- 160 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Boolean Algebra
About this book
Famous for the number-theoretic first-order statement known as Goodstein's theorem, author R. L. Goodstein was also well known as a distinguished educator. With this text, he offers an elementary treatment that employs Boolean algebra as a simple medium for introducing important concepts of modern algebra.
The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a detailed examination of three different axiomatizations, and an outline of a fourth system of axioms appears in the examples. The final chapter, on lattices, examines Boolean algebra in the setting of the theory of partial order. Numerous examples appear at the end of each chapter, with full solutions at the end.
The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a detailed examination of three different axiomatizations, and an outline of a fourth system of axioms appears in the examples. The final chapter, on lattices, examines Boolean algebra in the setting of the theory of partial order. Numerous examples appear at the end of each chapter, with full solutions at the end.
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Yes, you can access Boolean Algebra by R. L. Goodstein in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.
Information
CHAPTER ONE
The informal algebra of classes
1.0. Classes. Collections of objects, whether they are identified by a survey of their members or by means of some characteristic property which their members have, are called classes. The students in a particular room at a particular time form a class, the voters on an electoral roll of a certain town form a class (as do their names on the roll), the hairs on a man’s head, the blood-cells in his body, the seconds of time he has lived, all these form classes. Featherless bipeds and mammals with the power of speech are classes characterized by common properties of their members; they are classes with a common membership, equal classes, as we shall say.
1.1. Membership. We shall use capital letters as names of classes. If an object a is a member of a class A we shall write
and say that “a belon...
Table of contents
- Cover
- Title Page
- Copyright Page
- Preface
- Contents
- Chapter I. The Informal Algebra of Classes
- Chapter II. The Self-Dual System of Axioms
- Chapter III. Boolean Equations
- Chapter IV. Sentence Logic
- Chapter V. Lattices
- Solutions to Examples
- Bibliography
- Index