 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-4/7e/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Yes. Put

α = sup S

and

β = sup T

. Every

s + t \leq α + β

, so this is an upper bound. Given

ε > 0

, choose

s \in S

with

s > α - ε /2

and

t \in T

with

t > β - ε /2

. Then

s + t > α + β - ε

. Hence

sup (S + T) = sup S + sup T .

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