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: The metric topology on $\mathbb{Q}$ is the same as its subspace topology from $\mathbb{R}$, so a subset of $\mathbb{Q}$ is both closed and open iff it is both the intersection of a closed subset of $\mathbb{R}$ with $\mathbb{Q}$ and the intersection of an open subset of $\mathbb{R}$ with $\mathbb{Q}$.
Spoiler:

 $[-\sqrt{2},\sqrt{2}] \cap \mathbb{Q} = (-\sqrt{2},\sqrt{2}) \cap \mathbb{Q}$

