On Mar 22, 7:38 am, WM <mueck...@rz.fh-augsburg.de> wrote: > On 21 Mrz., 16:46, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Mar 21, 2:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote: > > > > > > But you think that after all finite and unnecessary lines another one > > > > > is lurking like a dragon? > > > > > Now I think that after any finite set of unnecessary lines has > > > > been removed, there still remains an unnecessary line.- > > > > I know. That's what I wished to prove. In order to believe in the > > > existence of actually infinite sets, it is necessary to have another > > > element after all ordinary elements have been removed. > > > Nope. I only talk about removing finite sets of ordinary > > elements. I do not talk about removing all ordinary elements. > > Do you know that set theory is timeless? Induction holds for all > natural numbers (not for the set though - but that is out of > interest). This proves that we can remove all finite lines from the > list without changing the contents of the remaining list.
No, it only proves that you can remove any finite set of lines.