[iclaudius]

Some stuff I want to address:

Quote by: ZNFYRH Infinity is a concept.

In the same way that numeric value is a concept. It can be attributed to things as condition, a description of quantity, etc.

Quote by: ZNFYRH How many times does infinity go into infinity? Once. ∞ / ∞ = 1

Quote by: Yasa wrong, INF/INF is undefined.

First, "infinity" is not one number -- it's a set of numbers that cannot be quantified by finite numeric value (unlike numbers like "3" or " 7.2"). If a number is infinite, that just means it isn't finite (which means that its value is always unquantifiable, either on a huge scale or an infinitesimal one).

Second, dividing any infinite number by another infinite number does not usually yield a specific number (like 1). For example: if it's unquantifiably huge, how would you know how many times it goes into another unquantifiably huge value? The question is just not specific enough -- we have no value to weigh how many times one goes into another. It's not undefined, it just it's just too broad.

For purposes of clarification: Infinity is a term generally used in math to explain the behavior of an equation. For example: If I asked, "How far up do numbers go?" your response would probably be something like "infinite." That designation means "it goes on forever, and for the purposes of communication, we don't need to bother specifying which infinite number; we need only know that the number it goes up to is definitely not finite, only meaning that it cannot be classified by values like '3'."

Quote by: ZNFYHR How large is a segment if you divide something into an infinite number of segments? Not zero. 1 / ∞ != 0

Correct. It's an infinitely small number.

Quote by: ZNFYRH How many times does nothing go into nothing? Forever. 0 / 0 = ∞

Actually, anything divided 0 times is the singular encompassing value of everything. Not infinity, but a representation of all numeric value.

Quote by: Lullaby Thus the equation is absurd and infinity cannot be treated as a number.

Infinity must be treated as an unquantifiable number, not as a concept or a finite number. Just because you conclude that it doesn't behave like a finite number does not mean that it should be abolished from finite math entirely.

Quote by: Lullaby Chainer Is it even POSSIBLE for space and the real world to be infinite? I remember hearing some pretty good arguments against it in the other thread. (or maybe I'm just remembering my own arguments )

Of course it is. Why wouldn't it be?

Quote by: 5010 According to Infinity (Wikipedia) x/∞ = 0 (where x is a real number) but 0·∞ is indeterminate (except in some contexts). It also states that [x/∞ = 0] is not equivalent to [0·∞=x]. So is there an error in this wiki, or is there disagreement, or is it coming from a different context? And could one say x/∞ = dx? The infinite slice is infinitessimal?

Wiki states, essentially, that x/INF = 0 and x = 0 * INF are not equivalent because that would mean that all numbers are equal. Assuming both equations are correct (they are not), the assertion is true, but wiki fails to acknowledge that they aren't even remotely the same statement. Let's start with the basic beginning, and try to get the second equation from the first (and let us, for sake of debate, assume that the statement is true in the first place):

We start with x/INF = 0. Habit might tempt us to multiply both sides by INF. Let's see what happens when we do that.

x/INF * INF = 0 * INF

x * 1/INF * INF = 0 * INF

x * INF/INF = 0 * INF

What have we established? Nothing. Not only are we not guaranteed that we can even multiply by INF, we must remember that INF/INF is non-conclusive (or, by wiki's standards, undefined). Even if x/INF = 0 were true, the second statement, x = 0 * INF is entirely unlinked. They are not the same, and infinite numbers do not reflexively cancel themselves out, because we have no guarantee that they are the same. We can't divide by x because dividing anything by zero (or even anything that could potentially be zero) yields an incomprehensible mathematic operation. Therefore the first statement exists and the second one is just wrong.

But the first one is wrong, anyway. 1/INF = an infinitely small number, not 0. And for the record, 0 * INF is still 0. And number that is unquantifiably huge may not have quantifiable value, but its pain property is that the value is too large to be quantified. Therefore, it still has value, and that value times 0 is 0.


Any other questions?