Date: Jan 26, 2013 4:40 PM Author: mueckenh@rz.fh-augsburg.de 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.

Regards, WM