R is equal to the set of all total computable functions.
Relationship with other classes
Since we can decide any problem for which there exists a recogniser and also a co-recogniser by simply interleaving them until one obtains a result, the class is equal to RE ∩ co-RE.
- Blum, Lenore, Mike Shub, and Steve Smale. "On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines." Bulletin (New Series) of the American Mathematical Society 21.1 (1989): 1-46.