 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-24/1/a/iii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

f \leq^{*} g ⟺ \exists N \in ω \forall n \geq N f (n) \leq g (n) .

C \subseteq ω^{ω}

satisfies

\forall f \in ω^{ω} \exists g \in C (f \leq^{*} g) .

It must dominate every function, and the exceptional finite initial interval may depend on both functions.

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