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>> >>"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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