The Resource Roads to infinity : the mathematics of truth and proof, John Stillwell
Roads to infinity : the mathematics of truth and proof, John Stillwell
Resource Information
The item Roads to infinity : the mathematics of truth and proof, John Stillwell represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Yuma County Library District.This item is available to borrow from 1 library branch.
Resource Information
The item Roads to infinity : the mathematics of truth and proof, John Stillwell represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Yuma County Library District.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- xi, 203 p.
- Contents
-
- 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
- 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
- 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
- Logic : Propositional logic ; A classical system ; A cut-free system for propositional logic ; Happy endings ; Predicate logic ; Completeness, consistency, happy endings ; Historical background
- Arithmetic : How might we prove consistency? ; Formal arithmetic ; The systems PA and PA ; Embedding PA and PA; Cut elimination in PA ; The height of this great argument ; Roads to infinity ; Historical background
- Natural unprovable sentences : A generalized Goodstein Theorem ; Countable ordinals via natural numbers ; From generalized Goodstein to well-ordering ; Generalized and ordinary Goodstein ; Provably computable functions ; Complete disorder is impossible ; The hardest theorem in graph theory ; Historical background
- Axioms of infinity : Set theory without infinity ; Inaccessible cardinals ; The axiom of determinacy ; Largeness axioms for arithmetic ; Large cardinals and finite mathematics ; Historical background
- Isbn
- 9781568814667
- 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
- 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
- Bibliography note
- Includes bibliographical references (p. 183-188) and index
- Contents
- 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 -- 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 -- 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 -- Logic : Propositional logic ; A classical system ; A cut-free system for propositional logic ; Happy endings ; Predicate logic ; Completeness, consistency, happy endings ; Historical background -- Arithmetic : How might we prove consistency? ; Formal arithmetic ; The systems PA and PA ; Embedding PA and PA; Cut elimination in PA ; The height of this great argument ; Roads to infinity ; Historical background -- Natural unprovable sentences : A generalized Goodstein Theorem ; Countable ordinals via natural numbers ; From generalized Goodstein to well-ordering ; Generalized and ordinary Goodstein ; Provably computable functions ; Complete disorder is impossible ; The hardest theorem in graph theory ; Historical background -- Axioms of infinity : Set theory without infinity ; Inaccessible cardinals ; The axiom of determinacy ; Largeness axioms for arithmetic ; Large cardinals and finite mathematics ; Historical background
- Control code
- ocn460058722
- Dimensions
- 24 cm.
- Extent
- xi, 203 p.
- Isbn
- 9781568814667
- Isbn Type
- (alk. paper)
- Lccn
- 2010014077
- Other physical details
- ill.
- System control number
- (OCoLC)460058722
- Label
- Roads to infinity : the mathematics of truth and proof, John Stillwell
- Bibliography note
- Includes bibliographical references (p. 183-188) and index
- Contents
- 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 -- 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 -- 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 -- Logic : Propositional logic ; A classical system ; A cut-free system for propositional logic ; Happy endings ; Predicate logic ; Completeness, consistency, happy endings ; Historical background -- Arithmetic : How might we prove consistency? ; Formal arithmetic ; The systems PA and PA ; Embedding PA and PA; Cut elimination in PA ; The height of this great argument ; Roads to infinity ; Historical background -- Natural unprovable sentences : A generalized Goodstein Theorem ; Countable ordinals via natural numbers ; From generalized Goodstein to well-ordering ; Generalized and ordinary Goodstein ; Provably computable functions ; Complete disorder is impossible ; The hardest theorem in graph theory ; Historical background -- Axioms of infinity : Set theory without infinity ; Inaccessible cardinals ; The axiom of determinacy ; Largeness axioms for arithmetic ; Large cardinals and finite mathematics ; Historical background
- Control code
- ocn460058722
- Dimensions
- 24 cm.
- Extent
- xi, 203 p.
- Isbn
- 9781568814667
- Isbn Type
- (alk. paper)
- Lccn
- 2010014077
- Other physical details
- ill.
- System control number
- (OCoLC)460058722
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.yumalibrary.org/portal/Roads-to-infinity--the-mathematics-of-truth-and/06NGCiCcdw8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.yumalibrary.org/portal/Roads-to-infinity--the-mathematics-of-truth-and/06NGCiCcdw8/">Roads to infinity : the mathematics of truth and proof, John Stillwell</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.yumalibrary.org/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.yumalibrary.org/">Yuma County Library District</a></span></span></span></span></div>
