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Proof WritingHardExistence, Uniqueness and Counterexamples

Existence, Uniqueness and Counterexamples · Hard problem

Claim: if f:Z→Zf: \mathbb{Z} \to \mathbb{Z} satisfies f(f(n))=nf(f(n)) = n for every integer nn, then f(n)=nf(n) = n for all nn or f(n)=−nf(n) = -n for all nn. Which function is a counterexample?