\begin{definition}[Definition:Operation/N-Ary Operation]
Let $S_1, S_2, \dots, S_n$ be sets.
Let $\circ: S_1 \times S_2 \times \ldots \times S_n \to \mathbb U$ be a mapping from the cartesian product $S_1 \times S_2 \times \ldots \times S_n$ to a universal set $\mathbb U$:
That is, suppose that:
:$\circ: S_1 \times S_2 \times \ldots \times S_n \to \mathbb U: \forall \tuple {s_1, s_2, \ldots, s_n} \in S_1 \times S_2 \times \ldots \times S_n: \map \circ {s_1, s_2, \ldots, s_n} \in \mathbb U$
Then $\circ$ is an '''$n$-ary operation'''.
\end{definition}