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Axiom — For any set X of nonempty sets, there exists a choice function f defined on X.Read: for every indexed family S(i) of nonempty sets there exists an indexed family x(i) of elements such that x(i) element S(i) for every i element I. For any set S there exists a function f such that for any non-empty subset c of S, f(c) lies in c . Careful with that axiom, Eugene!