Definition:Power Set/Class Theory

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


 * $\powerset S := \set {T: T \subseteq S}$

It is clear from the definition that:
 * $T \in \powerset S \iff T \subseteq S$

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