Definition:Additive Inverse/Field
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This page is about additive inverse in a 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 $-a$:
- $a + \paren {-a} = 0$
Also see
- Results about additive inverses can be found here.