This might seem simplistic experiment, but I believe it proves infinity of space cannot exist.

x% of infinity is infinity. eg, 5% of infinity is infinity.
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Now think about it, the room you occupy now, your computer, living or bedroom is a percentage of overall space. The space of your computer room is a constiuent of infinity and thus it can be expressed as a percentage of infinity.

Thus, If the space of your room is a percentage of infinite space, then the room itself must have infinite space. Does it?

What is zero percent of infinity?

Right, at best you can prove that any fixed space is 0% of the infinite total space, or more broadly that percentages don't work normally when talking about infinite quantities.

As an aside, I think most current cosmologies postulate that the universe currently occupies only a finite space-only that the limit of the expanding universe is infinite. I could be wrong about this however, but at any rate the argument here doesn't prove that space isn't infinite.

Forgive my ignorance, but I calculate 0% of infinity to be 0 (or nothing).

I suppose it makes sense, if anything measured must be zero percent, then any fixed measure can be expressed as 0 percent, and this makes sense when you compare something finite to something infinite. as something finite must be 0 percent of infintie.

zero% = anything less than infinity.

Consider x* (1/x) which we know equals one. Well now imagine x getting larger an larger. x tends to infinity and 1/x tends to 0. So "in the limit" we have infinity multiplied to zero. Yet it equals 1.

It turns out that it can be anything, depending on how you calculate it. I can make something that looks like 0 * infinity = 17. (See uke's comment.)

Infinity is not an object to be trifled with carelessly. And what you say about it mathematically has no direct bearing on anything about the actual physical universe.

There are two basic types of infinity: actual and potential.

Those that believe in actual infinity say that the set of all natural numbers {0, 1, 2, ..} exists.

Those that don't believe in actual infinity regard the natural numbers as a non-terminating process 0, 1, 2, .. called counting. This process never actually generates the set of all natural numbers, although every natural number does at some point get counted.

Nobody can prove that the set of all natural numbers exists and so its existence has to be affirmed as an axiom, called the axiom of infinity.

http://en.wikipedia.org/wiki/Actual_infinity
http://en.wikipedia.org/wiki/Axiom_of_infinity

percentages are measurable ratios; and as such are only applicable to finite concepts; as a measurable ratio of infinity is an illogical concept.

I think that's where the problem is, you can't take a percentage of infinity, because a percentage implies a finite state

This.

A great read on infinity: http://www.amazon.com/Everything-Mor...506796&sr=8-15

It's a great introduction but also very enjoyable for all of you math wiz's out there. The dude is a phenomenal writer and pretty much tells the story of infinity in a more entertaining and literary way than some of the best works of fiction out there.

The only problem with this is it's equally true for any number A, x*(A/x) = A. As x goes to zero, we have zero times infinity. Yet it equals A. That's why we say division by zero in undefined, not that it's infinity. I think this is Aaron W.'s point as well.

Here is a case in which it makes a difference, solve the equation A*x = x. If you divide both sides by x, you get A = 1, which is indeed one solution. But it appears to be the only solution. In fact, x = 0 is another solution. That's why you can't divide by zero, not because the result in infinity, but because you lose solutions. There are alternative ways to define arithmetic in which you can divide by zero.

Where this gets interesting is when you can define how a numerator and denominator approach zero. For example, suppose you have (e^x - 1)/x. As x approaches zero, both numerator and denominator approach zero, but the ratio approaches 1.