Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 200
Posted:
Jan 29, 2013 7:33 PM


In article <e5f29877208a4b7da33760a13aaf2d23@u7g2000yqg.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 29 Jan., 00:19, Virgil <vir...@ligriv.com> wrote: > > In article > > <0c93f65aee924f8cb63dcf37933f2...@u20g2000yqo.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > > On 28 Jan., 20:32, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > > <a687f86fa7424956ad8aea1964165...@w3g2000yqj.googlegroups.com>, > > > > > > WM <mueck...@rz.fhaugsburg.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.hsaugsburg.de/~mueckenh/KB/KB%208011000.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! 

