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