Date: Mar 21, 2013 3:46 AM
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:
> > 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.
> > 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
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?