\begin{definition}[Definition:Power Set]
The '''power set''' of a set $S$ is the set defined and denoted as:
:$\powerset S := \set {T: T \subseteq S}$
That is, the set whose elements are all of the subsets of $S$.
Note that this is a set all of whose elements are themselves sets.
It is clear from the definition that:
:$T \in \powerset S \iff T \subseteq S$
\end{definition}