In article <firstname.lastname@example.org>, email@example.com wrote:
> On Tuesday, 11 June 2013 19:18:34 UTC+2, Julio Di Egidio wrote: > > > > Therefore it is not possible to enumerate all rational numbers > (always > > > infinitely many remain) by all natural numbers (always > infinitely many > > > remain) or to traverse the lines of a Cantor list (always > infinitely > > > many remain). > > > It is not possible to do so effectively... Julio > > It is only possible by applying the axiom of infinity.
Surjecting the naturals onto the rationals is usually done by formula, of which formulae many are already known.
The existence of such surjections can also be proved by injecting the rationals into the naturals, which is even easier. --