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The Theory of Counting

Chapter
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Abstract

The theory of counting, or enumeration, is the theoretical counterpart of everyday practical counting. The chapter starts by defining an experiment to be any activity with well-defined, observable outcomes or results, and an event as a set of outcomes. Tree diagrams are introduced to represent sequences of events.

The multiplication principle and the rule of sum are introduced. Venn diagrams are used to describe events and in counting the number of outcomes in unions and intersections of events. The principle of inclusion and exclusion is introduced.

One-to-one correspondences are discussed, as are finite and infinite and countable and uncountable sets. Selections and arrangements are studied, leading to the binomial theorem.

Keywords

Venn Diagram British Airways Flight Track Team Positive Integer Index Scrabble Tiles 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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