Axiom of power set

The elements of the power set of the set {x, y, z} ordered with respect to inclusion.

In mathematics, the axiom of power set[1] is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set the existence of a set , the power set of , consisting precisely of the subsets of . By the axiom of extensionality, the set is unique.

The axiom of power set appears in most axiomatizations of set theory. It is generally considered uncontroversial, although constructive set theory prefers a weaker version to resolve concerns about predicativity.

  1. ^ "Axiom of power set | set theory | Britannica". www.britannica.com. Retrieved 2023-08-06.