f(x)={0 if x is irrational | 1/n if x = m/n ∈ Q}

I need to prove that f is continuous at every irrational point and that f has a simple discontinuity at every rational point.

I have no idea where to begin because for all irrational x, there will always be a rational number in an arbitrarily small neighborhood around it.

Please help me. Any input is appreciated.