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.
Monotone Subseqences
0
$\begingroup$
real-analysis
limsup-and-liminf
-
0What have you found out so far? – 2012-10-18
-
0Does monotone include constant sequences? It doesn't change the answer, but it makes one side easier. – 2012-10-19