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Biased generalizing
Biased sample
-2 is the additive inverse of +2
2 1/2
The main idea is the most important one! If you have fewer pigeon holes than pigeons and you put every pigeon in a pigeon hole, then there must result at least one pigeon hole with more than one pigeon. Expand the idea perhaps using a finite example. 21 pigeons and 10 holes. Try and see how at least one hole must have more than 2 pigeons. Then think about generalizing it. The real power comes from seeing this all in action. A commonly used example is: Among any N positive integers, there exists 2 whose difference is divisible by N-1.