Finite Precision Measurement Nullifies the Kochen-Specker Theorem

Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in $S^2$, can be colored so that the contradiction with hidden variable theories provided by Kochen-Specker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantum-overclassical advantage for information processing can be derived from the Kochen-Specker theorem alone.