(1.6) (2 points) Let f be a continuous real function on R and let Z(f) be the set of all at which f(p) = 0. Then Z(f) is closed.

(4) (20 points) Every rational t can be written in the form, where n> 0, and m and n are integers without any common divisors. When a = O, we take n = 1. Consider the function f defined on R by Prove that f is continuous at every irrational point, and that f has a discontinuity at every rational point.