Question: let k 01 r be defined by k...

Let k : (0,1) → R be defined by k (x) = 0 whenever, x is irrational, and k (x) = n when x = m/n

where m, n have no common factor other than 1. Prove that k is unbounded in any (a, b) which is a subset of (0, 1), and that k is not continuous on (0, 1).