Surjection/Examples/Negative Function on Integers
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Example of Surjection
- $\forall x \in \Z: \map f x = -x$
Then $f$ is a surjection.
- $\forall y \in \Z: \exists x \in \Z: -x = y$
This is the case by setting $ x = -y$, which is an integer since $y$ is an integer.
Thus $f$ is a surjection by definition.