I think there is a great opportunity to apply the Surreals to probability questions. E.g., in *some* sense, if you pick a random number from J = [0,1), once for each index in I = [0,1), then the probability of never picking 1/3 should heuristically be (1 - 1/c)^c (where c denotes the Surreal that is the least ordinal of cardinality 2^aleph_0). Then in the Surreals, (1 - 1/c)^c = 1/e, up to an infinitesimal. Then again, it's necessary to be careful about *what sense* is meant by this problem. For, using x |-> 2x there is a simple bijection from I = [0,1) to 2I = [0,2). This leads to the paradox that the probability of never picking 1/3 is both 1/e and 1/e^2. --Dan On 2013-06-23, at 11:04 AM, rcs@xmission.com wrote:
Are you using Conway Numbers as density values?