On Mar 21, 4:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 21 Mrz., 14:29, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Mar 21, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote: > > > > > > In fact? That's amazing. So we cannot prove that all lines of the > > > > > infinite set of lines are unnecessary? > > > > > We can prove that something is true for every > > > > member of an infinite set. We cannot > > > > prove that something is true for the set > > > > itself unless the set is finite. > > > > But I am not interested in the set itself. Not at all! My claim is > > > that every member of the set of lines can be removed > > > Yes, removed one at a time > > > >such that no member remains > > > nope, working one at a time you will not get > > to the point that no member remains. > > Induction does not need time. > The conclusion from n on n+1, if valid, is valid for every natural at > one instance.
Yes, valid for every natural, but not valid for the *set* of all naturals.