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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 7:54 AM

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 we
have:
1) The limit of the cardinals in set theory: aleph_0
2) The cardinality of the limit in set theory: 0
3) The limit of the number of digits in analysis: oo
4) The number of digits of the limit in analysis: oo

There 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