```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 aninfinite 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 removablelines is infinite, no? If you object to this simple and clear theoremof mine, then give a counter example please.Regards, WM
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