Date: Nov 22, 2012 11:06 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 154: Consistency Proof!

On 22 Nov., 16:27, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 22, 3:30 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> > Can we estimate by means of set theory how many digits *left* to the
> > decimal point will be present in the limit (as calculated by
> > analytical means) of the real sequence

>
> > > > 01.
> > > > 0.1
> > > > 010.1
> > > > 01.01
> > > > 0101.01
> > > > 010.101
> > > > 01010.101
> > > > 0101.0101
> > > > ...

>
> > ?

> Yes, The set of digits left of the decimal point is the
> empty set.


This is in contradiction to analysis (although analysis is said to be
based upon set theory). Just my point.

>  Simplest argument.  Start with
>
> 100.000...
> 10.000...
> 1.000...
> 0.1000...
> 0.01000...
> ...
>
> The 1 does not exist in the limit.  This 1 corresponds to
> the digit with index 5.  We conclude that for
> each index the digit corresponding to the digit does
> not exist in the limit.  Thus the set of digits in the limit
> is the empty set.  Thus, in the limit, the set of digits to
> the left of the decimal point is the empty set.


What has this problem to do with my question? I explicitly used
alternating sequences 010101... (moving from left to right, - so your
next example is completetly off topic). Analysis gives a result. Set
theory gives another result which is incompatible with analysis.

Regards, WM