Date: Jan 26, 2013 7:54 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 200
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