Re: Cantor's diagonal proof wrong?

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 11/28/04 

Date: Sun, 28 Nov 2004 18:20:58 -0500

In <fb701d3c.0411271334.cca9c93@posting.google.com>, on 11/27/2004
   at 01:34 PM, mueckenh@rz.fh-augsburg.de (W. Mueckenheim) said:

>What does distinguish the "limit" from the diagonal?

What distinguishes a banana from a townhouse? They're not remotely
similar.

The diagonal is a sequence of digits, not a number. In the case of the
Cantor diagonal argument you're referring to, you take the sequence of
digits as coefficients in a series and it is trivial to prove that the
series converges.

>Do we need different words here?

We need words that are applicable, and we need to ensure that we have
a common understanding of what they refer to. In particular, the term
limit has a precise meaning.

>However, how, then, can Cantor change all the digits of this
>"limit"?

He doesn't "change" anything. He defines a new number in terms of a
sequence of representations of numbers.

>And why can't we consider my proof in the limit?

What proof?

>So don't stop, but consider the limit of my proof.

What limit? 

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Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
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