Distance to the nearest integer ($\Vert x{\Vert }_{\mathbb{R}/\mathbb{Z}}$)

For a real number $x$, define $\Vert x{\Vert }_{\mathbb{R}/\mathbb{Z}}={\min }_{k\in \mathbb{Z}}|x-k|$. It lies in $[0,1/2]$ and obeys $\Vert \ell x\Vert \le |\ell |\Vert x\Vert$ for an integer $\ell$. It is a distance on the circle, rather than a norm on the real vector space.