A set "A" is said to have cardinality smaller than or equal to the cardinality of a set "B", if there exists a one-to-one function (an injection) from "A" into "B". This is denoted |"A"| ≤ |"B"|. If "A" and "B" are not equinumerous, then the cardinality of "A" is said to be strictly smaller than the cardinality of "B". This is denoted |"A"| < |"B"|. If the axiom of choice holds, then the law of trichotomy holds for cardinal numbers, so that any two sets are either equinumerous, or one has a strictly smaller cardinality than the other. The law of trichotomy for cardinal numbers also implies the axiom of choice.