Definition:Standard n Product

Definition
Let $\left({S, \circ}\right)$ be a semigroup.

Let $a_1, \ldots, a_n$ be a sequence of elements over $S$.

Then we denote the standard n product of $a_1, \ldots, a_n$ as:


 * $\displaystyle \prod_{i \mathop = 1}^n a_i$

We define it inductively as follows:

If $n = 1$ then:


 * $\displaystyle \prod_{i \mathop = 1}^1 a_i = a_1$

If $n > 1$ then:


 * $\displaystyle \prod_{i \mathop = 1}^n a_i = \left({\displaystyle \prod_{i \mathop = 1}^{n-1} a_i}\right) a_n$