Date: Feb 7, 2013 8:32 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 7 Feb., 10:50, William Hughes <wpihug...@gmail.com> wrote:

For esay reference:

1) For every n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).
2) For every n: (a_n1, a_n2, ..., a_nn) is terminating.
3) For every n: (d_1, d_2, ..., d_n) is terminating.

4) For all n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n).
5) For all n: (a_n1, a_n2, ..., a_nn) is terminating.
6) For all n: (d_1, d_2, ..., d_n) is terminating.

> WM uses induction to show that for every natural
> number n, d is not the nth line of the list.
> He then uses the fact that this is equivalent to
> "there does not exist an m, such that d is the mth
> line of the list".  At no time does he assume that
> "all" lines exist.-


I assume that all lines exist.
I do not agree that 4 follows from 1 and 5 follows from 2 while ~6
follows from 3.

Regards, WM