If $\displaystyle S$ $\displaystyle \subseteq$ $\displaystyle R$ is a nonempty bounded set, and $\displaystyle I_s$ := [inf S, sup S], show that $\displaystyle S$ $\displaystyle \subseteq$ $\displaystyle I_s$. Moreover, if $\displaystyle J$ is any closed bounded interval containing $\displaystyle S$, show that $\displaystyle I_s$ $\displaystyle \subseteq$ $\displaystyle J$.

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