Date: Mar 21, 2013 7:51 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 21 Mrz., 11:36, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 21, 11:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 21 Mrz., 08:57, William Hughes <wpihug...@gmail.com> wrote:
>
> <snip>
>

> > > There is such a thing as a sufficient set of
> > > lines  (all sufficient sets are composed
> > > entirely of unnecessary lines, which means
> > > that you can remove any finite set of lines

>
> > Why only finite sets?
>
> You can only use induction to prove
> stuff about finite sets.


For finite sets induction is not required.
It is required however, to define the infinite set |N:

If 1 is in M and if from n we can conclude on n+1, then M is an
infinite set.

> Once we remove one line, we are left with
> a new set of unnecessary lines.  We can
> remove one of these lines.
> From induction we get that
> any finite set of lines can
> be removed.


Exactly. And we can prove by induction that the set of all removable
lines is infinite, no? If you object to this simple and clear theorem
of mine, then give a counter example please.

Regards, WM