<-- Go Back Last Updated: 10/06/2025

Supremum**

Given a Partial Order \((P,\leq)\) and a subset \(A\subseteq P\), the supremum of \(A\), if it exists, is the least upper bound of \(A\), i.e. the element \(\sup A\in P\) such that \(\forall x\in P:(\forall a\in A:a\leq x\Rightarrow \sup A\leq x)\). If the supremum exists it must be unique.