\begin{definition}[Definition:Product Notation (Algebra)/Index Variable]
Consider the '''product''', in either of the three forms:
:$\ds \prod_{j \mathop = 1}^n a_j \qquad \prod_{1 \mathop \le j \mathop \le n} a_j \qquad \prod_{\map R j} a_j$
The variable $j$, an example of a bound variable, is known as the '''index variable''' of the product.
\end{definition}