On Apr 10, 10:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 10 Apr., 22:25, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Apr 10, 10:00 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 10 Apr., 20:14, William Hughes <wpihug...@gmail.com> wrote: > > > > > When using induction you can only prove that a finite thing > > > > has some property. > > > > This can be proved for infinitely many finite things. > > > Correct, but all of the things are finite. > > > > For instance, we > > > can prove for infinitely many natural numbers n > > > all of which are finite > > > > that the sum of the > > > FISON is S(n) = n(n+1)/2. So we construct a bijection > > > f(n) : n --> S(n). > > > Is this bijection finite or infinite? > > > The bijection is an infinite set with finite elements. > > And why should we not remove all these infinitely many finite > elements,
We can remove the colliction of all these elements. What we cannot do is remove the collection of all finite lines without changing the union of the remaining lines.
Thus, the fact that there is no line (along with all its predecessors) that cannot be removed is not a contradiction.