Corollary
21
[20K](Solved on 2022-11-24) Having fixed a set \(Aββ\) not empty, then \(\sup A\) is the only number \(πΌβββͺ\{ +β\} \) which satisfies these two properties
\begin{align*} β xβ A,xβ€ πΌ \\ β h{\lt}πΌ, β xβ A,x{\gt} h \end{align*}
as already seen in [22S] for the more general case of totally ordered sets.