Definition:Additive Inverse/Field

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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 $-a$:

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