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In page Pigeonhole principle:
"This principle is not a generalization of the pigeonhole principle for finite sets however: It is in general false for finite sets. In technical terms it says that if A and B are finite sets such that any surjective function from A to B is not injective, then there exists an element b of B such that there exists a bijection between the preimage of b and A.[citation needed] This is a quite different statement, and is absurd for large finite cardinalities.
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