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