Date: Jan 13, 2013 4:33 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 191
On 13 Jan., 21:19, Virgil <vir...@ligriv.com> wrote:

> > A listing of all finite initial segments of all possible tails is

> > possible.

> > Cantor's diagonal argument leads to an anti-diagonal that differs from

> > every finite initial segment by a finite initial segment which is a

> > self-contradiction since all possible finite initial segments that

> > possibly could differ are already there.

>

> Any non-finite sequence, such as an anti-diagonal, NECESSARILY differs

> from every finite sequence

at a finite place, i.e., within a finite initial segment of the anti-

diagonal. (Elsewhere it is impossible to fix a digit which could

differ.) Therefore, if the list contains all possible finite initial

segments, then the anti-diagonal necessarily differs and necessarily

cannot differ from all entries of the list.

How long have you needed to understand the former when you were young?

Have you meanwhile grown too senile to understand the latter, which is

as easy to comprehend?

Regards, WM