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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 200
Posted: Jan 26, 2013 6:52 AM

On 26 Jan., 12:31, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 26, 9:24 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
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> > 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. Therefore analysis
cannot result from set theory.

Regards, WM