> [!NOTE] Axiom (Power Set) > Every [[Zermelo Frankel set theory (ZFC)|set]] has a powerset. $\forall a \exists b \forall x (x\in b \leftrightarrow x\subseteq a)$ # Properties Note that [[Cantor's Theorem|Cantor's theorem]] guarantees that the cardinality of the power set is strictly greater than the set.