Prove that the set $A =\displaystyle \left \{ \frac{1}{n+1} : n \in \mathbb N \right \} $ is a nowhere dense subset of $\displaystyle{ \mathbb R }$.
I have think two ways but I can't finish it. Here it is
I tried to prove that $ \text{int} (\bar{A}) = \emptyset$. For this it is enough to prove that $ \bar A =\mathbb Q $ but I can't show this.
I tried to prove that every interval of $ \mathbb R$ contains a subinterval whose intersection with $A$ is the empty set.
Any help?
Thank's in advance!