Supremum and inmum Lemma 2.1. Let a and b be real numbers such that a

Supremum and infimum Lemma 2.1. Let a and b be real numbers such that a < b. Then there exists a rational number q e Q such that a < q < b, i.e. q e (a, b). a.) Let A = {A = x + y: 1 < x S 0, 2 < y 3) a subset of real numbers. Find the infimum. Justify your answer. b.) Let a bea real number. Consider a set A = { e R: m e Z, n e N, a < . Using the lemma 2.1, prove that the infimum of A is a, i.e. infA = a.