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Is a set containing [see page 4, all] the subsets of the parent set.

\begin{align*} \mathcal{P}(A) &= \{ x : x \subseteq A \} \
y \in \mathcal{P}(A) &\iff y \subseteq A \
A &\in \mathcal{P}(A) \
\varnothing &\in \mathcal{P}(A) \
\end{align*}