axiom of choice

== English == === Etymology === A calque of German Axiom der Auswahl (now more commonly Auswahlaxiom), which first appeared in print with a description of the axiom in 1908, Ernst Zermelo, Untersuchungen über die Grundlagen der Mengenlehre I ["Investigations in the foundations of set theory I"], Mathematische Annalen, 65 (although the paper was dated 1907). === Noun === axiom of choice (plural axioms of choice) (set theory) One of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made. ==== Synonyms ==== choice (ellipsis) AC (initialism) ==== Derived terms ==== axiom of countable choice, axiom of denumerable choice axiom of dependent choice ==== Translations ==== === See also === ZFC === References === === Further reading === Zermelo–Fraenkel set theory on Wikipedia.Wikipedia