# The Number System

## H. A. Thurston

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The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.
This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti:

Part I: Explanatory Treatment 1. Counting 2. Whole Numbers 3. The Laws of Arithmetic 4. Fractions 5. Negative Numbers 6. Fields 7. Irrational Numbers 8. Powers 9. Complex Numbers 10. Verification of the Axioms 11. Alternative Treatments Part II: Systematic Treatment 1. Whole Numbers 2. Hemigroups and Groups 3. Integers 4. Fields 5. Rational Numbers 6. Ordered Fields 7. The Order-Relation for Rationals 8. Exponentiation 9. Cauchy Numbers 10. Real Numbers 11. Complex Numbers Bibliography Key to the Exercises Index

Product Description:

This book explores arithmetic's underlying concepts and their logical development. It offers an informal and intuitive understanding of the rigorous logical approach, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. Numerous exercises help students test their progress and practice concepts. 1956 edition.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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### Altre edizioni note dello stesso titolo

#### Edizione in evidenza

ISBN 10:  1114475777 ISBN 13:  9781114475779
Casa editrice: Blackie and Son, 1956
Rilegato

Dover ..., 1968
Brossura

## 1.The Number System

ISBN 10: 0486458067 ISBN 13: 9780486458069
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Descrizione libro 2007. PAP. Condizione: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice articolo IB-9780486458069

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## 2.The Number System (Paperback)

Editore: Dover Publications Inc., United States (2007)
ISBN 10: 0486458067 ISBN 13: 9780486458069
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Descrizione libro Dover Publications Inc., United States, 2007. Paperback. Condizione: New. Language: English. Brand new Book. The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts. Codice articolo AAC9780486458069

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## 3.The Number System (Paperback)

Editore: Dover Publications Inc., United States (2007)
ISBN 10: 0486458067 ISBN 13: 9780486458069
Nuovo Paperback Quantità: 10
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Valutazione libreria

Descrizione libro Dover Publications Inc., United States, 2007. Paperback. Condizione: New. Language: English. Brand new Book. The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts. Codice articolo AAC9780486458069

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## 4.The Number System (Dover Books on Mathematics)

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## 5.The Number System Format: Paperback

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## 7.The Number System (Dover Books on Mathematics)

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## 8.The Number System (Paperback or Softback)

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ISBN 10: 0486458067 ISBN 13: 9780486458069
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Descrizione libro Dover Publications 4/19/2007, 2007. Paperback or Softback. Condizione: New. The Number System. Book. Codice articolo BBS-9780486458069

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## 10.The Number System (Paperback)

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Descrizione libro Paperback. Condizione: New. Paperback. This book explores arithmetic's underlying concepts and their logical development. It offers an informal and intuitive understanding of the rigorous logical approach, in addition to a deta.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 134 pages. 0.159. Codice articolo 9780486458069

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