H. A. Thurston The Number System

ISBN 13: 9780486458069

The Number System

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9780486458069: The Number System
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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.

Altre edizioni note dello stesso titolo

9781114475779: The Number-System

Edizione in evidenza

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

9780486618487: The Number System

Dover ..., 1968
Brossura

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H. A. Thurston
Editore: Dover Publications (2007)
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Descrizione libro Dover Publications, 2007. Paperback. Condizione: New. Never used!. Codice articolo 0486458067

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Descrizione libro Dover Publications Inc., United States, 2007. Paperback. Condizione: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. 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 BTE9780486458069

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H.A. Thurston
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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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H.A. Thurston
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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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