Sorry, I was having trouble giving the question because I can't figure out how to type in mathematical symbols. Let me try again:
$\{q\}$ is an enumeration of the rational numbers, and
$f(x)=\sum_{q_n< x}\frac1{n^2}$
for $x\in\Bbb R$.
Or $f(x)=\sum(1/n^2)$, the index of summation $q_n< x$, and $q$ is an enumeration of the rational numbers.
The goal is to prove that $f$ is continuous at each irrational and discontinuous at each irrational.
I'm having trouble visualizing this series so I'm not sure why it is supposed to be different at irrational as opposed to a rational $x$ ...
I think I need to use the epislon-delta definition of continuity but I'm not sure what epsilon to use.