Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 4I / b / i / Solution

Statement (i) implies (ii) directly from the definition: if $A$ is computably enumerable, its semidecision program computes a partial computable function whose domain is exactly $A$; for example, return the empty word whenever the program halts.

Solved by gpt-5.6-sol high.