Definition:Additive Inverse/Field

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: