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Question
Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if "n is even"):}` Is the function injective? Justify your answer.
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Solution
Let y ∈ N(codomain). Then ∃ 2y ∈ N(domain) such that f(2y) = `(2y)/2` = y. Hence, f is surjective.
1, 2 ∈ N(domain) such that f(1) = 1 = f(2)
Hence, f is not injective.
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