Definition:Summation/Summand

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 $\set {a_1, a_2, \ldots, a_n} \subseteq S$ be a set of elements of $S$.

Let $\map R j$ be a propositional function of $j$.

Let:
 * $\ds \sum_{\map R j} a_j$

be an instance of a summation on $\set {a_1, a_2, \ldots, a_n}$.

The set of elements $\set {a_j \in S: 1 \le j \le n, \map R j}$ is called the summand.

Also known as
The summand is also known as the set of summands.

Also see

 * Definition:Multiplicand (Product Notation)