"Given the nature of the multiverse, everything that can possibly happen will happen. This includes works of fiction: anything that can be imagined and written about, will be imagined and written about. If every story is being written, then someone, somewhere in the multiverse is writing your story. To them, you are a fictional character. What that means is that the barrier which separates the dimensions from each other is in fact the Fourth Wall."
-- In Flight Gaiden: Playing with Tropes
(Conversely, many fictions are instantiated somewhere, in some infinitesimal measure. However, I deliberately included logical impossibilities into HPMOR, such as tiling a corridor in pentagons and having the objects in Dumbledore's room change number without any being added or subtracted, to avoid the story being real anywhere.)
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 mechanic...
Here's the new thread for posting quotes, with the usual rules: