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.