Am Freitag, 6. Dezember 2013 23:56:10 UTC+1 schrieb Virgil:
> > Let d differ from r, then there is a first digit where both differ. Let d > > > differ from p, q, r, then there is a first digit where d differs from all > > > three. Let d differ from all rationals, then there is a first digit where d > > > differs from all rationals. >
> > Let d first differ from r1 at digit 1 > > let d first differ from r2 at digit 2 > > let d first differ from r3 at digit 3 > > ...
Then it differs at digit 3 from all three rationals. > > let d first differ from r_n at digit n > > > > and so on.
"and so on" means: there are always infinitely many rationals that do not differ. > > > > Then, while for every n in |N, > > d DOES differ from n rationals by line n,
there remain infinitely many rationals from which it does not differ. > > > > and ultimately differs from all listed rationals
Then either you can index the "ultimate" digit d_u or you cannot. In the latter case you either have to assume a digit without natural index u, namely index d_oo, which is out of mathematics, or you have to confess that the ultimate case does never appear. That is tantamount that d does never differ from all rationals.
> Actually it is WM's "proof" that, as usual, has been shown not to hold. > > See counter-proof above!
You have a strange use of language: ultimate = never.
But it is ridiculous to claim that your "never" differs from my "never", only because you call it ultimate.