# Supremum of a series

Let $( x_n )$ be a bounded sequence, and define for each $m \in \Bbb{N}$, the number $u_m := \sup{x_n : n \le m}$. Show that $(u_m)$ is a bounded, decreasing sequence. I'm having trouble even conceptualizing this question, specifically, how to define $(x_n)$ in terms of each ($m \in \Bbb N$). Any insight would be much appreciated.

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