Limit points of $\left\{ \frac{m}{2^{n}} \right\}$ where $m,n$ are natural numbers.
The set of limit points of the sequence $1,\frac12,\frac14,\frac34,\frac18,\frac38,\frac58,\frac78,\frac1{16},\frac3{16},\ldots$