> On Tuesday, 11 June 2013 20:43:30 UTC+2, Zeit Geist wrote: > > > I think your algorithm fails at the limit stage. > > That's the same with enumerating the rationals and with the diagonal of > the list. No limits available in all these cases. > If we enumerate the rationals, we do it up to n (since there is no > infinite natural number).
WM may be so constrained but those not imprisoned in his Wolkenmuekenheim are not.
Consider the following infinitely-many-to-one SURJECTION from the set of naturals, |N, ONTO the set of rationals, |Q:
for m and n in |N 2^m*3^n -> m/n 5^m*7^n -> -m/n all other naturals map to the 0 of the rationals.
Then for every rational, positive, negative or zero, there are more than any finite number of naturals mapping to that rational.
Which shows that there are no more rationals than naturals. --