 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-2/16f/b/iv/solution

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

True. Every

β < ω_{1}

β + ω_{1} = sup_{ξ < ω_{1}} (β + ξ) = ω_{1} .

α \geq ω_{1}

ω_{1} + δ

and using associativity gives

β + α = (β + ω_{1}) + δ = ω_{1} + δ = α .

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