ENGLISH

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

By Edward Scheinerman

Book information

Publisher
Cambridge University Press
Year
2024
ISBN
1009538640, 1009538675, 9781009538640, 9781009538657, 9781009538671
DOI
10.1017/9781009538657
LCC
QA247.5
Language
english
Format
PDF
Filesize
10 MB (10795035 bytes)
Edition
1
Pages
228\231
Topic
Mathematics
Orientation
no
Paginated
no
Scanned
portrait
Time added
2024-12-07 18:24:36
complex numbersMathematics; Natural Numbersreal numbersRelationsSets

Description

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.

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