Definition:Summation/Inequality

Definition
Let $\struct {S, +}$ be an algebraic structure where the operation $+$ is an operation derived from, or arising from, the addition 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 summation of $\tuple {a_1, a_2, \ldots, a_n}$ can be written:
 * $\ds \sum_{1 \mathop \le j \mathop \le n} a_j = \paren {a_1 + a_2 + \cdots + a_n}$