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Topic: Matheology § 203
Replies: 202   Last Post: Feb 10, 2013 3:34 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 203
Posted: Jan 31, 2013 3:48 AM

On 30 Jan., 22:38, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 30, 10:24 pm, WM <mueck...@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.

>

The question is not properly defined.
Do you mean "every" in the potential sense of "all from 1 to n"? Or do
you mean "every" in the sense of "all" of set theory?

The latter is wrong, the former is correct.
(Note also every potentially infinite sequence only consist of finite
initial segments.)

Regards, WM

Date Subject Author
1/29/13 mueckenh@rz.fh-augsburg.de
1/29/13 William Hughes
1/29/13 mueckenh@rz.fh-augsburg.de
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