Definition:Iterated Binary Operation over Finite Set

Definition
Let $G$ be a commutative semigroup.

Let $S$ be a finite nonempty set.

Let $f : S \to G$ be a mapping

Commutative Monoid
Let $G$ be a commutative monoid.

Let $S$ be a nonempty set.

Let $f : S \to G$ be a mapping