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Let A be the set of your pigeons, and let B be the set of pigeonholes in which they live. The Generalized Pigeonhole Principle states

Let A be the set of your pigeons, and let B be the set of pigeonholes in which they live. The Generalized Pigeonhole Principle states that for a natural number k, if |A| > k|B|, then there exists a pigeonhole in which more than k pigeons live. Prove the Generalized Pigeonhole Principle by contradiction.

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