Date: Feb 1, 2013 10:48 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 1 Feb., 16:35, William Hughes <wpihug...@gmail.com> wrote:
> Let P(n) be
>  0.111...  is not the nth line
>  of
>
>  0.1000...
>  0.11000...
>  0.111000...
>  ...
>
> Clearly for every natural number n
> P(n) is true.
>
> This means there is no natural
> number m for which P(m) is true.
>
> It is not simply that we cannot find m,
> we know that m does not exist.


More. We know that P(n) = 0.111... = 1/0 does not exist as an
actually infinite sequence of 1's. Only finite initial segements exist
in potential infinity.

Compare the Binary Tree. There is no path for 1/9 that could be
distinguished from all its approximations.

Regards, WM

Regards WM