Date: Mar 23, 2013 12:05 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 23 Mrz., 01:08, Virgil <vir...@ligriv.com> wrote:
> In article
> <cab606ea-29e6-48ae-97c1-56cd1fd39...@f5g2000yqp.googlegroups.com>,
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 22 Mrz., 16:24, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > And what is in your opinion beyond any finite set of lines?
>
> > > There is no such thing
> > > as "beyond every finite set of lines".
> > > Infinite sets are different from finite sets
> > > but they do not contain anything
> > > "beyond any finite set".

>
> > The decimal expansion of pi is not beyond any finite (i.e. rational)
> > approximation?

>
> Since the decimal expansion of p is made up of digits in sequence, WM
> needs to tell us which is the first of its digits tot exceeds finite
> approximation?
> --


If there is not more then all finite approximations, then there is no
uncountability, because all rational approximations belong to a
countable set.

Same holds for the FISONs of |N. Without a set that has more than
every finite number of naturals, there is no uncountable power set of
naturals.

Regards, WM