Date: Mar 21, 2013 3:46 AM
Subject: Re: Matheology § 224

On 21 Mrz., 08:28, William Hughes <> wrote:
> On Mar 21, 7:54 am, WM <> 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