Date: Mar 21, 2013 3:46 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 21 Mrz., 08:28, William Hughes <wpihug...@gmail.com> wrote:

> On Mar 21, 7:54 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> <snip>

>

> > If no line is necessary, then there is no necessary line.

>

> Correct, but the fact that you need to choose a line

> does not mean that you need to choose a necessary line.

> You can choose an unnecessary line.

Why should I do so? And what would it help.

>

> <snip>

>

> > Every not necessary line can be removed.

>

> by definition.

>

> > Why do you think there should remain unnecessary lines?

>

> Because you have to choose lines, and the lines

> you choose must be unnecessary lines.

It is necessary that I choose unnecessary lines?

Would it not be preferable to apply mathematics?

> > And if they are needed, which it the first

> > unnecessary line that must remain?

>

> The first line depends on which lines you choose.

My question remains: What is the subset of necessary lines?

is it the intersection of all sufficient lines?

Unless this intersection is empty, it has to have a first element.

If the intersetion is empty, then it cannot contain any line.

And this can in fact be proved: The set M of lines that are not

necessary obeys:

a) 1 is in M.

b) From n in M we can conclude that n+1 in M.

Therefore |N is a subset of M.

Any objections towards induction?

Regards, WM