Articoli correlati a From Counting to Continuum: What Are Real Numbers,...

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

Scheinerman, Edward

 
9781009538640: From Counting to Continuum: What Are Real Numbers, Really?
Rilegato
ISBN 10: 1009538640 ISBN 13: 9781009538640
Casa editrice: Cambridge Univ Pr, 2024

Sinossi

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 p, 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.

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

Informazioni sull'autore

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.

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

Editore
Cambridge Univ Pr
Data di pubblicazione
2024
Lingua
Inglese
ISBN 10 
1009538640
ISBN 13 
9781009538640
Rilegatura
Copertina rigida
Numero di pagine
212
Contatto del produttore
Cambridge University Press
https://www.cambridge.org/

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