Description
This text is a textbook on set theory for undergraduate students. It begins with a discussion of the physical world and how set theory can be used to understand it. It then progresses to discussing finite sets, which are based in arithmetic, and permutations and combinations, which are based in mathematics. The book then discusses general set theory, including ordered sets and the paradoxes of set theory. The book also includes an appendix with helpful information, such as a glossary.
Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from concrete finite sets to cardinal numbers, infinite cardinals, and ordinals.
Although set theory begins in the intuitive and the concrete, it ascends to a very high degree of abstraction. All that is necessary to its grasp, declares author Joseph Breuer, is patience. Breuer illustrates the grounding of finite sets in arithmetic, permutations, and combinations, which provides the terminology and symbolism for further study. Discussions of general theory lead to a study of ordered sets, concluding with a look at the paradoxes of set theory and the nature of formalism and intuitionalism. Answers to exercises incorporated throughout the text appear at the end, along with an appendix featuring glossaries and other helpful information.
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