Re: infinitely many nn's = infinite nn's?

On Mon, 05 Mar 2007 18:01:20 GMT, Phil <toob-headman@xxxxxxxxxxxxx> wrote:


I don't suppose you could come up with a logical train of thought that
shows why we CAN mix-and-match potential and actual infinity?

Well, actually Cantor wrote something about that question!

His argument in a nutshell: The notion of potential infinity only makes
sense on the "basis" of [the notion of] actual infinity. (But even if he's
wrong concerning this question, clearly the acceptance of "actual infinity"
allows for arguments referring to "potential infinity". The problem is just
the other way round. :-)


Remember, so I don't waste YOUR time, I have no disagreement with either
the argument proving infinitely many numbers, nor the argument proving
they are all finite. It's the combination that I think violates the rules
of mathematics,

It doesn't. There are infinitely many natural numbers, but each and any is
finite.

I'll agree that this MIGHT _sound_ strange. Maybe the following formulation
is easier to digest:

Each and any natural number is finite.

But the set of _all_ natural numbers is not bound.
(I.e. it does not have an upper boundary.) With other
words, there is no biggest natural number. (I guess
that's immediately clear, no? If W would be this number,
W+1 would be another natural number, but bigger. Which
is an aburdity.)


F.

--

E-mail: info<at>simple-line<dot>de
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