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