= Maximum of a subset of a total order
{title2=$\max S$}
= Maximum
{synonym}
= Maxima
{synonym}
A maximum of a subset $S$ of a <total order> is an element $m\in S$ with $s\leq m$ for every $s\in S$. If it exists it is unique. Every nonempty finite subset has a maximum, by repeated pairwise comparison. Unlike a supremum, a maximum must belong to the subset. The completion time of jobs processed on finitely many parallel machines is the maximum of the machine completion times.
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