Classic Set Theory: For Guided Independent Study

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9780412606106: Classic Set Theory: For Guided Independent Study

Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:

  • The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers
  • Defining natural numbers in terms of sets
  • The potential paradoxes in set theory
  • The Zermelo-Fraenkel axioms for set theory
  • The axiom of choice
  • The arithmetic of ordered sets
  • Cantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.

    The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.

    Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
  • Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

    Contenuti:

    INTRODUCTION
    Outline of the book
    Assumed knowledge

    THE REAL NUMBERS
    Introduction
    Dedekind's construction
    Alternative constructions
    The rational numbers

    THE NATURAL NUMBERS
    Introduction
    The construction of the natural numbers
    Arithmetic
    Finite sets

    THE ZERMELO-FRAENKEL AXIOMS
    Introduction
    A formal language
    Axioms 1 to 3
    Axioms 4 to 6
    Axioms 7 to 9

    CARDINAL (Without the Axiom of Choice)
    Introduction
    Comparing Sizes
    Basic properties of ˜ and =
    Infinite sets without AC-countable sets
    Uncountable sets and cardinal arithmetic without AC

    ORDERED SETS
    Introduction
    Linearly ordered sets
    Order arithmetic
    Well-ordered sets

    ORDINAL NUMBERS
    Introduction
    Ordinal numbers
    Beginning ordinal arithmetic
    Ordinal arithmetic
    The Às

    SET THEORY WITH THE AXIOM OF CHOICE
    Introduction
    The well-ordering principle
    Cardinal arithmetic and the axiom of choice
    The continuum hypothesis

    BIBLIOGRAPHY
    INDEX

    Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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    Goldrei, D.C.
    ISBN 10: 0412606100 ISBN 13: 9780412606106
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    Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97804126061060000000

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    Descrizione libro Taylor Francis Ltd, United Kingdom, 2013. Paperback. Condizione libro: New. 249 x 213 mm. Language: English . Brand New Book. Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes: * The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers * Defining natural numbers in terms of sets * The potential paradoxes in set theory * The Zermelo-Fraenkel axioms for set theory * The axiom of choice * The arithmetic of ordered sets * Cantor s two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these. The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed. Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory. Codice libro della libreria AAU9780412606106

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    D. C. Goldrei
    Editore: Taylor Francis Ltd, United Kingdom (2013)
    ISBN 10: 0412606100 ISBN 13: 9780412606106
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    Descrizione libro Taylor Francis Ltd, United Kingdom, 2013. Paperback. Condizione libro: New. 249 x 213 mm. Language: English . Brand New Book. Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes: * The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers * Defining natural numbers in terms of sets * The potential paradoxes in set theory * The Zermelo-Fraenkel axioms for set theory * The axiom of choice * The arithmetic of ordered sets * Cantor s two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these. The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed. Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory. Codice libro della libreria AAU9780412606106

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    Goldrei, D.C.
    Editore: Taylor & Francis Inc (1996)
    ISBN 10: 0412606100 ISBN 13: 9780412606106
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    Descrizione libro Taylor & Francis Inc, 1996. Condizione libro: New. 1996. 1st Edition. Paperback. Designed for undergraduate students of set theory, this book presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. It aims to give students a grounding to the results of set theory as well as to tackle significant problems that arise from the theory. Num Pages: 296 pages, 30 line illustrations. BIC Classification: PBCH. Category: (UU) Undergraduate. Dimension: 253 x 210 x 18. Weight in Grams: 666. . . . . . . Codice libro della libreria V9780412606106

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    Descrizione libro Taylor & Francis Ltd 1996-07-01, London, 1996. paperback. Condizione libro: New. Codice libro della libreria 9780412606106

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    Descrizione libro Chapman and Hall/CRC, 2017. Paperback. Condizione libro: NEW. 9780412606106 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Print on Demand title, produced to the highest standard, and there would be a delay in dispatch of around 10 working days. Codice libro della libreria HTANDREE0247368

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    Descrizione libro Taylor & Francis Inc. Condizione libro: New. 1996. 1st Edition. Paperback. Designed for undergraduate students of set theory, this book presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. It aims to give students a grounding to the results of set theory as well as to tackle significant problems that arise from the theory. Num Pages: 296 pages, 30 line illustrations. BIC Classification: PBCH. Category: (UU) Undergraduate. Dimension: 253 x 210 x 18. Weight in Grams: 666. . . . . . Books ship from the US and Ireland. Codice libro della libreria V9780412606106

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    Descrizione libro Springer Berlin Springer Netherlands Jan 2013, 2013. Taschenbuch. Condizione libro: Neu. Neuware - Designed for undergraduate students of set theory, this book presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. It aims to give students a grounding to the results of set theory as well as to tackle significant problems that arise from the theory. Englisch. Codice libro della libreria 9780412606106

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    Descrizione libro Taylor and Francis, 1996. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria VT-9780412606106

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