I should probably also mention that if you actually used rationals, the way you would do it (when running into the tough integrals) would be by just phrasing everything in terms of bounded approximations, which is basically just unrolling a construction of the real numbers. So you might as well just use real numbers.
I should probably also mention that if you actually used rationals, the way you would do it (when running into the tough integrals) would be by just phrasing everything in terms of bounded approximations, which is basically just unrolling a construction of the real numbers. So you might as well just use real numbers.