You may have missed the point. Although fractions may have infinite representations, the question of which sum of fractions is larger is a much easier problem t

You may have missed the point. Although fractions may have infinite representations, the question of which sum of fractions is larger is a much easier problem to solve: "On the other hand, comparing the sums of fractions is pretty easy, because division is nice and well behaved. So the question is how complicated square roots are."