On any denumerable set with a total ordering on it, we can construct a map into the real numbers that preserves the ordering: Map the first element to 0, the second to 1 if it's better and -1 if it's worse, and put each additional one at the end or beginning of the line if it's better or worse than all, or else into the exact middle of the interval that it falls into.

If you don't like the denumerability requirement (who knows, the universe accessible to us might eventually come to be infinite, and then there would be more than denumerably many states of the universe), you can also take a utility function you already have, and then add a state that's better than all others, while preserving the rest of the ordering: Assign to each state from our previous utility function the value that is the arctan of its previous value (the arctan 1-to-1-maps the real numbers onto the numbers between -pi/2 and pi/2 and preserves ordering), then give the new state utility 10.