Prove that lim(inf(x_n)) is lessthan or equal to lim(sup(x_n)), for every bounded sequence x_n of real numbers.
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$\begin{array}{l}{\text { Prove that if } \lim _{n \rightarrow n \rightarrow 0} a_{n}=0 \text { and }\left\{b_{n}\right\} \text { is bounded, then }} \\ {\lim _{n \rightarrow \infty}\left(a_{n} b_{n}\right)=0.}\end{array}$
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