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Fiction "Division by Zero" By Ted Chiang

I read the fiction story "Division by Zero" By Ted Chiang

My interpretation is the character finds a proof that arithmetic is inconsistent.

Is there a formal proof the fiction can't come true? (I don't suggest the fiction can come true).

EDIT: I see someone tried

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    Possibly worth saying, though - there are some people who claim it's possible to taking a ratio of the largest useful number to the smallest useful number based on physics and astronomy, and give infinity a finite value. Do this and arithmetic is trivially proven to be self-contradictary.2010-12-18

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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".

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    Is this scenario possible: No matter if arithmetic is consistent or not, it can prove that a counterexample of its consistency can't be constructed, well, within itself (sorry if that doesn't make any sence, I mean, a counterexample will need more axioms).2010-12-20