- In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by choosing one element from each set, even if the collection is infinite.
“Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them.
Matthew 5:17 NIV