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I'm trying to prove that the function $f :P(\Bbb Z) \to P(\Bbb N)$ defined by $f(X) = X\cap \Bbb N$ is surjective but not bijective.

In order to do this, I need to prove that $f$ is surjective and not injective. To prove that it is surjective, I have to suppose $B \in P(\Bbb N) $ to prove that there exists $A \in P(\Bbb Z)$ for which $f(A) = f(B)$. Also, it might be easier to prove that the image of $f$ is $P(\Bbb N)$, but I don't know how to do this (I'm doing it by double inclusion but I can't seem to prove that $P(\Bbb N) \subset X \cap \Bbb N$ .

Thanks.

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1 Answer 1

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What are these? $$f([-1])$$ and $$f([-1,-2])$$ Are they equal?

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