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