How would I express multiple intervals in this problem? I'm told to find which intervals $\left[a,b\right]$ in $\mathbb R$ is the intersection $\left[a,b\right]\cap\mathbb Q$ a clopen subset of the metric space $\mathbb Q$? My first thought was that one could be $\left[-\sqrt2,\sqrt2\right]$, but then I realized that both ends of the interval would be closed. So how would I express multiple intervals if I'm having a hard time trying to express one?

Hint: If you want to find all intervals that satisfy your requests, you could consider density of $Q$ on $R$ to verify that a set such as $[-\sqrt(2),\sqrt(2)]$ is open if you intersect with $Q$. For closure you should consider that the border of you given set is empty.
