Definition:Operation/N-Ary Operation

Definition
An $n$-ary operation is a mapping $\circ$ from a cartesian product of $n$ sets $S_1 \times S_2 \times \ldots \times S_n$ to a universal set $\mathbb U$:


 * $\circ: S_1 \times S_2 \times \ldots \times S_n \to \mathbb U: \forall \left({s_1, s_2, \ldots, s_n}\right) \in S_1 \times S_2 \times \ldots \times S_n: \circ \left({s_1, s_2, \ldots, s_n}\right) = t \in \mathbb U$

An $n$-ary operation needs to be defined for all tuples in $S_1 \times S_2 \times \ldots \times S_n$.

Also known as
An $n$-ary operation is also referred to as a finitary operation.

Also see

 * Operation