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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 200
Posted: Jan 28, 2013 3:33 PM

On 28 Jan., 20:32, Virgil <vir...@ligriv.com> wrote:
> In article
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 27 Jan., 23:25, Virgil <vir...@ligriv.com> wrote:
> > > In article
>
> > > > The cardinality of the indexes of this limit in
> > > > analysis is aleph_0.

>
> > > > The sequence of cardinalities is 2, 1, 3, 2, 4, 3, ... The limit of
> > > > this sequence is aleph_0 too.

>
> > > > > The limit you calculate is not a limit set, nor the
> > > > > cardinality of a limit set.

>
> > > > Analysis shows that the cardinality of the digits is 1 + logn. This
> > > > does not break down for n = oo.

>
> > > Since we are talking about a sequence of sets, not a sequence of
> > > numbers. "1+log(n)" is irrelevant.

>
> > I am talking about a sequence of sets, namely the indexed digits of
> > numbers, and their cardinality is 1 + log(n).

>
> The indexed digits of numbers are not sets, unless you are using
> something like the von Neumann naturals in which naturals are themselves
> sets.

Have you some other advice what, in your opinion, are not sets? Look,
Cantor took the seven colours of the rainbow and the seven tones of
the octave as examples of sets*). Why should indexed digits have to
stay outside of set theory?

*) Look here
http://www.hs-augsburg.de/~mueckenh/KB/KB%20801-1000.pdf
number 831. I have not had the time to translate this amusing
Kalenderblatt. And it would lose much of its humour unless it was
translated by an eloquent native speaker.

Regards, WM