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Unformatted text preview: S that converges to z . 5. a. What can you say about unions, intersections, and complements of closed sets? State without proof the strongest statements that you know to be true. b. Prove that the intersection of two open sets is open. c. Give an example of a countable collection of closed intervals whose union is the open interval (1 , 1). 6. Suppose that ( a n ) n =1 and ( b n ) n =1 are sequences of real numbers that converge to L R and M R \{ } , respectively. Show that if b n 6 = 0 for all n then the sequence a n b n n =1 converges. 1 For the test also review the pair of sequences n a n = (1 + 1 n ) n and n b n = (1 + 1 n ) n +1 which are easily shown to be monotonically increasing and decreasing by considering the quotients a n +1 a n and b n +1 b n of successive terms....
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This note was uploaded on 04/02/2009 for the course MAT 371 taught by Professor Thieme during the Spring '07 term at ASU.
 Spring '07
 thieme
 Calculus

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