Definition:Ordered Tuple/Definition 2

Definition
Let $n \in \N$ be a natural number.

Let $\N^*_n$ be the first $n$ non-zero natural numbers:
 * $\N^*_n := \left\{{1, 2, \ldots, n}\right\}$

Let $\left\langle{S_i}\right\rangle_{i \mathop \in \N^*_n}$ be an family of sets indexed by $\N^*_n$.

Let $\displaystyle \prod_{i \mathop \in \N^*_n} S_i$ be the Cartesian product of $\left\langle{S_i}\right\rangle_{i \mathop \in \N^*_n}$.

An ordered tuple of length $n$ of $\left\langle{S_i}\right\rangle$ is an element of $\displaystyle \prod_{i \mathop \in \N^*_n} S_i$.

Also see

 * Equivalence of Definitions of Ordered Tuple