Consider it from a measure theory point of view, at least colloquially. If you could assign a mass of 1 (lb/kg/g/whatever) to the reals and separate them into

Consider it from a measure theory point of view, at least colloquially. If you could assign a mass of 1 (lb/kg/g/whatever) to the reals and separate them into two piles: rational and irrational then weigh again. The irrational pile would weigh 1 and the rationals, 0. So yes you took something out, but also in some sense, it doesn't matter.