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