Date: Feb 1, 2013 10:12 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 1 Feb., 13:50, William Hughes <wpihug...@gmail.com> wrote:
> Let a potentially infinite list, L,
> of potentially infinite 0/1 sequences
> have the property that every
> (in the sense of "all from 1 to n")
> potentially infinite 0/1 sequence
> is a line of L


Let us take an example to visualize your ideas:

1) 0.000...
2) 0.1000...
3) 0.11000...
...
n) 0.111...1000...

Here the "..." does not mean actual infinity but only for every nth
figit there is a digit at position n+1.
>
> Let s be a potentially infinite
> 0/1 sequence.


0.111...
>
> Does this imply that there is
> a natural number m, such that s
> is the mth line of L
>
> ?


In the case sketched above, every initial segment of 0.111... is in a
line of the list. And in potential infinity there is not more than
every initial segment. Nevertheless, we cannot fix a line number m
where we could find it. An infinite list has no last line although it
has no line number that is larger than every natural (and also no
number of lines that is larger than every natural number).

Regards, WM