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. On the other hand, are not most of all the natural numbers, all except for a finite number of natural numbers, specifically indescribable? The tough question might be: is this chatting or programming?
________________________________ From: John Dixon <[email protected]> To: Programming forum <[email protected]> Sent: Monday, August 24, 2009 10:14:05 PM Subject: Re: [Jprogramming] Unforgettable times The interesting thing about real numbers is that they form an uncountable set, but there are only countably many sentences in English (or any other language with a finite alphabet). This means that almost all real numbers are indescribable- we cannot even talk about most of them as individuals even though we can prove elaborate theorems about them as a set. John. On 2009-08-24 6:00 PM, Zsbán Ambrus wrote: > On Mon, Aug 24, 2009 at 9:19 PM, R.E. Boss<[email protected]> wrote: > >> To me (when I was in university) it was proven by contradiction: >> if there would exist an uninteresting integer, there would be a smallest one >> / one closest to 0. >> A very interesting number. QED. >> > > I wonder, can you also prove that all real numbers are interesting? I > can't think of a proof. > > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
