REAL ANALYSIS I
Prove the following exercises (please show all yourwork)-
Exercise 1.1.2: Let S be an ordered set. Let A? S be a nonempty finite subset. Then A is bounded. Furthermore,inf A exists and is in A and sup A exists and is in A.Hint: Use induction.
Exercise 1.1.9: Let S be an ordered set and Ais a nonempty subset such that sup A exists. Suppose there is a B ?A such that whenever x ? A there is a y ? B such that x ? y. Showthat sup B exists and sup B = sup A.
