On 3/22/2013 4:01 AM, WM wrote: > On 22 Mrz., 08:19, William Hughes <wpihug...@gmail.com> wrote: >> 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.- > > And what is in your opinion beyond any finite set of lines? > > Do you believe that induction does not hold for all natural numbers? > Why do you believe that the axiom of infinity, that has the same > structure, reaches further?
