  He says in this case that \(x\) and \(y\) are independent, since for each values of \(x\) an infinity of values for \(y\) in any interval in its range are possible. The very fact that Boltzmann considers intervals for the values of \(x\) and \(y\) of arbitrary small sizes, and stressed the distinction between rational and irrational values of the ratio \(a/b\), indicates that he did not silently presuppose that phase space was essentially discrete, where those distinctions would make no sense.