Well, that might be true, but is there any sense (maybe measure theory?), even if I don't have a nicely defined concept of picking a value at random, where I can still talk about the relative probability? --Bill C. -----Original Message----- From: math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com [mailto:math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com] On Behalf Of franktaw@netscape.net Sent: Friday, November 10, 2006 9:47 AM To: math-fun@mailman.xmission.com Subject: Re: [math-fun] derangements Picking an infinite permutation at random is not a well defined concept. It comes down to the similar but simpler problem of picking a (positive) integer at random. Each integer must have probability zero (lim_{n->infinity} 1/n} of being chosen; but that means you can't ever pick one. For a random infinite permutation p, p(1) needs to be a positive integer picked at random. --- If you choose a probability distribution for infinite permutations, the probability that one will be a derangement will depend on what probability distribution you choose. There really isn't any obvious choice for the distribution. Franklin T. Adams-Watters -----Original Message----- From: wrcordw@sandia.gov For n objects, the fraction of permutations that are derangements is about 1/e. Does this extend to an infinite number of objects; i.e. is the probability of picking a permutation "at random" that is a derangement = 1/e? --Bill C. ________________________________________________________________________ Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun