"Albrecht" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Thursday, October 17, 2013 3:06:55 AM UTC+2, Julio Di Egidio wrote: >> "fom" <fomJUNK@nyms.net> wrote in message <snip> >> > You are correct concerning the necessity of infinity. >> >> But, is he? "Actual infinity" is logically necessary, Zeno docet. And >> quite reasonable too, just levels of abstraction. > > Oh, you are also live in the dream that Cantor has anything to do with > Zeno's paradoxa? Okay. Give me an idea in which way "actual infinity" > changes anything in that concern.
It's you who are still making confusion, infinite sets as only completed sets is one thing, the uncountability of the reals is another, and completed sets is not in fact Cantor's setting, despite overloads on terminology: Cantor didn't use an extended set of naturals as the domain of his functions. Then, whether extended sets (and non-well-founded ordinals? Oh how I wish people would also concentrate sometimes on *matters of fact*, the ones that count), change anything to the validity of Cantor's arguments is just beside the present point, although I would guess it does not, really, not just by itself.