Date: Feb 7, 2013 2:17 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 7 Feb., 20:12, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 7, 8:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > On 7 Feb., 19:46, William Hughes <wpihug...@gmail.com> wrote:
>
> > > Gosh, you are really running away
> > > from the fact that induction can
> > > show d is not in the list.
>
> > Induction can show that *your* d does not exist.
>
> My d?  You are the one who defined d to be
> the antidiagonal of the list.

The antidiagonal of a list is not always in the list, but the diagonal
of the list

1
11
111
...

is with certainty in this very list - since it is nothing else but a
potentially infinite sequence of 1' and not longer than the lines.


>  You also
> show by induction that the antidiagonal of
> a list is not in the list.

No, that depends on the list.

The antidiagonal of the list

0.0
0.1
0.11
0.111
...
when changing 0 to 1 is in the list, when changing 0 to 2 it is not.

Regards, WM