Definition:Product Notation (Algebra)/Multiplicand

Definition
Let $\left({S, \times}\right)$ be an algebraic structure where the operation $\times$ is an operation derived from, or arising from, the multiplication 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 a composite 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 multiplicand.

Also known as
The multiplicand is also known as the set of multiplicands.

Linguistic Note
The word multiplicand means that which is to be multiplied.

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