> Is there a formal proof the fiction can't come true?
No, by Gödel's second incompleteness theorem, formal systems can prove their own consistency if and only if they are inconsistent. So given that arithmetic is consistent, we'll never be able to _prove_ that it is. ( **EDIT** : Actually not quite true; see Alon's clarification below.)
As an aside, if you liked "Division by Zero," you might also like Greg Egan's pair of stories in which arithmetic isn't consistent: "Luminous" and "Dark Integers".