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    Cauchy Sequence and Limit Supremum

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    Suppose that {a_n}_n is a real Cauchy sequence. Prove that lim superior n--> infinity (a_n) = lim inferior n--infinity (a_n) so as to conclude that lim n--infinity (a_n) exists.

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    Suppose that {a_n}_n is a real Cauchy sequence. Prove that lim superior n--> infinity (a_n) = lim inferior n--infinity (a_n) so as to conclude thatlim n--infinity (a_n) exists.

    Solution:

    Let {a_n} be a sequence of real ...

    Solution Summary

    Cauchy sequence and limit supremum are investigated. The infinity functions are provided.

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