If convergent sequences are bounded and convergent sequences are Cauchy

hestyllvql

hestyllvql

Answered question

2022-04-20

If convergent sequences are bounded and convergent sequences are Cauchy sequences, can't you conclude that Cauchy sequences are bounded? If it's true, please, prove it.

Answer & Explanation

zavesiljid

zavesiljid

Beginner2022-04-21Added 21 answers

You logic is a bit incorrect.
It is correct that you say "Convergent means Bounded" and "Convergent means Cauchy". But you cannot use transitivity of implication to conclude "Cauchy means Bounded" unless, as Mhenni hints, you are working in a complete space, in which case we also have "Cauchy means Convergent" as well.

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