Date: Nov 22, 2012 11:06 AM
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
> 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.