(3) (15 points) Let (M,d) be metric space and M. Show that the set {x1, x2, x3,...] is compact set.

(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.