Right, but is this not just a variation of some mathematicians' argument? That is, are you not assuming by your own concept of "interesting number" that an "interesting number" has to have a certain "constructive" characteristic? (Mind you, I am just playing the devil's advocate.)
________________________________ From: Zsbán Ambrus <[email protected]> To: Programming forum <[email protected]> Sent: Tuesday, August 25, 2009 9:50:46 AM Subject: Re: [Jprogramming] Unforgettable times 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
