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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}
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 $\mathcal{P} X$.
Subdefinitions
» D5348: Set of binary relations
Child definitions
» D5464: Hyperpower set sequence
Results
» R255: Power set of empty set
» 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
» R4158: Power set is multiplicative
» R4159: Power set is not empty