Possible Duplicate:
Density of a Set on $\mathbb{R}$?
I have to show that show that $A=\{ \frac{m}{2^n}:m\in \mathbb {Z},n\in \mathbb {N}\} $ is dense in $\mathbb {R}$.
A set A is dense in $\mathbb {R}$ if $\overline A=\mathbb {R}$.
But also $Y$ is a subset of $X$, we say that $Y$ is dense in $X$, if for every $x\in X$ , there is $y \in Y$ that is arbitary close to $x$.
So ,I have to prove that for every $x \in \mathbb {R}$ ,there is a number $\frac{m}{2^n}$ arbitrarily close to $x$.So $\forall \epsilon,x ,\exists y$ such that $|y-x|<\epsilon$.
I got a little stuck at this point...Could anyone give me a hint?Thanks a lot!