Let A be an infinite subset of the real numbers that is bounded above and let u=supA. Show that there exists an increasing sequence $\displaystyle (x_n)$ with $\displaystyle x_n \in A \forall n \in \mathbb{N}$ such that $\displaystyle u=lim(x_n)$.

The only way I can think of starting this question is to form some sort of sequence involving u, but can't think of how to do this. Help?