From Counting to Continuum (Paperback)

Edward Scheinerman

ISBN 10: 1009538675 / ISBN 13: 9781009538671

Published by Cambridge University Press, Cambridge, 2024

About this Item

Paperback. 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. Whole numbers, fractions, decimals: we frequently use them, but what are they exactly? How about exotic numbers like the square root of 2 or p? You don't need to be a graduate student to explore the core ideas behind the construction of the real numbers: just read this book. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9781009538671

Bibliographic Details

• Title: From Counting to Continuum (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2024
• Language: English
• ISBN 10: 1009538675
• ISBN 13: 9781009538671
• Binding: Paperback
• Condition: new

About this title

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.

About the Author

Edward Scheinerman is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He is the author of various books including textbooks, a research monograph, and a volume for general readership, The Mathematics Lover's Companion (2017). He has twice been awarded the Mathematical Association of America's Lester R. Ford Award for outstanding mathematical exposition and has received numerous teaching awards at Johns Hopkins. His research publications are in discrete mathematics.