# Definition:Negation Function

## Definition

The negation function is the function defined on the various standard number systems as follows:

### Integer Negation Function

The negation function $h: \Z \to \Z$ is defined on the set of integers as:

$\forall n \in \Z: \map h n = -n$

### Rational Negation Function

The negation function $h: \Q \to \Q$ is defined on the set of rational numbers as:

$\forall x \in \Q: \map h x = -x$

### Real Negation Function

The negation function $h: \R \to \R$ is defined on the set of real numbers as:

$\forall x \in \R: \map h x = -x$

### Complex Negation Function

The negation function $h: \R \to \R$ is defined on the set of complex numbers as:

$\forall z = x + i y \in \C: \map h z = -x - i y$