Re: Cantor's diagonal proof wrong?

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 12/01/04 

Date: Wed, 01 Dec 2004 00:06:01 -0500

In <fb701d3c.0411300738.6336bb2c@posting.google.com>, on 11/30/2004
   at 07:38 AM, mueckenh@rz.fh-augsburg.de (W. Mueckenheim) said:

>It is not a matter of order type, but a matter of finity.

Your "at least one line enumerated by omega or infinity" would seem to
rule out finitude. Adding a terminal element to an infinite ordered
set creates an ordered set with a different order type.

>It is not a matter of order type, but a matter of finity. Each n is
>finite. Each line-number of Cantors list is finite. Otherwise we
>could not find and change the diagonal element a_nn.

The list, however, is infinite.

>As long as we are capable of doing so, the number of exchanged
> digits is finite.

The Cantor proof is not a construction or process. There is no
sequencing or temporality in it. It uses a purely functional
definition of the antidiagonal number in terms of the numbers on the
list.

>The infinite set of finite numbers is a contradicito in adjecto.

No. There is no contradiction, because there are an infinit number of
finite numbers.

>Yes = No to No.

If there is a contradiction in "finished infinity" then produce it
with a logical argument rather than handwaving. 

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