Date: Feb 1, 2013 10:48 AM
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
> 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.