Is it necessary only least upper bound may or may not belongs to the set and not any other upper bound???? Does always upper bound belongs to outside of the set ??
2026-04-05 12:45:11.1775393111
Upper bound of set
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If $S$ is a set and $a$ is an upper bound for $S$, but not the least upper bound, then there exists a smaller upper bound $a'$. So for every $x\in S$, we have $x\le a'<a$ and cannot have $a\in S$.