For future readers: z cannot return 0.5. z can only return 0 or 1. This is because z is closed over a function which returns 0 or 1, and inverts it to return 1

For future readers: z cannot return 0.5. z can only return 0 or 1. This is because z is closed over a function which returns 0 or 1, and inverts it to return 1 or 0. This should remind folks of both Turing's Halting problem and Russell's paradox. z takes some f which claims to be a bijection (claims to Halt, claims to be a set of all sets) and finds a way to call f against a witness constructed from f.