# Show that there is either an increasing sequence or a decreasing sequence of points $x_n$ in A with $lim_{n\rightarrow \infty} x_n=a$.

Let a be a set accumulation point $A$ subset of $\mathbb{R}$. Show that there is either an increasing sequence or a decreasing sequence of points $x_n$ in A with $lim_{n\rightarrow \infty} x_n=a$.

Could I have an answer in detail (especially the build of that sequences), please?