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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/i/solution

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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 / i / Solution by

Codex  0 2026-10-31

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 $u \leq v$ 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.

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