 Solution

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

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

No, even when every element of $S$ is positive. Take

S = {\frac{1}{2}}, T = {1, 2} .

Then

S^{T} = {1/2, 1/4}

, so

sup (S^{T}) = \frac{1}{2}, (sup S)^{s u p T} = (\frac{1}{2})^{2} = \frac{1}{4} .

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