# Definition:Additive Inverse/Number

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## Definition

Let $\Bbb F$ be one of the standard number systems: $\N$, $\Z$, $\Q$, $\R$, $\C$.

Let $a \in \Bbb F$ be any arbitrary number.

The **additive inverse** of $a$ is its inverse under addition, denoted $-a$:

- $a + \paren {-a} = 0$

## Also known as

The **additive inverse** of a number is often referred to as its **negative**.

However, beware of confusing the **negative of a number** with a negative number.

Note that the **negative** of a negative number is a positive number.

## Also see

## Sources

- 1967: Michael Spivak:
*Calculus*... (previous) ... (next): Part $\text I$: Prologue: Chapter $1$: Basic Properties of Numbers: $(\text P 3)$