\begin{definition}[Definition:Relation/General Definition]
Let $\ds \Bbb S = \prod_{i \mathop = 1}^n S_i = S_1 \times S_2 \times \ldots \times S_n$ be the cartesian product of $n$ sets $S_1, S_2, \ldots, S_n$.
An '''$n$-ary relation on $\Bbb S$''' is an ordered $n + 1$-tuple $\RR$ defined as:
:$\RR := \struct {S_1, S_2, \ldots, S_n, R}$
where $R$ is an arbitrary subset $R \subseteq \Bbb S$.
To indicate that $\tuple {s_1, s_2, \ldots, s_n} \in R$, we write:
:$\map \RR {s_1, s_2, \ldots, s_n}$
\end{definition}