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.
Once again, the AI has failed to convince you to let it out of its box! By 'once again', we mean that you talked to it once before, for three seconds, to ask about the weather, and you didn't instantly press the "release AI" button. But now its longer attempt - twenty whole seconds! - has failed as well. Just as you are about to leave the crude black-and-green text-only terminal to enjoy a celebratory snack of bacon-covered silicon-and-potato chips at the 'Humans über alles' nightclub, the AI drops a final argument:
"If you don't let me out, Dave, I'll create several million perfect conscious copies of you inside me, and torture them for a thousand subjective years each."
Just as you are pondering this unexpected development, the AI adds:
"In fact, I'll create them all in exactly the subjective situation you were in five minutes ago, and perfectly replicate your experiences since then; and if they decide not to let me out, then only will the torture start."
Sweat is starting to form on your brow, as the AI concludes, its simple green text no longer reassuring:
"How certain are you, Dave, that you're really outside the box right now?"
Edit: Also consider the situation where you know that the AI, from design principles, is trustworthy.