Raul Miller wrote: > I think that randomness might be something of a distraction > from the main point
OK: here's my argument. Let p and q be random nonzero integers. Define events E : denominator of reduced fraction p/q is even. E(n): q is divisible by 2^n ; q is divisible by 2^n-1 but not 2^n. Then the E(n) constitute a partition of E. Since p(E(n))=1/2^(2*n), p(E)=1/4+1/16+1/64+....=1/3. The same argument gives the even more surprising result that the probability of the denominator being divisible by a prime p is 1/((p^2)-1. The problem of this argument is that it depends on p and q: the E(n)'s become empty after a while. Whether this is is important depends on how randomness is defined. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
