Date: Mar 16, 2013 8:16 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 16 Mrz., 12:26, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 16, 10:30 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 15 Mrz., 23:27, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Mar 15, 8:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > Let's first prove that already two cannot be necessary by the fact
> > > > that two always can be replaced by one of them without changing the
> > > > contents.

>
> > > This is true but the fact that the two lines are
> > > necessary has nothing to do with their contents.  Two lines
> > > cannot be replaced by one of them without changing the number
> > > of lines.

>
> > Why should line-numbers be changed? Perhaps we are misunderstanding
> > each other.

>
> I said "number of lines" not "line-numbers".
> If you replace two lines by one of them, you do
> not change the contents, but you do change the number
> of lines.  Since the number of lines is important
> and the contents are not, you cannot replace
> two lines with one line.


Ok, I understand. Anyhow, if the number of lines is not empty, then
there must remain at least one line as a necessary line. That line has
a line-number in the original list. I think that if one more more
lines are necessary, as you claim, then there must be a set of line-
numbers which is not empty and, therefore, has a least element.

Do you think that this is unmathematical?

Regards, WM