# Four tuple/Modulus of differences/R/Infinite dilation/Exercise

We consider the mapping

which assigns to a four tuple the four tuple

Show that there exists a tuple , for which arbitrary iterations of the mapping do never reach the zero tuple.

We consider the mapping

- $\Psi \colon \mathbb {R} _{\geq 0}^{4}\longrightarrow \mathbb {R} _{\geq 0}^{4},$

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

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

Show that there exists a tuple ${}(a,b,c,d)$, for which arbitrary iterations of the mapping do never reach the zero tuple.