Show that (a,b) = $\displaystyle \bigcup_{n\in N}$($\displaystyle a_{n},b_{n}$) , where $\displaystyle a,b\in\mathbb{R}$ , {$\displaystyle a_{n}$} is a decreasing sequence of rational numbers with $\displaystyle a_{n}\rightarrow a$ , {$\displaystyle b_{n}$} is an increasing sequence of rational numbers with $\displaystyle b_{n}\rightarrow b$ .