# Definition:Distributive Operation/Distributand

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## Definition

Let $S$ be a set on which is defined *two* binary operations, defined on all the elements of $S \times S$, which we will denote as $\circ$ and $*$.

Let $\circ$ be distributive over $*$.

Then $*$ is a **distributand** of $\circ$.

### Linguistic Note

The word **distributand** means **that which is to be distributed**.

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

The term **distributand** was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$ to ease discussion of the details of the general **distributive operation**.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.