On 4/12/2013 3:16 PM, WM wrote: > On 12 Apr., 19:31, Ralf Bader <ba...@nefkom.net> wrote: >> WM wrote: >>> On 12 Apr., 17:24, Dan <dan.ms.ch...@gmail.com> wrote: >> >>>> They do not contradict each other : >>>> Cantor's affirmation (in its full form) is : >> >>>> 1) forall k , exist n , d_n =/= q_kn >> >>> Tricky! No, please be careful. Cantor shows exactly: >>> forall k: d_k =/= q_kk >>> Not more and not less. >> >> And that is precisely what he wanted to show - assertion 1) is true with >> taking n=k. > > I know that. But Cantor's proof is valid only for n =< k. >
No. The Cantor argument only stipulates conditions on what must be given in order for it to be applied.
The argument is irrelevant if what is given corresponds to your statement. It cannot be applied in such a case.