Re: Cantor's diagonal proof wrong?

From: Dave Seaman (dseaman_at_no.such.host)
Date: 11/14/04 

Date: Sun, 14 Nov 2004 21:44:00 +0000 (UTC)

On 14 Nov 2004 18:42:13 GMT, 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.

It's been pointed out already that the flaw in your "proof" is at the
point where you claim ...11111 is an "integer."

A "table", in the context of this proof, is a mapping defined on the
natural numbers. The identity map, given by f(n) = n, obviously covers
all of the naturals, meaning the range of f contains all the naturals.

What Cantor proved is that for any f: N -> R, there exists x in R such
that x is not in the range of f. 

-- 
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>

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