For any [[Set]] $A$, the [[Power Set]] of $A$, denoted as $\mathcal P(A)$ is the [[Set]] of all [[Subset|Subsets]] of $A$. For any set $A$, the [[Cardinality]] of its [[Power Set]] is always greater than $A$. $\huge \forall A \,:\,|\mathcal P(A)| > A $ >[!note] Note about the [[Empty Set]] >Because the [[Empty Set]] is a [[Subset]] of all [[Set|Sets]], the [[Power Set]] of any [[Set]] will always contain the [[Empty Set]], and will never have a [[Cardinality]] of 0. > $\huge \forall A \,:\, \emptyset \in \mathcal P(A) $