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 $a + b = c$:
- $a$ is the augend
- $b$ is the addend
- $c$ is the sum.
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.
- Use of this concept in the context of sum notation.
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): addend
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): addend