------------------------------------------------------------------------------------ David Wilson writes: I'm looking at the Mathworld article "Relatively Prime". I see this: The probability that two integers m and n picked at random are relatively prime is [6/pi^2, equation elided]. When we say "random element of set S" without further qualification, the assumption is a uniform distribution. For example, if you pick a random number form 1 to 10, the assumption is each number has probability 1/10. However, no such uniform distribution exists for Z, so an "integer picked at random" is ill-defined, I guess this is well-known. I think what is meant here is: The density of pairs of coprime integers over ZxZ is 6/pi^2. Is that a common interpretation of the original statement? ------------------------------------------------------------------------------------- Actually I've found a way to pick an integer from Z such that all integers have the same chance of being picked (using the Axiom of Choice). But never mind that. And yes, what people mean when they say "the chance that two random integers are coprime = 6/pi^2" is that 6/pi^2 is the limit of A(n) / n^2 as n -> oo, where A(n) is the number of coprime pairs K,L with 1<= K,L <= n. --Dan Asimov _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun