In the set-agreement problem, n processes seek to agree on at most n−1 different values. This paper determines the weakest failure detector to solve this problem in a message-passing system where processes may fail by crashing. This failure detector, called the Loneliness detector and denoted L, outputs one of two values, “true” or “false” such that: (1) there is at least one process where L outputs always “false”, and (2) if only one process is correct, L eventually outputs “true” at this process.