Coverart for item
The Resource Roads to infinity : the mathematics of truth and proof, John Stillwell

Roads to infinity : the mathematics of truth and proof, John Stillwell

Label
Roads to infinity : the mathematics of truth and proof
Title
Roads to infinity
Title remainder
the mathematics of truth and proof
Statement of responsibility
John Stillwell
Creator
Subject
Language
eng
Summary
Offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. --from publisher description
Cataloging source
DLC
http://library.link/vocab/creatorName
Stillwell, John
Dewey number
511.3/22
Illustrations
illustrations
Index
index present
LC call number
QA248
LC item number
.S778 2010
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Set theory
  • Infinite
  • Logic, Symbolic and mathematical
Label
Roads to infinity : the mathematics of truth and proof, John Stillwell
Instantiates
Publication
Bar code
31223094683175
Bibliography note
Includes bibliographical references (p. 183-188) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- 1. The Diagonal Argument. -- Counting and Countability -- Does One Infinite Size Fit All? -- Cantor's Diagonal Argument -- Transcendental Numbers -- Other Uncountability Proofs -- Rates of Growth -- The Cardinality of the Continuum -- Historical Background -- 2. Ordinals. -- Counting Past Infinity -- The Countable Ordinals -- The Axiom of Choice -- The Continuum Hypothesis -- Induction -- Cantor Normal Form -- Goodstein's Theorem -- Hercules and the Hydra -- Historical Background -- 3. Computability and Proof. -- Formal Systems -- Post's Approach to Incompleteness -- Gödel's First Incompleteness Theorem -- Gödel's Second Incompleteness Theorem -- Formalization of Computability -- The Halting Problem -- The Entscheidungsproblem -- Historical Background -- 4. Logic. -- Propositional Logic -- A Classical System -- A Cut-Free System for Propositional Logic -- Happy Endings -- Predicate Logic -- Completeness, Consistency, Happy Endings -- Historical Background -- 5. Arithmetic. -- How Might We Prove Consistency? -- Formal Arithmetic -- The Systems PA and PAω -- Embedding PA and PAω-- Cut Elimination in PAω -- The Height of This Great Argument -- Roads to Infinity -- Historical Background -- 6. Natural Unprovable Sentences. -- A Generalized Goodstein Theorem -- Countable Ordinals via Natural Numbers -- From Generalized and Ordinary Goodstein -- Provably Computable Functions -- Complete Disorder Is Impossible -- The Hardest Theorem in Graph Theory -- Historical Background -- 7. Axioms of Infinity. -- Set Theory without Infinity -- Inaccessible Cardinals -- The Axiom of Determinacy -- Largeness Axioms for Arithmetic -- Large Cardinals and Finite Mathematics -- Historical Background
Dimensions
24 cm
Extent
xi, 203 p.
Isbn
9781568814667
Lccn
2010014077
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
ill.
System control number
  • 460058722
  • (OCoLC)460058722
Label
Roads to infinity : the mathematics of truth and proof, John Stillwell
Publication
Bar code
31223094683175
Bibliography note
Includes bibliographical references (p. 183-188) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- 1. The Diagonal Argument. -- Counting and Countability -- Does One Infinite Size Fit All? -- Cantor's Diagonal Argument -- Transcendental Numbers -- Other Uncountability Proofs -- Rates of Growth -- The Cardinality of the Continuum -- Historical Background -- 2. Ordinals. -- Counting Past Infinity -- The Countable Ordinals -- The Axiom of Choice -- The Continuum Hypothesis -- Induction -- Cantor Normal Form -- Goodstein's Theorem -- Hercules and the Hydra -- Historical Background -- 3. Computability and Proof. -- Formal Systems -- Post's Approach to Incompleteness -- Gödel's First Incompleteness Theorem -- Gödel's Second Incompleteness Theorem -- Formalization of Computability -- The Halting Problem -- The Entscheidungsproblem -- Historical Background -- 4. Logic. -- Propositional Logic -- A Classical System -- A Cut-Free System for Propositional Logic -- Happy Endings -- Predicate Logic -- Completeness, Consistency, Happy Endings -- Historical Background -- 5. Arithmetic. -- How Might We Prove Consistency? -- Formal Arithmetic -- The Systems PA and PAω -- Embedding PA and PAω-- Cut Elimination in PAω -- The Height of This Great Argument -- Roads to Infinity -- Historical Background -- 6. Natural Unprovable Sentences. -- A Generalized Goodstein Theorem -- Countable Ordinals via Natural Numbers -- From Generalized and Ordinary Goodstein -- Provably Computable Functions -- Complete Disorder Is Impossible -- The Hardest Theorem in Graph Theory -- Historical Background -- 7. Axioms of Infinity. -- Set Theory without Infinity -- Inaccessible Cardinals -- The Axiom of Determinacy -- Largeness Axioms for Arithmetic -- Large Cardinals and Finite Mathematics -- Historical Background
Dimensions
24 cm
Extent
xi, 203 p.
Isbn
9781568814667
Lccn
2010014077
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
ill.
System control number
  • 460058722
  • (OCoLC)460058722

Library Locations

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      100 Larkin Street, San Francisco, CA, 94102, US
      37.779376 -122.415795
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