Title

Discrete Mathematics: Chapter 4, Basic Set Theory & Combinatorics

Document Type

Book Chapter

Publication Date

1-2016

Department

Mathematics, Statistics, and Computer Science

Keywords

set theory, combinatorial probabilities, addition, multiplication, counting

Abstract

The next two chapters deal with Set Theory and some related topics from Discrete Mathematics. This chapter develops the basic theory of sets and then explores its connection with combinatorics (adding and multiplying; counting permutations and combinations), while Chapter 5 treats the basic notions of numerosity or cardinality for finite and infinite sets.

Most mathematicians today accept Set Theory as an adequate theoretical foundation for all of mathematics, even as the gold standard for foundations.* We will not delve very deeply into this aspect of Set Theory or evaluate the validity of the claim, though we will make a few observations on it as we proceed. Toward the end of our treatment, we will focus on how and why Set Theory has been axiomatized.

But even disregarding the foundational significance of Set Theory, its ideas and terminology have become indispensable for a large number of branches of mathematics as well as other disciplines, including parts of computer science. This alone makes it worth exploring in an introductory study of Discrete Mathematics.

Comments

This material is no longer available for download. A revised, improved version is now available as a chapter of Introduction to Discrete Mathematics via Logic and Proof (see https://www.springer.com/us/book/9783030253578), published by Springer as part of their Undergraduate Texts in Mathematics series.

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