OK, I think I understand the problem now. It's that the actual answer can be very small but non-zero. You can put error bars on your calculations but that doe

OK, I think I understand the problem now. It's that the actual answer can be very small but non-zero. You can put error bars on your calculations but that doesn't necessarily tell you which side of zero the answer is on. In fact you would need to do the calculation with enough bits to represent the true answer which you don't know a priori. What you can do though is put an upper bound on the size of the difference between the two sums and you can make that bound as small as you want by using more bits.