Open Measurable Sets Containing All Rational Numbers So I am trying to figure out a proof for the following statement, but I'm not really sure how to go about it.  The statement is: "Show that for every $\epsilon>0$, there exists an open set G in $\mathbb{R}$ which contains all of the rational numbers but $m(G)<\epsilon$."  How can it be true that the open set G contains all of the rational numbers but has an arbitrarily small measure?

Hint:  if you order the rationals, you can put an interval around each successive one and take the union for your set.  If the intervals decrease in length quickly enough....  
