# Definition:Addition/Sum

## Definition

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

Then the result $a + b$ is referred to as the **sum** of $a$ and $b$.

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.

## Linguistic Note

In natural language, the word **sum** is often used to mean the process of operation of *any* arithmetical calculation.

This probably originates from elementary school, where the first excursions into arithmetic occurs via (natural number) addition.

Consequently, at that level, *all* such arithmetic lessons are often referred to as **sums**.

To those with math anxiety, the very word **sums** may be distressing, while in the humour of children's comics, a popular punishment for a child would be to be sat down at a desk in front of a book titled **hard sums**.

## Sources

- 1974: Murray R. Spiegel:
*Theory and Problems of Advanced Calculus*(SI ed.) ... (previous) ... (next): Chapter $1$: Numbers: Real Numbers: $1$ - 1981: Murray R. Spiegel:
*Theory and Problems of Complex Variables*(SI ed.) ... (previous) ... (next): Chapter $1$: Complex Numbers: The Real Number System: $1$