Date: Jan 30, 2013 4:22 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 30 Jan., 10:05, William Hughes <wpihug...@gmail.com> wrote:
> On Jan 30, 9:57 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 30 Jan., 09:40, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Jan 30, 9:28 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 30 Jan., 00:16, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > On Jan 29, 10:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > > On 29 Jan., 21:28, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > <snip>
>
> > > > > > > It does, however, imply that d in not one
> > > > > > > of the lines of the list L

>
> > > > > > For that sake you must check all lines. Can you check what is not
> > > > > > existing?

>
> > > > > So now your claim is
>
> > > > > We can know
>
> > > > >   There does not exist a natural number n
> > > > >   such that d is equal to the nth line
> > > > >   of L

>
> > > > > but we cannot know
>
> > > > >   d is not one of the lines of L
>
> > > > You are trying hard to misunderstand!
>
> > > Do you agree
>
> > >  i. There does not exist a natural number n
> > >     such that d is equal to the nth line
> > >     of L

>
> > > and
>
> > >  ii.  d is one of the lines of L
>
> > > are mutually exclusive?-
>
> > In existing finite sets this is true. In actually infinite sets it is
> > not true,

>
> Does
>
>   ii.  d is one of the lines of L
>
> imply
>
>   iii.  there is a natural number n such that
>         d is equal to the nth line of L


In finite sets or potentially infinite sets this is true, of course.
Reason: Every line n can be checked since we can go to line n+1.

In actually infinite sets it is not true, since there must be more
lines than every number n can reach. Remember: Beyond every n there
follow more loines than can be reached by a natural number or can be
measured by a natural number or can be enumerated by natural numbers.

Regards, WM