Definition:Product Notation (Algebra)/Inequality

Definition
Let $\left({S, \times}\right)$ be an algebraic structure where the operation $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.

Let $\left({a_1, a_2, \ldots, a_n}\right) \in S^n$ be an ordered $n$-tuple in $S$.

The product of $\left({a_1, a_2, \ldots, a_n}\right)$ can be written:
 * $\displaystyle \prod_{1 \mathop \le j \mathop \le n} a_j = \left({a_1 \times a_2 \times \cdots \times a_n}\right)$