Chapter 2 - The Language of Sets

Abstract

This chapter explores the concept of a set, which is so fundamental that it unifies mathematics and its cognates. It has revolutionized mathematical thinking, enabling ones' expression in clear and concise terms. This chapter presents the language of sets stating the concept of a set, the various ways of describing a set, the construction of new sets from known sets, a variety of applications, and a brief introduction to fuzzy sets. It also describes the various ways of constructing new sets from known sets and highlights some of the tricky problems involved in finding out the number of positive integers, subsets, and the definition of sets of legally paired parentheses. The questions explored in this chapter include: (1) finding out the number of positive integers ≤ N and divisible by a, b, or c, (2) finding out the number of subsets in a finite set with n elements; (3) defining a set of legally paired parenthesis; and (4) finding out the number of sequences of legally paired parentheses can be formed using n pairs of left and right parentheses.