how can I show that $\bigcap\bigcup_{k=0}^{n-1} [{k \over n}, {k+1 \over n}]^2=\{(x,x):x\in [0,1]\}$

Let $X=[0,1]$ given $\Delta=\{(x,x):x\in X\}$\begin{equation}\Delta_n = \bigcup_{k=0}^{n-1} \left[{k \over n}, {k+1 \over n} \right]^2 \end{equation}How can I show that $\Delta=\cap\Delta_n$? It's ok showing $\Delta\subset\cap\Delta_n$ because every $\Delta_n$ contains $\Delta$but I don't know how to do the opposite .