Date: Jan 31, 2013 4:04 AM
Author: William Hughes
Subject: Re: Matheology § 203

On Jan 31, 9:48 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> 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.

>
> > This does not answer the question.  Please answer the question.-
>
> 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.)
>


Let L be the potentially infinite
list of natural numbers

1
2
3
...

Does L have the property that
every (in the sense of "all from 1 to n")
natural number is a line of L
?