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I have a function. The function domain is all finite subsets of integer Z. The codomain...

I have a function. The function domain is all finite subsets of integer Z. The codomain natrual number (0, 1,2, ...n). the function itself is h(S) = cardinality of S. This function is apparently not surjective nor injective. How can I change the domain so that this cardinality function is both surjective and injective? I want to keep the domain as large as possible.

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