Virgil
Posts:
4,655
Registered:
1/6/11
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Re: Matheology � 200
Posted:
Jan 29, 2013 7:33 PM
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In article
<e5f29877-208a-4b7d-a337-60a13aaf2d23@u7g2000yqg.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 29 Jan., 00:19, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <0c93f65a-ee92-4f8c-b63d-cf37933f2...@u20g2000yqo.googlegroups.com>,
> >
> >
> >
> >
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 28 Jan., 20:32, Virgil <vir...@ligriv.com> wrote:
> > > > In article
> > > > <a687f86f-a742-4956-ad8a-ea1964165...@w3g2000yqj.googlegroups.com>,
> >
> > > > 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?
> >
> > Actually Cantor, and everyone else, would more properly take the seven
> > colors of the rainbow as MEMBERS of a set, not as sets themselves.
>
> No, he takes one colour as one member and the seven colours as the
> set.
> >
> > Such ambiguity is a common source of many errors.
>
> No again. This distinction has become necessary to maintain matheology
> for more than 100 years.
Then what WM calls "matheoogy" is what real mathematicians call
mathematics.
> Cantor himself did not even distinguish
> between element and singleton. Didn't you know that, did you?
If so, things have improved considerably since then. Today the
distinction between being a set and being a member of that set is
carefully established and preserved in every set theory in general use.
> >
> >
> > > *) Look here
> > >http://www.hs-augsburg.de/~mueckenh/KB/KB%20801-1000.pdf
>
> Anyhow, even in modern set theory the sets of indexed digits are sets.
And the distinction between a set and one of its elements is carefully
preserved in every current generally accepted set theory despite WM's
desperate attempts to obscure the distinction!
--
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