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Subject: Nods head

Author:
Damoclese

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Date Posted: 09/11/04 10:45pm
In reply to: Duane 's message, "Yes - I agree" on 09/11/04 2:27am

>
>"approaching" infinity is impossible - infinity "is."
>The whole idea of "getting to" infinity by subsequent
>addition is doomed to fail (you can always add one
>more).

I meant more like "creeping up towards infinity" like a limit. Newton's ideas come in handy for cheating around infinity.

>
>This is intuitively true. And I don't disagree with
>you. However, this paradox is a product of the axioms
>of Cantor set theory.

Yes, but Cantor set theory places itself at odds with the rest of mathematics. Two things behaving as a limit aren't really ever an infinity.

>
>
>Actually, I have to disagree with you on this point.
>When talking about mathematics, we use the phrase,
>"goes to infinity."

That's basically what I meant. I was trying to describe what a function does as it continues to run. Really, it's only the values of the function that matter at any point, and those values remain put for as long as you want to show it.

>
>"Unfortunately", that's a byproduct of our
>reality-based minds. (insert sarcasm here) Things
>don't "go to" infinity - they are infinite, or they
>are not.

Well, that's true, but then you get into a sticky situations with motion and everything else. Have you traveled one mile? Not really according to calculus. You converge on a mile.

>
>
>The fallacy is that a light microscope is only a tool
>to see things we normally couldn't. Atoms exist.
>We've seen them using "particle" microscopes (I say
>"particle microscopes" meaning particle accelerators,
>which are a type of microscope). Just because a
>limited tool cannot be used to elucidate everything
>does not mean that those things don't exist.

That's a good analogy. I've also read some of the history concerning Cantor and magnitudes of infinity, and your version seems to jibe with everything else I've read.

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