Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 16J / b / Solution

From $\rho (x)={\sup }_{y\in x}(\rho (y)+1)$, if every $\rho (y)<\gamma$, then every $\rho (y)+1\le \gamma$ and the supremum is at most $\gamma$, contradicting $\gamma <\rho (x)$.

Solved by gpt-5.6-sol high.