. F. e. 11112=1234321 or 1111112=12345654321 or 112=121
Ethnikoi · 1 points · Posted at 10:20:49 on February 14, 2016 · (Permalink)
The sum of all positive integers is equal to -1/12
The_Specialest_K · 1 points · Posted at 10:21:08 on February 14, 2016 · (Permalink)
It's three in the fucking morning why the hell did I click on this thread
userfriendly4 · 1 points · Posted at 10:21:19 on February 14, 2016 · (Permalink)*
ei*Pi + 1 = 0 , where e = Euler's number and Pi = the ratio of a circle's circumference to its diameter, both are irrational numbers. i = square root of -1.
schlongtoolong · 1 points · Posted at 10:23:05 on February 14, 2016 · (Permalink)
Euler's identity
[deleted] · 1 points · Posted at 10:25:36 on February 14, 2016 · (Permalink)*
He is choosing a book for reading
luncht1me · 1 points · Posted at 10:25:59 on February 14, 2016 · (Permalink)
I just finished writing / drawing this on paper just now. Something to do with spheres, and pyramids, and fitting them together into the same space what ratios of volumes there are. Basis for some tetryonics.
Guess I like to do some geometry when I'm bored.
Jugglingknottier · 1 points · Posted at 10:27:32 on February 14, 2016 · (Permalink)
This limerick - ((12+144+20+3x✔️4)/7)+5x11=92+0
(Sorry, best I can get on mobile!)
A dozen, a gross and a score, Plus three times the square root of four, Divided by seven, Plus five times eleven, Equals nine squared and not a bit more!
Z_9 · 1 points · Posted at 10:27:37 on February 14, 2016 · (Permalink)
A coffee cup and a doughnut/bagel are essentially the same thing: a solid with a one hole.
Thanks topology.
iHaveAgency · 1 points · Posted at 10:27:57 on February 14, 2016 · (Permalink)
That the sum of all the positive integers (1 to infinity) is not infinity, but -1/12. Negative one twelfth. Yes.
This is obviously crazy, yet it is true. There is a not-too-insanely-difficult proof (also one that IS insanely difficult involving the Riemann zeta function). FURTHERMORE, just as many mathematical formulas have real-world application, this one does too, in String Theory for one.
Proof
I guess this implies that the sum of all the negative integers is 1/12.
J_hoff · 1 points · Posted at 10:28:28 on February 14, 2016 · (Permalink)
There are enough molecules in one breath of air that when evenly distributed around the world, each following breath of air from anyone on the planet would contain 1-2 molecules from the first breath.
SaberSamurai · 1 points · Posted at 10:28:30 on February 14, 2016 · (Permalink)
I remember this from middle school, my teacher asked us this and I was one of the only two to get it correct.
How do you make 8 8s equal 1000?
The answer was 888+88+8+8+8.
dejus · 1 points · Posted at 10:28:37 on February 14, 2016 · (Permalink)
The result of 999 is a number larger than atoms in the universe.
homerghost · 1 points · Posted at 10:29:33 on February 14, 2016 · (Permalink)
If you had a teaspoonful of carbon and removed one atom per second, every second, since the dawn of the universe approximately 14 billion years ago, today you would not have even removed one millionth of the total number of carbon atoms in that teaspoonful.
Pablo_Hassan · 1 points · Posted at 10:30:03 on February 14, 2016 · (Permalink)
That any even number can be created by adding 2 prime numbers together
hectoring · 1 points · Posted at 10:30:26 on February 14, 2016 · (Permalink)
1+2+3+4+... = -1/12
SyrValker · 1 points · Posted at 10:30:42 on February 14, 2016 · (Permalink)
If you integrate log of cabin you get log cabin plus the c.
embracing_insanity · 1 points · Posted at 10:31:06 on February 14, 2016 · (Permalink)
Jesus. I thought I was bad at math before, but reading this thread makes me feel like I can't even comprehend...well, just about every fucking thing I'm reading.
[deleted] · 1 points · Posted at 10:31:30 on February 14, 2016 · (Permalink)
Take the imaginary number i, raise it to the imaginary power i, and you get a real (although irrational) number: ii = e-pi/2
Tactical_Wolf · 1 points · Posted at 10:32:54 on February 14, 2016 · (Permalink)
Finally!
Four is the only number with the same number of letters in its name as its numeric value.
FireKatNK · 0 points · Posted at 10:52:05 on February 14, 2016 · (Permalink)
Make me?
Tactical_Wolf · 1 points · Posted at 11:21:22 on February 14, 2016 · (Permalink)
What do you mean?
zangent · 1 points · Posted at 10:34:34 on February 14, 2016 · (Permalink)
Any integer with no 9s divided by an equal number of 9s makes a repeating decimal of the top number.
E.g. 1024/9999 = 0.102410241024...
Daradex · 1 points · Posted at 10:35:27 on February 14, 2016 · (Permalink)
If you add together all of the whole numbers from 1 all the way to infinity I.e 1+2+3+4+5... etc the result is -1/12. This number is also used in a lot of calculations in string theory where it's necessary to know the result of adding all of the numbers together.
I_am_the_visual · 1 points · Posted at 10:35:43 on February 14, 2016 · (Permalink)
Any possible number you can think of, no matter how long, exists within pi.
bysam · 1 points · Posted at 10:36:49 on February 14, 2016 · (Permalink)
The sum of all (infinite) natural numbers (1+2+3+4+..) is: 1/12th.
And this is not just some fun math party trick either, physicists use this to calculate stuff.
iHaveAgency · 1 points · Posted at 10:36:51 on February 14, 2016 · (Permalink)
That the golden ration squared is the golden ration plus one, while the golden ration inverted is the golden ration minus one.
bigdumbstupididiot · 1 points · Posted at 10:36:51 on February 14, 2016 · (Permalink)
U + me = us
marloutoyou · 1 points · Posted at 10:37:19 on February 14, 2016 · (Permalink)
that the continued/chain fraction of only 1's is the Golden Ratio: 1 + (1/(1 + 1/(1 + 1/(1 + 1/(............))))) = 1.618................ = the perfect number for everything (photography, paintings, advertisements etc) https://en.wikipedia.org/wiki/Golden_ratio http://mathworld.wolfram.com/ContinuedFraction.html
CeeArthur · 1 points · Posted at 10:37:49 on February 14, 2016 · (Permalink)
A geologist I met while working abroad explained Mandelbrot and fractals occurring in nature to me when I was a little drunk and stoned sitting by a fire roasting some marshmallows. My mind imploded on itself.
Ehsan763 · 1 points · Posted at 10:38:43 on February 14, 2016 · (Permalink)
Quadratic formula... D1 Math and Algebra
[deleted] · 1 points · Posted at 10:39:12 on February 14, 2016 · (Permalink)
E=MC2
Pinkum · 1 points · Posted at 10:39:37 on February 14, 2016 · (Permalink)
17 1+7=8 17-8=9
62 6+2=8 62-8=54 5+4=9
574 5+7+4=16 574-16=558 5+5+8=18 1+8=9
6482 6+4+8+2=20 6482-20=6462 6+4+6+2=18 1+8=9
ETC...
27569416953 2+7+5+6+9+4+1+6+9+5+3=57 27569416953-57= 27569416896 2+7+5+6+9+4+1+6+8+9+6=63 6+3=9
t0b4cc02 · 1 points · Posted at 10:40:39 on February 14, 2016 · (Permalink)
the mandelbrot set is so endless and always different but similliar
https://en.wikipedia.org/wiki/Mandelbrot_set
[deleted] · 1 points · Posted at 10:44:16 on February 14, 2016 · (Permalink)
That 1+1 CAN equal 3.
sirgog · 1 points · Posted at 10:44:16 on February 14, 2016 · (Permalink)
1/1 + 1/4 + 1/9 + 1/16 + 1/25 + .....
is equal to (pi2 )/6.
asosaffc · 1 points · Posted at 10:45:21 on February 14, 2016 · (Permalink)
Dividing the Great Pyramid's perimeter by twice its height will get Pi to the fifteenth digit
Nuwanda84 · 1 points · Posted at 10:46:11 on February 14, 2016 · (Permalink)
Graham's number is so large you can't even write out the digits of it in all of the available space of the universe. Thought that was pretty neat.
TrustN · 1 points · Posted at 10:46:49 on February 14, 2016 · (Permalink)
How to square any corner with 3,4,5. Geometry mf'n Geometry
CaptainTone · 1 points · Posted at 10:46:59 on February 14, 2016 · (Permalink)
69 x 69 = 4761... I used to do that every time I had a calculator and I don't know why...
Arekousu · 1 points · Posted at 10:47:27 on February 14, 2016 · (Permalink)
1 + 1 = 2...
Even in binary.
VeniVidiVixen · 1 points · Posted at 10:47:28 on February 14, 2016 · (Permalink)
Phi (1.61803398...) is the only number that becomes its own square by adding 1, and its own reciprocal by subtracting 1.
[deleted] · 1 points · Posted at 10:48:13 on February 14, 2016 · (Permalink)
The moon is 400 times smaller than the sun but is also 400 times closer to it (than Earth), so it appears to be the same size.
FireKatNK · 1 points · Posted at 10:50:18 on February 14, 2016 · (Permalink)
The number 4 is the only number with the same number of letters as its value. Mind blown.
chandu1504 · 1 points · Posted at 10:50:34 on February 14, 2016 · (Permalink)
This kind of amazed me https://www.youtube.com/watch?v=ZLiPr8xvCe8
[deleted] · 1 points · Posted at 10:50:36 on February 14, 2016 · (Permalink)
Every number of three or less digits that is a multiple of 37 will still be if its digits are cyclically permuted. A few examples :
And it works in any base !
Edit : got that from bash.org a long time ago (when it was still active) but I don't seem to be able to retrieve the source.
jammu · 1 points · Posted at 10:50:40 on February 14, 2016 · (Permalink)
that the number of real numbers between 1 and 2 is same as that between 1 and 3, and that the number of rational numbers between 1 and 2 though infinite is less than number of reals between 1 and 2.
Scotteo · 1 points · Posted at 10:51:50 on February 14, 2016 · (Permalink)
That 0.999... equals 1
https://en.wikipedia.org/wiki/0.999...
FrankieG726 · 1 points · Posted at 10:52:33 on February 14, 2016 · (Permalink)
Girls = Evil proof
https://www.youtube.com/watch?v=HyRGLDqSPRA
QWERASDYX · 1 points · Posted at 10:53:23 on February 14, 2016 · (Permalink)
The sum of all natural numbers (positive) is -1/12
The-red-Dane · 1 points · Posted at 10:55:37 on February 14, 2016 · (Permalink)
There are more numbers between 1 and 2 than we have ever counted to, with or without mechanical aid.
Because you can always just add a decimal after 1, meaning there is theoretically a infinite amount of numbers between 1 and 2 (and 2 and 3, etc)
sb120985 · 1 points · Posted at 10:56:00 on February 14, 2016 · (Permalink)
80083
POINTEEEE · 1 points · Posted at 10:58:11 on February 14, 2016 · (Permalink)
don't you mean 38008
sb120985 · 1 points · Posted at 11:02:53 on February 14, 2016 · (Permalink)
Oh, yes. I forgot that its 80085 when its turned upside down. Thanks for catching that. Also, 35071.
jfb1337 · 1 points · Posted at 10:59:46 on February 14, 2016 · (Permalink)
ei*pi + 1 = 0
o0_bigchief_0o · 1 points · Posted at 11:01:55 on February 14, 2016 · (Permalink)
987654312 / 8 = 123456789
falaicha · 1 points · Posted at 11:04:30 on February 14, 2016 · (Permalink)
152207*73=11111111
o0_bigchief_0o · 1 points · Posted at 22:27:34 on February 14, 2016 · (Permalink)
11111111111111111111 / 987654321 = 11249999999.9
the-h8ful-m8 · 1 points · Posted at 11:03:33 on February 14, 2016 · (Permalink)
Add 1 to Product of 4 consecutive numbers to get a perfect square! i.e. 1+x(x+1)(x+2)*(x+3) = (1+3x+x2 )2 , => a perfect square. Theorem is MATHEMATICALLY applicable to all numbers, but a definition of "perfect square" requires x to have integer value.
Inventorclemont · 1 points · Posted at 11:06:14 on February 14, 2016 · (Permalink)
29009
[deleted] · 1 points · Posted at 11:07:24 on February 14, 2016 · (Permalink)
If you deduct from a number its reverse enough times, you'll end up with either zero or some palindrome number. Example:
I once got bored as a kid and had only a calculator to play with. Many years later, I've yet to found an exception.
lonsdale992 · 1 points · Posted at 11:08:08 on February 14, 2016 · (Permalink)
Mine is
you see where I am going..
McAwesome_Face · 1 points · Posted at 11:08:26 on February 14, 2016 · (Permalink)
I can't wrap my head around that the sum of all integers =-1/12 https://youtu.be/w-I6XTVZXww
engineeringsForAll · 1 points · Posted at 11:10:37 on February 14, 2016 · (Permalink)
Not really math, but the melting point of gold is 1337 kelvin. Mind = blown.
unazim · 1 points · Posted at 11:12:18 on February 14, 2016 · (Permalink)
10=1
MissBelly · 1 points · Posted at 11:17:03 on February 14, 2016 · (Permalink)
The sum of all positive integers approaches -1/12
Gladix · 1 points · Posted at 11:17:36 on February 14, 2016 · (Permalink)
Sum of all integers (1 + 2 + 3 + 4 + ...) is - 1/12 calculated with partial sums. Kinda neat when you think about it. The sum of all whole positive numbers is partial negative number.
Fenrime · 1 points · Posted at 11:18:10 on February 14, 2016 · (Permalink)
372 is divisible by 3 because 3+7+2=12 , 1+2 is divisible by 3. Just add up the numbers to find out if it's divisible by 3.
TheAviot · 1 points · Posted at 11:19:58 on February 14, 2016 · (Permalink)
ITT
Infinityharry · 1 points · Posted at 11:20:41 on February 14, 2016 · (Permalink)
Pi = 3.14
MeshachBlue · 1 points · Posted at 11:21:42 on February 14, 2016 · (Permalink)
1 + 2 + 4 + 8 + 16 + ... = -1
mesofire · 1 points · Posted at 11:23:51 on February 14, 2016 · (Permalink)
Divide by 0.
[deleted] · 1 points · Posted at 11:25:29 on February 14, 2016 · (Permalink)
calculater joke i learned in 3rd grade A woman's boobs weighed 69 pounds, which she though was 2, 2, 2 much. So she went down 51st street to see DR. X he gave her 8 pills.....which left her....
6922251x8= BOOBLESS
troglidite1000 · 1 points · Posted at 11:32:46 on February 14, 2016 · (Permalink)
I learnt it in primary school (uk) as there was a girl who was 13 and had size 84 books but wanted size 45 so she went to the doctor and the doctor said 0h take these tablets 2 X (times) a day and she ended up boobless
rezdm · 1 points · Posted at 11:26:00 on February 14, 2016 · (Permalink)
1 + ei*Pi = 0
[deleted] · 1 points · Posted at 11:27:15 on February 14, 2016 · (Permalink)
My favourite things:
The platonic solids.
Hexagons are the regular polygon with the highest number of sides you can tile on a plane
Triangles have the fewest number of sides possible to create a 2d polygon, making triangles the fundamental polygon. It's easy to make any other polygon out of triangles.
Golden ratio.
Euler's number, e
tfriggink314 · 1 points · Posted at 11:27:38 on February 14, 2016 · (Permalink)
(3x)2 + (4x)2 = (5x)2
antsofretribution · 1 points · Posted at 11:27:43 on February 14, 2016 · (Permalink)
The number of potential chess games there are. I would try and explain it but couldn't do it justice.
sdo17yo · 1 points · Posted at 11:28:14 on February 14, 2016 · (Permalink)
From grade school, that you can do the nine times table with your ten fingers spread out on your desk.
9x1=spread out all ten fingers, hide the first finger. The answer is the remaining fingers=9.
9x2=spread out all ten fingers, hide the second finger. The answer is the amount of fingers on the left of the second finger put together with the number of fingers on the right=18.
9x3=spread out all ten fingers, hide the third finger. The answer is the amount of fingers on the left of the third finger put together with the number of fingers on the right=27.
Etc.
Ownejj · 1 points · Posted at 11:28:26 on February 14, 2016 · (Permalink)
If you keep halving your steps as you walk towards a door you will never leave the room.
Javssoccer · 1 points · Posted at 11:30:04 on February 14, 2016 · (Permalink)
Anything to do with Topology.
dannyquads · 1 points · Posted at 11:30:16 on February 14, 2016 · (Permalink)
Balthegor's prime (1000000000000066600000000000001) is a vaguely interesting number, a palindromic prime number that the superstitious think is significant due to the 13 0's either side of the number of the beast. https://en.wikipedia.org/wiki/Belphegor%27s_prime
Aznreka · 1 points · Posted at 11:35:24 on February 14, 2016 · (Permalink)
But what is it used for?
lfeuerbach · 1 points · Posted at 11:30:42 on February 14, 2016 · (Permalink)
That if you scaled down the earth to the size of a pool/billiard ball, it would be just as smooth.
Observante · 1 points · Posted at 11:31:43 on February 14, 2016 · (Permalink)
6 is afraid of 7.
TonyMatter · 1 points · Posted at 11:31:47 on February 14, 2016 · (Permalink)
I've heard that pies are squared.
SirSteve_ · 1 points · Posted at 11:33:13 on February 14, 2016 · (Permalink)
If you flip 3.14 (Pi) upside horizontally and vertically it looks like the word "PIE". Feel free to write a paper on this. I'm expecting a nobel prize.
arcs · 1 points · Posted at 11:33:22 on February 14, 2016 · (Permalink)
If you do a contour integral around the pole of a complex function f(z) you will get the same answer as the first term of the Taylor approximation of said function at that point. (Times 2 pi i)
[deleted] · 1 points · Posted at 11:33:23 on February 14, 2016 · (Permalink)
The ratio of the length of and A4 sheet of paper to its breath is square root of 2.
This works for all A- papers (A0, A1, A2, A3, A4,... )
drdaddyzen · 1 points · Posted at 11:33:25 on February 14, 2016 · (Permalink)
If this is true, then this: if you divide a number by half, and then again, and again, and so on, you never reach 0.
qevlarr · 1 points · Posted at 11:33:41 on February 14, 2016 · (Permalink)
Gödel's incompleteness theorems
In any mathematical system capable of describing anything useful, there are theorems which are true, but can never be proven.
OrangeDit · 1 points · Posted at 11:33:56 on February 14, 2016 · (Permalink)
Just a simple thing: That the area of the function ex from -infinity to 0 is 1. It's infinitely growing and growing, but the sum is the finite number 1. Blew my mind, when I learned it.
johkih · 1 points · Posted at 11:35:18 on February 14, 2016 · (Permalink)
I always found it pretty cool that if the sum of the digits in a number is divisible by 3, then the whole number is divisible by three. For instance, 441231, 4+4+1+2+3+1 = 15, 1+5 = 6, 6 is divisible by three, therefore 441231 is divisible by three. Also works with 9.
SaturnMoth · 1 points · Posted at 11:36:08 on February 14, 2016 · (Permalink)
Jet fuel can't melt steel beams.
[deleted] · 1 points · Posted at 11:37:10 on February 14, 2016 · (Permalink)
1 + 1 = 10
yet
1 + 10 = 11
ecco311 · 2 points · Posted at 11:37:40 on February 14, 2016 · (Permalink)
what
skydiveguy · 2 points · Posted at 12:09:16 on February 14, 2016 · (Permalink)
its a poor attempt at a binary joke.... 1+1=2.... 2 in binary is 00000010
ecco311 · 1 points · Posted at 12:16:43 on February 14, 2016 · (Permalink)
oh... well...
ethanpo2 · 1 points · Posted at 11:38:08 on February 14, 2016 · (Permalink)
Really annoying but really cool.
Also, the everything formula. It graphs itself, and can graph almost anything.
ecco311 · 1 points · Posted at 11:41:07 on February 14, 2016 · (Permalink)
Typing 71346315 in a calculator and turning it around will turn you into Adolf Hitler
user5577 · 1 points · Posted at 11:42:50 on February 14, 2016 · (Permalink)
eipi + 1 = 0
Aznreka · 1 points · Posted at 11:43:27 on February 14, 2016 · (Permalink)
"Dek, el, and do." The power of twelve.
aaegler · 1 points · Posted at 11:46:02 on February 14, 2016 · (Permalink)
If you add the individual numbers of multiples of 9 they will always add up to 9, or multiples of 9 (the higher you go). Eg, 9 x 4 = 36. 3 + 6 = 9.
Mad_Jas · 1 points · Posted at 11:49:12 on February 14, 2016 · (Permalink)
All numbers divisible by 3 add up to 3, 6, 9. Despite the fact that I "discovered" this in my own little world, I'm sure I'm hundreds of years behind the curve.
Ex1) 519. 5+1+9=15; 1+5=6... therefore 519 is divisible by 3.
Ex2) 12321. 1+2+3+2+1=9; therefore divisible by 3
[deleted] · 1 points · Posted at 11:56:01 on February 14, 2016 · (Permalink)
If you add up all the positive integers, I.e. 1+2+2+4+5+... All the way up to infinity, the answer which pops out is -1/12. The positive whole numbers add up to give a negative fraction. Have a nice day.
monsterjager · 1 points · Posted at 11:56:12 on February 14, 2016 · (Permalink)
That 60% of the time, it works every time.
bengals02 · 1 points · Posted at 11:56:46 on February 14, 2016 · (Permalink)
You're always within 20 moves of solving a Rubik's cube. Also Zeno's Paradox. Basically to go anywhere you have to get halfway there but then you have to get halfway there but then you have to get halfway there and so on and so forth. Infinity is everywhere.
Edit: Words
oighen · 1 points · Posted at 11:57:09 on February 14, 2016 · (Permalink)
Take a cup full of water, gently mix it with a spoon without touching the walls of the cup. Brower fixed point theorem says that there is at least one molecule in the exact same place it was before you mixed.
Now the weather. Someone already said that there's always at least a cyclone on Earth. A neater fact is that at any moment there are at least two antipodal points with the exact same temperature and atmospheric pressure. This is due to Borsuk-Ulam theorem.
Oh, on a useful note. Everybody knows that a three legged table can't wobble since three points define a plane. Unfortunately four legged tables often wobble. If the wobbling is due to the terrain and not to the fact that you are a cheap ass and bought a shit table and the table is square, simply turning it at most 90° will fix the wobble.
Epicritical · 1 points · Posted at 11:58:14 on February 14, 2016 · (Permalink)
e to the i pi plus 1 equals 0
Heisenbuggered · 1 points · Posted at 11:58:41 on February 14, 2016 · (Permalink)
That 0.999999999999999 (recurring) = 1
popsicle_cat · 1 points · Posted at 11:58:51 on February 14, 2016 · (Permalink)
That there is a 240 sided shape called a rhombicosidodecahedron
synapticimpact · 1 points · Posted at 11:59:49 on February 14, 2016 · (Permalink)
I love this thread
cometbird · 1 points · Posted at 12:00:32 on February 14, 2016 · (Permalink)
I used to know loads, all seems to have been forgotten for now
Not_Snoo · 1 points · Posted at 12:00:47 on February 14, 2016 · (Permalink)
The sum of all natural numbers is equal to -1/12
ApocryphalCanon · 1 points · Posted at 12:03:46 on February 14, 2016 · (Permalink)
2cool 2be 4gotten
[deleted] · 1 points · Posted at 12:03:50 on February 14, 2016 · (Permalink)
a way t remember e.
There are 2 things i want you to remember about andrew jackson. He was the 7th president elected in 1828... 2.71828 he was elected twice so we'll write it twice. 2.718281828. his face was very angular... so we'll the degrees of a special traingle... 45 90 45. 2.718281828459045. the angular/triangle thing is a stretch, but he really was the 7th president and was elected twice... the first time in 1828
FortunateGreg · 1 points · Posted at 12:04:13 on February 14, 2016 · (Permalink)
My favourite example of the Mean Value Theorem is this : "imagine you've just stumbled out of a pub and start to head home. You sway back and forth going in the wrong direction a heap of times. Eventually you make it home. To have made it home there was at least one time you were facing in the exact correct direction you should've headed after leaving the pub." That is how my Real Analysis lecturer explained it to us.
marktx · 1 points · Posted at 12:05:35 on February 14, 2016 · (Permalink)
the sum of all natural numbers all the way up to infinity = -1/12
moon_ninja · 1 points · Posted at 12:06:01 on February 14, 2016 · (Permalink)*
A couple of ones I always like are:
The sum of all positive integers up to infinity is equal to one 12th (1+2+3+4+....=-1/12).
There are no parallel lines in the universe, if you have two straight line on the same plane they will eventually meet, twice!
Edit: made a positive into a negative
dWintermut3 · 1 points · Posted at 12:06:24 on February 14, 2016 · (Permalink)
In physics to move between acceleration, velocity, and position you use integrals and derivatives, but you can keep going, finding the rate of change in acceleration (jerk) and the rate of change in jerk, which is snap.
These are important to a lot of fields, most notably moving and braking systems (because jerk is what causes whiplash and other unpleasant physiological effects) and robotics (where jerk and snap not only define how fluid a motion looks but how much stress it places on mechanical joints).
But you can keep going even further! The fifth derivative is crackle, and the sixth is pop.
These have less practical use than jerk and snap, and are mostly of interest to mathematicians because the rate at which the rate of change of acceleration is changing is hardly a vital mechanical statistic.
gordo65 · 1 points · Posted at 12:09:17 on February 14, 2016 · (Permalink)
0-273.15=0
Chronogos · 1 points · Posted at 12:10:21 on February 14, 2016 · (Permalink)
The number 47 seems to be the most common number when found in a random amount of numbers.
I have noticed that many online-only digitally downloaded products are usually $47...
Mosarwa · 1 points · Posted at 12:11:10 on February 14, 2016 · (Permalink)
Any number multiplied by zero is zero. So choosing not to multiply whatever you have will leave you with nothing.
sommarland · 1 points · Posted at 12:12:09 on February 14, 2016 · (Permalink)
Not really as cool as most other posts, but i felt so fucking smart when I as a kid realized that 9*x would always end up with a number that could be turned into a new 9:
9*2=18 | 1+8=9
9*7=63 | 6+3=9
9*43=387 | 3+8+7=18 | 1+8=9
9x386,72=3480,48 | 3+4+8+0+4+8=27 | 2+7=9
Golmin3 · 1 points · Posted at 12:13:48 on February 14, 2016 · (Permalink)
Everyone in the world is connected by 7 people.
Graathor · 1 points · Posted at 12:13:52 on February 14, 2016 · (Permalink)
I have always thought encryption and RSA cryptography to be interesting. I mean it basically makes the internet possible.
Izzy42 · 1 points · Posted at 12:14:02 on February 14, 2016 · (Permalink)
That the temperature when both the Celsius and Fahrenheit scales are the same is -40 degrees.
It's 'cool' because, you know, below freezing.
thehighschoolgeek · 1 points · Posted at 12:15:01 on February 14, 2016 · (Permalink)
Ah! The geeky side of reddit meets the funny one
francisdavey · 1 points · Posted at 12:15:15 on February 14, 2016 · (Permalink)
This is a bit obscure, but, the number of "differential structures" (explanation below) for the very simple space Rn is:
1 - for n not equal to 4
uncountably infinite - for n=4
What I think is cool about that is not only that 4 dimensions is different, but how much the difference is. Also that we may well live in a 4D space.
"Differential structure" is a bit of a complicated idea, but. Imagine you want to draw a map of something. Sometimes you can do that find with a nice Euclidean drawing (eg a map of a football field, can be drawn on a 2D picture), but sometimes you can't, eg you can't draw a map of the Earth on a flat piece of paper without distorting something impossibly (eg by having the pole a line across the top).
So, you could do this by having a number of pictures (known technically as "charts"). You can do this with two charts for a sphere for instance.
A differential structure is (roughly speaking) one where you use n-dimensional charts and where the charts overlap you can convert from one chart's co-ordinate system to the other in a way that is differentiable (in the high school sense).
Obviously some ways of doing this aren't fundamentally different from others. Eg you could take two charts of the Earth and move teeny bits of one to the other in a neatly differentiable way and that would make no difference (in technical language the two systems are equivalent as differential structures).
A differential structure is one of these systems of charts where the overlaps are all nicely differentiable. For R2 (say) there's only one really distinct way of doing this. For R4 there are lots.
myztry · 1 points · Posted at 13:24:08 on February 14, 2016 · (Permalink)
We don't actually live in 3D space, as in x, y & z which are constructs for convenience replaceable by things like spherical co-ordinates. Our real existence is more akin to vectors where everything is merely direction with a magnitude.
Perhaps one day FTL travel will be achieved not by moving but by reducing the magnitude of distance ahead of the vessel while increasing the magnitude behind the vessel, in a given direction.
loptthetreacherous · 1 points · Posted at 12:16:07 on February 14, 2016 · (Permalink)
Integral t squared dt
From one to the cubed root of 3
Times the cosine
Of three pi over nine
Is the log of the cube root of e
TheBames · 1 points · Posted at 12:17:13 on February 14, 2016 · (Permalink)
6 is afraid of 7 because 7 8 9!
anthem47 · 1 points · Posted at 12:17:52 on February 14, 2016 · (Permalink)
Binomial distribution is a favourite of mine, and while the Gambler's Fallacy (the belief that past performance is an indicator of future performance) is perfectly valid, it frequently gets mistakenly applied in conversations regarding dice rolls and slot machines.
Say you're trying to roll a 1 on a six sided dice, so you have a one in six chance of winning a roll. Anyone will tell you that the odds never improve and you are never "due" for a win. This is technically true but ignores the fact that while the odds of rolling a one remain constant per roll, the odds of finding a success in a sample of rolls do increase as the sample size gets larger.
To put it another way, if you roll one million dice, the odds of rolling a 1 are a constant 16.66% per dice, but 99.99% over the entire sample. And while continuing to roll dice will never "guarantee" you a win, the event of never rolling a win will become increasingly improbable the more dice you roll.
So gamblers, a machine is never "due" for a win, but if it has been pulled a 100 billion times and not paid out, it's either a statistical anomaly, or broken.
Cindibot9000 · 1 points · Posted at 12:18:35 on February 14, 2016 · (Permalink)
80085!
[deleted] · 1 points · Posted at 12:18:38 on February 14, 2016 · (Permalink)
That you can get the correct last n digits of a power using modulo even if the exponent is insanely large. This is what RSA encryption uses.
CyborgSlunk · 1 points · Posted at 12:18:47 on February 14, 2016 · (Permalink)
ITT: Every single Numberphile video.
[deleted] · 1 points · Posted at 12:19:01 on February 14, 2016 · (Permalink)
111,111 x 111,111 = 12,345,654,321
derrickcope · 1 points · Posted at 12:21:58 on February 14, 2016 · (Permalink)
Wow, cool and mathematical fact used in the same sentence. We're not in Kansas any more Toto.
AvoidApathy · 1 points · Posted at 12:22:00 on February 14, 2016 · (Permalink)
probably already been posted, but just in case it hasn't
the sum of all positive integers = -1/12
Tee_Hee_Wat · 1 points · Posted at 12:22:54 on February 14, 2016 · (Permalink)
That the sequence 1+2+3+4+5...+n = -(1/12)
The entirety of our number system to infinity equals -(1/12)
clopensets · 1 points · Posted at 12:23:09 on February 14, 2016 · (Permalink)
Well in honor of my reddit user name, one of my favorite mathematical objects is a clopen set. A open set Ais a generalization of the metric space concept of an open set, basically you can create a tiny ball around any point in the set. A closed set B is a set whose compliment--i.e. all of the space that is not in the set B--is open. A clopen set is both open and closed. Now in the metric space of real numbers, the only clopen sets are all of the real numbers and the empty set. But there are topological spaces who sets are all clopen! It's crazy.
peanutismint · 1 points · Posted at 12:24:41 on February 14, 2016 · (Permalink)
I've posted this before and some people replied to point out how I was wrong, but here goes anyway:
The idea that 'Pi' can be represented by an infinitesimally long number of seemingly random (but obviously not 'random') digits means that, theoretically, if you assigned every number a value, say a letter or even just 1s and 0s in binary, somewhere along that infinite number of decimal places you would find the entire written works of Shakespeare, for example.
is that right??!
emirp799 · 1 points · Posted at 12:24:58 on February 14, 2016 · (Permalink)
When a prime number is prime when it is reversed, like 13 and 31, it's called an emirp. Which is prime backwards.
QuargRanger · 1 points · Posted at 12:25:28 on February 14, 2016 · (Permalink)
By extending the notion of functions to complex numbers, then pretty much for free you get out that a bunch of super difficult things can be integrated by performing differentiation.
Was just mindblowing the first time I saw it.
(Cauchy Residue Theorem, for anyone interested)
Blood_Type_Pepsi · 1 points · Posted at 12:26:24 on February 14, 2016 · (Permalink)
my favourite fact is more of a statistical fact that most people have more than the average number of Limbs
FenixthePhoenix · 1 points · Posted at 12:27:11 on February 14, 2016 · (Permalink)
The amount of numbers between 1 and 2 are the same as the amount of numbers between 1 and 3 or 1 and 100. Still find the concept of infinity crazy.
Lone_some · 1 points · Posted at 12:28:56 on February 14, 2016 · (Permalink)
Yay...another math post that makes no sense to me. I'm so smart.
SkyComesFalling · 1 points · Posted at 12:29:33 on February 14, 2016 · (Permalink)
Euler's identity is awesome.
ei*pi + 1 = 0
jellsprout · 1 points · Posted at 12:29:46 on February 14, 2016 · (Permalink)
ii is a real number.
NagNella · 1 points · Posted at 12:32:11 on February 14, 2016 · (Permalink)
3n+1 principle
pequatri · 1 points · Posted at 12:34:06 on February 14, 2016 · (Permalink)
My elementary school students love how in the 9x table (up to 10x9) if you add the tens digit and ones digit together you always get 9. This is how the finger trick works. For example 7x9=63, 6+3=9.
ExcitedFox · 1 points · Posted at 12:34:40 on February 14, 2016 · (Permalink)
E=MC²
I'm not very good at math.
alexb507 · 1 points · Posted at 12:37:52 on February 14, 2016 · (Permalink)
That the answer to everything in the universe is 42.
MpMerv · 1 points · Posted at 12:39:40 on February 14, 2016 · (Permalink)
I'm not too knowledgeable in math so I'm sure there are much cooler facts than this, but I think it's weird how there is no exact number to describe pi, the ratio of a circle's radius to its area. 3.14159 just goes on forever so it begs the philosophical question, do we really know the area of a circle ever?
kronopovici · 1 points · Posted at 12:40:52 on February 14, 2016 · (Permalink)
2+2=4
Kefass · 1 points · Posted at 12:42:03 on February 14, 2016 · (Permalink)
It is never proved that 1+1=2
Kolabunyi · 1 points · Posted at 12:44:42 on February 14, 2016 · (Permalink)
I like cake, too, and that's a cool explai ation, but it's a METAPHOR, not an analogy.
LigerZerOJaegaer · 1 points · Posted at 12:45:59 on February 14, 2016 · (Permalink)
sum of all positive integers is -1/12
jo_annev · 1 points · Posted at 12:47:04 on February 14, 2016 · (Permalink)
This question and answers are so cool!! My answer seems less intelligent but I still find it interesting. The Pythagorean theorem is interesting to me. I think it is fascinating that if the hypotenuse of a right triangle were made out of steps, no matter how small the steps, at some point it changes into a straight line with a different length.
bacami47 · 1 points · Posted at 12:47:54 on February 14, 2016 · (Permalink)*
In mathematics zero stands for nothing. However, nothing cannot be represented by anything.... not even a 0
gaussjordanbaby · 1 points · Posted at 15:04:01 on February 14, 2016 · (Permalink)
That's so stupid
fenderrocker · 1 points · Posted at 12:48:19 on February 14, 2016 · (Permalink)
The digits of any multiple of 9 add up to 9.
9 = 9
18 --> 1 + 8 = 9
27 --> 2 + 7 = 9
...
8,991 --> 8 + 9 + 9 + 1 = 27 --> 2 + 7 = 9
...
111,105 --> 1 + 1 + 1 + 1 + 5 = 9
I have no idea how to actually prove this (maybe with mathematical induction?), but I came across it a few years ago and thought it was interesting.
CommodoreKrusty · 1 points · Posted at 12:48:41 on February 14, 2016 · (Permalink)
Exponential growth isn't a thing. It's actually called Geometric growth.
djabor · 1 points · Posted at 12:48:53 on February 14, 2016 · (Permalink)
infinitely summing integers yields -1/12
1+2+3+4+...+n = -1/12
it is actually know as "one of the most remarkable formulae in science".
the 'result' actually has use in quantum field theory among others.
src: https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
shifted1119 · 1 points · Posted at 12:49:30 on February 14, 2016 · (Permalink)*
That 1+2+3+4+5+6+.... = -1/12
No joke. It's actually used in complex physics like string theory and the "proof" is really easy to follow. You just have to accept that 1-1+1-1+1-1+... all the way to infinity averages out to 1/2, then it's like 3 steps.
https://www.youtube.com/watch?v=w-I6XTVZXww
alignedletters · 1 points · Posted at 12:51:11 on February 14, 2016 · (Permalink)
Monstrous Moonshine!
There's a surprising connection between the j-invariant, a modular function (well, its Laurent series representation, which is like a way to write down a function as an "infinite polynomial") and the Monster group. The fucking monster group. WTF? How the fuck are those two even connected??!
Well, they are and it's mind-boggling.
CommodoreKrusty · 1 points · Posted at 12:51:48 on February 14, 2016 · (Permalink)
A math Postulate is something unproven (or so self-evident that nobody's bothered going through the trouble of proving it) and just taken for granted to be true.
sachinyadav2 · 1 points · Posted at 12:51:52 on February 14, 2016 · (Permalink)
Match trick
bburghokie · 1 points · Posted at 12:58:37 on February 14, 2016 · (Permalink)
this--> 1=0.999...
Heisenmountain · 1 points · Posted at 13:00:25 on February 14, 2016 · (Permalink)
0.33333333... x 3 = 1 As 1/3 x 3 = 1 And 0.333333... = 1/3 As there is no Number existing between 0.9999... and 1 it is considered the same number. I did not want to accept this the first time i heard this but finally I had to :(
blueblast88 · 1 points · Posted at 13:00:28 on February 14, 2016 · (Permalink)
If you want to know if a number is evenly divisible by 3 without a calculator, add all the digits of the number. EX: 123 1+2+3 = 6 which is divisible by three and so is 123
HolesHaveFeelingsToo · 1 points · Posted at 13:00:48 on February 14, 2016 · (Permalink)
Jenny's phone number, 867-5309, from the Tommy Tutone song is a twin prime
8923805610 · 1 points · Posted at 13:02:19 on February 14, 2016 · (Permalink)
Not using grid paper shows you lack 20% of the understanding necessary, its that important
sjroberts9 · 1 points · Posted at 13:02:45 on February 14, 2016 · (Permalink)
Imaginary numbers, where i2 = -1
[deleted] · 1 points · Posted at 13:02:53 on February 14, 2016 · (Permalink)
The square root of 69 is 8 somthing.
mormotomyia · 1 points · Posted at 13:03:55 on February 14, 2016 · (Permalink)
you have always two opposite points in earth where the temperature is the same.
Rytannosaurus_Tex · 1 points · Posted at 13:05:40 on February 14, 2016 · (Permalink)
The sum of 1+1-1+1-1+1-1+1-1... is equal to not 1, not 0, but 1/2.
More interestingly, the sum of all natural numbers isn't infinity like one would think it is - it's equal to -1/12.
ck2839 · 1 points · Posted at 14:05:48 on February 14, 2016 · (Permalink)
1+1-1+.. is called Grandi's series.
1+2+3+... = -1/12 is an example of Ramanujan summation being used. It's a different kind of summation.
[deleted] · 1 points · Posted at 13:05:43 on February 14, 2016 · (Permalink)
eipi= -1
widden · 1 points · Posted at 13:07:09 on February 14, 2016 · (Permalink)
Fibonacci Number
[deleted] · 1 points · Posted at 13:09:44 on February 14, 2016 · (Permalink)
Take all the digits of any multiple of 9 and add them together until one digit remains. The answer is always 9.
9 * 9 = 81 8 + 1 = 9
Its a fast way to figure out if a number is divisible by 9.
9801 9 + 8 + 1 = 18 1+8=9.
This number is divisible by 9.
percival__winbourne · 1 points · Posted at 13:10:48 on February 14, 2016 · (Permalink)
According to every primary/elementary school ever: rote repetition of times tables = math brain
thefrado · 1 points · Posted at 13:13:33 on February 14, 2016 · (Permalink)
An infinite nuber of actions can be performed in a finite amount of time. For example: Cut a piece of paper in half in one minute. Then cut one of those halves in half in 30 seconds. A half of that in 15 seconds and so on. You will never exceed 2 minutes.
IThinkTheClockIsSlow · 1 points · Posted at 13:17:49 on February 14, 2016 · (Permalink)
2 + 2 = 5
sonanz · 1 points · Posted at 14:43:37 on February 14, 2016 · (Permalink)
But only for very large values of 2
IThinkTheClockIsSlow · 1 points · Posted at 21:12:15 on February 14, 2016 · (Permalink)
Only in "1984"
Damn_sun · 1 points · Posted at 13:19:23 on February 14, 2016 · (Permalink)
E=Mc squared
theslack · 1 points · Posted at 13:19:53 on February 14, 2016 · (Permalink)
0 Kelvin
[deleted] · 1 points · Posted at 13:21:41 on February 14, 2016 · (Permalink)
conway created a way of telling if you can fill a surface with a given tile. you know the classical question can you fill a 8x8 chess board with dominoes if u cut out 1 corner square?; what if u cut 2 opposite corner squares?; this evolved into more complicated questions, and therefore his way of finding out; it involves an algebraic way of describing the surface ; suppose that this algebraic expression of the tile is equal to the neutral element of the group we re working in ( the elements that help us describe this surfaces are in this group); if this equality implies the fact that the expression that describes the big surface is also = to e, then it can be covered in such tiles; i read this a while ago in a book and it blew my mind
Educated_Spam · 1 points · Posted at 13:24:16 on February 14, 2016 · (Permalink)
X*X = Y (X-1)(X+1) = Y-1
Works with all numbers. I just randomly discovered it, I'm not sure if it has a name as a real fact or anything.
E.g. 13 x 13 = 169 12 x 14 = 168
Swate- · 1 points · Posted at 13:49:50 on February 14, 2016 · (Permalink)
I use this in my head all the time for multiplication. I'm not sure if this application of it has a name but it ties in to the difference of perfect squares:
(a+b)(a-b) = a2 - b2
Therefore, for your example, a=13 (the original squaring number) and b=1 (the amount of deviation either side of a).
14*12 = (13+1)(13-1) = 132 - 12 = 169 - 1 = 168
Educated_Spam · 1 points · Posted at 14:44:49 on February 14, 2016 · (Permalink)
I'm confused. 132 - 12 = 168?
Swate- · 1 points · Posted at 14:50:12 on February 14, 2016 · (Permalink)
Oh, those 2's are squares. The superscript code that reddit uses might not be working for you, it looks fine to me.
It's supposed to look like: 13 squared - 1 squared = 168.
Educated_Spam · 1 points · Posted at 00:32:58 on February 18, 2016 · (Permalink)
Alright cool. Yeah the superscript triangle without a bottom symbol doesn't show up I guess. I'm on mobile as well so that may be a problem. Oh well, I understand now.
JedasRiddler · 1 points · Posted at 13:30:02 on February 14, 2016 · (Permalink)
if you square any odd integer and subtract one, the result is divisible by eight.
Swate- · 2 points · Posted at 13:46:30 on February 14, 2016 · (Permalink)
This is a cool one, I like it. The multiples of eight seem to follow a triangle number scheme.
In a formulaic form (where n is an integer):
(2n + 1)2 - 1 = 8 * n(n + 1) / 2
Mrhegel · 1 points · Posted at 13:31:23 on February 14, 2016 · (Permalink)
The smallest uninteresting number is 11630
datalies · 1 points · Posted at 13:34:46 on February 14, 2016 · (Permalink)
If you want to estimate the value of, say, a crowd at a foorball game, answer these two questions:
What is the smallest estimate you would believe? ... in other words, the smallest value that if someone said, "the value is [this]", you would say, "ehhhh, yeah I guess that's possible, but I don't think it cam be any lower than that
Similarly, what is the largest estimate you would believe?
... add the two values and divide by two. I feel this is better than just trying to guess a point estimate.
I also like to consider how off I feel the result is and adjust my estimate from there.
I've guessed stadium capacities to within a few hundred people. Concerts are hard to verify because you can't really get the actual number from anybody.
The point is, this method instills greater confidence in me when I need to estimate a number.
Not a mathematical truism, per se, but it's statistics... there is a variance around truth unknown. This method helps me.
Swate- · 1 points · Posted at 13:39:53 on February 14, 2016 · (Permalink)
I do something similar but I feel like a multiplication-based result yields more accuracy personally. I do my best to multiple the two answers and then square root the product.
Obviously addition is easier, and I'm just pulling at pedantic strings lol, but ye
MorRobots · 1 points · Posted at 13:39:06 on February 14, 2016 · (Permalink)
If N mod 2 = 0 then set N to N/2 else set N to 3N + 1
There is no mathematical proof to show that this will not always decay into a stedy state of 1, 4, 2, 1, 4, 2, 1, ..
piperluck · 1 points · Posted at 13:41:14 on February 14, 2016 · (Permalink)
Birthday Problem
https://en.m.wikipedia.org/wiki/Birthday_problem
compguytracy · 1 points · Posted at 13:47:23 on February 14, 2016 · (Permalink)
i do not know the formula, i just know that if you take to consective numbers, lets say 4 and 5, add them up equals nine. now the squared version of 4 is 16 and 5 is twenty five, the difference between the two is nine. this works all the way up 5 plus 6, 6 plus 7, etc
sut123 · 2 points · Posted at 13:54:10 on February 14, 2016 · (Permalink)
Formula for the lazy: (x + 1)² - x² = x + (x + 1)
SIrPsychoNotSexy · 1 points · Posted at 13:50:16 on February 14, 2016 · (Permalink)
The area of one ball, regardless of size, is equal to two balls of the same size as the original ball. Or something like that.
TehSuckerer · 1 points · Posted at 13:54:25 on February 14, 2016 · (Permalink)
The geometric mean of the coefficients of the continued fractions of almost every real number is Khinchin's constant (≈2.685452).
Continued fractions is a way to describe real number using integers, very different from a numeral system. To write a number as continued fractions, you write down its integer part as the first digit and continue with the reciprocal of the rest. The integer part of THIS number is the second digit and you keep on going like that. For example 3.14159265359... would be 3 + .14159265359..., so 3 is the first digit. The reciprocal of .14159265359... is 7.06251330592..., so 7 is the 2nd digit. The reciprocal of .06251330592... is 15.9965944095..., so 15 is the 3rd digit. Pi can therefor be written as the integer sequence 3,7,15,1,292,1,1,1...
The geometric mean of a set of numbers is a kind of average that is different from our usual average. The arithmetic means adds n numbers and divides by n. The geometric means, on the other hand, multiplies n (positive) numbers and takes the nth root of that.
The amazing thing is, that, for almost all real numbers, the geometric mean of the digits of the continued fractions converges towards a single number, called Khinchin's constant. Obviously not ALL numbers do, it's easy to create counterexamples. The continued fractions of the number 4 is just '4' and can't converge to anything. The same is true for any rational number. Other examples of numbers that don't have this property are all roots of quadratic equations and Eulers number.
In fact, there is not a single number of interest (that means not specifically constructed for this purpose) that we know for sure has this property. Not even Khinchin's constant itself. Yet it can be proven almost all numbers do.
As one final note, we know very little about Khinchin's constant as of now. We do not even know if it is rational.
LaTalpa123 · 1 points · Posted at 13:54:59 on February 14, 2016 · (Permalink)
If you have a deck of card with N cards in it and you riffle it in the natural way (split it in 2 parts, insert one of the two in the other one) the entropy of the deck, how "random" it becomes, increase drastically after 3/2 Log_2(N).
It is quite flat before and after that point.
That means that you need 7 riffles to have a randomized deck of 52 cards.
It was studied by Persi Diaconis. Great guy, mathematics and magician.
databasedgod · 1 points · Posted at 13:57:17 on February 14, 2016 · (Permalink)
When you're trying to divide a fraction by a fraction, just use the outties-over-innies method. (2/5)/(1/3) = (32)/(51) = 6/5
[deleted] · 1 points · Posted at 13:57:35 on February 14, 2016 · (Permalink)
0.9 recurring = 1
[deleted] · 1 points · Posted at 13:58:20 on February 14, 2016 · (Permalink)
The difference between the squares of two consecutive numbers is the sum of those two numbers, i figured it out during a maths test in highschool and was really chuffed with myself.
Roskarnolkov · 1 points · Posted at 13:58:27 on February 14, 2016 · (Permalink)
The square numbers are separated in succession by the odd numbers.
1(1) = 1 2(2) = 4 3(3) = 9 4(4) = 16
1 is separated from 4 by 3, 4 is separated from 9 by 5, 9 is separated from 16 by 7, etc. 3, 5, 7, 9, 11... Someone a little more privy to mathematics can probably whip up a cohesive equation for this.
JstAnthrAnymsAct · 1 points · Posted at 13:58:35 on February 14, 2016 · (Permalink)
7/7 really fucks that up
[deleted] · 1 points · Posted at 13:58:39 on February 14, 2016 · (Permalink)
Multiples of 9 are very easy to remember. The first number always increases by one, while the second number decreases by one.
09
18
27
36
45
54....
GatemouthBrown · 1 points · Posted at 14:00:19 on February 14, 2016 · (Permalink)
I don't know if it is my favorite per se, but I was just explaining to my 3rd grader that 9 times any single digit number will yield a quantity with where the digit in the tens place is one digit smaller than that number and the sum of both digits will be 9. Or 9x where x is a single digit integer = a two digit answer wherein the digit in the tens place is (x-1) and the the digit in the ones place is 9 - (x-1).
jasnoc · 2 points · Posted at 14:13:10 on February 14, 2016 · (Permalink)
I'm a 4th grade teacher, read them the book "The Best of Times" by Greg Tang. I read my 4th graders this book the beginning of each year. Excellent tips for working multiplication facts 1-9.
GatemouthBrown · 1 points · Posted at 14:22:42 on February 14, 2016 · (Permalink)
Thank very much, I will!
mickskitz · 1 points · Posted at 14:00:30 on February 14, 2016 · (Permalink)
That any number which has re-occurring decimals (at some point) can be turned into an exact fraction
[deleted] · 1 points · Posted at 14:00:58 on February 14, 2016 · (Permalink)
To determine if. a number is divisible by 11, add upthe numbers n every other digit. Then, add up the others. If they both equal the same amount, the number is divisible by 11.
For example: 121... 1+1=2, and 2=2, it's divisible by 11.
5731.. 5+3=8, and 7+1=8, it's divisible by 11 (521×11)
Brave_Bird · 1 points · Posted at 14:03:09 on February 14, 2016 · (Permalink)
e{i \pi} +1 = 0. So simple, using values from trigonometry, calculus and complex numbers.
offmychest_is_cancer · 1 points · Posted at 14:03:51 on February 14, 2016 · (Permalink)
ei*pi + 1 = 0
Weird but awesome!
[deleted] · 1 points · Posted at 14:05:37 on February 14, 2016 · (Permalink)
Terrence Howard thinks 1 X 1 = 2
nitro813 · 1 points · Posted at 14:07:05 on February 14, 2016 · (Permalink)
Faces of math 0.o
Multiman125 · 1 points · Posted at 14:09:32 on February 14, 2016 · (Permalink)
-40 degrees Celsius, when converted into Fahrenheit, is -40 degrees, and vice versa
Celsius to Fahrenheit -40*1.8 + 32 -72 + 32 = -40
Fahrenheit to Celsius (-40 - 32)/1.8 -72/1.8 = -40
Otsdarva23 · 1 points · Posted at 14:11:16 on February 14, 2016 · (Permalink)
That to be certain that x =/= y implies that x is mathematically distinct from y, we need to be in a complete normed space.
RhinoBarbarian · 1 points · Posted at 14:12:20 on February 14, 2016 · (Permalink)
There are 10120 possible games of chess played to 40 moves.
There are 1080 number of atoms in the observable universe.
fuzzzybear · 1 points · Posted at 14:39:57 on February 14, 2016 · (Permalink)*
There are 867th different combinations in a deck of cards.
Edit: how did you show it properly?
RhinoBarbarian · 1 points · Posted at 19:19:14 on February 14, 2016 · (Permalink)
Make the 8 and the 67 one word and put ^ between them. So 8*67, just replace * with ^ .
fuzzzybear · 1 points · Posted at 23:54:39 on February 14, 2016 · (Permalink)
Thank you.
Ihateracism-zionism · 1 points · Posted at 14:14:38 on February 14, 2016 · (Permalink)
ei(pi) + 1 = 0
mathurbater · 1 points · Posted at 14:18:24 on February 14, 2016 · (Permalink)
111,111,111 x 111,111,111 = 12345678987654321
Phishguy · 1 points · Posted at 14:18:38 on February 14, 2016 · (Permalink)
Infinity is as fascinating to me as how, what or why the universe was created... I became so interested in it when I heard from somewhere if a monkey had infinite time and infinite attempts, it would eventually type the entire works of Shakespeare..
https://en.m.wikipedia.org/wiki/Infinite_monkey_theorem
If infinity is real, everything and anything is true or will become true
NotUrMomsMom · 1 points · Posted at 14:22:03 on February 14, 2016 · (Permalink)
Pi squared is pretty goddamn close to earth's gravitational constant.
[deleted] · 1 points · Posted at 14:24:39 on February 14, 2016 · (Permalink)
The infinite sum of positive integers = -1/12
See specific values of the reman zeta function: -1
kevinatari · 1 points · Posted at 14:24:59 on February 14, 2016 · (Permalink)
In school we once had to invent a "mathematical trick". I was never good at maths so I was sure that I couldn't come up with anything clever at all. I fiddled a bit with numbers on my calculator and found a "trick" to easily find out a secret number multiplied by 99. All Information I needed to find it was the number of digits the secret number has.
So, for example, a person asks me what the number is if the sum is 2277 and the number has 2 digits the secret digit is 23. The "calculation" works like this:
Now if the secret number has two digits you take the last 2 numbers (77) and add up to them until both are 0, starting from the right e.g.
The number is 23. The simplest example is a single-digit number:
I hope I explained it well. People usually tent to not get it when I try to explain. You can do this with any length of secret digit length, the calculations get "harder" the more secret digits there are. Anyway, casual people are usually super impressed when you tell them you're able to find out any number they multiplied by 99 just by knowing the digits in the secret number and the end sum.
ck2839 · 1 points · Posted at 14:26:48 on February 14, 2016 · (Permalink)
666 = 1 + 2 + 3 + ··· + 6·6 = 22 + 32 + 52 + 72 + 112 + 132 + 172
It's the sum of the first 6·6 positive integers and the squares of the first 7 primes.
666 = 16 - 26 + 36 = 1 + 2 + 3 + 4 + 567 + 89
666 = 123 + 456 + 78 + 9 = 9 + 87 + 6 + 543 + 21
666 is also a Smith number:
666 = 2·3·3·37 and 6 + 6 + 6 = 2 + 3 + 3 + 3 + 7
Φ(666) = 6·6·6, where Φ is Euler's Totient Function.
The golden ratio is equal to -[sin(666°)+cos(6·6·6°)].
cos(6·6·6°) = cos(66·6°) = cos(666°) = cos(666666°)
There are exactly 6 6's in the number 6666.
I took most of this from this link. 666 is called a Beast Number.
pinkfloyds · 1 points · Posted at 14:27:20 on February 14, 2016 · (Permalink)
Most of us know Pythagorean Theorem that states a2 + b2 = c2, where it is possible to have a,b and c as all integers. For example: 32 + 42 = 52. But did you know this fact:
an + bn ≠ cn for all a,b,c,n ≥ 3 (where a,b,c,n are all natural numbers). This is called Fermat's Last Theorem and took centuries for mathematicians to prove.
lolhawk · 1 points · Posted at 14:31:30 on February 14, 2016 · (Permalink)
You can create 2 identically-shaped potato chips from two completely different potatoes by intersecting the potatoes with each other. The outline of the intersection appears once overall - but twice on the two separate potatoes.
MidnightSun77 · 1 points · Posted at 14:32:20 on February 14, 2016 · (Permalink)
each pair of opposite sides on a di = 7 e.g. 6+1, 4+3, 5+2
operationarmchair3 · 1 points · Posted at 14:34:31 on February 14, 2016 · (Permalink)
Pretty simple one to wrap the mind around, but there are infinitely equal amount of numbers between 0.0 and 1.0 as there are whole numbers in existence.
thisModerate · 1 points · Posted at 14:34:52 on February 14, 2016 · (Permalink)
Honestly once I got the idea of limits, I was pretty astonished.
Mark_Zajac · 1 points · Posted at 14:34:56 on February 14, 2016 · (Permalink)
I have always been partial to the divergence theorem:
∫∫∫ ∇ ⋅ V⃗ dV = ∫∫ V⃗⋅ dA⃗
Also, we now use the Leibniz notation for derivatives:
dx/dt = vₓ
and integrals:
∫ vₓ dt = x + x₀
but Newton called these the fluxion:
ẋ = vₓ
and the fluent:
ṽₓ = x + x₀
for which he had is own notation. Physicists still use ẋ for the time derivative.
mspahr4 · 1 points · Posted at 14:35:46 on February 14, 2016 · (Permalink)
This is more philosophy of math/set theory, but there is a very compelling proof for there being at least two different sizes of infinities.
[deleted] · 1 points · Posted at 14:36:03 on February 14, 2016 · (Permalink)
E to the power of iπ = -1
Irish_Airsofter · 1 points · Posted at 14:36:59 on February 14, 2016 · (Permalink)
That the sum of all natural numbers, to infinity, is -1/12
all4hurricanes · 1 points · Posted at 14:37:29 on February 14, 2016 · (Permalink)
Not exactly a fact more of a game. Try to fill a square with pentagons, there rules are there cannot me any gaps, there must be a finite amount of polygons and the most complex rule two polygons cant share some than one side. I guess my fact is there is a solution and every polygon can be constructed with these constraints just quadrilaterals are the hardest.
Mantis--Toboggan_MD · 1 points · Posted at 14:37:39 on February 14, 2016 · (Permalink)
∑ 1/(21+n ) [n=0 initially] for any number of iterations, the number will never be equal to or greater than 1. Basically, add up 1/2 + 1/4 + 1/8 +... the number will always be lower than 1. It's not that cool of a fact, but it's the best I've got. lol
lutinopat · 1 points · Posted at 14:38:16 on February 14, 2016 · (Permalink)
http://www.numberphile.com/
Ainjyll · 1 points · Posted at 14:38:50 on February 14, 2016 · (Permalink)
1.618033:1 is considered by many to be the most aesthetically pleasing ratio in the world. It's also called the Golden Ratio and can be found in countless places in nature, art, architecture and other places.
It is still highly contested by experts as to whether or not this ratio is really found in nature as much as claimed, but it's still pretty damn cool to me.
sixnew2 · 1 points · Posted at 14:39:23 on February 14, 2016 · (Permalink)
Graham's Number
paurwar · 1 points · Posted at 14:39:56 on February 14, 2016 · (Permalink)
The Fibonacci sequence is an excellent tool for making quick coversions from miles to kilometers and vice versa. E.g. if the sequence is 1, 2, 3, 5, 8, 13... 3 mi is roughly 5 km and 8 mi is roughly 13 km! This is because the golden ratio, on which the Fibonacci is based, is 1.618 and the conversion of km to mi is 1 mi = 1.609 km.
ARAR1 · 1 points · Posted at 14:40:00 on February 14, 2016 · (Permalink)
I have a question. A lot of answers in this thread have facts for repeating sequences and other numerical alignment. Would that be true if we were using a different numeral system? i.e would prime numbers be different if we were counting using a hexadecimal system?
candyman_forever · 1 points · Posted at 14:40:37 on February 14, 2016 · (Permalink)
Binary changed the world.
ck2839 · 1 points · Posted at 14:41:09 on February 14, 2016 · (Permalink)
987654321 / 123456789 ≈ 8.000000073
MeMuzzta · 1 points · Posted at 14:41:29 on February 14, 2016 · (Permalink)
Looking through these comments makes me feel small and dumb.
weaselking · 1 points · Posted at 14:41:47 on February 14, 2016 · (Permalink)
Numbers on a calculator look like words. 1337 80085!!
malarie · 1 points · Posted at 14:42:39 on February 14, 2016 · (Permalink)
If you could fold a piece of paper 50 times, it would be as thik as the distance to go to the moon.
ck2839 · 1 points · Posted at 14:43:33 on February 14, 2016 · (Permalink)
http://math.stackexchange.com/q/729033/236182
Dontcallmekatey · 1 points · Posted at 14:44:54 on February 14, 2016 · (Permalink)
There's different sizes of infinity. So the amount of numbers between 0 & 1 is infinite but the amount of numbers between 0 & 100 is infinite and so on, even though the difference between 0 & 100 is bigger.
random314 · 1 points · Posted at 14:45:08 on February 14, 2016 · (Permalink)
If you take infinity out of infinity, you still have infinity remaining...
Hard to wrap your head around it, but the proof makes a lot of sense.
2+3+4+5+6... = inf
1+2+3+4+5... = inf
First line minus second line
1+1+1+1+1... = inf
transmembrane_alpha · 1 points · Posted at 14:46:41 on February 14, 2016 · (Permalink)*
The sum of all positive numbers 1+2+3+4+5+... equals -1/12 !
A = 1 - 1 + 1 - 1 + 1 - 1 + ....
-A = -1 + 1 - 1 + 1 - 1 + ...
1 - A = A
A = 1/2
B = 1-2+3-4+5-6+...
A+B= 2-3+4-5+6-7+...
-1+A+B= -1+2-3+4-5+...
-1/2+B =-B
C = 1+2+3+4+5+6+7+...
-B =-1+2-3+4-5+6-7+...
C-B = 4+ 8+ 12+ 16+ ....
C -1/4 = 4C
fun fact , this has consequences in physics such as casimirs force
ck2839 · 1 points · Posted at 14:53:30 on February 14, 2016 · (Permalink)
You mean -1/12 ? 1+2+3+... = -1/12 is only true in a different sense. The summation used is a different kind of summation called Ramanujan summation.
transmembrane_alpha · 1 points · Posted at 16:33:48 on February 15, 2016 · (Permalink)
You are correct, in fact the minus in -1/12 in the casimir force means that it is an attractive force.
[deleted] · 1 points · Posted at 14:46:43 on February 14, 2016 · (Permalink)
When you're squaring numbers the distance between the product of the last square and the product of the current square is always increasing by two. It goes like this:
11=1, the product being 1. 22=4, and the distance between 1 and 4 is 3. 3*3=9, and if you add 2 to the distance between the last square that makes it 5, and if you add that to the last square you get the next one, which is 9.
It's kinda obscure and I figured it out myself so idk whether or not people already know it or if it's even useful, but that's the basics of how it works.
ck2839 · 2 points · Posted at 14:54:51 on February 14, 2016 · (Permalink)
It follows from (x+1)2 - x2 = 2x + 1.
vivabellevegas · 1 points · Posted at 14:52:28 on February 14, 2016 · (Permalink)
DNA splits to replicate at places in the stand where the nucleobases form a palindromic sequence.
vivabellevegas · 1 points · Posted at 14:56:29 on February 14, 2016 · (Permalink)
A "Crab Canon" is a piece of music that has two lines that are palindromes of one another. The piece can be played from the start or the end. Bach messed around with this and even wrote a piece of music where one player played the music normally and another flipped the sheet music upside down and played it that way. Fun stuff.
PMPG · 1 points · Posted at 14:57:00 on February 14, 2016 · (Permalink)
TIL: im retarded.
wowitshaines · 1 points · Posted at 15:01:29 on February 14, 2016 · (Permalink)
I just love the fact we plucked it out of thin air and it explains pretty much fucking everything!
FatGordon · 1 points · Posted at 15:02:24 on February 14, 2016 · (Permalink)
All the numbers that devide into a certain number are added together and make new number . All the numbers that de ide into that one add together and give you the first number.
Marsleo · 1 points · Posted at 15:07:46 on February 14, 2016 · (Permalink)*
I don't kown,but I want to say "1+1=2" is the coolest mathematical fact which I know even that had ever never been proved yet,yes,it could named Morden Goldbach conjecture I think.Our subconscious still think "1 + 1 = 2" is real cause it's the basic of other most of math theories in my opinion.
In 1920, Norway's brown proved "9 + 9". In 1924, the German's Mach proved the "7 + 7". In 1932, the British Mr Sterman proved "6 + 6". In 1937, the Italian Tracy has proved that the "5 + 7", "4 + 9", "3 + 15" and "2 + 366". In 1938, the Soviet union buchholz skarn is Bob proved that the "5 + 5". In 1940, the Soviet union buchholz skarn is Bob proved that the "4 + 4". In 1956, the Chinese king yuan proves the "3 + 4".Later proved that the "3 + 3" and "2 + 3". In 1948, Hungary's proved that the "1 + c", where c is a great natural Numbers. And the Soviet union in 1962, the Chinese Pan Cheng hole barr bain proves that the "1 + 5", China's king yuan proves the "1 + 4". In 1965, the Soviet union by evening too cuny and small dimension noguera madoff, and Italian friend Billy proved the "1 + 3". In 1966, China's trained Chen jingrun proved the "1 + 2".
The above data from the Internet.
AKA_Squanchy · 1 points · Posted at 15:25:47 on February 14, 2016 · (Permalink)
All the multiplications of 9 from 1-10 have products that when added together equal 9. (9x6=54, 5+4=9)
Agamoomnon · 1 points · Posted at 15:44:08 on February 14, 2016 · (Permalink)
That I could count to eleven, if I imagined I had one more finger.
SAGNUTZ · 2 points · Posted at 18:57:36 on February 14, 2016 · (Permalink)
Toes get you to 20!
kittykittysnarfsnarf · 1 points · Posted at 15:47:33 on February 14, 2016 · (Permalink)
The birthday paradox. ((364/365)((# of people(# of people - 1))/2))(-1)—1×100 That's the persentage someone in a room shares a birthday. So in a room of 30 people there's a 90% chance someone shares a birthday with someone else
dekindling · 1 points · Posted at 15:48:51 on February 14, 2016 · (Permalink)
Not really math per se, but there are more ways to arrange a deck of cards than there are atoms on earth. There are 80,000,000.... (+60 more 0s) unique ways to shuffle a 52 card deck.
yerPalSal · 1 points · Posted at 15:48:59 on February 14, 2016 · (Permalink)*
Rule of 72 tell you how long it will take to double your money at any given fixed annual interest rate. 72/rate=years
For example: 6% interest = 72/6 = 12 years to double your money.
Or you can use the same idea to learn what rate you need in order to double your money within your time frame. 72/rate=years
12 years = 72/12 = 6% needed in order to double your money in 12 years.
enckling · 1 points · Posted at 16:03:05 on February 14, 2016 · (Permalink)
I'm not exactly a math person, so this may seem obvious to some of you. I found that if you multiply a number (lets say 50 x 50) and get the result, then you take those same numbers and decrease one side by one and increase the other side by one (49 x 51), it's always one less than the first result.
50 x 50 = 2,500 49x 51 = 2,499
3,000 x 3,000 = 9,000,000 2,999 x 3,001 = 8,999,999
This is just something I found interesting. Not that it's overly useful though.
Springstof · 1 points · Posted at 16:03:26 on February 14, 2016 · (Permalink)
You can calculate any squared number that ends with a 5 by multiplying the number before the 5 with that same number + 1. Then multiply it by 100 and add 25. Works everytime.
Examples:
detexion · 1 points · Posted at 16:04:10 on February 14, 2016 · (Permalink)
take an odd number and square it. now take the consecutive numbers that add up to the squared odd number. these three now form a pythagorean triple.
32 = 9.
9 = 4 + 5
32 + 42 = 52.
72 = 49
49 = 24 + 25
72 +242 = 252
getbixi · 1 points · Posted at 16:07:53 on February 14, 2016 · (Permalink)
1729 it is the smallest number expressible as the sum of two cubes in two different ways. 1729 = 13 + 123 = 93 + 103
1729 is one of four positive integers which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number: 1 + 7 + 2 + 9 = 19 19 × 91 = 1729
Appetite4destruction · 1 points · Posted at 16:11:22 on February 14, 2016 · (Permalink)
The difference between two consecutive squares is the sum of their roots.
22 = 4 32 = 9 9-4 = 5 2+3 = 5
yerPalSal · 1 points · Posted at 16:11:42 on February 14, 2016 · (Permalink)
When constructing something, you can ensure square corners by making marks
3 units of measure down one side and
4 units down the other side.
Now make sure the distance between the marks is 5 units.
MrCantBeBothered · 1 points · Posted at 16:15:42 on February 14, 2016 · (Permalink)
Proof for 1 + 1 = 2 can be one or two pages long
[deleted] · 1 points · Posted at 16:21:44 on February 14, 2016 · (Permalink)
One is the loneliest number.
WoollyWalrus · 1 points · Posted at 16:32:37 on February 14, 2016 · (Permalink)
To quickly square a number ending in 5: Take the digits preceding 5 and multiply by next ascending (Natural) number, then put a 25 on the end of this. Example, square 35:
3*4=12 352 =1225
yerPalSal · 1 points · Posted at 16:33:58 on February 14, 2016 · (Permalink)
there are 10 kinds of people in the world... those who understand binary and those who don't.
Brainsonastick · 1 points · Posted at 16:46:37 on February 14, 2016 · (Permalink)
Claim: All positive integers are interesting.
Proof: Assume, for contradiction, that there exists a non-empty set of all positive integers that are not interesting. One of them is smaller than all the others, so it is the smallest uninteresting positive integer. That's an interesting trait, making it an interesting number. But our hypothesis assumes it is uninteresting! This creates a contradiction. Therefore the set of uninteresting positive integers cannot be non-empty. So all positive integers are interesting.
HavelockVe · 1 points · Posted at 16:49:44 on February 14, 2016 · (Permalink)
The sum of all Natural numbers is equal to -1/12...
Edit: https://plus.maths.org/content/infinity-or-just-112 This site is critical of whether numberphile cheated or not, but well... they didnt cheat :D
PW248 · 1 points · Posted at 17:02:15 on February 14, 2016 · (Permalink)
5318008
Kidlambs · 1 points · Posted at 17:03:47 on February 14, 2016 · (Permalink)
4(.5!)2 = π
π is pi
FavoriteNumberIs121 · 1 points · Posted at 17:04:27 on February 14, 2016 · (Permalink)
11 is the square root of 121 no matter what base number system is used, from base 3 up.
In base 3:
In base 4:
In base 5:
And so on.
MonkeyBombG · 1 points · Posted at 17:05:44 on February 14, 2016 · (Permalink)
Given any integer in base 10, one can easily check it's divisibility of 3 by summing up all it's digits to see whether that sum is divisible by 3 or not. For example, 53358 is divisible by 3 because 5+3+3+5+8=24, which is divisible by 3.
The reason is remarkably simple: one can write 53358 into
5x10000+3x1000+3x100+5x10+8
=5x(9999+1)+3x(999+1)+3x(99+1)+5x(9+1)+8
=[5x9999+3x999+3x99+5x9]+[5+3+3+5+8]
The number inside the first square bracket is obviously divisible by 3, so if the number inside the second square bracket(which is the sum of the digits) is also divisible by 3, then the whole number is divisible by 3.
You can apply the same idea to check for divisibility of 9.
The divisibility of 11 is a bit more complicated. To check whether an integer in base 10 is divisible by 11, you sum up it's odd and even digits separately, then you check whether their difference is divisible by 11. Example: 30624 is divisible by 11 because the odd digits add up to 3+6+4=13 and the even digits add up to 0+2=2, their difference is 11.
I'll let you figure out how to prove this ;)
Thrownaway_4_2_day · 1 points · Posted at 17:08:04 on February 14, 2016 · (Permalink)
This thread reminds me that, no matter how smart I am (or how smart I think I am), I will never be smart at this shit.
Z_brah21 · 1 points · Posted at 17:12:33 on February 14, 2016 · (Permalink)
If you start at zero, and you either add 1 or subtract 1 (50/50 chance) continuously for infinite time, every single number will occur eventually
dontgetupinmyjam · 1 points · Posted at 17:20:08 on February 14, 2016 · (Permalink)
The number 9's products. 9×9=81 8+1=9. 9×3=27 2+7=9. It goes on
monders337 · 1 points · Posted at 17:20:44 on February 14, 2016 · (Permalink)
6 is scared of 7, because 7, 8, 9.
Skaleks · 1 points · Posted at 17:21:58 on February 14, 2016 · (Permalink)*
It's a simple one but 9 when multipled by any number under 10 adds up to nine. Also the first digit goes up one and the other makes it add up to nine.
However I also think it works past 10. Correction it does not work with every number for example 510 doesn't work.
1x9 = 9
2x9 = 18
3x9 = 27
4x9 = 36
5x9 = 45
6x9 = 54
7x9 = 63
8x9 = 72
9x9 = 81
9x10 = 90
9x11 = 99 Digits add to 9 when you add them up
9x12 = 108 Digits add to 9
9x13 = 117 Digits add to 9
9x14 = 126 Digits add to 9
9x15 = 135 Digits add to 9
Snaaaaaaaaaake · 1 points · Posted at 17:22:26 on February 14, 2016 · (Permalink)
1+2+3+4+.....+infinity is................
-1/12
fun proof on numberfile showing this
JohnBakedBoy · 1 points · Posted at 17:26:39 on February 14, 2016 · (Permalink)
Way late to the party so its ever gonna see the light of day, but my personal favorite.
11*11=121
111*111=12,321
1,111*1,111=1,234,321
11,111*11,111=123,454,321
111,111*111,111=12,345,654,321
And so on and so on.
arvid_g · 1 points · Posted at 17:30:16 on February 14, 2016 · (Permalink)
Prime numbers are pretty friggin cool aswell.
sturmhauke · 1 points · Posted at 17:33:16 on February 14, 2016 · (Permalink)
eiπ + 1 = 0
[deleted] · 1 points · Posted at 17:35:06 on February 14, 2016 · (Permalink)
There are more possible chess moves than there are atoms in the observable universe.
Blue_Dog_Democracy · 1 points · Posted at 17:45:12 on February 14, 2016 · (Permalink)
I've never been much of a math whiz, but an easy way to calculate time occurred to me only a few years ago, while writing a program.
Say it's 4:33 and you want to figure out the time 36 minutes after that. Simply add 33 and 36 to get 69, subtract 60, and add an hour (since the result is >60). Your new time is 5:09.
My teachers tried to teach me this in elementary school, but I just didn't get it in those days. It seems easy and obvious now as an adult (with pre-calculus and Calculus classes under my belt).
Tyreefosho · 1 points · Posted at 17:48:52 on February 14, 2016 · (Permalink)
The square root of 69 is 8 something... Right?
Zerstorend · 1 points · Posted at 17:55:33 on February 14, 2016 · (Permalink)
How everything that have been written, or will be written ever is already "stored" in https://libraryofbabel.info
The old "an infinite number of monkeys with typewrittens can write Shakespeare books" problem, solved with an algorithm on a computer.
https://m.youtube.com/watch?v=GDrBIKOR01c
MWatson17 · 1 points · Posted at 18:08:21 on February 14, 2016 · (Permalink)
The commutative property of addition (rearranging the numbers will give you the same sum) does not apply to some kinds of infinite sums. Meaning if you change the order of addition in certain kinds of infinite sums, you can change the answer.
SuperRip · 1 points · Posted at 18:12:30 on February 14, 2016 · (Permalink)
The Pigeonhole Principle. If n items are put into m containers, with n > m, then at least one container must contain more than one item. For example, if you have 13 people together, there's a guarantee that at least two of them share the same birth month.
Kvasir0 · 1 points · Posted at 18:04:26 on May 30, 2016 · (Permalink)
I thought that it was if you had 23 people you would have a 50% chance to have two people with the same birthday
Takeabyte · 1 points · Posted at 18:36:05 on February 14, 2016 · (Permalink)
Without it, non of us would exist.
eabznax · 1 points · Posted at 18:41:51 on February 14, 2016 · (Permalink)
1 +2 +3 +4 + ... = -1/2 https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
jpconn1 · 1 points · Posted at 18:53:12 on February 14, 2016 · (Permalink)
You can quickly determine if a number is divisible by 3 by adding up the digits. If the sum of the digits is divisible by 3, then the number is divisible by 3. Example 111111 is divisible by 3.
matti77 · 1 points · Posted at 18:57:14 on February 14, 2016 · (Permalink)
I figured out that there are APPROX the same number of drops in a gallon as there are seconds in a day.
I'm a plumber, so it's helpful to get a rough estimate how much water is being wasted. 1 drip/second is about 1 gal/day wasted.
reddiuniquefool · 1 points · Posted at 19:26:50 on February 14, 2016 · (Permalink)
Best thread ever!
Elu_suario · 1 points · Posted at 19:39:23 on February 14, 2016 · (Permalink)
Way too late, but still:
I love 585 because it is a palindromic number on base 2, base 8 and base 10.
shylocxs · 1 points · Posted at 19:44:50 on February 14, 2016 · (Permalink)
Slamming it down on the stage was a reference to another comment about how this was turning into a rap battle. Your comments were excellent, even if I'm inclined to an anti-realist position myself.
icantbenormal · 1 points · Posted at 20:22:42 on February 14, 2016 · (Permalink)
The phrase "twelve plus one" is an anagram of "eleven plus two."
error_98 · 1 points · Posted at 20:23:56 on February 14, 2016 · (Permalink)
Take the closest divice capable of drawing graphs to you and put in (-1)x
and think about what it intales.
alternatively, take your favorite formula and multiply it by (-1)x
Groatolfs · 1 points · Posted at 20:25:09 on February 14, 2016 · (Permalink)
The sum of all natural numbers up to infinity is -1/12 (I say up to infinity even though infinity is merely an idea just because it's easier to say).
Badidzetai · 1 points · Posted at 20:31:08 on February 14, 2016 · (Permalink)
exp(i*pi)=minus one
complex number will never stop being so cool
[deleted] · 1 points · Posted at 20:48:44 on February 14, 2016 · (Permalink)
Late to the party, but:
There's an infinite amount of numbers between 0 and 1, 1 and 2, etc.
bobby8375 · 1 points · Posted at 21:11:41 on February 14, 2016 · (Permalink)
Further, there is the same "amount" of infinite numbers between 0 and 1 as there are in total on the number line.
Texttool · 1 points · Posted at 20:59:32 on February 14, 2016 · (Permalink)
A force of projectile gas, however brief, from the Gluteus Maximus while in space will propel the offender forward. Causing a trajectory to the planetary's atmosphere which burns to ashes the offender to death. So be warned, no matter what, do not eat last weeks bean burrito while floating in space with no space suit on, dua!
jdquinn · 1 points · Posted at 21:01:15 on February 14, 2016 · (Permalink)
You can determine if any number is divisible by 3 very easily without a calculator. Remove all digits that are 3, 6 or 9, then add the remaining digits, repeat if necessary until you obtain a single-digit number. If the result is 3, 6 or 9, the original number is divisible by 3.
826479166143, remove all digits that are 3, 6 or 9: 8247114, add these digits together: 27, add these digits together (since none are 3, 6 or 9): 9. 826479166143 is divisible by 3.
A shortened way of doing this is after step 1, as soon as you have an answer that you can identify as being divisible by 3 or not, that will indicate if the input is divisible by 3.
73397, 7+7=14, not divisible by 3.
Triquetra4715 · 1 points · Posted at 21:40:50 on February 14, 2016 · (Permalink)
I think limits are fascinating. It's almost a way of sneaking impossibilities through until we can deal with them. Like the definition of derivatives. We sneak h=0 through an expression in which that's undefined until it is defined. Plus, it's like we're sneaking the secant line closer and closer to being a tangent line, and we end up with the slope at a single point.
Math is really cool if you've got instructors who explain it well, which I didn't learn until college.
adrianmonk · 1 points · Posted at 21:56:00 on February 14, 2016 · (Permalink)
There's actually a really simple formula for pi:
Basically alternating addition and subtraction, 4 in the numerators, odd numbers in the denominators.
Granted, it's not a great formula. It takes hundreds of terms before you even hit 3.14. But it's still nice to know that it can be boiled down to something that simple.
saladaz · 1 points · Posted at 21:57:30 on February 14, 2016 · (Permalink)
that einstein equations are still being proved right
Hello_NL · 1 points · Posted at 22:02:51 on February 14, 2016 · (Permalink)
The answer to life the universe and everything = 42
JeaniousSpelur · 1 points · Posted at 22:16:17 on February 14, 2016 · (Permalink)
1+2+3+4...... All the way to infinity =-1/12.
Some guy proved it in a number phone video
oxeimon · 1 points · Posted at 22:21:45 on February 14, 2016 · (Permalink)
This all depends on how you define the notion of limits, "distance", and convergence. There is a very special notion of convergence for which this is true, but it is of course false for the usual notion of distance (obviously 1+2+3+4+... gets arbitrarily large and doesn't converge to any finite number)
EDIT: Your statement is only true in some special p-adic topology
vatsallfolks · 1 points · Posted at 22:40:06 on February 14, 2016 · (Permalink)
Thank you for introducing Dr. Tadashi Tokieda to me. I don't study math, but his teaching style and passion are lessons in themselves. He reminds me of how Richard Feynman can break something down.
thisisathrwwyy · 1 points · Posted at 22:53:39 on February 14, 2016 · (Permalink)
The limit does not exist
Koisame · 1 points · Posted at 23:40:41 on February 14, 2016 · (Permalink)
Something related has been mentioned by u/Felix_Tholomyes, but if you were to chose a real number at random you would get a so called normal number with a 100% probability. The twist being that no normal number is known to us at all.
[deleted] · 1 points · Posted at 23:54:51 on February 14, 2016 · (Permalink)
[deleted]
Keetlady · 1 points · Posted at 00:13:02 on February 15, 2016 · (Permalink)
Wow, these are complicated....I just came here to say the multiplication wit the number 9 with your fingers thing...
w3woody · 1 points · Posted at 00:13:04 on February 15, 2016 · (Permalink)
Euler's Identity, which ties together 4 fundamental constants: e, i = √-1, π and -1.
Cottenswab · 1 points · Posted at 01:05:33 on February 15, 2016 · (Permalink)
If things aren't adding up, try subtracting some things.
Its_Krypo · 1 points · Posted at 01:06:14 on February 15, 2016 · (Permalink)
9+10=21
fishead62 · 1 points · Posted at 01:52:35 on February 15, 2016 · (Permalink)
The sum of all positive integers from 1 to infinity equals -1/12.
https://m.youtube.com/watch?v=w-I6XTVZXww
bootshick · 1 points · Posted at 02:20:32 on February 15, 2016 · (Permalink)
Came in looking for the birthday thing. Was not disappointed.
like_smith · 1 points · Posted at 02:26:37 on February 15, 2016 · (Permalink)
Collatz Conjecture. Take any positive number n. If n is even, divide it by 2, if n is odd, multiply it by 3 and add 1. Repeat unil you get to one.
Nicepotato · 2 points · Posted at 05:25:43 on February 17, 2016 · (Permalink)
You won't get to 1 will you ?
like_smith · 1 points · Posted at 06:13:15 on February 17, 2016 · (Permalink)
We have for every number we've tried, though we haven't been able to prove it for all numbers.
like_smith · 1 points · Posted at 06:14:24 on February 17, 2016 · (Permalink)
Sorry, for all positive integers.
alex4point0 · 1 points · Posted at 02:44:08 on February 15, 2016 · (Permalink)
the bible has the best and worst approximations for pi depending on what you believe and what version of the text you have
preposey · 1 points · Posted at 03:01:03 on February 15, 2016 · (Permalink)
2+2=4
KittyHammer · 1 points · Posted at 03:08:13 on February 15, 2016 · (Permalink)
1
121
12321
1234321
123454321
12345654321
1234567654321
123456787654321
12345678987654321
Congrats: you know how to multiply:
1x1, 11x11, 111x111, 1111x1111, 11111x11111, 111111x111111, 1111111x1111111, 11111111x11111111, 111111111x111111111 in a song format if you ever took chorus class with a teacher that used that method.
BartlebyX · 1 points · Posted at 04:40:44 on February 15, 2016 · (Permalink)
0.9999999... == 1
Cellblockbrew · 1 points · Posted at 06:26:39 on February 15, 2016 · (Permalink)
12345679.0125*8=98765432.1
rarelyposts · 1 points · Posted at 17:32:43 on February 15, 2016 · (Permalink)
1+2+3+4+5+...=-1/12
Still blows me away. Proof
WhiteGrapeGames · 1 points · Posted at 20:14:38 on February 15, 2016 · (Permalink)
10,000th comment motherfuckers
stiffleryuu · 1 points · Posted at 13:58:48 on February 16, 2016 · (Permalink)
1 + 1 = a window. Haha nah but when I was a kid it literally blew my mind that when drawn on paper it made out to be a window, I begun to question how it ever equaled 2.
JustFinishedBSG · 1 points · Posted at 16:00:01 on February 19, 2016 · (Permalink)
The Dubins-Schwarz theorem ( roughly stating that any martingale is actually a brownian motion ) makes me uncomfortable.
Actually all the things relating to the Brownian Motion makes me uncomfortable
lilkobi · 1 points · Posted at 18:31:03 on February 26, 2016 · (Permalink)
Someone mentioned divisible by 9 integers adding up to 9. Pretty sure this stands true for divisible-by-3 as well. If the final result is 3, 6, or 9, the value is divisible by 3. 1149 -> 1+1+4+9=15 -> 1+5=6 1149/3=383
ProjectSnipe · 1 points · Posted at 06:28:32 on March 6, 2016 · (Permalink)
Take a book. Any book. Now count each time a word occurs, like how many times 'the' is written, but for every word. Take the most occurring word and halve the amount of times it was in the book, thats about how many times the second most common word appeared in the book. Now take 1/3rd of the original number and you have about how many times the 3rd most common word appears. Its called the zipf mystery
theintrepidscientist · 1 points · Posted at 22:34:09 on March 6, 2016 · (Permalink)
Circles don't actually exist in nature they are a human idealism as no real shape can have infinite sides so if you zoom in it will always be a super large number of sides shape ... I always find this one weird
jrmanny5 · 1 points · Posted at 23:52:43 on March 6, 2016 · (Permalink)
987654321/123456789=8
It's truly 8.0000007 but close enough. Always thought that was a cool tid bit!
heyhihowdyhey · 1 points · Posted at 17:44:04 on May 4, 2016 · (Permalink)
10+10
[deleted] · 1 points · Posted at 12:08:55 on May 23, 2016 · (Permalink)
0.9 recurring=1
0.9.=x
10x=9.9.
9x=9
x=9/9
x=1
spihsllat · 1 points · Posted at 15:02:49 on June 1, 2016 · (Permalink)
In 9-times tables, to a point, adding the two resulting numbers equals nine:
3x9=27 (2+7=9)
5x9=45 (4+5=9) and so on until 11x9
Lordhardstick · 1 points · Posted at 01:56:22 on June 26, 2016 · (Permalink)
2+2=5
[deleted] · 1 points · Posted at 02:06:16 on June 26, 2016 · (Permalink)
Thanks man. Bit of an old post though.
not_a_fangirl · 1 points · Posted at 19:52:47 on July 18, 2016 · (Permalink)
for every n>0, between 2 and 2n there is at least one prime.
aBluntCunt · 0 points · Posted at 19:07:31 on February 13, 2016 · (Permalink)
zero plus a number will always equal that number. wtf that's crazy it doesn't even make sense
Destructerator · 1 points · Posted at 04:51:53 on February 14, 2016 · (Permalink)
blew my mind
best of reddit
[deleted] · 1 points · Posted at 19:46:46 on February 13, 2016 · (Permalink)
[deleted]
MilitaryFish · 6 points · Posted at 21:00:57 on February 13, 2016 · (Permalink)
But three left turns make a right
mleventy · 6 points · Posted at 21:36:33 on February 13, 2016 · (Permalink)
But I'm not an ambiturner
chilly-wonka · 1 points · Posted at 21:57:58 on February 13, 2016 · (Permalink)
fortunately three right turns make a left turn, too
aixenprovence · 1 points · Posted at 23:00:06 on February 13, 2016 · (Permalink)
I'm a doctor.
Jim.
[deleted] · 0 points · Posted at 22:14:51 on February 13, 2016 · (Permalink)
[deleted]
MilitaryFish · 1 points · Posted at 07:33:40 on February 14, 2016 · (Permalink)
Three 90° left turns will, in fact, make a right.
DiamondMinah · 2 points · Posted at 21:33:09 on February 13, 2016 · (Permalink)
but two negatives make a positive
ananori · 1 points · Posted at 22:08:04 on February 13, 2016 · (Permalink)
Bears are fish and fish are mammals, therefore bears are mammals
heap42 · 1 points · Posted at 00:07:04 on February 14, 2016 · (Permalink)
But.. but, not not p by definition is p
YourCrohnie · 1 points · Posted at 00:27:49 on February 14, 2016 · (Permalink)
The square root of 69 is 8 (ate) something.
IZ3820 · 1 points · Posted at 08:21:36 on February 14, 2016 · (Permalink)
Right? Cause I been trying to work it out, ohhhhh
[deleted] · 2 points · Posted at 23:58:53 on February 13, 2016 · (Permalink)
The number 64.
Stemming from the 8x8 principle.
The genetic code by which DNA stores the genetic information consists of "codons" of three nucleotides. The functional segments of DNA which code for the transfer of genetic information are called genes. With four possible bases, the three nucleotides can give 43 = 64 different possibilities, and these combinations are used to specify the 20 different amino acids used by living organisms.
There are also 64 squares on a chess board.
There are also 32, and 64 bit operating systems.
64 is also used in a principle law of the universe; but I can't remember it off the top of my head, I'll have to look into it when I get home.
There are also other instances of the number 64 in a lot of religious documents. But I'm not going to get into that.
hypervelocityvomit · 1 points · Posted at 13:10:28 on February 16, 2016 · (Permalink)
Powers of two are just about everywhere. If there's 64, there are usually others, too.
43 = 64. To post that, you have to write
4^3 = 64, and copy-pasting doesn't play fair with exponents in reddit. :/OTOH, yes, 64 is a quite interesting number both in recreational math and application. It's a shame that your post ended up somewhere between "80085 on a calculator" and "root of 69" posts.
motoxer · 0 points · Posted at 00:57:23 on February 14, 2016 · (Permalink)
1+1= a window
dude_pirate_roberts · 1 points · Posted at 08:04:42 on February 14, 2016 · (Permalink)
My 9-year-old tried to explain this while we drove in the car.
I didn't get it. Thanks!
ZanderDogz · 1 points · Posted at 20:39:34 on February 13, 2016 · (Permalink)*
If you add 1/2, 1/4, 1/8, 1/16, 1/32, etc. for infinity, the sum somehow is 1
EDIT: Changed 2 to 1, my bad
sampeckinpah5 · 4 points · Posted at 21:12:33 on February 13, 2016 · (Permalink)
It's 1. If you also add 1 at the start, then it's 2.
ZanderDogz · 1 points · Posted at 21:14:50 on February 13, 2016 · (Permalink)
Fixed
ztrawsnoraa · 3 points · Posted at 22:32:50 on February 13, 2016 · (Permalink)
It's actually: If you add 1/1, 1/2, 1/4, etc., then you get 2. Make more sense? So what you were writing down actually adds up to one.
ZanderDogz · 1 points · Posted at 23:56:51 on February 13, 2016 · (Permalink)
Yes, I corrected that.
slacker0 · 2 points · Posted at 21:13:04 on February 13, 2016 · (Permalink)
1
FatKidsRHard2Kidnap · 1 points · Posted at 00:17:09 on February 14, 2016 · (Permalink)
that numbers dont lie, but they can be manipulated
vidcomm46 · 1 points · Posted at 00:52:44 on February 14, 2016 · (Permalink)
The fact that mathematics exists without Humans and has always existed...
[deleted] · 3 points · Posted at 02:51:42 on February 14, 2016 · (Permalink)
Found the platonist.
geared4war · 1 points · Posted at 01:27:05 on February 14, 2016 · (Permalink)
6 is afraid of 7 because 7 ate 9.
Slideydoge · 1 points · Posted at 02:18:54 on February 14, 2016 · (Permalink)
5/7 equals a perfect score
Outofthiswoah · 1 points · Posted at 02:53:32 on February 14, 2016 · (Permalink)
Without a doubt it has to be Euler's Identity - joining multiple disciplines of mathematics and identities
ei*pi + 1 = 0
Or maybe the endless fractals in the beautiful Mandelbrot Set takes it.
How about this little charm: you can prove 1 + 2 + 3 + 4 + ... = -1/12
For more I highly recommend checking out Brady Heron's YouTube channel Numberphile.
somadIcanteven · 2 points · Posted at 03:16:58 on February 14, 2016 · (Permalink)*
Okay, okay, since the whole -1/12 has been handled in other comments, no that sum is not equal to -1/12. -1/12 is the result of applying a regularization process to the series 1 + 2 + 3 + . . . . that is in now way what mathematicians mean when they write the series down, but is still incredibly important.
Fermats_Last_Account · 1 points · Posted at 04:09:52 on February 14, 2016 · (Permalink)
I still approve of that. Adding a positive to a positive equals a positive, so adding positive numbers forever to a positive number will always equal a positive number.
somadIcanteven · 1 points · Posted at 05:57:07 on February 14, 2016 · (Permalink)
Right. And that's why in standard summation, the sum's value is infinity -- it is a divergent series.
What the -1/12 is measuring is the growth rate of a function which measures how the sum goes to infinity when you apply smooth weights to its terms. It is absolutely not the value of the series.
prmcd16 · 1 points · Posted at 03:03:38 on February 14, 2016 · (Permalink)
Seconded.
Melba69 · 1 points · Posted at 05:22:50 on February 14, 2016 · (Permalink)
Square root of 69 is 8 something.
Euerfeldi · 0 points · Posted at 19:50:40 on February 13, 2016 · (Permalink)
Zero is an even number
MilitaryFish · 4 points · Posted at 21:00:08 on February 13, 2016 · (Permalink)
Well that makes sense. You never see 2 odd numbers of 2 even numbers when talking about numbers sequentially right? If 3 is odd and 2 is even, that makes 1 odd and 0 even.
chocapix · 3 points · Posted at 21:11:36 on February 13, 2016 · (Permalink)
One can't even!
acatcus · 1 points · Posted at 04:07:13 on February 14, 2016 · (Permalink)
I don't know why this is being downvoted. An even number is any integer n which can be written as n = 2k for some k ∈ ℤ, and 0 = 2*0, so 0 is even.
[deleted] · 1 points · Posted at 14:51:10 on February 14, 2016 · (Permalink)
I agree with you. But every math professor I've ever had disagrees with us.
Ramrod312 · 1 points · Posted at 20:02:34 on February 13, 2016 · (Permalink)
Take numbers 0-9 as individuals in any combination and it will always be divisible by 9
Acemcbean · 2 points · Posted at 20:19:11 on February 13, 2016 · (Permalink)
Sauce?
[deleted] · 2 points · Posted at 20:59:30 on February 13, 2016 · (Permalink)*
[deleted]
Acemcbean · 2 points · Posted at 21:03:43 on February 13, 2016 · (Permalink)
I.. Still can't wrap my head around it. Is there a quick example you could write up?
[deleted] · 2 points · Posted at 21:17:58 on February 13, 2016 · (Permalink)*
[deleted]
Acemcbean · 2 points · Posted at 21:19:20 on February 13, 2016 · (Permalink)
OK, I see what you meant. Sorry, didn't quite understand what was trying to be conveyed, thank you!
sampeckinpah5 · 1 points · Posted at 21:11:17 on February 13, 2016 · (Permalink)
All those numbers add up to 45, which is a multiple of 9, that's why it can be divided by 9 no matter the order.
FuckUHaveADownVote · 1 points · Posted at 13:44:12 on February 14, 2016 · (Permalink)
There is a trick to seeing if any number is divisible of 9. You sum up the digits together, and if the sum of the digits is divisible by 9, then the original number is also divisible by 9. If the sum is larger than 9, check to see if the sum equals 9 for ease. (Fun fact: same trick works for multiples of 3)
Examples:
09: 9+0=9
18: 1+8=9
72: 7+2=9
99: 9+9=18 ----> 18: 1+8=9
171: 1+7+1=9
So if you take any number that is using all the numbers 0-9, you can rearrange the numbers into these pairs:
(9+0)+(8+1)+(7+2)+(6+3)+(5+4)=9+9+9+9+9
and then sum them all together (each pair equals 9 independently).
And to finish it off, 9+9+9+9+9= 5(9)=45, 45 is divisible by 9 because 4+5=9. And yes, this last step i showed was redundant because you can already see that it is divisible by 9 because i just added only 9s together.
Ramrod312 · 0 points · Posted at 20:20:19 on February 13, 2016 · (Permalink)
A calculator
gabybo1234 · 1 points · Posted at 21:00:21 on February 13, 2016 · (Permalink)
I dont really understand what you mean, can you give me an example?
elyisgreat · 1 points · Posted at 21:30:30 on February 13, 2016 · (Permalink)
i.e. All pandigital numbers in base 10 divide 9
Similarly all pandigital numbers in base 4 are divisible by 3, and all pandigital numbers base 16 divide 15.
Would all pandigital numbers base n be divisible by n-1?
heap42 · 1 points · Posted at 00:08:29 on February 14, 2016 · (Permalink)
Guess what?, It is also divisible by 3 and said number by 3 will be 3 times as large as said number by 9.
Felixo77 · 1 points · Posted at 20:06:01 on February 13, 2016 · (Permalink)*
1x1=1 11x11=121 111x111=12321 1111x1111=1234321 11111x11111=123454321
JoshuaZ1 · -1 points · Posted at 20:37:35 on February 13, 2016 · (Permalink)*
Try this with 10 1s in a row. It won't work.
[deleted] · 1 points · Posted at 20:43:34 on February 13, 2016 · (Permalink)*
[deleted]
FashionableZebra · 1 points · Posted at 21:36:26 on February 13, 2016 · (Permalink)
Shit, as another thirty-something yr old, TIL.
hayberry · 1 points · Posted at 22:46:34 on February 13, 2016 · (Permalink)
I'm pretty sure the term root has to do with some Latin translation (mistranslation?) of the radix, the radical symbol for square root. We also have cube roots which goes against the multiplication table theory, if I'm understating you correctly. Also, what would the square root of 5 or 7 be in a multiplication table?
Kilo_G_looked_up · 1 points · Posted at 20:48:37 on February 13, 2016 · (Permalink)
0.9999999...=1
tiplinix · 1 points · Posted at 22:22:00 on February 13, 2016 · (Permalink)
This is just a question of notation. It's true because you have an infinite sum on the left side that converges to 1.
kikilio · 1 points · Posted at 21:11:46 on February 13, 2016 · (Permalink)
If you dropped any object into an airless, frictionless tunnel between any two points on Earth, it would take 42 minutes for that object to reach the other side of the tunnel.
[deleted] · 1 points · Posted at 21:45:51 on February 13, 2016 · (Permalink)
From the other side at some point, wouldn't it be acting against gravity?
Maggoony · 1 points · Posted at 22:16:07 on February 13, 2016 · (Permalink)
yes, but without friction/air resistance it would have enough momentum to carry on for the same distance once it passed that point.
Schwingzilla · 1 points · Posted at 21:49:29 on February 13, 2016 · (Permalink)*
The sizes of infinity. Let's just talk about positive real numbers here.
1) The positive integers. You know, 1, 2, 3, 4, 5, 6, 7 et cetera
2) The positive fractions (rationals). Integers divided by integers. You know, 1/2, 2/3, 1/3, 32/33, et cetera
3) The irrational numbers. Numbers whose decimal forms never repeat (so no 1/3 = .333333~), or numbers that can't be represented by a fraction. These are numbers like pi (3.1415...), e (2.7...), e + pi, sqrt(2), et cetera.
How many numbers are in 1) ? Why, infinity, of course. How many numbers are in 2) ? Why, infinity, of course. How many numbers are in 3) ? Why, infinity, of course.
Ahh, but are there more numbers in 2 than 1? Are there more numbers in 2 than 3 or 3 than 2?
Let's think about it intuitively. Take any two integers. Say, 4 and 5. There's an infinitie number of fractions between them (9/2, 19/4, et cetera). But take two fractions, say 1/2 and 2/3, and there are zero integers between them. So of course, there must be more fractions than integers, right? Similarly, take any two fractions, and there are an infinite number of irrational numbers between them. Also, take any two irrational numbers, and there's an infinite number of rational numbers between them. So 2) and 3) are the same size, right?
Wrong. 1) and 2) are the same size. And 3) is larger than either.
For some context and proof that 1) and 2) are the same size:
https://en.wikipedia.org/wiki/Countable_set
https://en.wikipedia.org/wiki/Uncountable_set
Cogswobble · 1 points · Posted at 23:03:42 on February 13, 2016 · (Permalink)
This interesting paradox:
http://i.imgur.com/ekvcNc0.jpg
[deleted] · 1 points · Posted at 23:32:27 on February 13, 2016 · (Permalink)
The largest factorial a scientific calculator can handle is 69!
Noob1239 · 1 points · Posted at 23:38:17 on February 13, 2016 · (Permalink)
Mitochondria is the powerhouse of a cell.
[deleted] · 1 points · Posted at 23:45:31 on February 13, 2016 · (Permalink)
4 farts = 1 poop
RedditsLittleSecret · 1 points · Posted at 23:53:19 on February 13, 2016 · (Permalink)
ITT: /r/theydidthemath
JustGOwiththem · 1 points · Posted at 00:05:13 on February 14, 2016 · (Permalink)
The mitochondria is the powerhouse of the cell
codythecoder · 1 points · Posted at 00:16:33 on February 14, 2016 · (Permalink)*
What kind of a mathematician doesn't know this, but I still think that eπi + 1 = 0 is the coolest thing ever.
Edit: messed up the signs
Hedgehogs4Me · 3 points · Posted at 01:34:32 on February 14, 2016 · (Permalink)
The more general form, eix = cosx+isinx, is even cooler. If you put in certain values for x things get really freaky (nsfw).
[deleted] · 2 points · Posted at 02:53:47 on February 14, 2016 · (Permalink)
I believe you mean "+1", or else "2πi"?
codythecoder · 1 points · Posted at 03:37:03 on February 14, 2016 · (Permalink)
Yep, I'd just mixed it up with eπi = -1.
chubbywalrus1123 · 1 points · Posted at 00:29:47 on February 14, 2016 · (Permalink)
I'm partial to epi*i= -1 just because logically it makes no sense.
But it's a fun little proof that involves Taylor series
heavyish_things · 1 points · Posted at 03:30:37 on February 14, 2016 · (Permalink)
Bullshit.
This really annoys me. The only reason people think it's cool is because it's unintuitive... if you don't know the more general, actually useful form of the equation.
It's like saying it logically makes no sense that the derivative of 2x includes ln(2), because why would 2 be related to e? Well because that's how e is defined.
PM_ME_UR_SKILLS · 1 points · Posted at 00:30:34 on February 14, 2016 · (Permalink)
Rivers have pi! The distance traveled is roughly the distance of source to mouth as the crow flies times pi. In other words, distance traveled : distance = pi, on average.
http://www.joyofpi.com/pifacts3.html
todtier27 · 1 points · Posted at 00:57:56 on February 14, 2016 · (Permalink)
Girls = (time)(money)...time=money...Girls=(money)(money)...Girls = (money)2...money=√evil......Girls = (√evil)2.....Girls = Evil
Cremasterau · 1 points · Posted at 01:10:24 on February 14, 2016 · (Permalink)*
Infinity really does leave us with -1/12.
What is seriously, seriously cool, is that with all the kerfuffle around the Numberphile video purporting to show infinity, or rather 1+2+3+4+5..., = -1/12 , it turns out that if you take all the numbers both positive and negative and graph them -1/12 pops up beautifully.
By that I mean the summing of all numbers including decimals and negative numbers. For instance ...-0.2 + -0.1 + 0 + .1 + .2 ....
The formula for summing sequential numbers is 1/2x(x+1) and if you plot this at Wolfram this is what you get).
If you calculate the small area under the x axis you get -1/12.
If you minus the area under the graph above the x axis on the left from the one on the right you get zero leaving the sum of all numbers through to infinity at -1/12!
I consider myself not all that mathematical but this little gem has intrigued me to no end. Love it.
Edit: Added image
AcellOfllSpades · 2 points · Posted at 03:37:06 on February 14, 2016 · (Permalink)*
Why would that area be equal to the sum? Shouldn't the sum be dependent on the behavior as it gets higher, not what happens between 0 and -1?
Also, that sum is entirely unrelated to the "sum of all numbers". There is no sum of all numbers.
Also, your sum "... + -.2 + -.1 + 0 + .1 + .2 + ... "misses an infinitely larger amount of numbers than it captures.
Also, that graph has a domain of all the real numbers, not all the integers. Integers are discrete.
I agree that it's interesting, and may even be relevant. It's disengenuous to call that the sum of all natural numbers, though, for several reasons.
Cremasterau · 1 points · Posted at 05:48:45 on February 14, 2016 · (Permalink)
All I'm doing is taking the area from the left side of the graph, which is a positive number even though it represents negative numbers and taking it away from the area on the right hand side of the graph which would leave us with zero. I don't claim this is legitimate since I don't have the mathematical skills to say so. But the area left is -1/12.
But the graph captures them. It doesn't matter how minute you go they will still represented in the graph, remember we are graphing sequential additions.
Perhaps, and I was at pains to point out my numerical illiteracy, but to have the Numberphile crew do their machinations and get a figure of -1/12th then to find the same number appearing when all the positive and negative sequential additions are graphed I thought was pretty bloody cool. To dismiss it as a fluke or merely interesting I felt doesn't do it justice which is why I thought it 'the most interesting fact I know'.
AcellOfllSpades · 1 points · Posted at 05:54:49 on February 14, 2016 · (Permalink)
The Numberphile video is wrong. There's a way to make it accurate, but nearly every statement there is blatantly false. (I wrote it up elsewhere in this thread.)
Also, that is not a graph of sequential additions. That is the graph of the analytic continuation of the sum of the first n natural numbers. The "analytic continuation" is just the function that behaves nicely that happens to pass through those points. It's not the same thing as the original function. The original function doesn't say anything at all about negative numbers or non-integers!
Oh, and there is no sum of all real numbers. There is no way to define it to make sense.
Yes, it's pretty cool, and it may even be related to how they get -1/12. However, calling that area the sum of anything is simply false. unless you get into the definition of area under a curve (aka integral) in calculus and even then it's not the sum but the limit of a sum
Cremasterau · 1 points · Posted at 06:16:57 on February 14, 2016 · (Permalink)*
More than happy to bow to your obviously superior grasp of mathematical nomenclature and concepts, especially since mine is so woeful.
I found the clash between the physics and the mathematical fraternities over the video really interesting and great fun for an outsider like myself.
What is obvious though is that physicists find -1/12 useful in their calculations and reflected in the real world. For it to appear visually tickled my fancy and my uneducated guess is that it will probably be found to have greater importance than it is given at the moment.
Edit: Additional thoughts.
The graph surely is the function of all numbers both negative and positive and of an infinite degree of minutia which must be a truer representation of infinity I would have thought.
Which might give cause to question Numberphile's presentation but doesn't negate what I have put.
AcellOfllSpades · 1 points · Posted at 06:37:01 on February 14, 2016 · (Permalink)
There's no clash, and we're fully aware that it has some importance (though not as much as you make it out to be). Often, the sudden appearance of -1/12 signals that there's a regularization hidden somewhere in the formula which "lets through" regular infinite series unchanged but assigns finite values to normally infinitely large sums.
Zeta regularization and Ramanujan summation are both used frequently in mathematics and physics.
Honestly, that video turned me off of Numberphile in general. If you want interesting math channels, I recommend these (none of them require any math knowledge past 6th grade; favorites bolded):
Stand Up Maths, a math professor and semi-comedian
3 Blue 1 Brown, a channel with intuitive explanations and smooth animation
Making Math Interesting (only one video so far unfortunately)
Mathologer, professor who connects math with pop culture.
And of course, Vi Hart, "mathemusician" extraordinaire.
Plus some other interesting educational channels for physics and other subjects (again, no prerequisite knowledge):
CGP Grey, videos about political systems and technology.
Frame of Essence, videos about quantum mechanics explained very simply.
Looking Glass Universe, more quantum mechanics (heavy calculation-free!) plus some calculus.
OskarPuzzle, Rubik's Cube-esque twisty puzzles.
Quirkology, magic tricks based on physics and psychology.
Veritasium, interesting explanations of physics and chemistry.
Tom Scott, who visits various places around the world to point out interesting facts. Also has an entirely unrelated but still interesting series on linguistics.
Big Shredder, in case you want to know what things look like when they get thrown into a big shredder.
Cremasterau · 1 points · Posted at 08:05:26 on February 14, 2016 · (Permalink)
Thank you for the links.
Well you seem to be very dismissive of the two physicists in the Numberphile video and by extension of Ramanujan.
"Dear Sir, I am very much gratified on perusing your letter of the 8th February 1913. I was expecting a reply from you similar to the one which a Mathematics Professor at London wrote asking me to study carefully Bromwich's Infinite Series and not fall into the pitfalls of divergent series. … I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + · · · = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. …"
I do like Feynman's take on the difference between the approaches of each fraternity.
He talks about understanding the connection of the words with the real world.
I would have thought if -1/12 is useful in understanding String Theory then it is the job of physicists to use the tool if they are comfortable doing so. It is the job of mathematicians to explain why it works in the real world.
I have enjoyed the debate between the two groups.
g-spot_adept · 1 points · Posted at 03:31:22 on February 14, 2016 · (Permalink)
No - this is a known hoax
Cremasterau · 1 points · Posted at 04:00:20 on February 14, 2016 · (Permalink)
Which one? The video or the graph?
g-spot_adept · 1 points · Posted at 06:52:30 on February 14, 2016 · (Permalink)
the whole thing is an over 100 year old hoax to show that you cannot use the same mathematical formula manipulation proofs on an infinite series that you would a normal equation.
as much as I hate to burst everyone's bubble, 1 + 2 + 3 + ...., = ∞
[deleted] · 1 points · Posted at 01:16:22 on February 14, 2016 · (Permalink)
If you shuffle a full deck of cards, it is extremely likely the cards have never been in the order you just put them in. Ever.
Xazrael · 1 points · Posted at 01:17:35 on February 14, 2016 · (Permalink)
There's a card trick I know that, using 21 cards, if you pick any card, and I shuffle its row into the middle of the deck, I can find your card by shuffling the deck back together 3 times - and it'll be the 8th card I draw from the top of the reshuffled deck.
Cant_standja · 1 points · Posted at 01:18:17 on February 14, 2016 · (Permalink)
That 1+2+3+4+...to infinity = -1/12
Proof: https://m.youtube.com/watch?v=w-I6XTVZXww
OuroborosSC2 · 1 points · Posted at 01:20:07 on February 14, 2016 · (Permalink)
Any number ending in 9 can be split up, multiplied, then added like so to equal the number.
tunersharkbitten · 1 points · Posted at 01:24:11 on February 14, 2016 · (Permalink)
Drakes equation https://en.m.wikipedia.org/wiki/Drake_equation
I am hopeful that we are not alone in this universe. This makes it that much easier to understand that we probably are not.
yuga_d · 1 points · Posted at 01:24:29 on February 14, 2016 · (Permalink)
epi * i +1 = 0
hackedhacker · 1 points · Posted at 01:31:30 on February 14, 2016 · (Permalink)
1+2+3+4+5+6....= - 1/12
[deleted] · 1 points · Posted at 01:39:57 on February 14, 2016 · (Permalink)
0.999... is equal to 1
Calius1337 · 1 points · Posted at 01:40:15 on February 14, 2016 · (Permalink)
I know the last digit of pi..
diabolical laughter
[deleted] · 1 points · Posted at 01:40:18 on February 14, 2016 · (Permalink)
If x is a single digit number and you multiply x by 9, if you add up the 2 digits together (i.e. 72 from 8 x 9) they'll add up to 9!
1x9 = 9 (9 + 0) 2x9 = 18 (9 + 1) 3x9 = 27 (2 + 7) 4x9 = 36 (3 + 6) etc.
mikemcgu · 1 points · Posted at 06:59:15 on February 14, 2016 · (Permalink)
(9+1)=10 last time I checked. Unless I have a fundamental misunderstanding of what the number '1' is.
[deleted] · 1 points · Posted at 15:37:27 on February 14, 2016 · (Permalink)
Well, it'd be 9 + 0
It's the 2 (or 1 in this case) digits added up together after you multiply by 9.
so for 1x9 you're doing 9 + 0 because there's no second digit.
peck8326 · 1 points · Posted at 01:43:30 on February 14, 2016 · (Permalink)
The Drake equation.. N = R* • fp • ne • fl • fi • fc • L.. a probabilistic argument used to arrive at an estimate of the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.
coloroftheskye · 1 points · Posted at 01:45:49 on February 14, 2016 · (Permalink)*
that 1 + 2 + 3 + 4 + 5 + ... = -1/12
There are various other divergent series with do have values that are not infinite. I can't understand it.
mikemcgu · 1 points · Posted at 06:50:35 on February 14, 2016 · (Permalink)
I might be an idiot, but - what?
coloroftheskye · 2 points · Posted at 19:14:53 on February 14, 2016 · (Permalink)*
I can't really explain it except in math terms.
The easiest way you can prove this is with a few different sums.
A = 1 - 1 + 1 - 1 + 1 ...
we can solve this by saying
1 - A = 1 - (1 - 1 + 1 - 1...)
which is original series again.
so 1 - A = A which means A = 1/2.
the next series we need is
B = 1 - 2 + 3 - 4 + 5...
this means we can do this.
B = 1 - 2 + 3 - 4 + 5...
+B = 1 - 2 + 3 - 4 + 5...
2B = 1 - 1 + 1 - 1 + 1 ...
and look 2B is equal to A. so B = 1/4
and Finally the series I was talking about is
C = 1 + 2 + 3 + 4 + 5...
We can do C - B.
C = 1 + 2 + 3 + 4 + 5...
-B = 1 - 2 + 3 - 4 + 5...
C-B=0 + 4 + 0 + 8 + 0...
C - B = 4 + 8 + 12 + 16...
C - B = 4 (1 + 2 + 3 + 4...)
C - B = 4C
we know that b = 1/4
C - 1/4 = 4C
-1/4 = 3C
C = -1/12
locotx · 0 points · Posted at 01:47:00 on February 14, 2016 · (Permalink)
I call it the "Where's your Math God now !?" formula
bnvjgj · 1 points · Posted at 01:56:54 on February 14, 2016 · (Permalink)
i gave up on math after 6th grade
rageofheaven · 1 points · Posted at 02:06:55 on February 14, 2016 · (Permalink)
Every whole number is divisible by one.
1o0m · 1 points · Posted at 02:07:15 on February 14, 2016 · (Permalink)
Anything multiplied by 0 is 9
[deleted] · 1 points · Posted at 02:10:58 on February 14, 2016 · (Permalink)
8675309 is a prime number. AND it has a twin!
richardec · 2 points · Posted at 02:17:28 on February 14, 2016 · (Permalink)
And it's a catchy tune
[deleted] · 2 points · Posted at 02:25:32 on February 14, 2016 · (Permalink)
For a good time, for a good time: CALL!
BASE_SEVEN · 1 points · Posted at 02:12:06 on February 14, 2016 · (Permalink)
A hexagon has the highest surface area to perimeter ratio of any shape. In layman's terms, if you have a rope of a given length and want to enclose as much space as possible with it, you should make a hexagon. This is why bees build hexagonal cells in their hives, and hexagons show up frequently in nature
SirBlobfish · 5 points · Posted at 02:17:25 on February 14, 2016 · (Permalink)
Bees use hexagons because they have a high surface area AND and they tile well (like squares). When it comes to just the surface area, circles are the best. That's why bubbles are spherical (3-d version of spheres)s
areemkay · 1 points · Posted at 02:19:53 on February 14, 2016 · (Permalink)
But how do bees know that?
[deleted] · 1 points · Posted at 08:15:30 on February 14, 2016 · (Permalink)
All the ones that tried octagons died.
FearHD · 1 points · Posted at 02:12:55 on February 14, 2016 · (Permalink)
0.9999999 = 1
1/3 = 0.333 2/3 = 0.666 3/3 = 0.999
donaldtrumpisacuck · 1 points · Posted at 02:13:40 on February 14, 2016 · (Permalink)
I have more money than you
[deleted] · 1 points · Posted at 02:19:59 on February 14, 2016 · (Permalink)
666 is the sum of every integer from 1 to 36.
superermonkey · 1 points · Posted at 02:22:29 on February 14, 2016 · (Permalink)
I always thought it was really cool that there are infinitely more decimal numbers between 0 and 1 than there are whole numbers between 0 and infinity.
iluvgrannysmith · 1 points · Posted at 03:08:31 on February 14, 2016 · (Permalink)
Yeah, the natural numbers are countable. However, the irrationals are uncountable. It is fascinating. You ought to consider looking into measure theory. Try reading up on the cantor set.
Davidred323 · 1 points · Posted at 02:26:04 on February 14, 2016 · (Permalink)
Four colors suffice
[deleted] · 1 points · Posted at 02:28:01 on February 14, 2016 · (Permalink)
There are only two operations, add and multiply. Subtraction is basically adding with a negative number; division is multiplying the number, inverted.
Sure would have made life easier in elementary.
heavyish_things · 1 points · Posted at 03:34:31 on February 14, 2016 · (Permalink)
What about AND, OR, etc.?
mcmcc · 1 points · Posted at 02:28:09 on February 14, 2016 · (Permalink)
1+2+3+4+ ... = -1/12
https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
[deleted] · 1 points · Posted at 02:30:26 on February 14, 2016 · (Permalink)
1 - 0.999… = 0.000...
0.000... = 0
1 = 0.999…
LochNessGinger · 1 points · Posted at 02:32:43 on February 14, 2016 · (Permalink)
The 9 times table is actually really simple to remember.
0123456789 9876543210 read each number from top to bottom. so 09, 18, 27, 36...
mazurkian · 1 points · Posted at 02:35:38 on February 14, 2016 · (Permalink)
The sum of all positive whole numbers to infinity is equal to - 1/12.
LiveAndDie · 1 points · Posted at 02:37:47 on February 14, 2016 · (Permalink)
Gabriel's horn: an object with infinite surface area, but finite volume. Gabriel's Horn
t3chb0ss · 1 points · Posted at 02:38:02 on February 14, 2016 · (Permalink)
The sum of all positive integers = -1/12 (sort of)
somadIcanteven · 1 points · Posted at 03:39:51 on February 14, 2016 · (Permalink)
You. You will be spared.
[deleted] · 1 points · Posted at 02:39:38 on February 14, 2016 · (Permalink)
The Birthday Paradox. In a room of 23 people there is a 50% change two people have the same birthday.
[deleted] · 1 points · Posted at 02:50:31 on February 14, 2016 · (Permalink)
[deleted]
brutalyak · 1 points · Posted at 02:53:26 on February 14, 2016 · (Permalink)
No, just no.
firebird50 · 1 points · Posted at 02:54:46 on February 14, 2016 · (Permalink)
i know this is going to sound impossible and blow your mind but did you guys know the coolest mathematical fact is that two plus two equals four.
Logan_W_Logan · 1 points · Posted at 02:57:19 on February 14, 2016 · (Permalink)
1+2+3+4+5+.......= -1/12
http://youtu.be/w-I6XTVZXww
prmcd16 · 1 points · Posted at 03:00:33 on February 14, 2016 · (Permalink)
+1 for Numberphile! :)
Silverbodyboarder · 1 points · Posted at 03:04:14 on February 14, 2016 · (Permalink)
.999999... = 1
Halfwayhome22 · 1 points · Posted at 03:05:34 on February 14, 2016 · (Permalink)
Graham's number is a number that is so big that the human brain cannot comprehend how big it is.
Daktush · 1 points · Posted at 03:10:27 on February 14, 2016 · (Permalink)
The sum of all numbers is equal to -1/12
https://www.youtube.com/watch?v=w-I6XTVZXww
brutalyak · 1 points · Posted at 03:11:22 on February 14, 2016 · (Permalink)
That's not true.
OverlordLork · 1 points · Posted at 05:01:59 on February 14, 2016 · (Permalink)
No. The Ramanujan sum of all positive integers is -1/12.
Here's a good article complaining about that video http://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/
[deleted] · 1 points · Posted at 03:13:28 on February 14, 2016 · (Permalink)
Why is 6 afraid of 7?
Because 7, 8, 9.
anuraj12 · 1 points · Posted at 03:13:58 on February 14, 2016 · (Permalink)
That you are one over cos c
tastes-like-chicken · 1 points · Posted at 04:01:45 on February 14, 2016 · (Permalink)
I sat here saying "secant c" in my head over and over until I finally got it.
[deleted] · 1 points · Posted at 03:14:55 on February 14, 2016 · (Permalink)
27 is the only xx birthday you will vividly remember.
11 = 1
22 = 4
33 = 27
44 = 256
robmox · 1 points · Posted at 03:15:41 on February 14, 2016 · (Permalink)
Q: What's the square root of 69?
A: 8 something.
-My Dad
[deleted] · 1 points · Posted at 03:17:21 on February 14, 2016 · (Permalink)
Would be so cool if this thread was translated for people without autism.
wheresmyadventure · 1 points · Posted at 03:23:47 on February 14, 2016 · (Permalink)
That six was afraid of 7.
[deleted] · 1 points · Posted at 03:26:50 on February 14, 2016 · (Permalink)
The sum of all positive integers (1+2+3+4... to infinity) equals -1/12
It can be proven and is used in many areas of physics
OverlordLork · 1 points · Posted at 05:04:40 on February 14, 2016 · (Permalink)
http://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/
[deleted] · 1 points · Posted at 05:16:30 on February 14, 2016 · (Permalink)
What I got from that article is that 1+2+3+4... can be assigned the value -1/12, but using the word "sum" or "equals" is misleading. The article complains about how it was explained, not that it's wrong.
Silvernocte · 1 points · Posted at 03:29:49 on February 14, 2016 · (Permalink)
the good old 0.999999... = 1 fact
nondescriptaccount · 1 points · Posted at 03:35:14 on February 14, 2016 · (Permalink)
ITT: things that make my brain shut down.
Sendmeloveletters · 1 points · Posted at 03:36:26 on February 14, 2016 · (Permalink)
U + Me = Us
fiesta119 · 1 points · Posted at 03:39:34 on February 14, 2016 · (Permalink)
1+2+3=123
Lunchables · 1 points · Posted at 04:03:32 on February 14, 2016 · (Permalink)
U + Me = Us
[deleted] · 1 points · Posted at 04:17:04 on February 14, 2016 · (Permalink)
Numbers add up to nothing
-Neil Young
lukeyj4212 · 1 points · Posted at 04:21:58 on February 14, 2016 · (Permalink)
My girlfriend is squareroot of negative one hundred. Shes a perfect ten, but just imaginary...
mlpiceking · 1 points · Posted at 04:28:09 on February 14, 2016 · (Permalink)
+1
alexandicity · 1 points · Posted at 04:23:47 on February 14, 2016 · (Permalink)
That pi would be better and more natural if it were actually twice as large...
(Tau ftw!)
snocat · 1 points · Posted at 04:25:52 on February 14, 2016 · (Permalink)
No matter how old I gets, college girls stay the same age! :D
OnePunkArmy · 1 points · Posted at 04:30:21 on February 14, 2016 · (Permalink)
With the exception of 2 and 3, all prime numbers are 1 away from a multiple of 6.
theembodimentofsleep · 1 points · Posted at 04:50:29 on February 14, 2016 · (Permalink)
Going farther out in the universe gives a high probability of meeting yourself.
Nicepotato · 1 points · Posted at 05:06:26 on February 14, 2016 · (Permalink)
Please explain
theembodimentofsleep · 1 points · Posted at 16:12:56 on February 14, 2016 · (Permalink)
I can't remember the exact theory, but if you travel out far enough in the universe, like trillions of lightyears, the combinations of atoms start repeating and running out if combinations.
firedropx · 1 points · Posted at 05:23:38 on February 14, 2016 · (Permalink)
5 + 5 = 55
2 + 2 = 22
Reala27 · 1 points · Posted at 06:04:35 on February 14, 2016 · (Permalink)
I think you mean "5" + "5" = "55"
snipermonkey789 · 1 points · Posted at 05:24:15 on February 14, 2016 · (Permalink)
8008135
RagingLeonard · 2 points · Posted at 05:27:49 on February 14, 2016 · (Permalink)
7734
The_Amazing_Shlong · 1 points · Posted at 05:38:54 on February 14, 2016 · (Permalink)
I'm telling!
snipermonkey789 · 1 points · Posted at 06:00:42 on February 14, 2016 · (Permalink)
You're going there!
[deleted] · 1 points · Posted at 08:23:20 on February 14, 2016 · (Permalink)
8675309
Aegmorgil_One · 1 points · Posted at 05:33:46 on February 14, 2016 · (Permalink)
I understand some of these words. This is warranted. http://i.imgur.com/bch6lqb.gif
steebo81 · 1 points · Posted at 05:39:21 on February 14, 2016 · (Permalink)
666 (devil) * 3 (digits in 666) = 1998 (year)
666 / 3 = 222 (anniversary)
1998 - 222 = 1776 (U.S. Independence)
Conclusion. America is the devil???
RainThunder0 · 1 points · Posted at 05:42:03 on February 14, 2016 · (Permalink)
Euler's identity.
NadaJava · 1 points · Posted at 05:43:52 on February 14, 2016 · (Permalink)
Sin x / n = six
Hapisok · 1 points · Posted at 05:45:56 on February 14, 2016 · (Permalink)
80085
Cadwae · 1 points · Posted at 05:47:37 on February 14, 2016 · (Permalink)
https://www.youtube.com/watch?v=1N6cOC2P8fQ
Day[9] talking and explaining Graham's Number. Found it very interesting.
justbeane · 1 points · Posted at 05:49:31 on February 14, 2016 · (Permalink)
ii is a real number. It is approximately 0.2079.
overconvergent · 1 points · Posted at 05:59:00 on February 14, 2016 · (Permalink)
The expression ii represents infinitely many real numbers, only one of which is approximately 0.2079.
[deleted] · 1 points · Posted at 05:54:15 on February 14, 2016 · (Permalink)
[deleted]
overconvergent · 1 points · Posted at 05:57:12 on February 14, 2016 · (Permalink)
No. A real number is either rational or irrational. By definition, a real number is rational if it is the ratio of two integers, and an irrational number is a number that is not rational. 1 is rational whether you write it as 1 or as 0.9999....
JackDallas · 1 points · Posted at 06:25:30 on February 14, 2016 · (Permalink)
That 42 is the answer to life, the universe and everything.
Thank you Douglas Adams for letting me in on this secret.
emcee_paz · 1 points · Posted at 06:41:55 on February 14, 2016 · (Permalink)
I know why 6 is scared of 7.
Gourry007 · 1 points · Posted at 06:46:25 on February 14, 2016 · (Permalink)
There was a man years ago; I'm sorry I don't remember his name or any integral information of the sort, but he proved to 100% mathematical certainty that human kindness was purely a survival tactic. He later killed himself due to his inability to reconcile such a discovery. His findings and formulas were also completely original; void of any sources or citations whatsoever.
CarpeCyprinidae · 1 points · Posted at 08:23:08 on February 14, 2016 · (Permalink)
George Price
SnapesFavoriteSong · 1 points · Posted at 06:52:20 on February 14, 2016 · (Permalink)
qt3.14 = Alison Brie
Skyros · 1 points · Posted at 06:57:50 on February 14, 2016 · (Permalink)
PI IS EXACTLY 3
tunnelvisie · 1 points · Posted at 07:08:50 on February 14, 2016 · (Permalink)
The sum of all possible integers to infinity is equal to -(1/12). See also this numberphile video: https://youtu.be/w-I6XTVZXww
flojo-mojo · 1 points · Posted at 08:57:14 on February 14, 2016 · (Permalink)
pi is exactly 3!!!
scaryclownzinmyhouse · 1 points · Posted at 09:22:53 on February 14, 2016 · (Permalink)
There are so many possible combinations of a deck of cards that if you shuffle a deck it is most likely that the arrangement you are holding has never before existed.
8.0767 arrangements of cards possible for a standard deck of 52 playing cards.
If you rearranged the deck in a new arrangement once every second since the big bang (13.8 billion years ago) you would still be making new combinations today and for millions of years to come.
Sabbaer · 1 points · Posted at 09:27:54 on February 14, 2016 · (Permalink)
1+1=2
awaqu · 1 points · Posted at 09:41:53 on February 14, 2016 · (Permalink)
58008 upside down is boobs
hihungryimdadDOTcom · 1 points · Posted at 13:38:25 on February 14, 2016 · (Permalink)
Type the following into a calculator: 5318008
Now turn it upside down. Prepare to weep.
HumansNotRobots · 1 points · Posted at 13:43:22 on February 14, 2016 · (Permalink)
6 is afraid of 7 because 7 ate nine
-Fugg-_ · 1 points · Posted at 14:07:41 on February 14, 2016 · (Permalink)
Mitochondria is the powerhouse of the cell
Rawr_Imma_duck · 1 points · Posted at 19:20:58 on February 13, 2016 · (Permalink)
24!
746865626c617a · 3 points · Posted at 20:18:21 on February 13, 2016 · (Permalink)
Is?
Cgcghost · 9 points · Posted at 20:39:39 on February 13, 2016 · (Permalink)
They're just excited about the number 24!
thestickystickman · 3 points · Posted at 20:50:21 on February 13, 2016 · (Permalink)
6.20448402x1023
antijudo · 0 points · Posted at 21:03:24 on February 13, 2016 · (Permalink)
Quite close to Avogadro's constant
thestickystickman · 9 points · Posted at 21:12:51 on February 13, 2016 · (Permalink)
Oh yeah, just 1,823,431,600,000,000,000,000 away.
MIKE6792 · 4 points · Posted at 21:41:14 on February 13, 2016 · (Permalink)
rek/t
thestickystickman · 1 points · Posted at 21:45:15 on February 13, 2016 · (Permalink)*
Internal resistance times energy to the power of kelvins per second?
MIKE6792 · 2 points · Posted at 04:03:53 on February 14, 2016 · (Permalink)
ek/t is usually used for exponential growth, r is a constant for radius, but could be used to represent anything, including original amount.
And energy is E aswell as temperature being T not k.
Thompy · 1 points · Posted at 02:30:25 on February 14, 2016 · (Permalink)
If you type in 58008 in the calculator and turn it upside down it spells "BOOBS" :)
jmckee3 · -1 points · Posted at 02:45:58 on February 14, 2016 · (Permalink)
You can spell out boobies on a calculator
ScoochMagooch · -2 points · Posted at 05:21:37 on February 14, 2016 · (Permalink)
80085 looks like "BOOBS" on a calculator
[deleted] · 0 points · Posted at 19:07:40 on February 13, 2016 · (Permalink)
[deleted]
shadowbananacake · 4 points · Posted at 19:14:44 on February 13, 2016 · (Permalink)
58008 918
dougie0341 · 3 points · Posted at 19:21:22 on February 13, 2016 · (Permalink)
55378008
chocopouet · 1 points · Posted at 19:41:43 on February 13, 2016 · (Permalink)
/r/counting
[deleted] · 0 points · Posted at 19:22:16 on February 13, 2016 · (Permalink)
In a right angle triangle, the hypotenous squared is equal to the sum of the... Oh, you know what I'm on about.
JugglingReferee · 1 points · Posted at 06:21:04 on February 14, 2016 · (Permalink)
I know who you are, Lore.
[deleted] · 0 points · Posted at 23:12:04 on February 13, 2016 · (Permalink)*
[deleted]
[deleted] · 1 points · Posted at 00:50:25 on February 17, 2016 · (Permalink)
Math bitch!
robinator8 · -1 points · Posted at 20:25:51 on February 13, 2016 · (Permalink)
My comments = 0 karma
Paultimate79 · -3 points · Posted at 02:47:32 on February 14, 2016 · (Permalink)
0.999_ does not = 1 becuse it would take infinite time and space for it to. It only theoretically = 1.
1/3 = 0.333_ 2/3 = 0.666_ 3/3 = 0.999_ = 1?
This is proof that math is imperfect when forced to define either infinity or zero and thus I theorize that "fractions" are a manmade construct and reality doe snot work in fractions, but in wholes and there comes a point where there is both an indivisible quantity and a finite quantity.
Fermats_Last_Account · -3 points · Posted at 04:07:46 on February 14, 2016 · (Permalink)
I agree. Just cause people can make it seem like they equal each other by writing it out, thinking in reality the fact that 0.999... is a different number than 1. 0.999... will equal 1 - .000000......1.
[deleted] · -3 points · Posted at 23:03:47 on February 13, 2016 · (Permalink)
[deleted]
ben1996123 · 3 points · Posted at 23:21:10 on February 13, 2016 · (Permalink)
no it isnt
[deleted] · 2 points · Posted at 23:48:16 on February 13, 2016 · (Permalink)
No.
YT_Reddit_Bot · 1 points · Posted at 23:03:57 on February 13, 2016 · (Permalink)
mylies43 · -2 points · Posted at 01:02:36 on February 14, 2016 · (Permalink)
ITT: Buncha nerds
Mac33 · 1 points · Posted at 11:43:10 on February 14, 2016 · (Permalink)
This guy fucks!
Wiiplay123 · -1 points · Posted at 02:06:58 on February 14, 2016 · (Permalink)
3 x 4 = 11
In common core.
Voxel_Brony · 2 points · Posted at 06:21:53 on February 15, 2016 · (Permalink)
Could you explain?
buffalo_fluff · -3 points · Posted at 02:07:08 on February 14, 2016 · (Permalink)
None, math is for nerds.
abductodude · -6 points · Posted at 19:30:09 on February 13, 2016 · (Permalink)
Pick me!
PICK ME!
The mitochondria is the powerhouse of a cell.
mrCHRIAS · 1 points · Posted at 20:03:16 on February 13, 2016 · (Permalink)
It is also hypothesized that mitochondria originally were independent prokaryotes that got engulfed by a larger bacteria, which then developed a symbiotic relationship!
Acemcbean · 2 points · Posted at 20:21:42 on February 13, 2016 · (Permalink)
Mitochondrion also have DNA seperate from the DNA of a cell which is passed down maternally
abductodude · 1 points · Posted at 20:11:25 on February 13, 2016 · (Permalink)
This is why I dropped biology.
razor5cl · 1 points · Posted at 21:25:44 on February 13, 2016 · (Permalink)
Endosymbiosis is one of the interesting and cool phenomena that made me stick with it.
hypervelocityvomit · 1 points · Posted at 13:14:08 on February 16, 2016 · (Permalink)
Cancer is the abductodude of a cell.
abductodude · 1 points · Posted at 18:08:42 on February 16, 2016 · (Permalink)
Can confirm, am the abductodude of a cell.
turtle-senpai · -1 points · Posted at 23:29:48 on February 13, 2016 · (Permalink)
1 + 2 + 3 + 4 ... = -1/12
lightsolgr · -1 points · Posted at 04:17:13 on February 14, 2016 · (Permalink)
that 6 is afraid of 7 because 7 8 9.
mlpiceking · 2 points · Posted at 04:30:16 on February 14, 2016 · (Permalink)
reboot taught me this joke
slowbrowsersarefunny · 0 points · Posted at 19:49:10 on February 13, 2016 · (Permalink)
the golden ratio, and also euler's identity
kionih · 0 points · Posted at 20:48:12 on February 13, 2016 · (Permalink)
According to the Giant Impact Hypothesis, a Mars-sized object collided with Earth at an oblique angle, obliterating a huge section of the existing upper layers and ejecting a massive amount of material into orbit. Much of this material coalesced and became the moon as we know it. Now....what is REALLY cool is that the moon used to be a lot closer. So much so that several billions of years ago the entire lunar cycle was on the order of hours, not days. The moons orbit has been slowing as its distance has been increasing from the Earth. Whilst the Earth was in a semi-molten, pre-crustal period of early development, the proximity to the moon, combined with the very short orbital period meant that the tidal forces that the moon exerted on the Earth were vastly stronger and more frequent. In effect, this means that the early moon was capable of producing a perpetual "Wave" that would be experienced across the Earth several times a day due to the effect of this tidal bulge. As the Earth's surface was still in a semi-molten state, this would have appeared to a static observer as a gigantic lava wave, circling the Earth multiple times per day.
YesMyNameIsGeorge · 0 points · Posted at 21:17:53 on February 13, 2016 · (Permalink)
It may not be the coolest one here. Personally I love so many of these but can we take some time to acknowledge our great lads Pythagoras and Newton. I know we learn their works in high school but just think how much this has opened up for us!!
heap42 · 1 points · Posted at 00:11:29 on February 14, 2016 · (Permalink)
Right?... I mean all these highly complicated are fucking useful and awesome and all... but sometimes i am just in awe when i think that a few thousand years ago people managed to come up with things like Pythagoras etc... and then we got days like these where we somehow managed to measure Gravity Waves and simultaneously still kill each other and hate each other and have Wars and all that shit.
upmostytoasty · 0 points · Posted at 21:38:17 on February 13, 2016 · (Permalink)
111,111,111² is 12345678987654321
Avatar_ZW · 0 points · Posted at 21:45:35 on February 13, 2016 · (Permalink)
The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.
Nettius2 · 2 points · Posted at 02:35:22 on February 14, 2016 · (Permalink)
Yes, The Wizard of Oz is ironical all over the place.
hypervelocityvomit · 1 points · Posted at 13:32:44 on February 16, 2016 · (Permalink)
What's that? The theorem of Isosceles?
Avatar_ZW · 1 points · Posted at 13:55:28 on February 16, 2016 · (Permalink)
I dunno, I just thought it sounded smart
sweetei · 0 points · Posted at 21:46:08 on February 13, 2016 · (Permalink)
Shuffle a deck of cards. Chances are ( by a huge degree), that no deck of cards has ever been in that exact order. There are precisely '52!' Possible arrangements for a deck of 52 cards. This number, 8.1 x 10 ^ 67, is greater than the number of stars in the known universe.
kingJoffi · 0 points · Posted at 21:52:26 on February 13, 2016 · (Permalink)
In a room of 23 people there is a 50-50 chance that 2 share the same birthday
A17L · 0 points · Posted at 21:53:40 on February 13, 2016 · (Permalink)
0.999... = 1 https://en.wikipedia.org/wiki/0.999...
BackburnerPyro · 0 points · Posted at 21:58:28 on February 13, 2016 · (Permalink)
epi*i =-1
Ponchieoo · 0 points · Posted at 22:00:27 on February 13, 2016 · (Permalink)
Ok, I didnt actually know this until I took Pre-Calc, but:
The reason that Pi is 3.14.... Is because it takes the radius 3.14 times to go once around the circle.
When we learned this fact in class we all wondered why we hadnt known it before since its such a simple fact..
CommutatorUmmocrotat · 1 points · Posted at 01:07:06 on February 14, 2016 · (Permalink)
It actually takes the diameter 3.14 times to go around a circle
89LXfiveoh510 · 0 points · Posted at 22:02:04 on February 13, 2016 · (Permalink)
1+1=2
femidom · 0 points · Posted at 22:02:11 on February 13, 2016 · (Permalink)*
This scene always inspires me to want to know more about math
graaahh · 0 points · Posted at 22:05:27 on February 13, 2016 · (Permalink)
The number of inches in a mile is equal to the number of astronomical units in a light year to within a fraction of a percent.
Also equal to within a fraction of a percent: the volume of a sphere with a radius of one kilometer and the volume of a cube with a side length of one mile.
galactapotamus · 0 points · Posted at 22:14:26 on February 13, 2016 · (Permalink)
-40°C = - 40°F
hypervelocityvomit · 2 points · Posted at 13:35:15 on February 16, 2016 · (Permalink)
And that's the freezing point of Mercury. If your thermometer runs on mercury, it'll freeze at -40 no matter if it's C or F.
[deleted] · 1 points · Posted at 23:43:48 on February 13, 2016 · (Permalink)
Didn't know that. But it's not surprising at all that such a degree would exist. Two nonparallel lines on a plane have to intersect somewhere.
DhroovP · 0 points · Posted at 22:18:53 on February 13, 2016 · (Permalink)
Opposite of infinity is infinitesimal
heavyish_things · 1 points · Posted at 03:39:15 on February 14, 2016 · (Permalink)
That depends on how you define opposite.
Urgullibl · 0 points · Posted at 22:19:08 on February 13, 2016 · (Permalink)
Absolute zero is at −273.15 degrees Celsius, which equates to −459.67 degrees Fahrenheit, or −218.5 degrees Réaumur.
[deleted] · 0 points · Posted at 22:19:34 on February 13, 2016 · (Permalink)
[deleted]
Sellerofrice · 0 points · Posted at 22:29:12 on February 13, 2016 · (Permalink)
Euler's Equation (Identity): ei*pi + 1 = 0. Not only is this equation incredibly useful, especially in complex arithmetic, there is a kind of beauty to it as well. It includes many important numbers such as e, i, pi, the additive identity 0, and the multiplicative identity 0.
malawisativa · 0 points · Posted at 22:41:30 on February 13, 2016 · (Permalink)
You can spell 80085 on a calculator
ineffablepwnage · 0 points · Posted at 22:44:42 on February 13, 2016 · (Permalink)
The number 6 is in wit-sec, because it knows 7 is a cannibal.
dpfw · 0 points · Posted at 22:57:56 on February 13, 2016 · (Permalink)
Take your age, divide by two, add six, subtract zero, multiply by two, subtract twelve. That's you're age.
[deleted] · 0 points · Posted at 22:59:13 on February 13, 2016 · (Permalink)*
There is a number so large, if you could think of it in terms of it's individual numerals all at once, that amount of data would cause your brain to collapse into a black hole.
edit: It is called Graham's number
Sadsharks · 1 points · Posted at 03:17:31 on February 14, 2016 · (Permalink)
That makes no sense. Black holes are caused by extreme densities (I.e. the mass of a star collapsing). Thinking about large amounts wouldn't cause your brain or anything inside your brain to increase in mass or density at all, since the brain operates by electricity.
[deleted] · 2 points · Posted at 04:28:07 on February 14, 2016 · (Permalink)*
Electricity works on the same physical properties everything else does and EVERYTHING has mass, or effects mass.
You can argue all day about what the number is, but since thoughts aren't magic, if you had enough thoughts in a confined space...Poof.
Found it, Graham's Number
muckluckcluck · 0 points · Posted at 23:01:49 on February 13, 2016 · (Permalink)
All math is fact, otherwise it isn't math
Cwmcwm · 0 points · Posted at 23:07:01 on February 13, 2016 · (Permalink)
An infinite number of engineers walk into a bar. The first one says "one beer, please". The second, "1/2 beer please". The third "1/4 beer, please". The fourth, "1/8 of a beer, please". The bartender/mathematician replied "okay, okay two beers, comin' up".
kvlxm · 0 points · Posted at 23:08:08 on February 13, 2016 · (Permalink)
I do not understand anything in this post.
GoldenMinge · 0 points · Posted at 23:12:05 on February 13, 2016 · (Permalink)
7 ate 9
lucasax21 · 0 points · Posted at 23:14:32 on February 13, 2016 · (Permalink)
5/7=10/10
GooseVersusRobot · 0 points · Posted at 23:15:04 on February 13, 2016 · (Permalink)
1 + 1 = fish
[deleted] · 0 points · Posted at 23:25:07 on February 13, 2016 · (Permalink)
The sum of all natural numbers, from one to infinity:
1+2+3.... = -1/12
bridgerdabridge1 · 0 points · Posted at 23:30:48 on February 13, 2016 · (Permalink)
ITT: NERDS
efie · 0 points · Posted at 23:57:28 on February 13, 2016 · (Permalink)
I think this one is fairly common, but I love how 1+1/2+1/4+1/8+1/16+...=2, and I love how elegant the proof is.
I also love how 1/3=0.33333333... and 2/3=0.66666666... yet 3/3=1 therefore 0.99999999...=1 exactly.
ccie_to_be · 0 points · Posted at 23:57:57 on February 13, 2016 · (Permalink)
Surely not the coolest, but there are 85 ordered pairs of positive integers (x,y) with x<y<=100 where both y/x and (y+1)/(x+1) are integers.
This was the only question I got right on the 1995 AIME. https://www.artofproblemsolving.com/wiki/index.php?title=1995_AIME
vekeso · 0 points · Posted at 00:01:05 on February 14, 2016 · (Permalink)
if you add 1 through 36 together sequentially (1+2+3+4 etc) it adds up to 666
Sedillio · 0 points · Posted at 00:03:08 on February 14, 2016 · (Permalink)
the square root of 69 is 8.something
urmomsballs · 0 points · Posted at 00:27:39 on February 14, 2016 · (Permalink)
1=1*32
English system is fucked.
Adeedee · 0 points · Posted at 00:39:48 on February 14, 2016 · (Permalink)
The square root of 69 is 8 something.
DevilleinaBlueDress · 0 points · Posted at 00:53:49 on February 14, 2016 · (Permalink)
The farther down this thread I read, the less intelligent I feel.
Littlewigum · 0 points · Posted at 00:54:03 on February 14, 2016 · (Permalink)
Infinity is a concept not a number.
http://youtu.be/kCMBxSUN4kc
netchemica · 0 points · Posted at 00:55:01 on February 14, 2016 · (Permalink)
5 out of 7 is a perfect score
This_User_Said · 0 points · Posted at 01:00:55 on February 14, 2016 · (Permalink)
Coolest mathematical fact I know of is the probability of me knowing any listed in comments.
I_be_who_I_be · 0 points · Posted at 01:06:23 on February 14, 2016 · (Permalink)
You're all equally pieces of shit and I can prove it mathematically.
McGootch · 0 points · Posted at 01:07:40 on February 14, 2016 · (Permalink)
According to Hasbro, zero is even.
frosted1030 · 0 points · Posted at 01:09:54 on February 14, 2016 · (Permalink)
0 is not a number. It's a concept.
[deleted] · 0 points · Posted at 01:10:25 on February 14, 2016 · (Permalink)
infinity is less than n, where n is the number of men your mom has been with
Davelulz · 0 points · Posted at 01:11:07 on February 14, 2016 · (Permalink)
The average human being has less than two arms.
shot-in-the-mouth · 0 points · Posted at 01:13:01 on February 14, 2016 · (Permalink)
Dolly Parton weighed 69 pounds. The doctor said that was too (2) too (2) too (2) much, so he told her to take 51 of these pills, 8 times a day, and then she was...
6922251 x 8 = 55378008
Raherin · 0 points · Posted at 01:19:26 on February 14, 2016 · (Permalink)
5318008 = BOOBIES
[deleted] · 0 points · Posted at 01:21:23 on February 14, 2016 · (Permalink)
6 is afraid of 7 because 7 8 9.
kasteriris · 0 points · Posted at 01:27:10 on February 14, 2016 · (Permalink)
Sin(666)=Cos(666)
Works only in degrees
Murmakun · 0 points · Posted at 01:30:40 on February 14, 2016 · (Permalink)
The 1+2+3+4+5+6... and so on sum is equal to... -1/12!
Brailledit · 0 points · Posted at 01:31:35 on February 14, 2016 · (Permalink)
Five sevenths is a perfect score.
ShadowBourne · 0 points · Posted at 01:32:14 on February 14, 2016 · (Permalink)
58008
benweiner · 0 points · Posted at 01:34:34 on February 14, 2016 · (Permalink)
-2-2 x = chim chim cheree
Zissou79 · 0 points · Posted at 01:38:35 on February 14, 2016 · (Permalink)
80085 was the sum of all calculator jokes back in the 80s.
SLARGMONSTER · 0 points · Posted at 01:42:29 on February 14, 2016 · (Permalink)
The sum of all integers (ie 1+2+3+4+5... +(n+1)... where n is any integer) is equal to -1/12. Numberphile did a simplified proof on their YouTube channel for everyone that doesn't study string theory.
XplicitVoltz · 0 points · Posted at 01:46:48 on February 14, 2016 · (Permalink)
9+10=21
Chicaben · 0 points · Posted at 01:48:54 on February 14, 2016 · (Permalink)
The universe works on a math equation
that never even ever really even ends in the end
Infinity spirals out creation
We're on the tip of its tongue, and it is saying
We ain't sure where you stand
McCash34 · 0 points · Posted at 01:49:29 on February 14, 2016 · (Permalink)
Supposedly, there is a theory that states that any two people in the entire world can be connected by 6 connections. Connections being people that you know. So like, I know a guy in Israel, who knows a guy in Jordan who knows a guy in Syria who knows a guy who works for Isis who knows the leader...etc. makes sense, but I'm sure there are some exceptions. But for the majority it seems plausible.
justmycrazyopinion · 0 points · Posted at 01:49:38 on February 14, 2016 · (Permalink)
And today I realized I really can't math.
ajfrosty19 · 0 points · Posted at 01:49:40 on February 14, 2016 · (Permalink)
2 + 2 = 5
MassiveLazer · 0 points · Posted at 01:52:30 on February 14, 2016 · (Permalink)
Santa Clause exists: Let S be the statement "if S is true then Santa exists". Try to prove by assumption and see if no contradiction is reached. So assume S is true. Then the statement "If S is true then Santa exists" holds, and since S is true, then Santa exists. So far we have proven that if S is true, then Santa exists, which is the statement S. So we know that S is true. And this is the statement "If S is true then Santa exists". So it follows that Santa exists.
streetbum · 0 points · Posted at 01:53:11 on February 14, 2016 · (Permalink)
The rule of 70. If you want to know roughly how long (in years) an investment will take until it doubles in value, just do 70/r (where r is the rate of return.)
CapTrips · 0 points · Posted at 01:53:31 on February 14, 2016 · (Permalink)
58008 upside down spells boobs.
ablack82 · 0 points · Posted at 01:53:41 on February 14, 2016 · (Permalink)
5/7 = 1
[deleted] · 0 points · Posted at 01:54:58 on February 14, 2016 · (Permalink)
The sum of all natural numbers from 1 to infinity is equal to -1/12, here is a video explaining why.
MjrPayne · 0 points · Posted at 01:55:03 on February 14, 2016 · (Permalink)
1+2+3+4+5+... = - 1/12
brutalyak · 2 points · Posted at 02:13:32 on February 14, 2016 · (Permalink)
No. The sum of all natural numbers doesn't equal a finite number, because it is a divergent series.
[deleted] · 0 points · Posted at 01:55:16 on February 14, 2016 · (Permalink)
[deleted]
brutalyak · 1 points · Posted at 02:10:29 on February 14, 2016 · (Permalink)
No, it's not.
nihilus666 · 0 points · Posted at 01:55:44 on February 14, 2016 · (Permalink)*
The infinite series 1+2+3+4+5... can be substituted with -1/12
[deleted] · 0 points · Posted at 02:22:14 on February 14, 2016 · (Permalink)
That math is tough!
snarp · 0 points · Posted at 02:24:43 on February 14, 2016 · (Permalink)
Pi is never ending.
5heepdawg · 0 points · Posted at 02:26:07 on February 14, 2016 · (Permalink)
PEMDAS. My math skill is very low.
cpu5555 · 0 points · Posted at 02:27:14 on February 14, 2016 · (Permalink)
22/7 is not pi but an approximation of pi
corner-case · 0 points · Posted at 02:30:05 on February 14, 2016 · (Permalink)
0.99... (repeating ad infinitum) is equal to 1. It doesn't just approach one, but they are in fact equal. Here's a proof.
(1/3) = 0.33...
3*(1/3) = 3 * 0.33...
1 = 0.99...
mitchell271 · 0 points · Posted at 02:36:44 on February 14, 2016 · (Permalink)
0.999.. = 1 As far as I know, here's the proof
1/9 = 0.111.. Since 9/9 = 1, and .111.. * 9 = 0.99.. therefore 0.999.. = 1
iluvgrannysmith · 1 points · Posted at 02:51:54 on February 14, 2016 · (Permalink)
Let x=.999...; So, 10x=9.999...; Thus, 10x-x = 9.999...-(.999); which implies 9x=9. Thus, x=1. There are many proofs for this.
madein1986 · 0 points · Posted at 02:39:28 on February 14, 2016 · (Permalink)
Six is afraid of seven because 7, 8, 9. Take that PHD's.
Ricepilaf · 0 points · Posted at 02:39:45 on February 14, 2016 · (Permalink)
I suppose this is more statistics than mathematics, but you know that saying "a million monkeys with a million typewriters will eventually create the complete works of Shakespeare"? Well, it's technically true, but people tend to underestimate just how unlikely it is of happening, by, uh, a lot. Statisticians are kind of upset by it because it gives people a poor sense of scale for both how long infinity is, and just how random events can be.
"Even if every proton in the observable universe were a monkey with a typewriter, typing from the Big Bang until the end of the universe (when protons no longer exist), they would still need a ridiculously longer time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10500 chance of success. To put it another way, for a one in a trillion chance of success, there would need to be 10360,641 universes made of atomic monkeys."
This is just for Hamlet, with a 26 character keyboard, ignoring punctuation, spacing, and capitalization.
Why_are_you_so_dumb_ · 0 points · Posted at 02:40:11 on February 14, 2016 · (Permalink)
You can divide any number by 5 by doubling it and moving the decimal one place over.
20 / 5
20 x 2 = 40.
Move the decimal.
4.0
Okay, fine. 20 is easy. How about 3.7 / 5?
3.7 x 2 = 7.4
0.74
Or even 3791.
3791 x 2 = 7582
Move the decimal - 758.2
3791 / 5 = 758.2
Aarons777 · 0 points · Posted at 02:43:46 on February 14, 2016 · (Permalink)
that .99 repeated=1
there are multiple proofs about this, but this one is the simplest
1/3 = .33 repeated
2/3 = .66 repeated
3/3 = .99 repeated and 1.
dandroid126 · 0 points · Posted at 02:43:54 on February 14, 2016 · (Permalink)
The slope of ex is ex for any given x.
maritimesies · 0 points · Posted at 02:47:16 on February 14, 2016 · (Permalink)
111,111,111 x 111,111,111 = 12,345,678,987,654,321
Andrei_Vlasov · 0 points · Posted at 02:55:30 on February 14, 2016 · (Permalink)
You + me = fun
[deleted] · 0 points · Posted at 02:55:52 on February 14, 2016 · (Permalink)
Impressive. I'd be more impressed if one of you got me a sandwich and would it kill you to toast the bread?
satismo · 0 points · Posted at 03:00:41 on February 14, 2016 · (Permalink)
0.99999999999999999(etc).. = 1. it makes infinity seem trivial and somehow understandable.
[deleted] · 0 points · Posted at 03:06:22 on February 14, 2016 · (Permalink)
[deleted]
meowcat187 · 2 points · Posted at 03:16:49 on February 14, 2016 · (Permalink)
Shit....how does that work? I cant find an error
EmptyRegrets · 0 points · Posted at 03:07:27 on February 14, 2016 · (Permalink)
Really late posting so no one will probably see this, but there is a relatively simple connection, for lack of a better word, between the squares of 2 numbers and the numbers themselves. I discovered this when I was in the 4th grade all by myself and was really proud of it at the time.
Take 6 and 7 for example. 62 is 36 and 72 is 49. Now if you take the original numbers and add them up you get 13, which just so happens to be the difference between the 2 squares. The formula, which I am just now making up on the spot, should be
b2 - a2 = a + b
where a and b are two positive whole numbers directly next to each other on the number line and b is the larger of the two numbers.
Not really that cool but it's cool to me because I independently thought of this at a young age.
meowcat187 · 2 points · Posted at 03:10:55 on February 14, 2016 · (Permalink)
It just happens to work for those numbers but doesnt work for every number
EmptyRegrets · 1 points · Posted at 03:20:09 on February 14, 2016 · (Permalink)
I might be wrong, but I have tested it with a few different numbers and it seems to work for them all that I've tried it with. Can you think of any of any of the numbers that don't go with it off the top of your head?
meowcat187 · 2 points · Posted at 03:23:19 on February 14, 2016 · (Permalink)
You are really wrong. 7 and 5.
meowcat187 · 2 points · Posted at 03:24:14 on February 14, 2016 · (Permalink)
Oh, it appears I am the one who is wrong
meowcat187 · 1 points · Posted at 03:27:59 on February 14, 2016 · (Permalink)
You are basically saying
b = a + 1
b2 - a2 = a + b
(a+1)2 - a2 = a + (a+1)
a2 + 2a + 1 - a2 = 2a+1
2a+1 = 2a+1
a = a
Mystery solved.
[deleted] · 0 points · Posted at 03:33:46 on February 14, 2016 · (Permalink)
Me + your mum = hot sex
owlsrule143 · 0 points · Posted at 03:38:11 on February 14, 2016 · (Permalink)
Cool? Well more like infuriating, but here.
1+2+3+4+5+...... To infinity is.......
-1/12. Let that sink in.
hypervelocityvomit · 2 points · Posted at 13:43:07 on February 16, 2016 · (Permalink)
http://cdn1.lockerdome.com/uploads/1af5d36fc8387f1cad769d0bf83bac849ed276175bd4afbf0f18f60c2c2c8803_large
sgdbw90 · 0 points · Posted at 03:40:10 on February 14, 2016 · (Permalink)
1+2+3+4+5... to infinity = -1/12
You'd think it's infinite, but apparently (and insanely) it's not.
Proof (literally): http://youtu.be/w-I6XTVZXww
sgdbw90 · 1 points · Posted at 03:43:31 on February 14, 2016 · (Permalink)
Looks like this is a frequently used fact! Glad to see it's as well known as it is. So cool.
GoCubsGo2016 · 1 points · Posted at 03:50:24 on February 14, 2016 · (Permalink)
I'm pretty sure I got dumber from watching that. That was the stupidest thing I've seen.
ginkomortus · 1 points · Posted at 04:49:37 on February 14, 2016 · (Permalink)
Why do you say that?
GoCubsGo2016 · 1 points · Posted at 05:19:03 on February 14, 2016 · (Permalink)
Because when you're talking in terms of pure math, literally everything he says is wrong.
ginkomortus · 1 points · Posted at 05:40:31 on February 14, 2016 · (Permalink)
Care to elaborate?
GoCubsGo2016 · 1 points · Posted at 05:53:22 on February 14, 2016 · (Permalink)
For starters the sum S1 that he claims equals 1/2. If you gave that to any mathematician, not a single one would say it's 1/2. The answer would be DNE.
ginkomortus · 1 points · Posted at 06:15:40 on February 14, 2016 · (Permalink)
He is a mathematician though, which throws a monkeywrench in that logic. And while it's divergent, it's Cesaro sum is 1/2, and though that only makes so much sense to me, it seems plausible.
godforsakenlightning · 0 points · Posted at 03:56:41 on February 14, 2016 · (Permalink)
The sum of all natural numbers is -1/12.
Vortico · 1 points · Posted at 07:09:02 on February 14, 2016 · (Permalink)
No, the sum diverges.
snakeshift · 0 points · Posted at 04:01:44 on February 14, 2016 · (Permalink)
the sum of all real numbers from 1 to infinity is -1/12 https://www.youtube.com/watch?v=w-I6XTVZXww
Vortico · 1 points · Posted at 07:04:16 on February 14, 2016 · (Permalink)
No, the sum diverges.
cobbs_totem · 0 points · Posted at 04:02:58 on February 14, 2016 · (Permalink)
The sum of all natural numbers, 1+2+3+4+... = -1/12
Vortico · 1 points · Posted at 07:04:06 on February 14, 2016 · (Permalink)
No, the sum doesn't exist.
cobbs_totem · 1 points · Posted at 14:54:20 on February 14, 2016 · (Permalink)
There are techniques that assign this divergent series a sum. And it's result has actual physics verification.
https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
Vortico · 1 points · Posted at 18:51:45 on February 14, 2016 · (Permalink)
Right, I just wanted to be clear that in order to get the result -1/12, you have to decide on an extension of the definition of an infinite sum. You could just as easily come up with another arbitrary method which "assigns" the sum the value 17, for example. Regardless, the sum doesn't exist in the traditional sense without stating your regularization method.
cobbs_totem · 1 points · Posted at 19:04:45 on February 14, 2016 · (Permalink)
Yes, understood. But, "arbitrary" is much more interesting when it actually has implications that we can demonstrate about the universe. The thing about our mathematical system is that it's abstract. Things like infinity doesn't really even make sense in a finite universe. Computation devices such as Turing machines don't even exist in a finite universe.
em3am · 0 points · Posted at 04:04:21 on February 14, 2016 · (Permalink)
The only five numbers you need: 0, 1, pi, e, and i.
matthew0517 · 0 points · Posted at 04:13:40 on February 14, 2016 · (Permalink)
ITT: Holy shit! Math has patterns!
HisRandomFriend · 0 points · Posted at 04:21:22 on February 14, 2016 · (Permalink)
I don't know quite how to word this but let's give it a shot. If you think of a number let's use 16 as an example, and then think of everything that ads up to it. For example:
16= 8+8 7+9 6+10 5+11 4+12 3+13 2+14 1+15
Then multiply each of them
8×8 = 64 7×9 = 63 6×10 = 60 5×11 = 55 4×12 = 48 3×13 = 39 2×14 = 28 1×15 = 15
Now look at the difference between each multiple.
8×8 = 64 = 64 - 0 7×9 = 63 = 64 - 1 6×10 = 60 = 64 - 4 5×11 = 55 = 64 - 9 4×12 = 48 = 64 - 16 3×13 = 39 = 64 - 25 2×14 = 28 = 64 - 36 1×15 = 15 = 64 - 49
As you can see each is a perfect square away from the highest reaching numbers, this always works.
engineerRob · 0 points · Posted at 04:21:49 on February 14, 2016 · (Permalink)
The sum of all natural numbers is -1/12 . wikipedia article . youtube
Vortico · 1 points · Posted at 07:01:12 on February 14, 2016 · (Permalink)
No, the sum diverges.
engineerRob · 1 points · Posted at 15:34:05 on February 14, 2016 · (Permalink)
Correct, it diverges because limits approach infinity but never quite get there. If the sum were to be carried out to infinity, it would result in -1/12. Which is ridiculous, but is apparently backed up by quantum theory.
Vortico · 2 points · Posted at 20:35:32 on February 14, 2016 · (Permalink)
"Carried out to infinity" isn't rigorous. If you were to say "The zeta renormalization of the sum is -1/12" you would be correct since you're extending the definition of infinite sums, but without state this, there is no number which is a limit point of the sequence of partial sums.
the_rabid_beaver · 0 points · Posted at 04:24:01 on February 14, 2016 · (Permalink)
Probably already mentioned, but this really blew my mind. I still don't know what to believe.
1 = 0.999...
https://en.wikipedia.org/wiki/0.999...
MetaMD · 0 points · Posted at 04:24:07 on February 14, 2016 · (Permalink)
1+2+3+...... = -1/12
Vortico · 1 points · Posted at 07:00:46 on February 14, 2016 · (Permalink)
No, the sum diverges.
MetaMD · 1 points · Posted at 07:25:12 on February 14, 2016 · (Permalink)
It doesn't actually. You can find several rigorous proofs of this. Crazy that you would just comment like that.
Vortico · 1 points · Posted at 07:41:05 on February 14, 2016 · (Permalink)
I would agree with you if you say "The zeta regularization of the sum 1+2+3+... is -1/12", but by the traditional meaning of an infinite sum, it certainly diverges.
bla4562 · 0 points · Posted at 04:24:13 on February 14, 2016 · (Permalink)
pi never repeats
[deleted] · 0 points · Posted at 04:27:02 on February 14, 2016 · (Permalink)
[deleted]
Vortico · 1 points · Posted at 07:00:21 on February 14, 2016 · (Permalink)
No, the sum diverges.
JamesBlitz00 · 0 points · Posted at 04:27:27 on February 14, 2016 · (Permalink)
One and one don't make two. One and one make one.
I learned many things from The Who.
haymonaintcallyet · 0 points · Posted at 04:27:42 on February 14, 2016 · (Permalink)
Surprised that this isn't at the top: sum of all natural numbers is -1/12
ie. 1+2+3+4+5+6+...=-1/12
Edit: natural numbers not the set of real numbers.
Vortico · 1 points · Posted at 06:59:07 on February 14, 2016 · (Permalink)
No, the sum diverges.
[deleted] · 0 points · Posted at 04:28:28 on February 14, 2016 · (Permalink)
The sum of the natural numbers (positive counting numbers) is equal to -1/12.
Vortico · 1 points · Posted at 06:57:37 on February 14, 2016 · (Permalink)
No, the sum diverges.
[deleted] · 1 points · Posted at 13:46:22 on February 14, 2016 · (Permalink)
The regularized sum converges, using the Riemann zeta function. This result is extremely important in quantum physics and string theory, and also explains many observed natural phenomena, including the Casimir effect
Stickyballs96 · 0 points · Posted at 04:28:29 on February 14, 2016 · (Permalink)
1+1=11
jbloom3 · 0 points · Posted at 04:33:16 on February 14, 2016 · (Permalink)
1+2+3+4... = 1/12
Actually though. Do the proof (or look it up)
Vortico · 1 points · Posted at 06:51:11 on February 14, 2016 · (Permalink)
No, the sum diverges.
TonyPajamas29 · 0 points · Posted at 04:36:23 on February 14, 2016 · (Permalink)
00=1 So if you take nothing and put it to the power of nothing you get 1.. I wish money worked this way.
Vortico · 0 points · Posted at 06:50:47 on February 14, 2016 · (Permalink)
No, the value is indeterminate.
TonyPajamas29 · 1 points · Posted at 16:37:20 on February 14, 2016 · (Permalink)
Technically either would be correct.
sardu1 · 0 points · Posted at 04:36:30 on February 14, 2016 · (Permalink)
3...is the magic number.
bloodyhell23 · 0 points · Posted at 04:39:22 on February 14, 2016 · (Permalink)
23 It is all 23. You can get 23 out of your phone number, your house number, everything. It all comes back to 23.
Jay_Bond · 0 points · Posted at 04:39:54 on February 14, 2016 · (Permalink)
From 'I Am Weasel' :- "Two plus two equals infinity"
TwentyPercentPlease · 0 points · Posted at 04:40:25 on February 14, 2016 · (Permalink)
8008132 on a calculator looks like "boobies"
88Reasons · 0 points · Posted at 04:41:12 on February 14, 2016 · (Permalink)
2 +2 = 5
[deleted] · 0 points · Posted at 04:41:59 on February 14, 2016 · (Permalink)
there are 10101000000 possible universes and there is such thing as a planck volume
dreadlord473 · 0 points · Posted at 04:43:16 on February 14, 2016 · (Permalink)
The sum of all the positive integers is equal to a negative number
1+2+3......= -1/12
And this equation is used in everyday physics.
Vortico · 1 points · Posted at 06:46:10 on February 14, 2016 · (Permalink)
No, the sum does not exist.
And it's not used every day in physics. Perhaps every decade?
[deleted] · 0 points · Posted at 04:47:40 on February 14, 2016 · (Permalink)
The sum of all natural numbers is equal to -1/12.
https://www.youtube.com/watch?v=w-I6XTVZXww
Vortico · 0 points · Posted at 06:39:57 on February 14, 2016 · (Permalink)
No, the sum doesn't exist.
[deleted] · 1 points · Posted at 07:03:33 on February 14, 2016 · (Permalink)*
Did you watch the video? It's a proven equation that is used "in many areas of physics" according to one of the men in the video.
And just because it's an infinite sequence doesn't mean it doesn't have a sum. Finding the sum of an infinite sequence is actually not that difficult.
Edit: Here's another video with further explanation.
https://www.youtube.com/watch?v=E-d9mgo8FGk
Vortico · 1 points · Posted at 07:20:04 on February 14, 2016 · (Permalink)
I wish this video didn't exist. It confuses way more people than helps. Zeta function regularization is used in a few areas of analytic number theory, which has strong applications in QFT. However, I've only seen the method used in computation, where another more difficult method could also do the job.
Regardless, the uses of this somewhat obscure technique doesn't change the fact that by the traditional meaning of a sum, it certainly diverges.
maddrabbits · 0 points · Posted at 04:48:38 on February 14, 2016 · (Permalink)
That .999...=1.
Dehsurbria · 0 points · Posted at 04:50:21 on February 14, 2016 · (Permalink)
Zipf's law
Watch81 · 0 points · Posted at 04:51:14 on February 14, 2016 · (Permalink)
32+42=52
lynnspiracy-theories · 0 points · Posted at 05:17:35 on February 14, 2016 · (Permalink)
Every conceivable pair of two straight lines in Euclidean space will meet at exactly one point.
Vortico · 1 points · Posted at 06:18:29 on February 14, 2016 · (Permalink)
...except parallel ones.
lynnspiracy-theories · 1 points · Posted at 07:36:34 on February 14, 2016 · (Permalink)
Parallel lines intersect at infinity, so says the theory. So yes, even parallel ones.
Vortico · 1 points · Posted at 07:44:19 on February 14, 2016 · (Permalink)
Euclidean space doesn't include the "point at infinity", but hyperbolic and projective spaces do, for example.
lynnspiracy-theories · 1 points · Posted at 18:14:00 on February 14, 2016 · (Permalink)
Aight we'll go with that then
Vortico · 1 points · Posted at 20:30:35 on February 14, 2016 · (Permalink)
Whoops, I made a small mistake. Hyperbolic spaces contain a point at infinity but there are geodesics which do not intersect. It's true about projective spaces.
Yurei2 · 0 points · Posted at 05:17:46 on February 14, 2016 · (Permalink)
Pi doesn't actually go on forever. Since there is a smallest possible small in the universe (see Plank length) and pi is an expression of a geometric length (the ratio of diameter to circumference) at the point where the distance expressed hits the plank limit pi stops. True, it technically keeps going but after that point its just irrational nonsense with no possible use or purpose.
Vortico · 1 points · Posted at 06:17:51 on February 14, 2016 · (Permalink)
The definition of pi has nothing to do with the discretization of the universe.
Yurei2 · 1 points · Posted at 06:55:45 on February 14, 2016 · (Permalink)
While true, that is also false, because if it can't exist in reality or doesn't exist in reality, it's fictional. Meaning after point X, further numbers of pi are fictional in nature.
Or in short, the laws of physics prove math is fictional stuff made up by humans and not the word of god as math lovers insist it is.
Vortico · 1 points · Posted at 07:23:14 on February 14, 2016 · (Permalink)
I can't debate this.
Yurei2 · 0 points · Posted at 12:07:36 on February 14, 2016 · (Permalink)
Welcome to the real world. Where light can be both a particle and a wave at once, certain subatomic strata can apparently spontaneously generate, and quantum superpositions prove things can exist in multiple states at once.
seran0 · 0 points · Posted at 05:19:17 on February 14, 2016 · (Permalink)
.999999 repeating infinitely equals exactly 1
marklein · 0 points · Posted at 05:19:56 on February 14, 2016 · (Permalink)
1/9 = .11111111... forever
2/9 = .222222222... forever
3/9 = .33333333... forever
...
8/9 = .888888888... forever
9/9 = 1. Our should it be .9999999...?
diet_pepsi_bottle · 0 points · Posted at 05:26:36 on February 14, 2016 · (Permalink)
.333... + .333.... + .333... = 1
matacks970 · 0 points · Posted at 05:33:06 on February 14, 2016 · (Permalink)
2 + 2 = 5!!
Vortico · 1 points · Posted at 06:05:16 on February 14, 2016 · (Permalink)
5 factorial factorial is 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000 :)
AlbertaVape403 · 0 points · Posted at 05:43:16 on February 14, 2016 · (Permalink)
Probably the mathematical constant e.. I am not really versed enough in Math to explain it, but when I learned it, how it was found and its relevance in the universe, it kind of blew my mind.
iluvgrannysmith · 2 points · Posted at 05:53:13 on February 14, 2016 · (Permalink)
It's the highest growth factor. In a sense that ex >= xe for any x that is a real number. If you take the limit as n goes to infinity of (1+1/n)n then you get e.
Psykerr · 0 points · Posted at 05:45:08 on February 14, 2016 · (Permalink)
Anything divided by infinity equals zero.
overconvergent · 1 points · Posted at 06:00:47 on February 14, 2016 · (Permalink)
At least in the real number system, infinity is not a number, so you cannot divide by infinity.
KaputFive · 0 points · Posted at 05:49:36 on February 14, 2016 · (Permalink)
I know where to find my x.
runninron69 · 0 points · Posted at 05:54:29 on February 14, 2016 · (Permalink)
Pie are square?
Party_With_Arty · 0 points · Posted at 05:56:38 on February 14, 2016 · (Permalink)
So I am in a public speaking class, and this one kid blew my mind with a math magic trick.
Pick and number between 1 and 100. Add 20 to that number. Subtract your number from that sum. The number in your head right now is 20.
Mic drop.
Help_Me_Im_Diene · 1 points · Posted at 06:10:03 on February 14, 2016 · (Permalink)
Well...that's saying you start with x. Then you do x+20-x=20, so that works with any number really, doesn't have to be between 1 and 100
Party_With_Arty · 1 points · Posted at 06:54:44 on February 14, 2016 · (Permalink)
Obviously. I should have added this is a college public speaking class. We were all waiting for this guy to go on with his "magic trick" but he just like stopped at that point and sat down.
untitled_redditor · 0 points · Posted at 05:58:11 on February 14, 2016 · (Permalink)
Not the coolest, but this one comes to mind...
Ever noticed numbers like this? When 142857 is multiplied the numbers usually only get rearranged.
142857 × 2 = 285714
142857 × 3 = 428571
142857 × 4 = 571428
142857 × 5 = 714285
142857 × 6 = 857142
infinitefoamies · 0 points · Posted at 06:03:06 on February 14, 2016 · (Permalink)
67.2% of all statistics are made up on the spot.
Chez_Rubenstein · 0 points · Posted at 06:06:48 on February 14, 2016 · (Permalink)
Euler's identity:
epi*i - 1 = 0
The idea that two seemingly unrelated mystical irrational numbers combined with an imaginary one gives -1 is absolutely magical. A co-worker claims that this is proof of divine creation.
https://en.wikipedia.org/wiki/Euler%27s_identity
Waex · 0 points · Posted at 06:09:22 on February 14, 2016 · (Permalink)
Pablo
iamerror87 · 0 points · Posted at 06:21:21 on February 14, 2016 · (Permalink)
E= MC2
Ceejae · 0 points · Posted at 06:26:02 on February 14, 2016 · (Permalink)
PI IS EXACTLY 3!
Rafmasterflash · 0 points · Posted at 06:30:30 on February 14, 2016 · (Permalink)
Nothin' from nothin' leaves nothin' You gotta have somethin' if you Wanna be with me Theory by Billy Preston
ectopunk · 0 points · Posted at 06:32:16 on February 14, 2016 · (Permalink)
If you hold this number upside down you learn that Martian females are:
55378008
GaandKeAndhe · 0 points · Posted at 06:39:49 on February 14, 2016 · (Permalink)
1+1=3. Big brother is watching you.
navysbandit · 0 points · Posted at 06:42:32 on February 14, 2016 · (Permalink)
Here's my contribution:
This 1 girl who was 16 got f**ed 69 times by 3 men, how did she feel? *This is where you rotate the calculator or phone 35007 11669x3 = 35007
Learned this one in middle school lol
Man-Among-Gods · 0 points · Posted at 06:43:19 on February 14, 2016 · (Permalink)
10=9.9999999999999999999999999999999999999999999 repeated to infinity
because
10/3=3.33333333333333333333333333333333333333333 repeated to infinity
(10/3)(3)
dimmu1313 · 0 points · Posted at 07:05:49 on February 14, 2016 · (Permalink)
Actually those equalities are both wrong. Any decimal requiring repetition to infinity is an approximated by the given fraction.
It's the same as Pi not having a definite fraction. So 1/3 ~= 0.333... and 0.333... = 333.../1000...
The thing to remember is that the decimal system is an expansion of fractions by use of exponent placeholders. So 123.456 is really just a shorthand way of writing out 1x102 + 2x101 + 3x100 + 4x10-1 + 5x10-2 + 6x10-3. A fraction is a ratio of two numbers in any given number base, and the decimal equivalent or approximation is just a way of representing that fraction in a different way. It's very possible to have a fraction that can only be represented as a fraction and not written into its decimal equivalent; in fact it happens all the time. A common misconception is that "rational" numbers are numbers that can be and are written in decimal form, but the only requirement for a number to be rational is that it can be written in "ratio" form (i.e., as a fraction of two numbers in the given base).
Shamroc_14 · 0 points · Posted at 06:48:16 on February 14, 2016 · (Permalink)
2+2=22
Wilreadit · 0 points · Posted at 06:53:11 on February 14, 2016 · (Permalink)
The basic terms of geometry are undefined.
JoXand · 0 points · Posted at 07:00:39 on February 14, 2016 · (Permalink)
1+2+3+4(...)=-1/12
HammSich · 0 points · Posted at 07:06:06 on February 14, 2016 · (Permalink)
The sum of all natural numbers is equal to -1/12
Redditmorelikeblewit · 0 points · Posted at 07:16:13 on February 14, 2016 · (Permalink)
The summation of all whole integers from 1 to infinity is -1/12. Think about that. Adding every single number from one to infinity gives you a negative number. And a fraction.
DaBratatatat · 0 points · Posted at 07:37:22 on February 14, 2016 · (Permalink)
Because Pi is an infinite number, it contains EVERYTHING represented in numbers. It holds the answer to all our questions, the fate of our futures, the code for all computing, absolutely everything... We just can't single out which part is what.
Kleenme · 0 points · Posted at 08:09:11 on February 14, 2016 · (Permalink)
.99 = 1
GenrlWashington · 0 points · Posted at 08:11:06 on February 14, 2016 · (Permalink)
You can mathematically prove that 1=2.
[deleted] · 1 points · Posted at 08:18:53 on February 14, 2016 · (Permalink)
[deleted]
GenrlWashington · 0 points · Posted at 08:30:18 on February 14, 2016 · (Permalink)
It was actually a lot more complicated than just that. But I had a calculus teacher show it to the class once. This was over a decade ago, or I'd post it all up.
vHAL_9000 · 0 points · Posted at 08:41:02 on February 14, 2016 · (Permalink)
1+2+3+4+5+ etc... is -1/12.
Don't believe me? Look it up.
Orange_Ash · 1 points · Posted at 09:03:25 on February 14, 2016 · (Permalink)
Only if you include negative integers. This is a consequence of the Riemann Zeta function.
Minihood1997 · 0 points · Posted at 09:01:04 on February 14, 2016 · (Permalink)
eipi = -1
Bigcats30 · 0 points · Posted at 09:05:56 on February 14, 2016 · (Permalink)
42
SpaghettiWalrus · 0 points · Posted at 09:09:12 on February 14, 2016 · (Permalink)
ei*pi = -1
butkaf · 0 points · Posted at 09:10:43 on February 14, 2016 · (Permalink)
Fibonacci sequence.
Algernoq · 0 points · Posted at 09:37:11 on February 14, 2016 · (Permalink)
e to the i * pi, plus one, equals zero.
greydalf_the_gan · 0 points · Posted at 09:55:26 on February 14, 2016 · (Permalink)
1+2+3+4+5+6+7+8+... = - 1/12
now_look_here · 0 points · Posted at 09:57:14 on February 14, 2016 · (Permalink)
1 + 2 + 3 + 4 + 5 + ... = - 1/12
Tall_dark_and_lying · 0 points · Posted at 10:08:44 on February 14, 2016 · (Permalink)
The sum of every positive integer equals -1/12
lilpopjim0 · 0 points · Posted at 10:10:22 on February 14, 2016 · (Permalink)
That 1+1 = window
xargon3333 · 0 points · Posted at 10:41:42 on February 14, 2016 · (Permalink)
Any wobbly table can be fixed by tilting the table by 45°.
domthetrout · 0 points · Posted at 10:55:57 on February 14, 2016 · (Permalink)
If you subtract the year of your birth from this year (2016), the resulting number will be your age! How freaky is that? And it gets even weirder; it works for other people's year of birth too!
falaicha · 1 points · Posted at 11:09:31 on February 14, 2016 · (Permalink)
TIL not
jimjatt1999 · 0 points · Posted at 10:58:03 on February 14, 2016 · (Permalink)
1 + 1 = 2
EddyTheMan · 0 points · Posted at 11:14:39 on February 14, 2016 · (Permalink)
The sum of all integers above 0 is -1/12
LazyTheSloth · 0 points · Posted at 11:24:51 on February 14, 2016 · (Permalink)
It hates me.
BruiserLeet · 0 points · Posted at 12:25:17 on February 14, 2016 · (Permalink)
My brother told me an easy way to 11xN. Like 11x11=121(1+1=2 then put it in the middle of the number).
[deleted] · 0 points · Posted at 13:10:26 on February 14, 2016 · (Permalink)
I am too stupid for this thread.
throwaway3366991 · 0 points · Posted at 13:40:10 on February 14, 2016 · (Permalink)
This is the only correct answer : 1+2+3+...+n = -1/12.
kenetha65 · 0 points · Posted at 13:49:39 on February 14, 2016 · (Permalink)
Pi. I mean. . . .SHIT.
fools-savage · 0 points · Posted at 13:55:20 on February 14, 2016 · (Permalink)
Six is afraid of seven.
TheStig1214 · 0 points · Posted at 14:05:19 on February 14, 2016 · (Permalink)*
I love the beauty of Euler's Identity. Such seemingly random, unrelated mathematical concepts fit together.
epi*i + 1 = 0
[deleted] · 1 points · Posted at 14:31:10 on February 14, 2016 · (Permalink)
[deleted]
TheStig1214 · 1 points · Posted at 14:32:57 on February 14, 2016 · (Permalink)
Yes, that one.
weezer13us · 0 points · Posted at 14:09:36 on February 14, 2016 · (Permalink)
The sum of all positive numbers is -1/12
Meruhnes · 0 points · Posted at 14:16:51 on February 14, 2016 · (Permalink)
6 and 8 went on a date, sat at table 48
Lame, i know, it still help is pre-calculus though
sarudesu · 0 points · Posted at 14:31:21 on February 14, 2016 · (Permalink)
that 1+1=3 if one of the ones is a male, and one of the ones is a female... yeah, math has never been my strong point.
TBSdota · 0 points · Posted at 14:41:29 on February 14, 2016 · (Permalink)
If you flip a coin 13 times Head, put it in your pocket until you need to bet everything, it will be guarunteed Tails next flip.
basednidoking · 0 points · Posted at 14:58:26 on February 14, 2016 · (Permalink)
8 is the infinity sign standing up.
BunchOfCircusAnimals · 0 points · Posted at 14:59:17 on February 14, 2016 · (Permalink)
When I started dating, my grandfather said this, "so...I hear you got yourself a girlfriend. Just remember, one plus one equals three." This counts, right?
Maximillianz · 0 points · Posted at 15:49:13 on February 14, 2016 · (Permalink)
The sum of all positive numbers from 1-infinity = -1/12
Pkmn_Gold · 0 points · Posted at 17:50:57 on February 14, 2016 · (Permalink)
fuck math
[deleted] · 0 points · Posted at 19:14:04 on February 14, 2016 · (Permalink)
Pi goes on and on? Okay, that's not really original, and I'm sure it's already been said, but...
falcorn70 · 0 points · Posted at 07:22:56 on February 17, 2016 · (Permalink)
If you could fold a piece of A4 paper 50 times, the resulting thickness would be enough to reach the sun
[deleted] · -1 points · Posted at 21:04:39 on February 13, 2016 · (Permalink)
[deleted]
ananori · 5 points · Posted at 22:15:16 on February 13, 2016 · (Permalink)
Nay. Just because it's irrational it doesn't mean there has to be any imaginable combination of numbers.
pdabaker · 1 points · Posted at 22:20:28 on February 13, 2016 · (Permalink)
Not actually known for sequences of arbitrary length, although I'm sure it's true for short sequences like those
Dinkir9 · -3 points · Posted at 21:12:02 on February 13, 2016 · (Permalink)
I fucking love mathematics so I have several...
The area under the equation: e-(x2) (thats -x2 im having trouble getting it to work right on my phone) is the square root of pi.
The ratio between consecutive fibonacci numbers approaches the golden ratio. ((1+sqrt5)/2)
The continued fraction form of e is 1:2,1,1,5,1,1,8,1,1,11,1,1,14....
e2(pi)i=1 (by changing that 2 to x its running on a cosine curve essentially)
Every single composite number can be defined as the sum of 2 prime numbers.
1-1/2+1/3-1/4+1/5-1/6.... is the ln(2) or 0.693.....
The Gamma function can be used to find the factorials of decimals... Factorials being... 8!=1×2×3×4×5×6×7×8 (see where the problem arises finding decimals?)
I've got more but I don't want to get too crazy here
Mazork · 2 points · Posted at 22:43:55 on February 13, 2016 · (Permalink)
Goldbach's conjecture remains unproven.
Dinkir9 · -4 points · Posted at 23:36:53 on February 13, 2016 · (Permalink)
Neither has the Riemann Hypothesis but we're pretty damn sure it's true.
Mazork · 3 points · Posted at 23:59:11 on February 13, 2016 · (Permalink)
Doesn't matter. Can't go around spitting facts that aren't true.
Dinkir9 · -3 points · Posted at 00:19:56 on February 14, 2016 · (Permalink)
You must be fun at parties.
somadIcanteven · 0 points · Posted at 03:30:55 on February 14, 2016 · (Permalink)
Sorry dude. You're just wrong.
Dinkir9 · 0 points · Posted at 03:49:28 on February 14, 2016 · (Permalink)
And you're a member of the Reddit hivemind. It's easy living agreeing with everybody else though isn't it?
somadIcanteven · 2 points · Posted at 05:59:00 on February 14, 2016 · (Permalink)
You're saying I'm part of the reddit hivemind because I agreed that you made a mistake? Wow, dude. Ok.
Math is all about proofs and rigor. You made a claim that something was a "mathematical fact" when it's not actually known yet. That's all.
Dinkir9 · -2 points · Posted at 06:27:17 on February 14, 2016 · (Permalink)
A lot of things aren't known yet we accept them as everyday fact. For all intents and purposes it's a fact, any,number you would care to test would work out. The only point of proving something in math is so that you can exploit it and connect it to other things in math, proving something works or doesnt work? Well that's kinda already known beforehand by the people working on this 'proof'.
Would it be better if I said "It's theorized that any composite number can be defined as the sum of two primes?" Still interesting and I thought it was cool, but you'd rather twist my words and nitpick at an individual point instead of accepting several cool little pieces of mathematical trivia. Oh and most people (such as the Reddit hivemind) would have simply accepted what I said and moved on without that guy stating that it wasn't actually a proven fucking fact. Yet it's so damn functional and practically true that it's like Einsteins Theory of Relativity, nobody knows how or why but it just works and you're gonna have to get over that, unless you want to take it up with the man himself?
somadIcanteven · 1 points · Posted at 13:35:52 on February 14, 2016 · (Permalink)
You realize number theory conjectures that had been checked to ludicrously large numbers have been later proven false, right? It's not nitpicking; it's the way mathematics works, which is fundamentally different to the nature of experimental sciences.
The only reason this exchange is happening is that, when presented with a comment that your facts were not yet facts (and might not be facts!) you tried to make fun of the commenter. He/she was just trying to make a polite point.
[deleted] · -3 points · Posted at 02:34:53 on February 14, 2016 · (Permalink)
1 black person = 3/5 of a white person
[deleted] · -2 points · Posted at 23:05:46 on February 13, 2016 · (Permalink)
[deleted]
ben1996123 · 4 points · Posted at 23:21:25 on February 13, 2016 · (Permalink)
no it isnt
Kiwi-kies · 0 points · Posted at 00:15:09 on February 14, 2016 · (Permalink)
Well, what is it?
ben1996123 · 2 points · Posted at 00:16:49 on February 14, 2016 · (Permalink)
infinity
[deleted] · -2 points · Posted at 00:57:09 on February 14, 2016 · (Permalink)*
[deleted]
ben1996123 · 5 points · Posted at 00:57:50 on February 14, 2016 · (Permalink)
i am well aware of this
the sum is not -1/12
somadIcanteven · 2 points · Posted at 03:35:53 on February 14, 2016 · (Permalink)
That video is incredibly misleading (in that it's completely wrong).
The only way to get from 1 + 2 + 3 + ... to the value -1/12 is through a regularization process. The identity is simply not correct as stated.
mseuleand · -3 points · Posted at 09:51:21 on February 14, 2016 · (Permalink)
0 is not a perfect 0. there are no absolute values. 0 is actually 0.000000000000000000000000000000000000000000000000000000000000000000000000000001 for example.
jos_kavalier · 3 points · Posted at 11:59:52 on February 14, 2016 · (Permalink)
this is wrong
xexir · -3 points · Posted at 20:54:24 on February 13, 2016 · (Permalink)
The lubricant in your knees is one of the slipperiest substances known.
RedditYankee · 6 points · Posted at 20:55:41 on February 13, 2016 · (Permalink)
Sir_Doughnut · -1 points · Posted at 19:39:19 on February 13, 2016 · (Permalink)
F epsilon naught.
[deleted] · -1 points · Posted at 19:52:11 on February 13, 2016 · (Permalink)
[deleted]
ThereOnceWasAMan · 6 points · Posted at 20:22:39 on February 13, 2016 · (Permalink)
You have it backwards.
Also, it is to be expected. The volume of the sphere can be made up of with lots of sums of infinitesimal surface areas at various different radii.
KayWhyElEe · -1 points · Posted at 20:11:45 on February 13, 2016 · (Permalink)
Is / of = x / 100
Kevlar98 · -1 points · Posted at 20:47:16 on February 13, 2016 · (Permalink)
The collatz conjecture. Any number can get to one by dividing by two if even or multiplying by 3 and adding one if it's odd and repeating with the results.
[deleted] · 1 points · Posted at 20:58:26 on February 13, 2016 · (Permalink)
Proof?
Kevlar98 · 1 points · Posted at 21:36:06 on February 13, 2016 · (Permalink)
That's the thing, it's unsolved but you can try any number (well, positive integer) you want and it will work. That's why I think it's cool.
For a random number: 1533 4600 2300 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
[deleted] · -1 points · Posted at 20:57:49 on February 13, 2016 · (Permalink)*
[deleted]
slacker0 · 1 points · Posted at 21:09:50 on February 13, 2016 · (Permalink)
Wut ? The domain of sin or cosine is any real number. The range is from -1 to +1.
almightySapling · 1 points · Posted at 23:10:48 on February 13, 2016 · (Permalink)
What he's saying is that sin and cos have a "fixed point" (a point where x=sin(x)) and further, that no matter what you start with, the sequence obtained by repeatedly applying sin (or cos) will always converge in that point.
See also: Banach fixed-point theorem
UffaloIlls · 1 points · Posted at 21:15:56 on February 13, 2016 · (Permalink)*
Try it. For example:
If y = Sin(sin(sin(...sin(x)...))) where x is any real number
y=sin(y)
sturio · -1 points · Posted at 20:57:57 on February 13, 2016 · (Permalink)
You can cool something to absolute zero (almost) by shining lasers at it. It works like this. Imagine there a bunch of people at the beach. These are the atoms in your substance. Now imagine them trying to walk around in the waves. The waves are the lasers beams traveling in one direction. When the people (atoms) try to walk against the waves, they slow down. However, walking in other directions doesn't really affect them at all. So the net effect is that the people keep walking slower and slower, until they have almost stopped. A similar thing happens to atoms. When they travel towards a laser beam, they see a certain energy from the laser. This energy makes them slow down. However, when they travel in different directions, they see different energy that doesn't effect them at all due to the doppler effect. The result is that the lasers only work to slow the atoms down (make things colder), but never to speed the atoms up. So if you keep the energy of the laser at the right energy, it will eventually slow the atoms down until they reach absolute zero (almost).
Ilostmycontrasena · -1 points · Posted at 22:04:16 on February 13, 2016 · (Permalink)
If Y=x1000 x will never go beyond 1.
Y=1(1/2)x and y will never go beyond 1 (this synthesizes the tale of Achilles never catching up to the turtle).
[deleted] · -1 points · Posted at 22:06:35 on February 13, 2016 · (Permalink)
[deleted]
ben1996123 · 1 points · Posted at 23:16:59 on February 13, 2016 · (Permalink)*
no it isnt
PDXtravaganza · -1 points · Posted at 22:30:56 on February 13, 2016 · (Permalink)
2+2 does NOT equal 22, but 1+1 can equal 3 or more.
zaqraw · -1 points · Posted at 22:34:16 on February 13, 2016 · (Permalink)
That there are 2 kinds of infinity, countable infinity and uncountable infinity.
Countable infinity:
Uncountable infinity:
carmium · -1 points · Posted at 22:51:29 on February 13, 2016 · (Permalink)
2 + 2 = 5 for extremely large values of 2.
carmium · 1 points · Posted at 05:56:27 on February 15, 2016 · (Permalink)
Downvotes? Really? I love this one; I'd wear it on a T-shirt.
[deleted] · -1 points · Posted at 23:19:40 on February 13, 2016 · (Permalink)
If you sum all the natural numbers, you get -1/12! Here's a Youtube video of it: https://www.youtube.com/watch?v=w-I6XTVZXww
baxter_1999 · -1 points · Posted at 23:49:58 on February 13, 2016 · (Permalink)
All positive integers added together to infinity equals -1/12. Blows my mind.
stigmaboy · -1 points · Posted at 00:00:49 on February 14, 2016 · (Permalink)
The sum of all real numbers from 0 to infinity is -1/12
INTERNALCARNAGE · -1 points · Posted at 00:13:06 on February 14, 2016 · (Permalink)
2+2 is 5
ITGuyLevi · -1 points · Posted at 00:13:23 on February 14, 2016 · (Permalink)
That 1 does not have to equal 1.
.99999999999 = 1
Calartian · -1 points · Posted at 00:14:45 on February 14, 2016 · (Permalink)
one plus one does not always equal two.
one glass of water plus one glass of sand does not equal two glasses of either.
just_gopher-it · -1 points · Posted at 00:26:09 on February 14, 2016 · (Permalink)
The sum of all positive integers equals -1/12. This videos does a good job of proving it http://youtu.be/w-I6XTVZXww
[deleted] · -1 points · Posted at 00:27:59 on February 14, 2016 · (Permalink)
Take the diameter of a circular object. Mark 3.1415... of those diameters. Roll the circular object and it will roll exactly one revolution.
Gibbelton · -1 points · Posted at 00:33:24 on February 14, 2016 · (Permalink)
The sum of all positive integers (1+2+3... All the way to infinity) is -1/12.
[deleted] · -1 points · Posted at 00:47:11 on February 14, 2016 · (Permalink)
The sum of all positive integers is -1/12
Frickinfructose · -1 points · Posted at 00:48:14 on February 14, 2016 · (Permalink)
Late to the game, but BY FAR the most interesting mathematical fact I've ever seen is that the sum of all integers from one to infinity equals negative one twelfth, or:
1 + 2 + 3 + 4 + ... = -1/12
This has actually been proven both mathematically and in observations in quantum mechanics. It is the craziest, most unintuitive math fact I've ever seen. 60 symbols does a great video on it here:
https://www.youtube.com/watch?v=w-I6XTVZXww
somadIcanteven · 1 points · Posted at 03:38:43 on February 14, 2016 · (Permalink)
Oh god, I think I'm gonna have a stroke responding to these for some reason. That identity isn't true; the sum used in quantum mechanics is a regularized sum and is quite different from standard summation.
RazarTuk · -1 points · Posted at 00:51:14 on February 14, 2016 · (Permalink)
1+2+3+4+5+... = -1/12
Dandistine · -1 points · Posted at 00:54:05 on February 14, 2016 · (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
Sleeveharvey · -1 points · Posted at 01:00:48 on February 14, 2016 · (Permalink)
The sum of all positive integers is -1/12 http://scitation.aip.org/content/aip/magazine/physicstoday/news/10.1063/PT.5.8029
VixVixious · -1 points · Posted at 01:15:44 on February 14, 2016 · (Permalink)*
1+2+3+4+5+6...= -1/12. It can be proven and it's a result that actually comes up in some experimental, empirical observations involving advanced physics. https://www.youtube.com/watch?v=w-I6XTVZXww
liamthorpe · -1 points · Posted at 01:18:30 on February 14, 2016 · (Permalink)
The sum of all positive whole numbers is -1/12. i.e. 1+2+3+4+5+...=-1/12
luke_in_the_sky · -1 points · Posted at 02:12:50 on February 14, 2016 · (Permalink)
That when I put 1+1 on a calculator and press = it shows 2. If I keep pressing = it add 1 to the result.
TotalCreative · -1 points · Posted at 02:17:25 on February 14, 2016 · (Permalink)
X0 = 1
gohikhierookal · -1 points · Posted at 02:30:23 on February 14, 2016 · (Permalink)
This will get burried but is too cool not to share:
1+2+3+4+5+...natural numbers...= (drums rolling...) -1/12
EDIT natural numbers, not integers
CJamezon · -1 points · Posted at 02:31:42 on February 14, 2016 · (Permalink)
THIS is the most astounding math fact anyone has ever known or WILL ever know, and I am not joking:
1+2+3+4+5+....[forever] = -1/12
This is not a prank, this is true: https://www.youtube.com/watch?v=w-I6XTVZXww
It appears in string theory and lots of other places in physics, but what it really shows us is that human intuition about math is very wrong, and that our understanding of even the topic of mathmatics is very limited as a human species.
brutalyak · 3 points · Posted at 02:35:52 on February 14, 2016 · (Permalink)
No, it doesn't.
iluvgrannysmith · 2 points · Posted at 02:58:34 on February 14, 2016 · (Permalink)
When you subtract infinity from infinity, the standard rules of math break. Real Analysis, at least at the foundations, does not attempt to define infinity - infinity. The intuitive argument for that proof is... Interesting though.
CJamezon · 2 points · Posted at 04:39:05 on February 14, 2016 · (Permalink)
There are plenty of places in math and physics where this "sum" appears, and astoundingly the math only works out if you plug in "-1/12". These occurrences are also unrelated to each other, so this is not a single "math trick", but is more of a truth of reality. It may be similar to how i (sqrt of -1) also needs to exist in mathematics even though it alone is nonsensical.
iluvgrannysmith · 1 points · Posted at 05:27:37 on February 14, 2016 · (Permalink)
Using root(-1) is adjoining the field of real numbers with i. Kind of like when you use an (x,y) coordinate plane. Only, multiplying everything by i gives a rotation of 90 degrees on your plane. If you worked with quaternions it's similar there. It's not in the least bit nonsensical.
Saying 1+... = -1/12 < 1 defies that the characteristic of the real numbers is 0. I believe the proof works, and that it can have some meaning in some places. Though, I would need to see them myself to agree they could be on the level of the development of the complex plane.
CJamezon · 1 points · Posted at 13:04:06 on February 14, 2016 · (Permalink)*
FYI: I have a degree in Mechanical Engineering, and have been doing robotics, machine simulation, inverse kinematics, since 1990, and have written over 1,000,000 lines of code involving complex numbers. I think perhaps you need to just get over yourself, and perhaps drop the "oh no it isn't" attitude. Just a life tip for ya.
As for your second disgruntlement, here's some help (or you can learn to google): https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
[deleted] · 1 points · Posted at 15:19:20 on February 14, 2016 · (Permalink)
[deleted]
CJamezon · 2 points · Posted at 18:02:27 on February 14, 2016 · (Permalink)
You're the kind of person who would have told Einstein "action at a distance" was not the least bit "spooky", despite knowing less about it than him...and when he corrected you, you'd call him disgruntled. You know that's precisely what just happened. Enjoy being you.
[deleted] · 1 points · Posted at 18:41:04 on February 14, 2016 · (Permalink)
[deleted]
CJamezon · 1 points · Posted at 20:59:33 on February 14, 2016 · (Permalink)
The Einstein analogy was about how you would react to the word "spooky" if he made the mistake of saying it to you in social media. It wasn't about my knowledge level, and you know it. Nice try pretending not to understand what my point was. Didn't believe a word of it.
About -1/12, I don't think anyone fully understands that. Math can be somewhat counter-intuitive at times, like in Quantum Mechanics, where two contradictory things can both be true at the same time, because a physical object can be in two locations simultaneously. You know the famous quote: "If you think you understand QM, then you definitely don't understand QM." The wikipedia page on "-1/12" has a section titled "Physics" that are the primary two examples of it's use, with one being so important that it would indicate there are 26 dimensions to our reality.
Benchriha · -1 points · Posted at 02:39:20 on February 14, 2016 · (Permalink)
If you add every number to each other infinitely Luke this:
1+2+3+4+5+6+...
it equals -1/12 There is a nice Video about that on YouTube somewhere.
(Sorry for bad english, i'm no native speaker. )
flexiverse · 1 points · Posted at 02:41:49 on February 14, 2016 · (Permalink)
Interestingly this is the first thing you are taught in string theory in the first few pages on string theory text books.
ThingsIAlreadyKnow · -1 points · Posted at 02:45:44 on February 14, 2016 · (Permalink)
The sum of all integers = -1/12
MrReddington · -1 points · Posted at 02:45:59 on February 14, 2016 · (Permalink)
1-1+1-1+1-1+1-1+1.....=1/2 (..... Means to go into infinite). Also when a person pedals a bicycle the point the tire contacts the ground is not moving. Some of the things I've learned in Calculus.
earnestadmission · -1 points · Posted at 02:47:47 on February 14, 2016 · (Permalink)
If you add 1 + 2 + 3 + 4 + 5 + ... and so on, from 1 to infinity, the sum is -1/12
brutalyak · 1 points · Posted at 02:48:26 on February 14, 2016 · (Permalink)
No its not
[deleted] · 1 points · Posted at 02:52:40 on February 14, 2016 · (Permalink)
[deleted]
brutalyak · 1 points · Posted at 02:54:55 on February 14, 2016 · (Permalink)
I've seen the video. It's still wrong. The sum of all natural numbers is a divergent series, meaning it doesn't equal any finite number.
earnestadmission · 1 points · Posted at 03:52:58 on February 14, 2016 · (Permalink)
brutalyak · 0 points · Posted at 03:58:23 on February 14, 2016 · (Permalink)
earnestadmission · 0 points · Posted at 04:33:12 on February 14, 2016 · (Permalink)
I'm not sure what you think you're accomplishing here. There is an interesting result from an obscure branch of number theory in which the equivalence I reported holds. This result turns out to have applications in physics, especially in predictive models about the real world. Thus there are both theoretical and empirical contexts in which the statement I made is "true."
Your complaints thus far are a bit like a Calculus student insisting that one must never divide by zero. In fact, l'Hopital's rule widens, though does not erase, the constraints on dividing by zero. Similarly, results about connectedness (for example) which hold for metric spaces might fail in more arcane topologies. That does not mean that you'd be justified in saying that a connected subspace is not closed and bounded (just because not every single topology has a metric).
When you insist that we must never repeat this interesting -1/12 result by Ramanujan, it says only that you aren't interested in playing with math the way that I'm playing with math. It doesn't prove me "wrong."
So to repeat, I'm not sure what you think you're accomplishing here.
Avron18381 · -1 points · Posted at 02:48:58 on February 14, 2016 · (Permalink)
1 - 1 + 1 - 1 + 1 - 1 + 1 ... = 0.5
https://www.youtube.com/watch?v=qJiVhfR_XVE
YT_Reddit_Bot · 1 points · Posted at 02:49:13 on February 14, 2016 · (Permalink)
[deleted] · -1 points · Posted at 02:52:28 on February 14, 2016 · (Permalink)
1 + 2 + 3 + ... = -1/12
Yup, look it up.
somadIcanteven · 1 points · Posted at 03:40:53 on February 14, 2016 · (Permalink)
Try looking it up further. It's still not right, and the actual reason why -1/12 is an important value for that (divergent to infinity) series is far more complicated.
[deleted] · -1 points · Posted at 03:03:16 on February 14, 2016 · (Permalink)
[deleted]
Felix_Tholomyes · 2 points · Posted at 03:21:56 on February 14, 2016 · (Permalink)
No, if you were to take out a calculator and start adding all natural numbers given infinite time your sum would not approach -1/12.
It's just a way to assign a value to a divergent sum.
JayneIsAGirlsName · -1 points · Posted at 03:05:12 on February 14, 2016 · (Permalink)
The sum of all natural numbers (1+2+3+4+...) = -1/12
NoGardE · -1 points · Posted at 03:05:12 on February 14, 2016 · (Permalink)
The sum of all natural numbers is - 1/12.
ranma_one_half · -1 points · Posted at 03:05:49 on February 14, 2016 · (Permalink)
1+1=1.
Don't belive me?
Let's say you have two groups of people.. if they come together how many groups do you have?
One.
Your welcome.
*also if you think about it everyone and anyone is still only one.
Sandisk4gb4 · -1 points · Posted at 04:32:45 on February 14, 2016 · (Permalink)
It suck.
ziippadiip · -1 points · Posted at 04:41:26 on February 14, 2016 · (Permalink)
Your mum can be divided by everything.
kresimirnovakovic · -1 points · Posted at 04:49:28 on February 14, 2016 · (Permalink)
1+2+3+4+... to infinity = -1/12. Blows my mind every time.
Vortico · 1 points · Posted at 06:39:38 on February 14, 2016 · (Permalink)
No, the sum doesn't exist.
H-Wood · -1 points · Posted at 04:50:31 on February 14, 2016 · (Permalink)
58008 on a calculator turned upsidedown spells BOOBS
mknisal102003 · -1 points · Posted at 04:51:27 on February 14, 2016 · (Permalink)
9+10=21
meonthew3 · -1 points · Posted at 05:28:32 on February 14, 2016 · (Permalink)
1 plus 1 equals 2, but, sometimes, it equals one.
PM_ME_UR_GOODIEZ · -1 points · Posted at 05:31:02 on February 14, 2016 · (Permalink)
1/3 =.333 repeating
.333 repeating * 3 =.999 repeating
1/3 * 3 = 3/3
1=.999 repeating
nemoking · -1 points · Posted at 05:42:03 on February 14, 2016 · (Permalink)
Graham's number is so big that if the human brain had the ability to be able to understand it, it would need to be so dense that it would reach the schwarzchild radius and collapse into a black hole.
Vortico · 1 points · Posted at 05:54:37 on February 14, 2016 · (Permalink)
What do you mean "understand"? You can write down the definition, compare it with other numbers, multiply and add it to other numbers.
nemoking · 1 points · Posted at 06:05:03 on February 14, 2016 · (Permalink)
You know how when you think of a number like 3 or 5 you can visualize that number, immediately recognise that number of items without thinking etc etc. Thats what I mean by 'understand'. I'm no maths proffessor (just a lowly law undergrad), but I remember seeing this in a series of videos on Youtube by the channel, NumberPhile.
Vortico · 1 points · Posted at 06:26:26 on February 14, 2016 · (Permalink)
If visualizing an array of n objects is your definition of understanding a number, you definitely don't need to go as high as Graham's number. 10100 will do it (with the rough assumption that you need as least n neurons to visualize n.)
nemoking · 1 points · Posted at 18:20:27 on February 19, 2016 · (Permalink)
Great
baronmad · -1 points · Posted at 05:43:23 on February 14, 2016 · (Permalink)
Fact is a bit misleading when it comes to this one.
That if you add all the positive numbers together, 1+2+3+4... all the way to infinity the answer you will get is -1/12 from nothing but positive numbers you come out with a negative number.
This is not a fact as such because in mathematics limits doesnt work on a convergent series because they dont have a limit.
tellohello · -1 points · Posted at 05:50:28 on February 14, 2016 · (Permalink)
Hella late, but 1+2+3+4+... = -1/12
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
overconvergent · 1 points · Posted at 06:00:04 on February 14, 2016 · (Permalink)
1+2+3+4+... does not equal -1/12. One way of associating a value to divergent series happens to associate the value -1/12 to this series, but that does not mean that the sum of this series is -1/12.
ChaozNacho · -1 points · Posted at 06:12:55 on February 14, 2016 · (Permalink)
Boring...
cacingintegral · -1 points · Posted at 06:49:27 on February 14, 2016 · (Permalink)
The sum of all positive numbers is... -1/12
https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
[deleted] · -1 points · Posted at 13:34:18 on February 14, 2016 · (Permalink)
the golden ratio
lennarn · -1 points · Posted at 13:52:47 on February 14, 2016 · (Permalink)
The amount of wrinkles around a camel's butt hole is equal to pi times the number of leaves in a tulip. Disprove at your own peril.
syndus · -1 points · Posted at 14:49:32 on February 14, 2016 · (Permalink)
2 + 3 = Chair
[deleted] · -1 points · Posted at 15:36:23 on February 14, 2016 · (Permalink)
I before E except after C
Ertj13s · -1 points · Posted at 16:43:25 on February 14, 2016 · (Permalink)
That 1+2+3+4+.....infinity = -1/12
NoobosaurusIdioticus · -8 points · Posted at 19:36:42 on February 13, 2016 · (Permalink)
1 + 1 = 69 ( ͡° ͜ʖ ͡°)
[deleted] · -2 points · Posted at 20:02:31 on February 13, 2016 · (Permalink)
[deleted]
weebiloobil · 1 points · Posted at 20:49:54 on February 13, 2016 · (Permalink)
00 is an interesting situation, but you can handwave by pointing out xx -> 1 as x -> 0
PantsMacKenzie · -2 points · Posted at 20:47:35 on February 13, 2016 · (Permalink)
We can get close to, but never reach 0K.
sampeckinpah5 · 1 points · Posted at 21:13:57 on February 13, 2016 · (Permalink)
Because 0 K is "absolute zero" and it isn't supposed to be reachable by normal means.
PantsMacKenzie · 2 points · Posted at 21:22:34 on February 13, 2016 · (Permalink)
Yes. It is therefore the coolest fact I know. I guess it's a physics fact and not math... :(
[deleted] · -2 points · Posted at 22:08:28 on February 13, 2016 · (Permalink)
[deleted]
ben1996123 · 2 points · Posted at 23:17:15 on February 13, 2016 · (Permalink)*
no it doesnt
luckyvonstreetz · 1 points · Posted at 23:33:10 on February 13, 2016 · (Permalink)
This is really bothering you or isnt it? Haha
[deleted] · -2 points · Posted at 22:34:16 on February 13, 2016 · (Permalink)
[deleted]
ben1996123 · 2 points · Posted at 23:19:39 on February 13, 2016 · (Permalink)
no
there are infinitely many kinds of infinity. one of them is countable, all of the others are uncountable
0.000...1 is equal to 0 so that has nothing to do with infinity (and there are only countably many 0s in "0.000..." anyway. also your first list is finite
luckyvonstreetz · -1 points · Posted at 23:31:47 on February 13, 2016 · (Permalink)
You're a retard ben xD stop acting like you know something about maths
Cogswobble · -2 points · Posted at 23:01:08 on February 13, 2016 · (Permalink)
If you take the sum of all the positive integers, you can show that it equals -1/12, not infinity. In other words:
1+2+3+4+5+6+... = -1/12
Here's a Numberphile video about it: https://www.youtube.com/watch?v=w-I6XTVZXww
ben1996123 · 2 points · Posted at 23:20:53 on February 13, 2016 · (Permalink)
no it isnt
Psycho_Robot · -2 points · Posted at 03:00:32 on February 14, 2016 · (Permalink)
The sum of all natural numbers (1, 2, 3, 4...) is -1/12
brutalyak · 0 points · Posted at 03:04:35 on February 14, 2016 · (Permalink)
No, it's not.
Psycho_Robot · 0 points · Posted at 03:11:34 on February 14, 2016 · (Permalink)
Oh, I didn't realise mathematicians everywhere are wrong. Say, what are your credentials for doubting them?
brutalyak · 0 points · Posted at 03:14:27 on February 14, 2016 · (Permalink)
The fact that the sum of natural numbers is divergent, and therefore does not equal a finite number.
Psycho_Robot · -1 points · Posted at 03:16:48 on February 14, 2016 · (Permalink)
Math didn't get that memo. You'd better it know. It's going to be so embarrassed.
hbcproeagle · 2 points · Posted at 03:23:42 on February 14, 2016 · (Permalink)
it's not quite an equality though, it's just a value that we can assign to a series even when it diverges. it doesn't really make sense to say that the sum is actually equal to -1/12.
Psycho_Robot · 1 points · Posted at 03:29:55 on February 14, 2016 · (Permalink)
Regularizing divergent series using a number of different methods has long been recognized as mathematically sound, and has been used in a number of useful ways in other areas of mathematics, and even in physics. This blog post by the one of the mathematicians who appears in the video links to a lot of resources, and provides a lot of explanation, for why this is not some mathematical bullshit, and why it is actually a useful and valid value to assign this sum.
hbcproeagle · 1 points · Posted at 03:51:01 on February 14, 2016 · (Permalink)
I'm not saying it's bullshit, I'm just being a little bit pedantic and justifying what the other poster mentioned. We don't say that the sum is actually equal to -1/12, but rather we are assigning the value to it because it makes it easier to manage (we don't want to deal with infinity, especially in physics). Look carefully at the language used, we never actually state that the sum is equal but rather that we associate/attach this particular value with the sum. There is a quite distinct difference.
It does sort of take away from the magic of it all, but this is not an arbitrary assignment, and as you mention, has many applications in other fields.
brutalyak · 2 points · Posted at 03:27:21 on February 14, 2016 · (Permalink)
I don't know what that link is supposed to prove, are you trying to say 1+2+3+4+5... is equal to a finite number, because it definitely isn't.
brutalyak · 0 points · Posted at 03:29:02 on February 14, 2016 · (Permalink)
If mathematicians everywhere disagree with me why don't you give me a link to one of those mathematicians instead of wikipedia?
Psycho_Robot · 1 points · Posted at 03:30:50 on February 14, 2016 · (Permalink)*
I already did. It's in the video, which you didn't watch, where three mathematics professors from the University of Nottingham explain why this is true.
brutalyak · 1 points · Posted at 03:38:58 on February 14, 2016 · (Permalink)
I guess you didn't read the description of the video because it clearly states "Tony Padilla and Ed Copeland are physicists at the University of Nottingham."
Psycho_Robot · 1 points · Posted at 04:04:40 on February 14, 2016 · (Permalink)
They're currently physicists, but Tony Padilla was formerly a professor in math, and has a BA in maths from Cambridge. You're right that Ed Copeland does not have a degree in math, but as a physicist he had to study the hell out of it nonetheless. But fine, if you'd like to split hairs, here's a video on the same subject from Edward Frenkel, a math professor at cambridge, and here's a paper by Terrance Tao, math professor at UCLA. Speaking of which, someone who is so confident in their understanding of math to doubt physics professors at Nottingham must have a pretty strong background in math. How many years have you studied it? Was it all the way through high school? Or did you need to do another year in college?
[deleted] · -2 points · Posted at 04:44:14 on February 14, 2016 · (Permalink)
6+9= me and yur mum
dukemetoo · -2 points · Posted at 04:59:35 on February 14, 2016 · (Permalink)*
The Sum of all natural numbers =-1/12
Source
Edit: I'm an idiot that can't copy the right link.
overconvergent · 1 points · Posted at 06:03:39 on February 14, 2016 · (Permalink)
The sum of all the natural numbers is not equal to -1/12.
Source: I'm a mathematician.
dukemetoo · 1 points · Posted at 06:39:32 on February 14, 2016 · (Permalink)
Would you mind telling me what the video is doing wrong then?
overconvergent · 2 points · Posted at 07:11:50 on February 14, 2016 · (Permalink)
You linked to a video about laptop batteries, so I'm not sure how to help you.
In any case, the series 1+2+3+4+... diverges. In other words, as you add more numbers, the sum gets larger and larger without bound. There is a way of assigning the value -1/12 to the expression "1+2+3+4+...", but that does not mean that the sum of the natural numbers is -1/12.
dukemetoo · 1 points · Posted at 07:20:26 on February 14, 2016 · (Permalink)
That's what logic tells me, but Infinity seems to always defy logic
Vortico · 1 points · Posted at 06:32:04 on February 14, 2016 · (Permalink)
No, the sum doesn't exist.
wyedg · -2 points · Posted at 05:35:03 on February 14, 2016 · (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
Vortico · 1 points · Posted at 06:04:17 on February 14, 2016 · (Permalink)
No, the sum doesn't exist and is certainly not -1/12.
Ozwegian · -2 points · Posted at 05:41:30 on February 14, 2016 · (Permalink)*
All this maths is considered cool? Haha, what nerds
I was joking, geez, for a site of people that like making controversial jokes, you sure don't like taking light hearted ones
Noah-R · -2 points · Posted at 06:05:53 on February 14, 2016 · (Permalink)*
1 is equal to 2
To demonstrate this, let's establish two variables, a and b. If we let them be equal, then we know the following is true:
If we add a2 to each side
Combine terms
If we subtract 2ab from each side
Combine some more terms
Factor out a constant from each side
Divide the (a2 - ab) from each side, and you finally get
Edited for formatting
aeglos · 2 points · Posted at 06:22:20 on February 14, 2016 · (Permalink)
As novel as it seems, it is a mathematical fallacy as you are dividing by zero.
Noah-R · 1 points · Posted at 06:40:38 on February 14, 2016 · (Permalink)
Exactly, the joke is that you can't always divide by a variable
LordFoster · -2 points · Posted at 14:25:02 on February 14, 2016 · (Permalink)
99% or people may or may not be gay
Chick22694 · -2 points · Posted at 14:54:08 on February 14, 2016 · (Permalink)
Jet fuel can't melt steel beams
the_real_nedflanders · -2 points · Posted at 15:24:53 on February 14, 2016 · (Permalink)
you type 8-0-0-8, and it spell boob. forward and backward
sjhock · -3 points · Posted at 21:50:39 on February 13, 2016 · (Permalink)*
Because pi is infinite, it
mustcould potentially contain, in binary, every novel ever written, that ever will be written, and that was never written.ben1996123 · 2 points · Posted at 23:23:05 on February 13, 2016 · (Permalink)
pi is finite, it is less than 4
also 0.101001000100001000001000000100... is "infinite" and doesnt repeat but it doesnt contain a 2 anywhere
[deleted] · -3 points · Posted at 22:08:33 on February 13, 2016 · (Permalink)
That the sum of 1+2+3+4....upto infinity is NOT Infinity. It is
-1/12
ben1996123 · 2 points · Posted at 23:17:21 on February 13, 2016 · (Permalink)
no it isnt
somadIcanteven · 2 points · Posted at 03:34:25 on February 14, 2016 · (Permalink)
Ugh, I am getting seriously sick of misinformation being spouted here. Read the other comments on the other 500 times this is mentioned in the thread, talking about what this "series" means, because that identity is flat out wrong at worst, and severely misleading at best.
boom456 · -3 points · Posted at 22:12:00 on February 13, 2016 · (Permalink)
The sum of all natural numbers (1+2+3 etc) equals -1/12 http://youtu.be/w-I6XTVZXww
ben1996123 · 3 points · Posted at 23:17:29 on February 13, 2016 · (Permalink)
no it doesnt
[deleted] · -2 points · Posted at 23:00:07 on February 13, 2016 · (Permalink)
the infinite sequence 1 + 2 + 3 + 4... does not sum up to infinity, it sums up to -1/12.
ben1996123 · 2 points · Posted at 23:20:45 on February 13, 2016 · (Permalink)
no it doesnt
luckyvonstreetz · -1 points · Posted at 23:25:54 on February 13, 2016 · (Permalink)
I would like to see you disprove it ben
ben1996123 · 5 points · Posted at 23:31:17 on February 13, 2016 · (Permalink)
alright
1+2+3+4+... is defined as lim n->inf (1+2+3+...+n) = lim n->inf (n(n+1)/2)
choose any positive integer k>1. then for n>k, n(n+1)/2 > k(k+1)/2 > k so the limit is infinite
luckyvonstreetz · -4 points · Posted at 23:46:27 on February 13, 2016 · (Permalink)
I meant that you had to disprove the proof that says that it's -1/12. Because the sum is both infinite and -1/12.
ben1996123 · 3 points · Posted at 00:04:49 on February 14, 2016 · (Permalink)
that makes no sense at all but ok
Z is a closed subset of R with the euclidean topology => limit of a sequence of integers is an integer => limit of a sequence of integers is not -1/12
luckyvonstreetz · -1 points · Posted at 09:19:21 on February 14, 2016 · (Permalink)
You still didn't show the error in the proof that the sum is -1/12.
This way I could disprove that the sum is an integer bij posting the proof for -1/12. But it doesn't work that way.
Snowayne2 · 1 points · Posted at 19:13:17 on February 14, 2016 · (Permalink)
If you are referring to this proof: The first sequence (1+1-1+1-1...) does not equal 1/2. Thus, the whole proof is rubbish.
[deleted] · -2 points · Posted at 05:16:37 on February 14, 2016 · (Permalink)
[deleted]
Vortico · 1 points · Posted at 06:19:02 on February 14, 2016 · (Permalink)
No, the sum doesn't exist.
RJrules64 · -4 points · Posted at 05:36:01 on February 14, 2016 · (Permalink)*
1+2+3+.... = -1/12 (or something along those lines.)
Most other things listed here I can almost wrap my head around some way or another. I cannot understand how the sum of positive integers can ever equal a negative. But apparently it's proven!
Edit: https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
overconvergent · 1 points · Posted at 06:02:25 on February 14, 2016 · (Permalink)
No. 1+2+3+... does not equal -1/12.
RJrules64 · 1 points · Posted at 07:45:29 on February 14, 2016 · (Permalink)
But... https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
overconvergent · 1 points · Posted at 16:25:47 on February 14, 2016 · (Permalink)
From your own link:
There are methods of associating a value to a divergent series. Some of these methods associate the value -1/12 to the series 1+2+3+4+..., but this does not mean that the series equals -1/12.
RJrules64 · 1 points · Posted at 00:07:57 on February 15, 2016 · (Permalink)
But it can Which is the mind blowing fact I mentioned.
Vortico · 1 points · Posted at 06:03:32 on February 14, 2016 · (Permalink)
No, your intuition is correct; the sum doesn't exist and is certainly not -1/12.
RJrules64 · 1 points · Posted at 07:44:56 on February 14, 2016 · (Permalink)
But... https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
Vortico · 1 points · Posted at 07:54:23 on February 14, 2016 · (Permalink)
From the article:
So you would be correct if you say "The zeta regularization of the sum 1+2+3+... is -1/12", but by the traditional meaning of an infinite sum, it diverges.
i_shud_b_studying · -3 points · Posted at 05:40:49 on February 14, 2016 · (Permalink)
The sum of all natural numbers is -1/12
Vortico · 1 points · Posted at 06:00:32 on February 14, 2016 · (Permalink)
No, the sum doesn't exist. The zeta function regularization of the sum yields -1/12, but that's less surprising since the definition requires the zeta function and analytic continuation methods, which might as well pop out a simple "-1/12" from that mess.
overconvergent · 1 points · Posted at 06:01:46 on February 14, 2016 · (Permalink)
No, it is not.
old_liberal · -2 points · Posted at 13:43:31 on February 14, 2016 · (Permalink)
eiπ=1
bicyclemom · 2 points · Posted at 13:48:21 on February 14, 2016 · (Permalink)*
-1
EDIT: Er....that's not a downvote indication, that's the real right hand side of the equation.
ClassyAmoeba · -4 points · Posted at 20:58:24 on February 13, 2016 · (Permalink)
i to the power of an odd number will always equal -1, and i to the power of an even number will always equal 1.
[deleted] · 2 points · Posted at 21:43:20 on February 13, 2016 · (Permalink)
False. And here's why
i0= 1
i1= i
i2= -1
i3= -i
i4= 1
i5= i
...
The same pattern repeats.
More Info
AcellOfllSpades · 1 points · Posted at 21:43:48 on February 13, 2016 · (Permalink)
That's not true. Not even close.
i2 = -1
i3 = -i
LiamsFriend · 1 points · Posted at 21:55:27 on February 13, 2016 · (Permalink)
i3=iii=-i
Hopkirk87 · -4 points · Posted at 21:33:09 on February 13, 2016 · (Permalink)
The Sum of all positive integers is equal to -(1/12)
ben1996123 · 6 points · Posted at 23:22:11 on February 13, 2016 · (Permalink)
no it isnt
user725 · -2 points · Posted at 01:04:52 on February 14, 2016 · (Permalink)
But it is
ben1996123 · 2 points · Posted at 01:10:22 on February 14, 2016 · (Permalink)
no it isnt
Geneticbrick · -5 points · Posted at 21:44:52 on February 13, 2016 · (Permalink)
1+2+3+4+5+6+7+8+9+10+........=-1/12
ben1996123 · 3 points · Posted at 23:22:17 on February 13, 2016 · (Permalink)
no it doesnt
user725 · -1 points · Posted at 01:05:03 on February 14, 2016 · (Permalink)
But it does
evanstravers · -4 points · Posted at 05:02:06 on February 14, 2016 · (Permalink)
Republican = Racist