Analysis 1 Midterm Solutions - Analysis I section 5...

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Analysis I, section 5 - Midterm (10/22/2013) [100 marks]Name:Please justify all your answers, unless otherwise instructed. No calculators allowed.Duration: 75 minutes.1. See Wade’s book2. See Wade’s book3. See Wade’s book4. Decide which of the following statements are true and which are false. Prove the true ones and give counterex-amples to the false ones(7 marks each).IfAandBare nonempty bounded subsets ofR, then sup(AB) = max{supA,supB}.
B.The other two cases (supA= supB, supA >supB) aresimilar.If{xn}and{yn}are Cauchy withyn6= 0 for alln, then{xn/yn}is Cauchy.

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