By the Bolzano-Weierstrass theorem, we know that any bounded sequence $\{x\_n\}$ has a convergent subsequence. Also, if there exists a converge subsequence, it's not always true that the sequence $\{x\_n\}$ is bounded($\{x\_n\}$ doesn't always have both upper bound and lower bound), but is it possible to conclude that $\{x\_n\}$ at least has one of them(have at least upper bound or lower bound) if there exists a converge subsequence $\{x\_{n\_k}\}$?