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This question already has an answer here:

Suppose that a set $A$ is denumerable. Prove that there is a partition $P$ of $A$ where $P$ is denumerable and every $X \in P$ is also denumerable.

I can see that this can be done but I cannot figure out how to construct it where every $X \in P$ is denumerable and not finite. Any ideas here?

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marked as duplicate by Asaf Karagila elementary-set-theory Jan 19 '15 at 18:08

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HINT: Let $A=\{x_n:n\in\Bbb N\}$, and use the inverse of the pairing function.

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