axiom of choice

名词 n.
中文释义

英文释义

名词 n.
  1. 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.
    — The axiom of choice is logically equivalent to the assertion that every vector space has a basis.

词形变化

axioms of choice plural

词源

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).
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