Show that lim inf $\{a_{n}\}$ $\leq$ lim sup $\{a_{n}\}$
Proof: let $\{a_n\}$ be a sequence such that $\{a_n\}$ is bounded, so by definition
lim inf $\{a_{n}\}$ = lim inf $\{a_{n}: n\geq k\}$ as n goes to infinity and,
lim sup $\{a_{n}\}$ = lim sup $\{a_{n}: n\geq k\}$ and, as n goes to infinity
thus i can conclude that lim inf $\{a_{n}\}$ $\leq$ lim sup $\{a_{n}\}$.
i feel like there is more to this problem than just using the definition to prove it...
