Power Set

The power set of $A$ (written $\mathcal{P}(A)$ or $2^A$) is the set of all subsets of $A$, including $\emptyset$ and $A$ itself.

For example, if $A = \{1, 2\}$, then $\mathcal{P}(A) = \{\emptyset, \{1\}, \{2\}, \{1, 2\}\}$. Notice there are $4$ subsets.

If $|A| = n$, then $|\mathcal{P}(A)| = 2^n$. This grows exponentially with the size of $A$.