Interactive Real Analysis
- part of Examples 5.2.2(c):
Is the set {1, 1/2, 1/3, 1/4, ...} compact ?
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This set is not compact. Take the sequence { 1/n } which is the set itself. It - and hence
every subsequence - converges to zero, which is not part of the set. Therefore, the set can
not be compact by our definition.
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