Unformatted text preview: convergent sequence s i together with its limit is a closed set; (b) Show that any set consisting of a (not necessarily convergent) sequence together with all of its accumulation points is a closed set. 12. Prove that if α,β > 0 satisfy 1 α + 1 β = 1 then for all x,y ≥ xy ≤ 1 α x α + 1 β y β as follows: (a) The inequality is clear for xy = 0, so we can assume xy n = 0....
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 Fall '08
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 Calculus, Topology, Inequalities, Metric space, Topological space, Closed set, convergent sequence si

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