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Re: Matheology § 162
Posted:
Nov 27, 2012 1:11 PM
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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
Regards, WM
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