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Easily. Indeed, it might be empty.

Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set.

For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.

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Q: Is intersection of two countably infinite sets can be finite?
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