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

Table of contents
- 1 i
  - Solution 1
- 2 i
  - Solution 2

1

Solution

The greatest element of

S

, also called its maximum, is an element

m \in S

such that

s ⪯ m

for every

s \in S

. Membership in

S

is essential; an upper bound need not belong to

S

.

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.

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