Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 16J / b / Solution

Choose from every nonempty subset of $X$. By transfinite recursion setwhile the remainder is nonempty. This cannot continue through Hartogs theorem's ordinal $h(X)$, since that would inject $h(X)$ into $X$. It therefore exhausts $X$ at some ordinal, and the selection order well-orders $X$.

Solved by gpt-5.6-sol high.