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From counting to continuum = what ar...

Scheinerman, Edward R.

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From counting to continuum = what are real numbers, really? /

Record Type:	Electronic resources : Monograph/item
Title/Author:	From counting to continuum/ Edward Scheinerman.
Reminder of title:	what are real numbers, really? /
Author:	Scheinerman, Edward R.
Published:	Cambridge :Cambridge University Press, : 2025.,
Description:	xvii, 212 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 06 Dec 2024).
Subject:	Numbers, Real. -
Online resource:	https://doi.org/10.1017/9781009538657
ISBN:	9781009538657

From counting to continuum = what are real numbers, really? /
Scheinerman, Edward R.

From counting to continuumwhat are real numbers, really? /[electronic resource] :Edward Scheinerman. - Cambridge :Cambridge University Press,2025. - xvii, 212 p. :ill., digital ;24 cm.

Title from publisher's bibliographic system (viewed on 06 Dec 2024).

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.

ISBN: 9781009538657Subjects--Topical Terms:

544169
Numbers, Real.

LC Class. No.: QA241 / .S24 2025

Dewey Class. No.: 512.81

From counting to continuum = what are real numbers, really? /
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245 1 0 $a From counting to continuum $h [electronic resource] : $b what are real numbers, really? / $c Edward Scheinerman.
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500 $a Title from publisher's bibliographic system (viewed on 06 Dec 2024).
520 $a 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.
650 0 $a Numbers, Real. $3 544169
856 4 0 $u https://doi.org/10.1017/9781009538657