This problem is from Zorich 3.1.5 and I have difficulty in solving it.
We mark all the points on a circle obtained from a fixed point by rotations of the circle through angles of $n$ radians, where $n\in\mathbb{Z}$ ranges over all integers. Describe all the limit points of the set so constructed.
My approach it that firstly, such limit points must be on the circle, since any point that is not on the circle will have a neighbourhood small enough to avoid intersecting to the circle. Hence the limit points that we need can be expressed into the form of an angle. And then the problem will turns into:
$$A=\left\{0\leqslant n+2m\pi<2\pi:n,m\in \mathbb{Z}\right\}$$
and find the limit points of $A$. What can I do now?
