Definition:Continued Product/Multiplicand

Definition

Let $\struct {S, \times}$ be an algebraic structure where $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.

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

Let:

$\ds \prod_{\map R j} a_j$

be a continued product on $\set {a_1, a_2, \ldots}$.

The set of elements $\set {a_j \in S}$ is called the multiplicand.

Also known as

The multiplicand of a continued product 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.