Cardinality of Power Set of Finite Set

Theorem
Let $S$ be a set such that:
 * $\card S = n$

where $\card S$ denotes the cardinality of $S$,

Then:
 * $\card {\powerset S} = 2^n$

where $\powerset S$ 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.