\begin{definition}[Definition:Product Notation (Algebra)/Inequality]
Let $\struct {S, \times}$ be an algebraic structure where the operation $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.
Let $\tuple {a_1, a_2, \ldots, a_n} \in S^n$ be an ordered $n$-tuple in $S$.
The '''product''' of $\tuple {a_1, a_2, \ldots, a_n}$ can be written:
:$\ds \prod_{1 \mathop \le j \mathop \le n} a_j = \paren {a_1 \times a_2 \times \cdots \times a_n}$
\end{definition}