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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?

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    $\begingroup$ Do you mean $\theta \in [0+ 2k\pi, \tau + 2k\pi)$ for some $k \in \mathbb Z$? $\endgroup$ – Andrew Mar 29 '17 at 13:49
  • $\begingroup$ @Andrew that seems appropriate, but needlessly complicated. $\endgroup$ – Frank Vel Mar 29 '17 at 13:52
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    $\begingroup$ How about $[0,\tau) + 2\pi \mathbb Z$ then? $\endgroup$ – Andrew Mar 29 '17 at 13:54
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As Andrew suggested, you can write: $$ [0,\tau)\ +\ 2\pi\mathbb{Z} $$ or using quotient spaces notation: $$ [0,\tau)\ /\ 2\pi\mathbb{Z} $$

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