In article <email@example.com>, firstname.lastname@example.org wrote:
> On Wednesday, 26 February 2014 22:19:35 UTC+1, Virgil wrote: > > > > If one does not have something like an axiom of choice, there is no > > guarantee that any infinite set need have any well-orderable subsets. > > The axiom of choice is no guarantee either. It is impossible to well-order > the uncountable set of real numbers.
No one claimed the set of reals could be well-ordered but it does have natually well-ordered subsets, the set of naturals, for instance.