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REAL ANALYSIS I Prove the following exercises (please show all your work)- Exercise 1.1.2: Let S be an...

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Advance Math

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.

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