Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Matheology § 200
Replies: 40   Last Post: Jan 29, 2013 7:33 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 200
Posted: Jan 26, 2013 5:24 PM

In article
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.-

> >
> > > 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

Then those "numbers of digits" cannot be cardinal numbers, but real
numbers.

> 4) The number of digits of the limit in analysis: oo

Then those "numbers of digits" cannot be cardinal numbers, but real
numbers.
>
> There is only one non-sensical result.

WM manages always to find lots of non-sensical results, but they are
only to be found in Wolkenmuekenheim.
--