Give an example of bounded sequence that does not converge.
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The most straightforward one : $\displaystyle (-1)^n$
Non-convergent Cauchy sequences will be bounded as well.
Originally Posted by redsoxfan325 Non-convergent Cauchy sequences will be bounded as well. For this to work you must be working in a non-complete metric space. So this isn't going to happen in $\displaystyle \mathbb{R}^n$
Originally Posted by putnam120 For this to work you must be working in a non-complete metric space. So this isn't going to happen in $\displaystyle \mathbb{R}^n$ We aren't in $\displaystyle \mathbb{R}^n$.
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