Definition:Square/Function/Integer

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Definition

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

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


IntegerSquareFunction.png


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.