```Date: Jan 26, 2013 7:54 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 200

On 26 Jan., 13:06, William Hughes <wpihug...@gmail.com> wrote:> On Jan 26, 12:52 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>>> > On 26 Jan., 12:31, William Hughes <wpihug...@gmail.com> wrote:>> > > On Jan 26, 9:24 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > Matheology § 200>> > > > We know that the real numbers of set theory are very different from> > > > the real numbers of analysis, at least most of them, because we cannot> > > > use them. But it seems, that also the natural numbers of analysis 1,> > > > 2, 3, ... are different from the cardinal numbers 1, 2, 3, ...>> > > > This is a result of the story of Tristram Shandy, mentioned briefly in> > > > § 077 already, who, according to Fraenkel and Levy ["Abstract Set> > > > Theory" (1976), p. 30] "writes his autobiography so pedantically that> > > > the description of each day takes him a year. If he is mortal he can> > > > never terminate; but if he lived forever then no part of his biography> > > > would remain unwritten, for to each day of his life a year devoted to> > > > that day's description would correspond.">> > > > This result is counter-intuitive,>> > > Correct.   But counter-intuitive does not mean contradictory.> > > Outside of Wolkenmeukenheim, the limit of cardinalites is not> > > necessarily equal to the cardinality of the limit.->> > Obviously you have not yet understood?> > In my proof the cardinality of the limit in set theory and the> > cardinality of the limit in analysis are different.>> Nope In analysis you take the cardinalities> of a sequence of sets, i.e. take a sequence of numbers,> and calculate a limit.  However, this limit is not the> cardinality of a limit set. In anylysis you calculate> the limit of the cardinalities not the cardinality of> the limit.-In order to correct your mistake, here are the details. In my proof wehave:1) The limit of the cardinals in set theory: aleph_02) The cardinality of the limit in set theory: 03) The limit of the number of digits in analysis: oo4) The number of digits of the limit in analysis: ooThere is only one non-sensical result. But it is necessary to assume(2) in order to get the desired result Card(N) = Card(Q).Regards, WM
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