Let be a space (a nonempty set) endowed with a distance function .

Let G be a group and S a nonempty set.

X is a nonempty set and F a field.

Choice: Let the members of B be disjoint nonempty sets.

A linear order where every nonempty set has a least element is called a well-order.

Every class of nonempty sets has a choice function.

AC states that every set of nonempty sets has a choice function.

Product numerical range forms a nonempty set for a general operator.

Simply ask the black box to find the subset that sums to zero, then check whether it returned a nonempty set.

Let be a (finite or infinite) nonempty set of individuals.