On Apr 10, 12:26 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 10 Apr., 08:59, William Hughes <wpihug...@gmail.com> wrote:
> > ... 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.
Thus, the fact that there is no line (along with all its predecessors) that cannot be removed is not a contradiction.