I need help showing that Dirichlet's function is discontinuous on the interval (0,1).
f(x)=
{1/q if x=p/q in lowest terms with p,q in N
0 if x is irrational}
This function is continuous at irrational . To prove it's discontinuous at , let . Since for all , contains an irrational point, such that .
There's a good picture of this function on MathWorld.