1. Let $A \subseteq \mathbb{R}^{n}$ and both $A$ and $A^{c}$ are dense in $\mathbb{R}^{n}$. Can we find $x \in A$ such that $x$ is NOT a limit point of $A$?
2. Let $B \subseteq \mathbb{R}^{n}$ and $B$ is dense in $\mathbb{R}^{n}$. Is the closure of complement of $B$ supposed to be contained in the boundary of B? In other words, is it always $cl(B^{c}) \subseteq bd(B)$?

Please give me hints. Thanks.