Date: Nov 27, 2012 1:21 PM
Author: William Hughes
Subject: Re: Matheology § 162

On Nov 27, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 27 Nov., 18:42, William Hughes <wpihug...@gmail.com> wrote:
>

> > On Nov 27, 4:37 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > <snip>
>
> > > According to set theory the limit set is empty.
>
> > Indeed.
>
> Nice to hear that.
>

> >  And the proof of this does not depend
> > on "actual infinity".

>
> Of course it does, because every digits moves to the right side.


Stick with

1
10
100
....

The 1 moves to the left.

We do not have to check the positions one by one.
It is easy to show by induction (which requires only
potential infinity) that for each n in |N
the nth position is not occupied. This is equivalent to
saying that the set of all possible occupied positions is empty.