Re: Cantor's "proof"

From: Dave Seaman (dseaman_at_no.such.host)
Date: 09/22/04 

Date: Wed, 22 Sep 2004 20:57:48 +0000 (UTC)

On Wed, 22 Sep 2004 21:23:27 +0300, Keckman wrote:

> We all know how Cantor proved (proofed? - sorry, not good in english) that
> real numbers can not be counted(listed).

> He supposed that they can. So that for example all numbers between 0..1
> could be listed so that they are connected to one natural number:

> 1: 0,597455716942474...
> 2: 0,474752319363838...
> 3: 0,231556132376985...
> 4: 0,629366777735563...
> .
> .

Nearly every posting to sci.math that begins like this one is based on
the same fundamental mistake.

Congratulations on breaking the pattern. Your argument is based on an
entirely different fundamental mistake.

<snip>

> This way the never ending list will contains all the decimal numbers
> between 0..1 as much as the list 1...n,n+1,... will contain all the
> natural numbers.

> So: real numbers are as much counted (listed) as are the natural numbers.

Let S be the subset of R consisting of all the numbers that are produced
by infinitely many (countably many) repetitions of the diagonal argument
according to the scheme you have described. You are correct in stating
that S is a countable set.

Is it your contention that, since S is infinite, it must therefore
contain all of R?

Why do you think that? 

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