20: Counting
- Page ID
- 83504
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- 20.1: Motivation
- You probably learned to count before you even started kindergarten. But efficiently counting large collections can be difficult!
- 20.2: Addition and subtraction rules
- As usual in mathematics, breaking a big problem into smaller parts is a useful strategy.
- 20.3: Multiplication Rule
- Counting a small Cartesian product. What is |A×B| for A={0,1,2,3} and B={−1,0,1}?
- 20.4: Division Rule
- 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.
- 20.5: Pigeonhole Principle
- Pigeonhole Principle (formal version). If A,B are finite sets with |B|<|A|, then no function A→B can be an injection.