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Re: Matheology § 203
Posted:
Jan 30, 2013 4:24 PM
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On 30 Jan., 22:14, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 30, 6:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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>
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> > On 30 Jan., 12:32, William Hughes <wpihug...@gmail.com> wrote:
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> > > 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.
Regards, WM
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