 Solution

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

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

True. If

x

is a nonempty finite set, then

rank (x) = sup_{y \in x} (rank (y) + 1) = max_{y \in x} (rank (y) + 1) .

This maximum is a successor ordinal, whereas the empty set has rank

0

. Hence a set of nonzero limit ordinal rank cannot be finite and must be an infinite set.

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