Hello! (Wave)
Let $(a_n), (b_n), (c_n)$ sequences such that $(a_n), (c_n)$ are bounded and $a_n \leq b_n \leq c_n$ for each $n=1,2, \dots$ I want to show that $(b_n)$ has a convergent subsequence.
I have thought the following:
Since $(a_n), (c_n)$ are bounded, $\exists m_1, m_2 \in...