```Date: Jan 14, 2013 1:40 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Finitely definable reals.

On 14 Jan., 14:23, forbisga...@gmail.com wrote:> On Saturday, January 12, 2013 12:24:46 AM UTC-8, WM wrote:> > On 12 Jan., 02:14, Virgil <vir...@ligriv.com> wrote:>> > > > Cantor managed to prove that there are more than countably many finite>> > > > binary strings possible. Remember, the part behind a_nn of a_n is not>> > > > relevant for his proof.>> > > Quite so, but that in no way weakens his proof.>> > It shows a self-contradiction by the fact that there must be an>> > antidiagonal that from every entry differs at a finite place. But if>> > the list is complete with respect to all finite binary strings, this>> > is obviously impossible.>> > Regards, WM>> I've been thinking about this assertion of your and beg to differ.> The decimal expansion of 1/3 only differs from all other reals at> the infinite.What do you understand by this statement?>  It takes the infinite to make it 1/3.  When one multiplies> a number by 10 one moves the decimal place one position to the right.> Only the infinite decimal expansion will do to restore the fraction.> Any finite expansion will have a delta from 1/3.In my opinion everything that in mathematics can be used to express1/3 as a decimal fraction is "all its finite digits". That means, onlyin the infinite we obtain 1/3, but a better phrase describing "theinfinite" is simply "never". We will never obtain 1/3 as a decimal.Alas, if Cantor was right, we must assume that "never" is a certainpoint in time that can be reached and surpassed. Therefore Cantor wasvery happy when he read in the Holy Bible "Dominus regnabit in eternam*et ultra*" (emphasis by Cantor).Regards, WM
```