Date: Mar 16, 2013 2:10 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 16 Mrz., 18:10, William Hughes <wpihug...@gmail.com> wrote:

> > Ok, I understand. Anyhow, if the number of lines is not empty, then
> > there must remain at least one line as a necessary line.

>
> Not a particular line.  This is similar to
> the case where any set of lines with an unfindable
> last line has at least one "necessary" findable line.
> This line has a line number in the original
> list but we can choose the  "necessary"
> findable line to have any line number we want.


No, it is always the last line. We call it unfindable or unfixable
because as soon as we have found it, it is no longer the last line.

> The fact that more than one findable line
> is "necessary" does not mean there must
> be a set of line numbers which is nonempty
> and has a least element.-


That is interesting. We have a set of natural numbers, so called line-
numbers of necessary findable lines. This fact does not mean that the
set of so called line-numbers of necessary findable lines is nonempty
and has a least element.

I understand that an empty set need not and can not have a least
element. What I not yet understand is that an empty set can house more
than zero elements, in fact more than one.

But with this premise accepted, set theory is certainly not provably
inconsistent.

Regards, WM