Date: Jan 30, 2013 5:06 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203
On 30 Jan., 10:52, William Hughes <wpihug...@gmail.com> wrote:

> On Jan 30, 10:46 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>

>

>

>

>

> > On 30 Jan., 10:31, William Hughes <wpihug...@gmail.com> wrote:

>

> > > For a potentially infinite list L, the

> > > antidiagonal of L is not a line of L.

>

> > Of course. Every subset L_1 to L_n can be proved to not contain the

> > anti-diagonal

>

> > > Does this imply

>

> > > There is no potentially infinite list

> > > of 0/1 sequences, L, with the property that

> > > any 0/1 sequence, s, is one of the lines

> > > of L.

>

> > Do you mean potentially infinite sequences?

>

> yes-

A potentially infinite sequence has *not* more elements than every

natural number. There are only, if we may apply this terminus,

countably many such sequences. A list of them can be complete (in set

theory, not in reality). If a complete list of them yields a digonal

that is not in the list, then the self contradictory character of the

diagonal argument is obvious.

Regards, WM