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