Date: Jan 29, 2013 3:28 PM
Author: William Hughes
Subject: Re: Matheology § 203
On Jan 29, 3:35 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 29 Jan., 14:27, William Hughes <wpihug...@gmail.com> wrote:

>

>

>

>

>

>

>

>

>

> > On Jan 29, 12:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > > On 29 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote:

>

> > > > To summarize

>

> > > > For every natural number, n, the antidiagonal,d, of a list L

> > > > is not equal to the nth line of L

>

> > > > A statement WM has made.

>

> > > > A) For every natural number n, P(n) is true.

> > > > implies

> > > > B) There does not exist a natural number n such that P(n) is

> > > > false.

>

> > > > A statement WM has made.

>

> > > > There does not exist a natural number n such that d is

> > > > equal to the nth line of L

>

> > > > A statement WM disputes

>

> > > I do not dispute this statement (as I erroneously had said yesterday,

> > > when being in a hurry). I dispute that this statement implies the

> > > statement:

> > > d is not in one of all lines of the infinite list L

>

> > It does, however, imply that d is not

> > of the the lines of the infinite list L.

>

> Here we have again the ambivalence required for set theory. No, your

> statement is incorrect if "infinite" is used in the sense of completed

> or actual,

It is not. No concept of "completed" is needed or used.

It does, however, imply that d in not one

of the lines of the list L

This is turn implies.

There is no list of binary sequences, L, with

the property that give any binary sequence, s,

s is one of the lines of L.

So we can divide collections into two groups.

Those, like the collection of all rational

numbers, that can be listed, and those

like the real number that cannot.