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Topic: Matheology § 200
Replies: 40   Last Post: Jan 29, 2013 7:33 PM

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 William Hughes Posts: 2,330 Registered: 12/7/10
Re: Matheology § 200
Posted: Jan 26, 2013 7:06 AM

On Jan 26, 12:52 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 26 Jan., 12:31, William Hughes <wpihug...@gmail.com> wrote:
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> > On Jan 26, 9:24 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > Matheology § 200
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> > > 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, ...

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> > > 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."

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> > > This result is counter-intuitive,
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> > 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.-

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> 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.