TITLE: Is the fact that there are more irrational numbers than rational numbers useful?
QUESTION [8 upvotes]: Although it is known that the cardinality of the set of irrational numbers is greater than the cardinality of the set of rational numbers, is there any usefulness/applications of this fact outside of mathematics?

REPLY [2 votes]: Outside of mathematics, the distinction between the irrational number $\pi$ and the rational number $10^{-10000}\lfloor 10^{10000}\pi\rfloor$ is irrelevant. In everyday life, even the distinction between $\pi$ and $\frac{22}7$ is of little importance.