# Notation for a periodic interval?

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?

• Do you mean $\theta \in [0+ 2k\pi, \tau + 2k\pi)$ for some $k \in \mathbb Z$? – Andrew Mar 29 '17 at 13:49
• @Andrew that seems appropriate, but needlessly complicated. – Frank Vel Mar 29 '17 at 13:52
• How about $[0,\tau) + 2\pi \mathbb Z$ then? – Andrew Mar 29 '17 at 13:54

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