For the math geeks

[Mordred]

Kmon guys, infinity is not a number. Once you make infinity a number, you make it finite.
What does it mean to divide a number by infinity? It's impossible since infinity is not a number. One might say, what about dividing a number infinite amount of times. Dividing infinitely by what? Say divide by a number x. Well then this dividing process will never, end will it, since you divide the number infinitely.

The flaw is in the problem, thus all the solutions that accept/ignore/don't notice the flaw are flawed themselves.

s3my0n actually has the most correct point.
First of all you cannot operate with infinity. It is not a number (although in mathematics for ease of use we accept is as one sometimes) but it is a concept denoted by a symbol.
Infinity is actually originating from limit theory. The problem was that there was no way to represent how an exponential function (as an example) behaves when the exponent is a very very large number.
Basically what is calculated is the tendency of the function. In the case of a normal exponential, the function converges to infinity when the exponent tends to infinity. This is the correct way of formulating from a mathematical point of view - and you'll notice that I never said "equals infinity" or the likes because that is illogical.

Now for the mathematical proof I will appeal to a simple idea of mathematics - If you can provide at least 1 counterexample to a rule, that rule cannot possibly be true.

I'm gonna stay away from the logical fallacy of "dividing infinity an infinite number of times" because as I explained before this already doesn't make sense from a mathematical P.O.V.

“You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large. But if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small. Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.”

So, if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small.

Let's take our non-infinite number to be 1. (doesn't matter what value it actually is, I could've called it "x", but like this it's easier)
We are dividing an "infinite number of times" which means that we have 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7 ... 1/∞ as our non-infinitely small pieces.

Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite.

Here is where the critical mistake is made. The claim is: an infinite number of non-infinite values added together sums up to infinity

Counter-proof: Our previous calculation left us with the series of 1/x where x -> ∞ (read as x tends to ∞).
lim[SUM(1/x)] = lim(1/1+1/2+1/3+1/4+...+1/∞) = lim (1/∞) = 0 (this is a proven theorem, if you don't believe me check WolframAlpha and compute it).
So the sum converges at 0, and not ∞. Why? Because you claimed that you're dividing a number P an infinite number of times, which means that although you might have a few values over 1 (i.e. x>y when you calculate x/y), most of them will be smaller than 1 (i.e. x<y when you calculate x/y).


This is a really ghetto solution because if I would've done it purely mathematical I was worried maybe you wouldn't get it.

The series that I used (1+1/2+1/3+1/4+...+1/∞) is called a Harmonic Series (http://en.wikipedia.org/wiki/Harmonic_series_%28mathematics%29#Divergence)

[silenthunder]

This guy, what is he? O.o that was beautiful Mordred.

[syk0b4bbl3]

This ever smaller theorem is what I have used to prove, at least in theory, that movement is not possible.

To get from point A to point B, you must first go through the midpoint at point C: A--C--B
But to get from point A to point C, you must first go through the midpoint at point D: A--D--C

and so on.

The are an infinite number of midpoint's that must be crossed in order to make forward movement, but for every midpoint there is an another one standing in the way, hence, movement isn't possible.

WE'RE ALL LIVING IN A DREAM!

[Deque]

Obviously people have a hard time understanding the concept of limits.
You are refering to "Achilles and the tortoise", syk0b4bbl3.

[Mordred]

Obviously people have a hard time understanding the concept of limits.
You are refering to "Achilles and the tortoise", syk0b4bbl3.

Heh, limits sucked when I first learned them also. But after the millionth limit that you have to work on 30 minutes just to get it to a shape where it's not an illegality (i.e. 0/0) you kinda get the hand of it 

Yeah it's basically the same thing, only the explanation is a bit different. In "Achilles and the tortoise" the logical fallacy is the assumption that both Achilles and the turtle have the same frame of reference, which they don't.

In syk0b4bbl3's story actually you need the same stuff from the OP's question. It's a matter of dividing an infinite number of times and the same counter-proof that I wrote a few posts up applies.

[EMOKDOOM]

0**-1 = 1

BOOYAH!!!