>>tromp+(OP)
I'm going to agree with the downvoted people and say that this sort of approach is largely meaningless if you allow arbitrary mappings. IMO the most reasonable mathematical formulation given the structure of the integers (in the sense of e.g. Peano) is that to truly represent an integer you have to represent zero and each other representable number has a representable predecessor, i.e. to say you can represent 5 you need 0,1,2,3,4, and 5 to be representable. By a straightforward counting argument, 2^64-1 is then the largest representable number, in other words the obvious thing is right.