On Wednesday, June 12, 2013 6:56:54 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Wednesday, 12 June 2013 02:31:50 UTC+2, Virgil wrote: > > > > 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. -- > > > > And for which k do you fail to well-order by size all rationals which have (m + n) < k? >
It will fail at no k, all k are natural numbers. It will fail for the set of all natural numbers.