\begin{definition}[Definition:Ordered Tuple/Definition 2]
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 $\ds \prod_{i \mathop \in \N_n} S_i$ 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 $\ds \prod_{i \mathop \in \N_n} S_i$.
\end{definition}