Virgil
Posts:
4,655
Registered:
1/6/11
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Re: Matheology � 200
Posted:
Jan 26, 2013 5:32 PM
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In article
<d9cbdc08-778c-4b2a-8c8a-3b0592bf0d48@u7g2000yqg.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> 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.-
>
> Aside: Of course this nonsense shows already that set theory is such.
> A limit is the continuation of the finite into the infinite. But that
> is not used in my proof.
I know of no such definition of any limit process.
> >
> > > Obviously you have not yet understood?
Why bother to understand nonsense?
> > > In my proof the cardinality of the limit in set theory and the
> > > cardinality of the limit in analysis are different.
Your proof, as usual, is only valid in your own private world of
Wolkenmuekenheim
> >
> > 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.-
>
> You are not well informed. Read my proof again (and again, if
> necessary, until you will have understood, if possible): In analysis
> you calculate the limit. This limit contains numbers or (in the
> reduced case of my proof) bits 0 and 1. The number of theses bits is
> the cardinality of the limit.
Then, according to WM, lim_(n -> oo) 1/n must have infinitely many bits.
> In set theory it is similar. The number of bits in the limit set is
> the cardinality of the limit set. And that is oo in analysis and it is
> empty in set theory.
Only in Wolkenmuekenheim.
>
> Regards, WM
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