 Solution

ID: 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

An element

m

S

if $m \in S$ 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.

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