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I tried to check the definition of divergent sequences in many places. All of them define divergent sequence as a sequence which is not convergent.

I wonder if a Cauchy sequence (which is not convergent in a non-complete normed space) is still called a divergent sequence.

Alex M.
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Waroth Kuhirun
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1 Answers1

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If you are in a non-complete space and find a Cauchy sequence which does not converge, then by definition yes, this sequence is divergent. Cauchyness has nothing to do with it.

Clement C.
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