Re: Cantor's diagonal proof wrong?

mueckenh_at_rz.fh-augsburg.de
Date: 12/19/04 

Date: 19 Dec 2004 01:29:17 -0800

Shmuel (Seymour J.) Metz wrote:
> In <1103206218.096524.51760@f14g2000cwb.googlegroups.com>, on
> 12/16/2004
> at 06:10 AM, mueckenh@rz.fh-augsburg.de said:
>
> >Hence the set of natural numbers cannot be actually infinite.
>
> Non sequitor.
>
> >You see it best, if you imagine Card{1,2,3,...,n} as a function f(n)
> >of n.
>
> You'd have to be hallucinating to see it that way.

You could even prove it by using set theory. In the finite realm,
ordinal number n is equal to cardinal number n of the sequence
1,2,3,...n. If we have a set of finite numbers only, then all the
ordinal numbers are finite, hence giving finite cardinal numbers. There
is no chance to form an infinite set with finite numbers. It is so easy
to see, but Cantor has spoiled many brains.
>
> >(and there are no others)
>
> That depends on what "is" is. It has no relevance to Mathematics,
> which does not depend on your philosophy.

There are no infinite natural numbers in all mathematics. You'd need no
philosophy to see that.

Regards, WM
>
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