
Continuous Functions
Let:
while: , and p,q are relatively prime.
How can I prove that f is continuous in every irrational point, and noncontinuous in rational points?
It looks as if it is not continuous at all (because between every irrational number there's a rational number, and viceverse) (Thinking)
*(Sorry for my bad English)
Can anyone please help me to find a way to solve this problem?
Thank you very much :)

This seems to explain this function in great detail:
Thomae's function  Wikipedia, the free encyclopedia