In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 27 Nov., 18:42, William Hughes <wpihug...@gmail.com> wrote: > > On Nov 27, 4:37 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > <snip> > > > > > According to set theory the limit set is empty. > > > > Indeed. > > Nice to hear that. > > > And the proof of this does not depend > > on "actual infinity". > > Of course it does, because every digits moves to the right side. In > potential infinity of analysis, this defect is not included. There > always an infinity remains left.
If there are no actual infinities, then there can never be any left. > > > Your problem is not between > > potential and actual infinity but between > > no infinity and infinity. > > Wrong. Analysis has infinity, but not completed. However, this is not > my problem (although I put it) but the problem of set theorists.
It is no problem at all to those set theorists for whom the actuality of infinities is no problem at all. > > There was no objection to a 'potential infinity' in the form of an > unending process, but an 'actual infinity' in the form of a completed > infinite set was harder to accept. (H. Enderton, Elements of Set > Theory)
But all sorts of eminent mathematicians manage to do so. > > the set of all integers is infinite (infinitely comprehensive) in a > sense which is "actual" (proper) and not "potential". > Fraenkel, Abraham A., Levy, Azriel: "Abstract Set Theory" (1976) --