On Tue, Aug 25, 2009 at 3:06 PM, Jose Mario Quintana<[email protected]> wrote: > One the one hand, if one assumes the axiom of choice then, not only the set > of all the real numbers, but every set is well ordered and you are back in > business because if you assume that the subset of uninteresting elements is > not empty then it has an interesting smallest element.
Sure, but the problem is that there's no one canonical well-ordering so you can get any smallest non-interesting number depending on the choice of the ordering. In contrast, natural numbers have a canonical ordering, and integers or rationals have at least one interesting canonical ordering as well. Ambrus ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
