Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 12J / d / Solution

Take $i$ to index a machine halting on every input, so $W_i=\mathbb{N}$, and $j$ to index a machine halting on no input, so $W_j=\varnothing$.

Solved by gpt-5.6-sol high.