Is $S = \left\{ \frac{m}{10^n}\,\Bigm|\, m,n\in\mathbb{Z}, n\geq 0\right\}$ dense in the set of real numbers ?
I guess that $S$ is dense in $\mathbb{R}$ and so I was tring to produce a sequence in $S$ that converges to any given real number . Thanks for any help .