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. > > >> Further in ZFC the sequence > >> 21., 2.1, 432.1, 43.21, 6543.21, 654.321, ... > >> has the limit < 1. > > No; it has no limit.
It has an improper limit in analysis, namely oo. It has a limit in set theory. 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.
Or do you need a proof? Take any epsilon = 1/k > 0. Then for all j > k: |1/a_j - 0| < epsilon.