Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 4, 2013 4:48 PM
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In article
<52da52b8-a093-4a27-8b52-8cee878dc323@r3g2000yqd.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 4 Feb., 13:19, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 4, 1:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > So we have according to WM
> >
> > 0.111...
> >
> > is not a single line of
> >
> > 0.1
> > 0.11
> > 0.111
> > ...
> >
> > and
> >
> > there is no list of every 0/1 sequence.
>
> You have to distinguish more carefully: There is nothing of such a 0/1-
> sequence that you can name and that was missing from every line of an
> appropriate list.
Ever such FIS corresponds to a member of |N, and every list of FIS's
that is not infinite has a last one, which has a successor.
So WM cannot produce a list which is complete.
>
> And there is no list of every FISON in exaxtly the same sense. Thus it
> is impossible to distinguish countability and uncountability in
> potential infinity.
But it is impossible to impose the nonsense of potential infiniteness on
ZF or most other set theories.
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