begin quoting boblq as of Thu, Jul 20, 2006 at 08:08:54PM -0700: > On Thursday 20 July 2006 08:00 pm, Stewart Stremler wrote: > > It's quite possible to prove that an answer exists to a given question, > > but to be unable to ever find out what that answer is. [snip] > > I wonder if answers exist for which there are no questions ...
42 > did Goedel have an inverse theorem? I don't think so. The problem with "answers for which there are no questions" is that most computability questions are either "yes" or "no". Even if we broaden our scope of answers, it's possible to construct a question around a given answer. Hm... Consider the set of all answers to which there are no questions. Order this set (lexigraphically, say). Construct a question: "What is the Nth answer in the ordered set of answers to which there are no questions?" There is now a question for the Nth answer. Therefore the Nth answer is not in the set of answers to which there are no questions. Consequently, the set of all answers to which there are no questions is the empty set. > BobLQ "my mind always seems to work backwards" A useful characteristic, I should think. -- _ |\_ \| -- [email protected] http://www.kernel-panic.org/cgi-bin/mailman/listinfo/kplug-list
