A factor is said to be of type II if there are no minimal projections but there are non-zero finite projections. This implies that every projection "E" can be “halved” in the sense that there are two projections "F" and "G" that are Murray–von Neumann equivalent and satisfy "E" = "F" + "G". If the identity operator in a type II factor is finite, the factor is said to be of type II1; otherwise, it is said to be of type II∞. The best understood factors of type II are the hyperfinite type II1 factor and the hyperfinite type II∞ factor, found by . These are the unique hyperfinite factors of types II1 and II∞; there are an uncountable number of other factors of these types that are the subject of intensive study. proved the fundamental result that a factor of type II1 has a unique finite tracial state, and the set of traces of projections is [0,1].