Definition:Ordered Tuple/Definition 2

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

Let $\N_n$ denote the first $n$ non-zero natural numbers:
 * $\N_n := \set {1, 2, \ldots, n}$

Let $\family {S_i}_{i \mathop \in \N_n}$ be a family of sets indexed by $\N_n$.

Let $\displaystyle \prod_{i \mathop \in \N_n} S_i$ be the Cartesian product of $\family {S_i}_{i \mathop \in \N_n}$.

An ordered tuple of length $n$ of $\family {S_i}$ is an element of $\displaystyle \prod_{i \mathop \in \N_n} S_i$.

Also see

 * Equivalence of Definitions of Ordered Tuple