CRC Press Classic Set Theory - For Guided Independent Study

Classic Set Theory by CRC Press provides a modern perspective on the foundational work of Georg Cantor and Richard Dedekin. This text is specifically designed for undergraduate students seeking a structured approach to set theory through guided independent study. It bridges the gap between historical mathematical concepts and modern applications, making it a valuable resource for those studying discrete mathematics. Readers will explore the fundamental construction of number systems, including how to define real numbers using rational numbers and eventually natural numbers. The text also covers the essential process of defining natural numbers in terms of sets. By navigating through potential paradoxes and the Zermelo-Fraenkel axioms, students gain a deep understanding of the mathematical frameworks that govern the field. This book serves as a comprehensive guide for mastering the arithmetic of ordered sets and the distinction between Cantor's two types of transfinite numbers: cardinals and ordinals.