# Math Help - [SOLVED] monotone sequence

1. ## # theory analysis

Let be a bounded sequence, and for each let $sup${>}. Prove that $(s_n)$ is monotone.

2. Originally Posted by perfectnumber
Let be a bounded sequence, and for each let $sup${>} and $t_n$ := $inf${>}. Prove that $(s_n)$ and $(t_n)$ are monotone and convergent. Also prove that if $lim(s_n) = lim(t_n)$, then $(x_n)$ is convergent.
All the details can be found in post #2 here.