Recursive enumerability

Recursive enumerability refers to sets or problems where, if the answer exists, there’s a systematic way (algorithm) to list all the valid instances or solutions, though it may not be able to decide quickly if a particular item belongs. Imagine having a process that can generate every valid example over time—if an item is in the set, it will eventually appear on the list. However, for some items not in the set, the process might run forever without confirming their absence. This concept helps distinguish problems that are partially, but not fully, algorithmically solvable.