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. But that axiom will also manage to well-order the rationals. After each one has been attached to a natural, we have the set of naturals that obviously can be re-ordered in any desired way.
(The power set of |N should even include the singleton of the last natural as an element.)