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Infimum**

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