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. And this is remarkable, isn't it?
Do you know and deny these basics of set theory? Or why do you argue against set theory?