Am Donnerstag, 5. Dezember 2013 20:35:08 UTC+1 schrieb Zeit Geist: > On Thursday, December 5, 2013 12:59:55 AM UTC-7, WM wrote: > > > Am Donnerstag, 5. Dezember 2013 08:49:37 UTC+1 schrieb fom: > > > > > > > > The property of differing or not depedns on the d_n only. Note that Cantor's diagonal argument only uses the d_n. > > > > > > > No. It also uses the fact that the listing may be > > > > arbitrarily given, > > > > > > Why say no? Of course the listing may be arbitrarily given. Nevertheless the decisive point is that d_n =/= a_nn. > > > > > > And it forgets two crucial aspects: 1) A list could contain all rational numbers. 2) No d_n is out of all rational numbers. > > > > > > > But, d might Not be rational, and if your given List contains only Rationals then the anti-diagonal is not.
If you insist that the irrational antidiagonal differs from every entry of the list, you must use a digit d_oo, because up to every d_n it does not differ. If you don't say so, you must agree that an irrational number cannot be defined by its digits but only by a formula supplying every digit.