Prove that the following propositions are true:

(g) If a real number r is not an integer, then there is an integer n in the interval (r 1, r) Clarification: the interval (r 1, r) consists of all real numbers x such that x > r 1 and x < r

(h) For any real number r, there exist unique numbers n and such that r = n + , n is an integer, and 0 < 1. Hint: The proposition from question g can be helpful