Norm in $\mathbb{R}/\mathbb{Z}$

Question

I have to prove some statements about some norm in $\mathbb{R}/\mathbb{Z}$, for example "Let $x$, $y$, $z$ be points in $\mathbb{R}/\mathbb{Z}$ such that x + y + z = 0. Prove that one of the options is valid: $||x|| + ||y|| + ||z|| = 2 \max\{||x||, ||y||, ||z||\}$

$||x|| + ||y|| + ||z|| = 1$

The problem is I have no idea how this norm is defined. Does anyone know what might this be? It's for an analytic number theory class, I missed the first lecture and we're not following any particular book

Answer 1

There is no naturally defined norm, so it is presumably something like the absolute value of a coset representative lying in $[-1/2, 1/2]$. To be certain, you should just ask your instructor.