Injection/Examples/Negative Function on Integers

Example of Mapping which is Not an Injection
Let $f: \Z \to \Z$ be the mapping defined on the set of integers as:
 * $\forall x \in \Z: \map f x = -x$

Then $f$ is an injection.

Proof
Let $x_1$ and $x_2$ be integers.

Then:

Hence $f$ is an injection by definition.