Does there exist a Cauchy sequence with an unbounded subsequence?
I know that all Cauchy sequences are bounded, so my guess is no. If there is, can someone provide me an example?
2026-03-29 11:05:57.1774782357
A cauchy sequence with an unbounded subsequence
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The answer is negative. A real sequence converges if and only if it is a Cauchy sequence. Every convergent sequence is bounded. If a sequence is a Cauchy sequence, it has to be bounded and it cannot have an unbounded subsequence.