ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Definition D80
Power set
Formulation 0
Let $X$ be a D11: Set.
The power set of $X$ is the D11: Set \begin{equation} \mathcal{P}(X) : = \{ E : E \subseteq X \} \end{equation}
Subdefinitions
D5348: Set of binary relations
Children
D5464: Hyperpower set sequence
Results
R1036: Power set is closed under complements
R1035: Power set is closed under intersections
R1034: Power set is closed under unions
R4157: Superadditivity of power set
Conventions
Convention 0 (Notation for power set)
If $X$ is a D11: Set, we denote its D80: Power set either by $\mathcal{P}(X)$ or by $\mathcal{P} X$.