Virgil
Posts:
4,661
Registered:
1/6/11
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Re: Matheology � 162
Posted:
Nov 27, 2012 2:19 PM
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In article
<3f2ae7b1-0063-417e-9b79-e780e0ae886a@m13g2000vbd.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> 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)
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