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If limsup$(p_k) \neq \infty$ and liminf$(p_k) \neq -\infty$, prove or disprove that $(p_k)$ has monotone increasing and monotone decreasing sub sequences.

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    What have you found out so far?2012-10-18
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    Does monotone include constant sequences? It doesn't change the answer, but it makes one side easier.2012-10-19

3 Answers 3