# Set Theory for Physicists

- Nicolas A Pereyra

- May 2019

### Description

This book provides a rigorous, physics-focused introduction to set theory that is geared towards natural science majors. The science major is presented with a robust introduction to set theory, which concentrates on the specific knowledge and skills that will be needed for calculus and natural science topics in general.### About Editors

Nicolas A Pereyra pursued his undergraduate studies in physics in Caracas at the Universidad Central de Venezuela, where he graduated in 1991. Following this, he studied physics at the University of Maryland at College Park where he obtained his MS and PhD in 1995 and 1997. Currently, Pereyra is an associate professor in astrophysics at the Physics and Astronomy Department of the University of Texas Rio Grande Valley. His research work has largely focused on the development of computational models of physical systems, and he is presently working on the development of computational models of accretion disk winds in QSOs.### Table of Contents

Contents

Preface

Acknowledgements

Author Biography

1 Equality '='

2 Fundamental Properties of Sets

2.1 What is a Set?

2.2 Defining a Set

2.3 Equality of Sets

2.4 A Set Can Be an Element of Another Set

2.5 A Set Cannot Contain Itself

2.6 A Set Can Be Empty (Null )

2.7 Subsets

2.7.1 Definition of Subsets

2.7.2 A ⊂ A

2.7.3 ∅ ⊂ A

3 Set Operators

3.1 What is a set operator?

3.2 The ∪ Operator (UNION)

3.2.1 The Commutative Property of ∪

3.2.2 The Associative Property of ∪

3.2.3 The ∪ operator and the empty set ∅

3.3 The ∩ Operator (INTERSECTION)

3.3.1 The Commutative Property of ∩

3.3.2 The Associative Property of ∩

3.3.3 The ∩ operator and the empty set ∅

3.4 Mixed Properties of ∪ and ∩

3.5 The \ Operator (SET SUBSTRACTION)

3.5.1 The \ operator and the empty set ∅

3.6 Mixed Properties of \ , ∪ and ∩

3.7 The × Operator (CARTESIAN PRODUCT)

3.7.1 The × operator and the empty set ∅

4 Universal Set Systems

4.1 What is a Universal Set?

4.2 Complement

4.3 Properties of the Complement

5 Relations and Functions

5.1 What is a Relation?

5.2 One-to-one Relations

5.3 What is a Function?

6 Equivalence Relations and Classes

6.1 What is an Equivalence Relation?

6.2 What is an Equivalence Class?

7 Mathematical Theory

7.1 Axiomatic Definitions and Definitions

7.2 Axioms and Theorems

8 Appendix

8.1 General Equations of Set Theory

8.2 Universal Set Systems

8.3 Relations and Functions

8.3.1 Relations

8.3.2 One-to-one Relations

8.3.3 Functions

8.4 Equivalence Relations and Classes

8.4.1 Equivalence Relations

8.4.2 Equivalence Classes### Bibliographic

Paperback ISBN: 9780750329866

Ebook ISBN: 9781643276496

DOI: 10.1088/2053-2571/ab126a

Publisher: Morgan & Claypool Publishers