Chapter 7.1, Problem 12E

(a)

To determine

To prove: When $\sup \left(A\right)$ exist, then $\sup \left(A\right)=\inf \left\{u:u\text{is}\text{an}\text{upper}\text{bound}\text{of}A\right\}$ .

(b)

To determine

To prove: When $\inf \left(A\right)$ exist, then $\inf \left(A\right)=\sup \left\{l:l\text{is}\text{an}\text{lower}\text{bound}\text{of}A\right\}$ .