Four tuple/Modulus of differences/Mapping properties/Exercise

We consider the mapping

$\Psi \colon \mathbb {N} ^{4}\longrightarrow \mathbb {N} ^{4}$

that assigns to a four-tuple ${}(a,b,c,d)$ the four-tuple

$(\vert {b-a}\vert ,\vert {c-b}\vert ,\vert {d-c}\vert ,\vert {a-d}\vert ).$

Determine whether ${}\Psi$ is injective and whether ${}\Psi$ is surjective.

Create a solution