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  • The Number System (Dover Books on Mathematics)

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H. A. Thurston
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The Number System (Dover Books on Mathematics)

by H. A. Thurston (Author)
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The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.
This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts.
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  1. ISBN-10
    0486458067
  2. ISBN-13
    978-0486458069
  3. Publisher
    Dover Publications
  4. Publication date
    April 19, 2007
  5. Language
    English
  6. Dimensions
    5.46 x 0.28 x 8.51 inches
  7. Print length
    144 pages
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H. A. Thurston

H. A. Thurston

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Customer reviews

4.4 out of 5 stars
17 global ratings

Top reviews from the United States

  • Jeremy Roach
    5.0 out of 5 stars Necessary and sufficient
    Reviewed in the United States on September 7, 2014
    Format: PaperbackVerified Purchase
    This is a better book than E. Landau's classic Foundations of Analysis in many ways. It has several insightful expository chapters that precede the rigorous systematic part. The integers are actually formalized (Landau only introduces negative numbers with the reals). And Cauchy sequences are used to model the irrational numbers instead of Dedekind cuts. Abstract algebraic structures (hemigroup, commutative group, field, ordered field) are defined and used to avoid duplicating theorems and proofs for the different types of numbers. Also Landau only defines integral powers whereas Thurston defines both rational and real powers.

    Thanks to Dover for publishing great books like this at such a low price.
    22 people found this helpful
    Helpful
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  • Jim Giese
    5.0 out of 5 stars thanks
    Reviewed in the United States on December 11, 2019
    Format: PaperbackVerified Purchase
    thanks
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  • Massimo Coletti
    5.0 out of 5 stars Five Stars
    Reviewed in the United States on February 11, 2017
    Format: PaperbackVerified Purchase
    Everything as expected, thanks.
    Helpful
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Top reviews from other countries

  • agingjb
    5.0 out of 5 stars Worth reading
    Reviewed in the United Kingdom on August 22, 2013
    Format: PaperbackVerified Purchase
    This is a detailed description of the definition of the reals starting from the natural numbers, informal and formal.

    Mathematicians should, at least once, make themselves familiar with this process.
    Report
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