Date: Feb 7, 2013 4:20 PM
Subject: Re: Matheology � 222 Back to the roots
WM <email@example.com> 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
> 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
and none of them are in the list itself.