Re: Cantor's diagonal proof wrong?

From: robert j. kolker (nowhere_at_nowhere.net)
Date: 11/21/04 

Date: Sun, 21 Nov 2004 17:45:10 -0500

Curt Welch wrote:

> Dave Seaman <dseaman@no.such.host> wrote:
>
>
>>Do you agree that |N| < |P(N)|?
>
>
> For finite sets, it's obvious that the size of N is < size of the P(N).
>
> For infinite sets, the question seems to me to be invalid to ask.
>
> It's exactly like the following word problem: If we built one machine to
> count to infinity which can count one number per second, and a second
> machine which can count at the speed 2^T numbers per second, where T is how
> long the machines have been running, which machine will finish first?

Constructability is not a requirement for theorizing about power sets.

The way you deal with infinite sets is to use a static definition. A set
is infinite if and only if there exists an injective surjection of the
the set to a proper subset of itself. We know the set of integers is
infinite because the correspondence n <-> 2*n is just such an injective
surjection of the integers onto the even integers.

Bob Kolker

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