 This function is unbounded both from above and from below, so its supremum and infimum are ∞ and −∞ respectively.However, from the point of view of the Lebesgue measure, the set of rational numbers is of measure zero; thus, what really matters is what happens in the complement of this set, where the function is given as arctan "x".It follows that the essential supremum is /2 while the essential infimum is −/2.