[math-fun] Random integer question

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?