Quote Originally Posted by rong View Post
Or another way of putting it is you're saying that

infinitelyxinfinity > Axinfinity > infinity (where A>1)

And I'm saying they're all equal.
What happens when you divide each of those terms by infinity?

If you say that it becomes infinity > A > 1, then you have proven that the greater than relationship you presented in fact correct, in which case not all infinites are equal.

If you say that you cannot assume that, then you are saying that infinity/infinity is not necessarily 1, but all equivalent values DO necessarily equal 1 when divided by each other, so then you are saying that not all infinites are equal.

Conclusion: Not all infinites are equal, regardless of your answer to the question.

Anyway, if I'm not mistaken, infinityXinfinity > Ainfinity > infinity is a false assumption. I think that 2(inf) can be "less than" just infinity (I realize I'm playing really fast and loose with the terminology from a mathematical standpoint). Infinity's too general of a term to know for sure. To use the Christian analogy, that would mean that two human Christian souls > God Himself.

I'll jump in from a more conceptual, non-mathematically, possibly flawed perspective and see if I can help. Let's imagine that we referred to all very big numbers (like anything greater 12,736) as simply "more than I can be fucked to count." So how many grains of sand are on the beach? More than I can be fucked to count, I'll tell you that much. How many USD is the US in debt? Again, more than I can be fucked to count. Are there more grains of sand on the beach than there are dollars that the US is in debt? Obviously the correct answer here is "I don't know."

Obviously if you subtract some number that is more than I can be fucked to count from the US debt, then it is more likely that this will leave more room in the debt or actually make for a surplus than it will make the debt exactly zero, because "more than I can be fucked to count" is just an entire massive class of numbers, most of which are not equivalent.

I'm sure it's not a perfect mathematical analogy, but it might be conceptually helpful to the idea of infinity. It's just anything that isn't finite; that doesn't mean that they're all some number that's just the greatest number ever wrought (in fact, it most definitely does NOT ever mean that). Some non-finite amount of something can (and most likely are) be different from another random non-finite amount of something else.