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In universal algebra, a finitary algebraic operation on a set $S$ is a functionfor a nonnegative integer $n$, its arity. A binary operation has $n=2$, as with addition on the integers. A unary operation has $n=1$, as with taking the additive inverse $a\mapsto -a$.

A nullary operation has $n=0$: since $S^0$ contains the single empty tuple, such an operation selects a distinguished element of $S$, such as zero in a ring. Thus constants are operations too. The fixed codomain $S$ expresses closure, while additional identities such as the associative property specify laws an operation may satisfy.