# Definition:Additive Inverse/Field

Jump to navigation
Jump to search

*This page is about Additive Inverse of Field. For other uses, see Additive Inverse.*

## Definition

Let $\struct {F, +, \times}$ be a field whose addition operation is $+$.

Let $a \in R$ be any arbitrary element of $F$.

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

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

where $0_F$ is the zero of $R$.

### Additive Inverse of Number

The concept is often encountered in the context of numbers:

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 $-a$:

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