```Date: Nov 22, 2012 1:22 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 154: Consistency Proof!

On 22 Nov., 17:16, William Hughes <wpihug...@gmail.com> wrote:> On Nov 22, 12:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>>> > 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?>> It answers it.>> <I explicitly used>> > alternating sequences 010101...>> And I deal with the simpler case firstNo, yours is a much more difficult case. That's why I conceived thesimplest case.Regards, WM
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