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Re: Matheology § 200
Posted:
Jan 26, 2013 6:31 AM
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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.
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