Solution
= Solution
An element $u\in A$ is a <least upper bound> of $S$ if it is an <upper bound>, meaning $s\leq u$ for every $s\in S$, and \b[$u\leq v$ for every <upper bound> $v\in A$ of $S$]. The candidate need not belong to $S$. Because a <partial order> is an <antisymmetric relation>, two <least upper bounds> must be equal. A <least upper bound> is also called the <supremum>.