 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/ii/paper-2/14h/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-10-05

True. If

α β = β α

, repeated use of associativity gives

α^{2} β^{2} = α (α β) β = α (β α) β = (α β)^{2} = (β α)^{2} = β^{2} α^{2} .

No unlicensed commutativity of ordinal multiplication is being used: only the assumed commuting pair is swapped.

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