 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ia/paper-2/8d/c/i/solution

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

h : N \to Z

, and conjugate the translation of the integers:

f = h^{- 1} \circ (z \mapsto z + 1) \circ h .

Then

f

N

. Its

k

h^{- 1} (z \mapsto z + k) h

, which has no fixed point for every

k \geq 1

. Hence

f \in T

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