Date: Jan 26, 2013 4:40 PM
Subject: Re: Matheology § 200
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.
In analysis the limit is a single number, not a real though, that
consists of infinitely many indexed digits. In analysis the set of
indices can be calculated.
Even if William Hughes tries to forbid that.