# 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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#### Solution Preview

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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