Concept explainers
Pigeonhole principle. Recall the Pigeonhole principle from the first section in Chapter 2. Restate this principle in terms of a correspondence. Suppose you try a method of assigning pigeons to holes and, after filling all the holes, some pigeons remain. If you remove the pigeons and try again, is there any hope of placing each pigeon in an individual hole the second time? Suppose you have an infinite number of pigeons and pigeonholes. Is it possible that a first attempt to give each pigeon an individual hole failed but a second attempt succeeded?

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Chapter 3 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)
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