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Given bounded sequence $\{a_n\}_{n=1}^{\infty}$ which doesn't have minimum or maximum - prove that $a_n$ doesn't converge.

Thanks a lot.

  • 1
    Something is wrong with the statement: $a_n=1/n$ is bounded, doesn't have minimum and maximum value in its sequence, but it does converge.2012-05-02
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    What is this $L$?2012-05-02
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    @lhf: It has a maximum of $1$.2012-05-02
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    @lhf: I think the OP means minimum or maximum.2012-05-02
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    I understand the assumptions as follows: If $\{a_n\}_n$ converges, then either $\inf_n a_n$ or $\sup_n a_n$ is attained.2012-05-02
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    @lhf the supremum of $\frac{1}{n}$ equal to the maximum which is 1 and hence a member of the sequence $\frac{1}{n}$ , therefore the example isn't relevant to the question.2012-05-02

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