An element $m$ is a <maximum> of $S$ if \b[$m\in S$ and $s\leq m$ for every $s\in S$]. Thus it is an <upper bound> that is itself a member. Every <maximum> is the <least upper bound>: any <upper bound> must lie above $m$ because $m\in S$. A <supremum> outside $S$ need not be a <maximum>.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 3 / c / ii / Solution

 Solution (source code)