As far as I know, let $S \subset \mathbb{R}$ which is bounded above, then $\operatorname{cl}(S)$ includes $\sup(S)$. Also, if $S$ is bounded below, then $\inf(S) \in \operatorname{cl}(S)$. But, does $\inf(S) \in \operatorname{cl}(S)$ when $S$ has bounded above? How do you prove that? I suppose the answer is no, but I could not construct any proof.
2026-04-04 14:53:07.1775314387
Does the closure of bounded above subset of reals includes both infinimum and supremum?
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