Definition:Additive Inverse/Number

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

• Negative of Ring Negative

• Results about additive inverses can be found here.

Sources

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