Date: Jan 30, 2013 5:06 AM
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?
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.