Virgil
Posts:
4,486
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Jan 30, 2013 8:15 PM
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In article
<8cb79e99-7c3a-4b4f-a835-312ac06e0ba2@h2g2000yqa.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 30 Jan., 22:14, William Hughes <wpihug...@gmail.com> wrote:
> > On Jan 30, 6:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >
> > > On 30 Jan., 12:32, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Jan 30, 12:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > On 30 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > > > Summary. We have agreed that
> >
> > > > > > For a potentially infinite list L, the
> > > > > > antidiagonal of L is not a line of L.
> >
> > > > Do you agree with the statement
> >
> > > > For a potentially infinite list, L,
> > > > of potentially infinite 0/1 sequences
> > > > the antidiagonal of L is not a line
> > > > of L
> >
> > > Yes, of course. We have a collection of which we can keep a general
> > > overview. And in finite sets (potential infinity is nothing but finity
> > > without an upper threshold) "for every" means the same as "for all".
> > > There is no place to hide.
> >
> > So now we have
> >
> > For a potentially infinite list, L,
> > of potentially infinite 0/1 sequences
> > the antidiagonal of L is not a line
> > of L
> >
> > Can a potentially infinite list, L,
> > of potentially infinite 0/1 sequences
> > have the property that every
> > potentially infinite 0/1 sequence
> > is a line of L?
>
> Potential infinity is the opposite of completeness like "infinite" is
> the opposite of "finished". So *every* line number n would not imply
> *all* possible line numbers of the set |N defined by AxInf.
>
Thus in WM's world of WMytheology what holds for every member of a set
need not hold for all members of that set,
or is it the what holds for all members need not hold for every member,
or is it both?
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