Suppose $X$ is a partially ordered set. Let $A$ be a finite subset of $X$. Is $A$ bounded? (That is, do there exist upper and lower bounds for $A$?)
It seems false but unable to find a counter example.
2026-04-07 19:02:16.1775588536
Is a finite subset of a partially ordered set bounded?
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Every finite partial order has a maximal (and minimal) element, and the subset of maximal/minimal elements make a boundary to $A$.
If you are talking about an element strictly larger than all the points in $A$ then the answer would be negative, for example $A=X=\{0,1\}$ in the discrete order.