Cardinality of Power Set of Finite Set

Theorem
Let $S$ be a set such that:
 * $\left|{S}\right| = n$

where $\left|{S}\right|$ denotes the cardinality of $S$,

Then:
 * $\left|{\mathcal P \left({S}\right)}\right| = 2^n$

where $\mathcal P \left({S}\right)$ denotes the power set of $S$.

Thus it can be seen that the power set's alternative notation $2^S$ is indeed appropriate.

However, because of possible confusion over the conventional meaning of $2^n$, its use is deprecated.