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From counting to continuumwhat are real numbers, really? /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	From counting to continuumEdward Scheinerman.
其他題名:	what are real numbers, really? /
作者:	Scheinerman, Edward R.
出版者:	Cambridge :Cambridge University Press,2025.
面頁冊數:	xvii, 212 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 06 Dec 2024).
標題:	Numbers, Real.
電子資源:	https://doi.org/10.1017/9781009538657
ISBN:	9781009538657$q(electronic bk.)

From counting to continuumwhat 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: 9781009538657$q(electronic bk.)Subjects--Topical Terms:

189607
Numbers, Real.

LC Class. No.: QA241 / .S24 2025

Dewey Class. No.: 512.81

From counting to continuumwhat are real numbers, really? /
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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 189607
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