# Definition:Addition/Summand

## Definition

Let $a + b$ denote the operation of addition on two objects.

The objects $a$ and $b$ are known as the **summands** of $a + b$.

Note that the nature of $a$ and $b$ has deliberately been left unspecified.

They could be, for example, numbers, matrices or more complex expressions constructed from such elements.

## Also known as

The word **addend** appears to mean the same thing as **summand**, such that the two words may be used interchangeably.

The word **term** is frequently seen for **summand**, but **term** also has other meanings.

If it is important to avoid ambiguity then it is recommended that **summand** is used.

The term **augend** can sometimes be seen for (specifically) the first of a pair of **summands**, so in the context of $a + b = c$:

In the context of **summations**, the **summand** is also known as the **set of summands**.

## Also see

- Use of this concept in the context of sum notation.

## Linguistic Note

The extensions **-and** and **-end** derive from the Latin gerundive forms which impart the meaning **that which must be ...** to a word.

Thus the word **summand**, and its synonym **addend**, literally mean: **that which must be summed (or added)**.

In natural language, the word **addendum** is more common than either, and similarly means **something which is to be added** (usually, by linguistic coincidence, to the **end**).

The archaic term **augend** has the same lingustic root as **augment**, which means **to make larger**.

Hence **augend** is interpreted as **something which is to be made larger** by adding an **addend**.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**addend** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**addend** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**addend** - 2021: Richard Earl and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(6th ed.) ... (previous) ... (next):**addend**