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# Class Note for MATH 425A with Professor Laetsch at UA 2

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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15
Math 4255251 Comparing Suprema 2008 l Prove using the de nition or basic properties of supremum or give a counterexample Suppose A and B are nonempty subsets of the real numbers which are bounded above Suppose that for each a in A there is b in B such that a S b Then supA S supB 2 Prove using the Problem 1 above or give a counterexample Suppose S is any nonempty set not necessarily a subset of the real numbers Let F and G be functions from S to R which are bounded above Suppose that for each s in S FS S Gs Then supF S S supGS 3 Explain in detail the relevance of the result of Problem 2 above to the solution proof in Exercise 5b in Section 61 4 Prove using the de nition or basic properties of supremum and infimum or give a counterexample Suppose S is any nonempty set not necessarily a subset of the real numbers Let F and G be functions from S to R which are bounded above Suppose that for each s in S FS S Gs Then supF S S infGS 5 Explain in detail the relevance of the result of Problem 4 above to inequalities 63 and 610 in Section 6 1 Is 610 a direct consequence of 63

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