The SlugMath Wiki is under heavy development!
State/Axiom of power sets
Axiom: (Axiom of Power Sets.) Suppose that $x$ is a set. There exists a set $y$, such that: $$\forall u, u \in y \Leftrightarrow u \subset x.$$
In other words, there exists a set, whose elements are precisely the subsets of $x$.
This is one of the Zermelo-Fraenkel axioms of set theory.
This statement logically relies on the following definitions and statements:
To visualize the logical connections between this statements and other items of mathematical knowledge, you can visit the following cluster(s), and click the "Visualize" tab: Clust/ZFC axioms of set theory