ThmDex – An index of mathematical definitions, results, and conjectures.

Result R1832 on D326: Cartesian product

Cardinality of a finite cartesian product of finite sets

Formulation 1

Let $X_1, \, \ldots, \, X_N$ each be a D17: Finite set.

Then \begin{equation} \left| \prod_{n = 1}^N X_n \right| = \prod_{n = 1}^N |X_n| \end{equation}

Also known as

Product rule of counting, Number of elements in a finite cartesian product of finite sets

Subresults

▶	R4315: Cardinality of a finite set raised to a finite power
▶	R5643: Cardinality of the set of bytes
▶	R1856: Cardinality of the set of maps between finite sets