Definition:Relation/General Definition

Definition
Let $\displaystyle \mathbb S = \prod_{i \mathop = 1}^n S_i = S_1 \times S_2 \times \ldots \times S_n$ be the cartesian product of $n$ sets $S_1, S_2, \ldots, S_n$.

An arbitrary subset $\mathcal R \subseteq \Bbb S$ is a called an $n$-ary relation on $\Bbb S$.

To indicate that $\left({s_1, s_2, \ldots, s_n}\right) \in \mathcal R$, we write $\mathcal R \left({s_1, s_2, \ldots, s_n}\right)$.