Authors who use this formulation often speak of the "choice function on A", but this is a slightly different notion of choice function. Its domain is the power set of "A" (with the empty set removed), and so makes sense for any set "A", whereas with the definition used elsewhere in this article, the domain of a choice function on a "collection of sets" is that collection, and so only makes sense for sets of sets. With this alternate notion of choice function, the axiom of choice can be compactly stated as