Re: Cantor's diagonal proof wrong?

From: Virgil (ITSnetNOTcom#virgil_at_COMCAST.com)
Date: 11/14/04 

Date: Sun, 14 Nov 2004 14:12:44 -0700

In article <20041114134213.860$7S@newsreader.com>,
 curt@kcwc.com (Curt Welch) wrote:

> José_Carlos_Santos <jcsantos@fc.up.pt> wrote:
> > So, when you state that there
> > is a bijection between the set of all natural numbers and *your* set of
> > real numbers, there is in fact no contradiction between you and Cantor,
> > since you are talking about different things.
>
> Ok, I see your position. I'm making assumptions that you do not accept.
> I'd need to convence you that my assumptions follow from some of your basic
> beliefs. And I don't have the power to do that right now because I don't
> understand all your basic beliefs and don't know your full langauge.
>
> But, still, I need someome to show me the error of my logic in my proof
> that the table of integers does not contain all the integers. That should
> not require us to build a common foundation about reals and integers to
> argue from. It only requires that we have a common foundation about
> integers, and the logic used in Cantor's diagonal proof. We can leave the
> definition of reals out of the argument.

The "contradiction" is that you cannot prove that *every* table of
integers is missing some integers whereas Cantor has proved that *every*
table of reals is missing some reals (in fact missing more than are
actually tabulated).

Relevant Pages

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