Answer Happy

11.2 Use Definition 11.2.1 to prove that if a set of real numbers has a maximum element then this element is unique. [Hint: Suppose that c, and c, are two maximum elements of a set A and use the definition to prove that C1 C2 C1 = C2.] =

or b= = min A Definition 11.2.1 Let A be a set of real numbers, i.e. A SR. Then b is a minimum element of A when (i) b is an element of A, i.e. b € A, (ii) b is less than or equal to every element of A, i.e. a eA-b<a. Similarly, c is a maximum element of A or c=max A when (i) c is an element of A, i.e. Ce A, (ii) c is greater than or equal to every element of A, i.e. a eAc> a.