Cardinality of Cartesian Product of Finite Sets/General Result

Theorem
Let $\displaystyle \prod_{k \mathop = 1}^n S_k$ be the cartesian product of a (finite) sequence of sets $\sequence {S_n}$.

Then:
 * $\displaystyle \card {\prod_{k \mathop = 1}^n S_k} = \prod_{k \mathop = 1}^n \card {S_k}$

This can also be written:
 * $\card {S_1 \times S_2 \times \ldots \times S_n} = \card {S_1} \times \card {S_2} \times \ldots \times \card {S_n}$