In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 10 Dez., 18:31, Shmuel (Seymour J.) Metz > <spamt...@library.lspace.org.invalid> wrote: > > In <virgil-F01676.16024408122...@BIGNEWS.USENETMONSTER.COM>, on > > 12/08/2012 > > at 04:02 PM, Virgil <vir...@ligriv.com> said: > > > > >In article > > ><47934f05-f8e1-4687-b590-af47fc4be...@8g2000yqp.googlegroups.com>, > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > >> On the contrary, ZFC is a deeply unlogical theory. It requires > > >>the belief that uncountably many elements can be distinguished > > >>whereas everybody knows that this is impossible even in ideal > > >>mathematics. > > > > That's one of the dumbest claims that I've ever read. Don't confuse > > your delusions with what everybody believes. > > I am not interested in everybody's beliefs but in mathematics. That is > completely free of beliefs - apart from some conjectures.
What you are interested in is imposing your prejudices on the whole of mathematics, instead of only on those poor souls in your classes. > > > > >> Further in ZFC the sequence > > >> 21., 2.1, 432.1, 43.21, 6543.21, 654.321, ... > > >> has the limit < 1.
Does your sequence continue on with digits larger than 9 or does digit 0 follow digit 9 cyclicly, or does it do something entirely different at that point?
As it stands, your sequence is far too ambiguous to have any defineable or determinable limit.
> > > > No; it has no limit. > > It has an improper limit in analysis, namely oo. It has a limit in set > theory.
Unless it is redefined as a sequence of sets, which it is not in its original form, set theory says nothing about any limit for it.
> Every natural number that appears left of the decimal point > disappears right of it.
> > > > >> In analysis the very same sequence has the (improper)imit oo. > > >Right, for once! > > > > No. For the sequence to have the limit oo, both lim sup and lin inf > > would have to be oo, not just one of them. > > Please do not mistake analysis and set theory. In analysis we have the > simple criterion: If lim 1/a_n = 0, then lim a_n = oo. That is here > the case. Obviously.
Not until you explain what happens to the terms of your as yet ambiguous sequence when you need to use digits following 9. Until ,then nothing about it is obvious. --