# Number Systems and the Foundations of Analysis

## Mendelson, Elliott

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Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.

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Contenuti:

Chapter 1. Basic Facts and Notions of Logic and Set Theory 1.1 Logical Connectives 1.2 Conditionals 1.3 Biconditionals 1.4 Quantifiers 1.5 Sets 1.6 Membership. Equality and Inclusion of Sets 1.7 The Empty Set 1.8 Union and Intersection 1.9 Difference and Complement 1.10 Power Set 1.11 Arbitrary Unions and Intersections 1.12 Ordered Pairs 1.13 Cartesian Product 1.14 Relations 1.15 Inverse and Composition of Relations 1.16 Reflexivity, Symmetry, and Transitivity 1.17 Equivalence Relations 1.18 Functions 1.19 Functions from A into (Onto) B 1.20 One-One Functions 1.21 Composition of Functions 1.22 Operations Chapter 2. The Natural Numbers 2.1 Peano Systems 2.2 The Iteration Theorem 2.3 Application of the Iteration Theorem: Addition 2.4 The Order Relation 2.5 Multiplication 2.6 Exponentiation 2.7 Isomorphism, Categoricity 2.8 A Basic Existence Assumption Supplementary Exercises Suggestions for Further Reading Chapter 3. The Integers 3.1 Definition of the Integers 3.2 Addition and Multiplication of Integers 3.3 Rings and Integral Domains 3.4 Ordered Integral Domains 3.5 Greatest Common Divisor, Primes 3.6 Integers Modulo n 3.7 Characteristic of an Integral Domain 3.8 Natural Numbers and Integers of an Integral Domain 3.9 Subdomains, Isomorphisms, Characterizations of the Integers Supplementary Exercises Chapter 4. Rational Numbers and Ordered Fields 4.1 Rational Numbers 4.2 Fields 4.3 Quotient field of an Integral Domain 4.4 Ordered Fields 4.5 Subfields. Rational Numbers of a Field. Chapter 5. The Real Number System 5.1 Inadequacy of the Rationals 5.2 Archimedean Ordered Fields 5.3 Least Upper Bounds and Greatest Lower Bounds 5.4 The Categoricity of the Theory of Complete Ordered Fields 5.5 Convergent Sequences and Cauchy Sequences 5.6 Cauchy Completion. The Real Number System 5.7 Elementary Topology of the Real Number System 5.8 Continuous Functions 5.9 Infinite Series Appendix A. Equality Appendix B. Finite Sums and the Sum Notation Appendix C. Polynomials Appendix D. Finite, Infinite, and Denumerable Sets. Cardinal Numbers Appendix E. Axiomatic Set Theory and the Existence of a Peano System Appendix F. Construction of the Real Numbers via Dedekind Cuts Appendix G.Complex Numbers Bibliography Index of Special Symbols Index

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## 1.Number Systems and the Foundations of Analysis

Editore: Dover Publications Inc. (2007)
ISBN 10: 0486457923 ISBN 13: 9780486457925
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Descrizione libro Dover Publications Inc., 2007. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486457925

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## 2.Number Systems and the Foundations of Analysis (Paperback)

Editore: Dover Publications Inc., United States (2008)
ISBN 10: 0486457923 ISBN 13: 9780486457925
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Descrizione libro Dover Publications Inc., United States, 2008. Paperback. Condizione libro: New. 213 x 135 mm. Language: English . Brand New Book. This study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Written by a noted expert on logic and set theory, it assumes no background in abstract mathematical thought. Undergraduates and beginning graduate students will find this treatment an ideal introduction to number systems, particularly in terms of its detailed proofs. Starting with the basic facts and notions of logic and set theory, the text offers an axiomatic presentation of the simplest structure, the system of natural numbers. It proceeds, by set-theoretic methods, to an examination of integers that covers rings and integral domains, ordered integral domains, and natural numbers and integers of an integral domain. A look at rational numbers and ordered fields follows, along with a survey of the real number system that includes considerations of least upper bounds and greatest lower bounds, convergent and Cauchy sequences, and elementary topology. Numerous exercises and several helpful appendixes supplement the text. Codice libro della libreria AAC9780486457925

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## 3.Number Systems and the Foundations of Analysis (Paperback)

Editore: Dover Publications Inc., United States (2008)
ISBN 10: 0486457923 ISBN 13: 9780486457925
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Descrizione libro Dover Publications Inc., United States, 2008. Paperback. Condizione libro: New. 213 x 135 mm. Language: English . Brand New Book. This study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Written by a noted expert on logic and set theory, it assumes no background in abstract mathematical thought. Undergraduates and beginning graduate students will find this treatment an ideal introduction to number systems, particularly in terms of its detailed proofs. Starting with the basic facts and notions of logic and set theory, the text offers an axiomatic presentation of the simplest structure, the system of natural numbers. It proceeds, by set-theoretic methods, to an examination of integers that covers rings and integral domains, ordered integral domains, and natural numbers and integers of an integral domain. A look at rational numbers and ordered fields follows, along with a survey of the real number system that includes considerations of least upper bounds and greatest lower bounds, convergent and Cauchy sequences, and elementary topology. Numerous exercises and several helpful appendixes supplement the text. Codice libro della libreria AAC9780486457925

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Descrizione libro Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-ING-00448222

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## 5.Number Systems and the Foundations of Analysis (Dover Books on Mathematics)

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## 8.Number Systems and the Foundations of Analysis

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Descrizione libro Dover Publications. Paperback. Condizione libro: New. Paperback. 358 pages. Dimensions: 8.4in. x 5.3in. x 0.9in.This study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Written by a noted expert on logic and set theory, it assumes no background in abstract mathematical thought. Undergraduates and beginning graduate students will find this treatment an ideal introduction to number systems, particularly in terms of its detailed proofs. Starting with the basic facts and notions of logic and set theory, the text offers an axiomatic presentation of the simplest structure, the system of natural numbers. It proceeds, by set-theoretic methods, to an examination of integers that covers rings and integral domains, ordered integral domains, and natural numbers and integers of an integral domain. A look at rational numbers and ordered fields follows, along with a survey of the real number system that includes considerations of least upper bounds and greatest lower bounds, convergent and Cauchy sequences, and elementary topology. Numerous exercises and several helpful appendixes supplement the text. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780486457925

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## 9.Number Systems and the Foundations of Analysis (Dover Books on Mathematics)

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Descrizione libro Dover Publications, Inc. PAPERBACK. Condizione libro: New. 0486457923. Codice libro della libreria Z0486457923ZN

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## 10.Number Systems and the Foundations of Analysis (Dover Books on Mathematics)

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ISBN 10: 0486457923 ISBN 13: 9780486457925
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Descrizione libro Dover Publications, Inc., 2008. Paperback. Condizione libro: New. Codice libro della libreria INGM9780486457925

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