Definition:Summation/Summand

Definition
Let $\left({S, +}\right)$ be an algebraic structure where the operation $+$ is an operation derived from, or arising from, the addition operation on the natural numbers.

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

Let:
 * $\displaystyle \sum_{\Phi \left({j}\right)} a_j$

be an instance of sum notation on $\left\{{a_1, a_2, \ldots, a_n}\right\}$.

The set of elements $\left\{{a_j \in S: 1 \le j \le n, \Phi \left({j}\right)}\right\}$ is called the summand.

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

Linguistic Note
The word summand means that which is to be added.

The -and derives from the gerundive form of Latin verbs, expressing future necessity: that which needs to be done.