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Pigeon-Hole Principle

It's amazing how a very simple and obvious thing in life become a mathematical principle and helps to prove many complex results. Pigeon-Hole principle is one such concept. At first it seems as a very obvious fact and one may wonder whether it deserves such a place in mathematics. But this principle becomes very useful in many occasions to prove that there exists some answer for a problem.

You should look up axiom of choice

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