Date: Mar 9, 2013 7:37 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<dd451c73-da29-4427-a669-ad023508e968@c10g2000vbt.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 9 Mrz., 21:42, Virgil <vir...@ligriv.com> wrote:
>

> > > Consider a Cantor-list with entries a_n and anti-diagonal d:
> >
> > > For every n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).
> > > For every n: (a_n1, a_n2, ..., a_nn) is terminating.
> > > For every n: (d_1, d_2, ..., d_n) is terminating.

> >
> > > For all n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).
> > > For all n: (a_n1, a_n2, ..., a_nn) is terminating.
> > > For all n: (d_1, d_2, ..., d_n) is *not* terminating.

> >
> > That last line could  only be true in weird places like
> > Wolkenmuekenheim, since outside Wolkenmuekenheim it can only read
> > For all n: the finite sequence (d_1, d_2, ..., d_n) terminates with d_n.

>
> Correct. But matheologians build d from the infinite set of all FISs
> and forget that every natural number closes a finite initial sequence
> of natural numbers.




The set d (and its more normal representation, |N) are built on the
basis that every natural number is required to have a successor in order
to be a natural number at all, so whatever things WM is working with
which do not all have to have successors, any set of them must contain
something which is not a natural number.

See http://en.wikipedia.org/wiki/Peano_axioms#The_axioms



And where is WM's proof that some mapping from the set of all binary
sequences to the set of all paths of a CIBT is a linear mapping?
WM several times claimed it but cannot seem to prove it.
--