This is homework. The problem was also stated this way:
Let A be a dense subset of $\mathbb{R}$ and let x$\in\mathbb{R}$. Prove that there exists a decreasing sequence $(a_k)$ in A that converges to x.
I know:
A dense in $\mathbb{R}$ $\Rightarrow$ every point in $\mathbb{R}$ is either in A or a limit point of A.
If x is a limit point of A, then there is a sequence in A that converges to x.
What if $x\in A$?
Also, how can I know if the sequence is increasing or decreasing?