From Counting to Continuum: What Are Real Numbers, Really? - Couverture rigide

Scheinerman, Edward

 
9781009538640: From Counting to Continuum: What Are Real Numbers, Really?
Couverture rigide
ISBN 10 : 1009538640 ISBN 13 : 9781009538640
Editeur : Cambridge University Press, 2024

Synopsis

Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like π, are, frankly, really difficult to describe rigorously. Instead of waiting to take a theorem-proof graduate course to appreciate the real numbers, readers new to university-level mathematics can explore the core ideas behind the construction of the real numbers in this friendly introduction. Beginning with the intuitive notion of counting, the book progresses step-by-step to the real numbers. Each sort of number is defined in terms of a simpler kind by developing an equivalence relation on a previous idea. We find the finite sets' equivalence classes are the natural numbers. Integers are equivalence classes of pairs of natural numbers. Modular numbers are equivalence classes of integers. And so forth. Exercises and their solutions are included.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Understanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like π, are, frankly, really difficult to describe rigorously. Instead of waiting to take a theorem-proof graduate course to appreciate the real numbers, readers new to university-level mathematics can explore the core ideas behind the construction of the real numbers in this friendly introduction. Beginning with the intuitive notion of counting, the book progresses step-by-step to the real numbers. Each sort of number is defined in terms of a simpler kind by developing an equivalence relation on a previous idea. We find the finite sets' equivalence classes are the natural numbers. Integers are equivalence classes of pairs of natural numbers. Modular numbers are equivalence classes of integers. And so forth. Exercises and their solutions are included.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2024
Langue
anglais
ISBN 10 
1009538640
ISBN 13 
9781009538640
Reliure
Relié
Nombre de pages
228
Coordonnées du fabricant
Cambridge University Press
https://www.cambridge.org/

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Pomezia
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Autres éditions populaires du même titre

9781009538671: From Counting to Continuum

Edition présentée

ISBN 10 :  1009538675 ISBN 13 :  9781009538671
Editeur : Cambridge University Press, 2024
Couverture souple