Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 200
Posted:
Jan 26, 2013 5:38 PM
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In article
<ebcd3b95-b93a-4410-bd7c-f12ee4c05e4a@u16g2000yqb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 26 Jan., 16:08, William Hughes <wpihug...@gmail.com> wrote:
> > On Jan 26, 1:42 pm, WM <mueck...@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.
> >
> > > > > 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.-
> >
> > > 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.
> >
> > Nope. The limit is a single number. In analysis there is no
> > limit set.-
>
> Like to drop logic? Nobody can hinder you.
We have no desire to follow you down that primrose path.
> In analysis the limit is a single number, not a real though, that
> consists of infinitely many indexed digits.
Since in analysis every real number is limit and every such limit that
actually exists as a real is a real, WM is saying that every real
"consists of infinitely many indexed digits".
> In analysis the set of
> indices can be calculated.
> Even if William Hughes tries to forbid that.
In analysis, most of the time there is no point to calculating any "set
of indices", even if one knew what indices WM was referring to.
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