 One difficulty with the formulation above is that ordinary physical systems admit of uncountably many physical states, whereas ordinary computational descriptions, such as TM tables, consist of countably many states. Thus, there are not enough computational states for the physical states to map onto. One solution to this problem is to reverse the direction of the mapping, requiring a mapping of the computational states onto (a subset of) the physical states. Another, more common solution to this problem—often implicit—is to select either a subset of the physical states or equivalence classes of the physical states and map those onto the computational states. When this is done, clause (i) is replaced by the following: (i′) there is a mapping from a subset of (or equivalence classes of) the physical states of S to the states of computational description C.