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.
> What property is changed if infinitely many are > there? If there are infinitely many unnecessary lines, they all can be > removed - by their property of being unnecessary.
Nope, their property of being unnecessary means that *any one* line can be removed.
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.