 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/16h/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Assertion (iii) can be false. Let

κ = ℵ_{0}

and

λ = 2^{ℵ_{0}}

κ^{λ} = 2^{λ}, λ^{κ} = (2^{κ})^{κ} = 2^{κ^{2}} = 2^{κ} = λ .

2^{λ} > λ

, and therefore

κ^{λ} \neq = λ^{κ} .

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