Date: Feb 7, 2013 4:20 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<8d610f94-e350-49b9-82c9-e2efc2a3b89e@fn10g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.


If it is not longer than all lines, then there must be a first such line
that it is not longer than.


So which is the first line that the diagonal is as short as?

No first line implies no line at all.

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


Actually, one should not speak of THE antidiagonal as there are at least
as many antidiagonals as lines in the original list.
>
> No, that depends on the list.



>
> The antidiagonal of the list


Which one? There are lots of them
>
> 0.0
> 0.1
> 0.11
> 0.111
> ...

and none of them are in the list itself.
--