```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 bebased 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 usedalternating sequences 010101... (moving from left to right, - so yournext example is completetly off topic). Analysis gives a result. Settheory gives another result which is incompatible with analysis.Regards, WM
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