predicate, then is one particular object that satisfies (if one exists, otherwise it returns an arbitrary object). Hence we may obtain quantifiers from the choice function, for example was equivalent to . However, Bourbaki's choice operator is stronger than usual: it's a global choice operator. That is, it implies the axiom of global choice. Hilbert realized this when introducing epsilon calculus. See also Axiom of countable choice Hausdorff paradox Hemicontinuity Notes References Basic concepts in set theory Axiom of choice