Definition:Power Set/Class Theory

Definition
The power set of a set $x$ is the class of all the subsets of $x$:


 * $\powerset x := \set {y: y \subseteq x}$

It is clear from the definition that:
 * $y \in \powerset x \iff y \subseteq x$

Class Theory
The concept of the power set is axiomatised in the Axiom of Powers in class theory:

Also see

 * Cardinality of Power Set of Finite Set


 * Definition:Set of All Mappings