Unformatted text preview: n holes, there is room for only n pigeons. This contradicts the fact that a total of n + 1 pigeons are within the n holes. Thus, the theorem must be correct. ✷ (b) Proof : i. Base case. For one pigeon hole and two pigeons, there must be two pigeons in the hole. ii. Induction Hypothesis. For n pigeons in n − 1 holes, some hole must contain at least two pigeons....
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- Fall '08
- Mathematical Induction, Mathematical logic, base case, induction hypothesis, Mathematical proof