Date: Jan 30, 2013 8:15 PM
Author: Virgil
Subject: Re: Matheology � 203
In article

<8cb79e99-7c3a-4b4f-a835-312ac06e0ba2@h2g2000yqa.googlegroups.com>,

WM <mueckenh@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.

>

Thus in WM's world of WMytheology what holds for every member of a set

need not hold for all members of that set,

or is it the what holds for all members need not hold for every member,

or is it both?

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