Date: Jan 31, 2013 4:23 AM Author: mueckenh@rz.fh-augsburg.de Subject: Re: Matheology § 203 On 31 Jan., 10:04, William Hughes <wpihug...@gmail.com> wrote:

> 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

>

Yes.

Regards, WM