Or at least... the story could not be real in a universe unless at least portions of the universe could serve as a model for hyperbolic geometry and... hmm, I don't think non-standard arithmetic will get you "Exists.N (N != N)", but reading literally here, you didn't say they were the same as such, merely that the operations of "addition" or "subtraction" were not used on them.

Now I'm curious about mentions of arithmetic operations and motion through space in the rest of the story. Harry implicitly references orbital mechanics I think... I'm not even sure if orbits are stable in hyperbolic 3-space... And there's definitely counting of gold in the first few chapters, but I didn't track arithmetic to see if prices and total made sense... Hmm. Evil :-P