Real Square Function is not Bijective

Theorem
Let $f: \R \to \R$ be the real square function:
 * $\forall x \in \R: \map f x = x^2$

Then $f$ is not a bijection.

Proof
From Real Square Function is not Injective, $f$ is not an injection.

From Real Square Function is not Surjective, $f$ is not a surjection.

The result follows by definition of bijection.