Notation for a periodic interval?

Question

For instance, if I want to describe the position on a circle I can write that the angle $\theta$ can be found in the interval $[0, \tau)$, but how can I express that this interval is periodic, e.g. that $0$ and $\tau^-$ are "glued" together?

Answer 1

As Andrew suggested, you can write: $$ [0,\tau)\ +\ 2\pi\mathbb{Z} $$ or using quotient spaces notation: $$ [0,\tau)\ /\ 2\pi\mathbb{Z} $$