"Zeit Geist" <firstname.lastname@example.org> wrote in message news:email@example.com... > On Saturday, July 13, 2013 7:40:24 AM UTC-7, Julio Di Egidio wrote: >> "Zeit Geist" <firstname.lastname@example.org> wrote in message >> news:email@example.com... >> > On Friday, July 12, 2013 1:41:31 PM UTC-7, muec...@rz.fh-augsburg.de >> > wrote: >> >> On Friday, 12 July 2013 19:13:19 UTC+2, Zeit Geist wrote: >> >> >> > It is rather silly to expect the process that creates each of the >> >> > Naturals would produce the set of all Naturals, as that set is, >> >> > itself, not a Natural. >> >> >> Each natural belongs to a finite initial segment. None of them >> >> requires a number that is larger than every natural number. In >> >> fact the contrary. If you do not talk about the set, then there is >> >> no reason to talk about alephs. >> >> > Yes, but for every Natural there is a larger natural, hence the number >> > of Naturals is larger than any Natural. >> >> Since the number of natural numbers is not itself a natural number, that >> is >> a non-sequitur, despite standardly the conclusive statement is correct: >> indeed, a fallacy of relevance. Plus, the standard here is in question, >> so >> one should rather qualify statements as well as objections (not that WM >> ever >> does it, of course). > > The are numbers that are not Natural Numbers. > The number of Naturals Numbers is a number, > and it greater than any finite number, that is to say, > It is greater than any Natural Number. > > Here, number means Cardinality, of course. > > In most Mathematical circles the standard is ZF(C). > Yes, standard Set Theory is being questioned here. > And most who question it here have not come up with > a good reason to reject. Nor have they come up with > a suitable replacement.
You still have this idea of the standard vs. the cranks, but the one with no arguments, the non-sequiturs and, in fact, no clue (e.g. as to the standard and the non-standard), here is still you.