Date: Jan 30, 2013 4:24 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203
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.

Regards, WM