What about contradictions?

⊥

Hm. Yes. x = x where x ∈ X and X is a totally ordered set. This precludes IEEE 754 which is totally ordered except for NaN, -0, and 0.

Also, what are you doing in a 3 month old thread? :)

Recursion

... not!

Here, FTFY

How would 7x + 2 evaluate to a Boolean value.

But this is about equations, not evaluation. Just P∧¬P is a contradiction, aka "literal false".

Until I can do something like

if (some_expression) {
    // do something
} else {
    // do something else
} idk {
    // run around in circles while the world goes up in flames
}

I will not be content.

(In a Satanic voice) You've been a good boy, a very good boy, /u/BasedSkarm...

I know, I just like spreading nodejs everywhere i possibly can. Almost as much as i try to spread Negima.

Post increment is syntax sugar for

a;
a=a+1;

You can use it as an arg:

f(a++);

Which returns a, and adds a command afterward to increment a 1:

a = a + 1;

Likewise, you have pre increment. It increment, then returns:

++a;

Like sex, programming involves loads of meticulous preparation and study, followed by a few minutes of flailing around like a dying fish, finding out it didn't work at all, and then being disappointed in yourself.

It's not necessarily meant as an actual feature--it's just a rather interesting interaction between two separate language features that ends up working together in that way. I'm sure there's some strange situations where it would be useful for actual code, but I can't quite think of any right now.

Mostly it just ends up being a problem for beginning C programmers that come from languages that use a single '=' as the comparison operator.

Thanks! All that Java made me forget the difference between pointers and references.

Taylor series:

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In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

The concept of a Taylor series was discovered by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor series is centered at zero, then that series is also called a Maclaurin series, named after the Scottish mathematician Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century.

It is common practice to approximate a function by using a finite number of terms of its Taylor series. Taylor's theorem gives quantitative estimates on the error in this approximation. Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial. The Taylor series of a function is the limit of that function's Taylor polynomials, provided that the limit exists. A function may not be equal to its Taylor series, even if its Taylor series converges at every point. A function that is equal to its Taylor series in an open interval (or a disc in the complex plane) is known as an analytic function in that interval.

Image ⁱ - As the degree of the Taylor polynomial rises, it approaches the correct function. This image shows sin(x) and its Taylor approximations, polynomials of degree 1, 3, 5, 7, 9, 11 and 13.

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^{Interesting: Davidon–Fletcher–Powell formula | Rational function | Taylor's theorem | Polygamma function}

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now nobody gives a fuck on how to do the real math any more and just uses a taylor approximation

Pretty sure the approximations are used because they're faster, not because we "can't do real math."
And for anyone interested, this is how a lot of CPUs do intrinsics for trigonometric functions. As you can imagine, you don't really need full accuracy for such stuff.

I see, thanks. I guess it's ok that there are things that I can't understand for now. Maybe in the future, when I'll be able to augment my brain, I'll understand these things easily.

The left hand 0 is from R while the right hand 0 is from C.

Now they're different.

That is not a valid number in mathematics. You might as well ask me what if x is a car. I have only proven it correct under the assumption that the laws of mathematics are true, which is not always the case on computer hardware. IEEE 754 is just an approximation to begin with.

The fact is that you made a bad assumption about me and you made an assumption, bad or not (but certainly unfair enough), about the teacher. The only assumption I'm making is that you're just trolling now because you're stubborn and have nothing really relevant to add, and that assumption seems justified given what you just posted.

How do you know when an equation is true? By evaluating both sides and comparing the values. If there are variables in one side of the equation, you have plug in values before you can evaluate it.

Yes, if you introduce a second variable with a zero coefficient, then the solution is independent of it.

x + 0 * y ?= 7

Is true when x is 7 and "whatever" for y. That's not what /u/Wodashit proposed as the solution though, it was

y ?= n

For the solution which, I said way the hell back when, the truth of that statement is indeterminate because the value of y is undefined, and unconstrained, so it could be true or false. Whether x is 7 or not.

If he meant to say: "x = 7" is a solution, and it is completely independent of the value of y! Well, no kidding. It is the preexisting solution that's already written down, and why the teacher wrote "Really?".

Yes, I understand the concept of independent variables / orthogonal axes and the set of possible solutions, its the basis for calling the proposed solution incorrect.

Let me make this much simpler and remove the second variable.

if you do not express x in there the expression is true for any x, especially if x=7

old: f(x) = x new: f(x) = 3

f(7) ?= 7

false

You would have to write 3 = 3, not introduce an undefined variable and compare it to a constant.

If the variables are truly independent, then knowing how many slices of ham are on the sandwich (or not) tells you nothing about how many slices of cheese are on the sandwich. Can you truly answer this question?

"There are seven slices of ham on the sandwich. Are there three slices of cheese on the sandwich?"

If not, you will understand why a system of equations with two unknowns in insoluble without a second equation.

y = 2x, y ?= 14

This is true when x = 7. The value of y is no longer unresolved.

They are actually a subset of rationals. Like rationals and integers, they are countable.

Real number aren't. The set of real number is very different from rationals, whereas rational looks a lot like integers.

Real number:

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In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356…, the square root of two, an irrational algebraic number) and π (3.14159265…, a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and complex numbers include real numbers.

Image ⁱ - A symbol of the set of real numbers (ℝ)

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^{Interesting: Extended real number line | Real line | 0.999... | Totally real number field}

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I'm well aware of what they said. I was just pointing something out.