On Apr 10, 4:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 10 Apr., 16:10, William Hughes <wpihug...@gmail.com> wrote: > > > > On Apr 10, 12:26 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 10 Apr., 08:59, William Hughes <wpihug...@gmail.com> wrote: > > > <snip> > > > > > ... we are agreed that it makes perfect > > > > sense to say that any one line (and all its predecessors) > > > > can be removed, but the collection of all lines > > > > cannot be removed > > > > By a single move. When applying induction, i.e., when n is removed, > > > also n+1 is removed, every finite line is removed. Then no finite > > > lines remain - only actually infinite lines remain. > > > Nope. You can only use induction to show that a finite > > collection of finite lines can be removed. > > You cannot use induction to prove > > that the collection of all finite lines can be removed. > > That's wrong (even if it is your opinion). Sorry. Induction holds for > all n.
Yes and each one of those n is finite. Induction does not hold for the collection of all n.
Thus, the fact that there is no line (along with all its predecessors) that cannot be removed is not a contradiction.