
Re: Matheology § 200
Posted:
Jan 29, 2013 4:00 AM


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. Cantor himself did not even distinguish between element and singleton. Didn't you know that, did you? > > > > *) Look here > >http://www.hsaugsburg.de/~mueckenh/KB/KB%208011000.pdf
Anyhow, even in modern set theory the sets of indexed digits are sets.
Regards, WM

