Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 1 / c / i / 2 / Solution

A least upper bound of $S$ is an element $u\in A$ such that $s⪯u$ for every $s\in S$, and such that $u⪯v$ for every other upper bound $v\in A$ of $S$. It need not belong to $S$. The antisymmetric relation axiom makes it unique whenever it exists.