Introduction to Set Theory by Karel HrbacekThoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
Set theory is concerned with the concept of a set, essentially a collection of objects that we call elements. Because of its generality, set theory forms the foundation of nearly every other part of mathematics. In order to make things easier for you as a reader, as well as for the writers, you will be expected to be familiar with a few topics before beginning. I hope to have some links to other Wikibooks here soon. Wikipedia has related information at Set theory.
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Lecturer: Dr Adam Epstein. Content : Set theoretical concepts and formulations are pervasive in modern mathematics. For this reason it is often said that set theory provides a foundation for mathematics. On a practical level, set theoretical language is a highly useful tool for the definition and construction of mathematical objects. On a more theoretical level, the very notion of a foundation has definite philosophical overtones, in connection with the reducibility of knowledge to agreed first principles.
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries. Either in that same course or early in a course on analysis, they also learn about the distinction between countable and uncountable sets. Every so often, however, an ambitious undergraduate or group of undergraduates wants to learn more. This book is intended to meet that need. It provides a careful introduction to axiomatic set theory that is accessible to smart and well-motivated undergraduates. Most graduate textbooks in axiomatic set theory require a large amount of mathematical logic just to get started.