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.
> 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.
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)
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)
Until then, no one envisioned the possibility that infinities come in different sizes, and moreover, mathematicians had no use for ?actual infinity.? The arguments using infinity, including the Differential Calculus of Newton and Leibniz, do not require the use of infinite sets, Thomas Jech, Set Theory Stanford.htm, Stanford Encyclopedia of Philosophy