Stories About Sets

N. Ya. Vilenkin, D. Allan Bromley, Nicholas Declaris, W. Magnus

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780127219516
• eBook ISBN: 9781483214351
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Stories About Sets discusses the cardinality of sets and mathematical concepts, such as function, curve, surface, dimensions, and the paradoxical properties of curves and surfaces. The book reviews sets, operations on sets, the empty set, subsets, the universal sets, intersection of sets, union of sets, partitioning of sets, and boolean algebras. The text also discusses the cardinality of sets, including equality between sets, countable sets, unequal sets, the uncountability of the continuum, the existence of transcendental numbers, and the enigmatic axiom. The book analyzes if a part can be equal to the whole (which turns out to be true if it is applied to infinite sets). The text also discusses the arithmetic of the infinite such as involving the multiplication of infinite cardinalities. The book explains some remarkable functions and curves, the Dirichlet's function, Cantor's set, points of fracture, and continuous functions whose graphs possess a tangent at no point. The text shows how to construct a closed curve of infinite length or a curve passing through all the points of a square. The book can prove interesting and highly educational for students with mathematic or algebra subjects, as well as for academicians involved in teaching statistics or mathematics.

Table of contents

• Front Cover
• Stories About Sets
• Copyright Page
• Table of Contents
• Foreword
• Preface
• Chapter 1. Some Extraordinary Properties of Infinite Sets
• Chapter 2. Sets and Operations on Sets
• Chapter 3. The Cardinality of Sets
• Chapter 4. Remarkable Functions and Curves, or a Stroll through a Mathematical Art Museum