 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/16i/iii/solution

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

True. For each

y \in x

{y}

is a finite subset of

x

, so the hypothesis gives

rank (y) + 1 = rank ({y}) \leq c .

Taking the supremum over all

y \in x

yields

rank (x) = y \in x sup (rank (y) + 1) \leq c .

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