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20.1: Motivation
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You probably learned to count before you even started kindergarten. But efficiently counting large collections can be difficult!
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20.2: Addition and subtraction rules
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As usual in mathematics, breaking a big problem into smaller parts is a useful strategy.
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20.3: Multiplication Rule
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Counting a small Cartesian product. What is |A×B| for A={0,1,2,3} and B={−1,0,1}?
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20.4: Division Rule
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Sometimes it is easier to count a related but more structured collection, where the collection we actually want to count corresponds to equivalence classes of the more structured collection.
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20.5: Pigeonhole Principle
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Pigeonhole Principle (formal version). If A,B are finite sets with |B|<|A|, then no function A→B can be an injection.
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20.6: Activities
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20.7: Exercises
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