Definition:Additive Inverse

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Definition

Let $\struct {R, +, \circ}$ be a ring whose ring addition operation is $+$.

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


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

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

where $0_R$ 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 sets of numbers

Let $a \in \Bbb F$ be any arbitrary number.


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

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


Sources