# Definition:Square/Function/Integer

## Definition

The (integer) square function is the integer function $f: \Z \to \Z$ defined as:

$\forall x \in \Z: \map f x = x^2$

## Properties

### Integer Square Function is not Injective

Let $f: \Z \to \Z$ be the real square function:

$\forall x \in \Z: \map f x = x^2$

Then $f$ is not an injection.

### Integer Square Function is not Surjective

Let $f: \Z \to \Z$ be the real square function:

$\forall x \in \Z: \map f x = x^2$

Then $f$ is not a surjection.

## Also see

• Results about the square function can be found here.