Roads to infinity : the mathematics of truth and proof /: the mathematics of truth and proof. (©2010)

• Record Type: Book
• Further Information: Note: John Stillwell.
• Other Names: Stillwell, John
• 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.
• Publisher Details: Natick, Mass : A K Peters
• Publication Date: 2010
• Copyright Date: 2010
• Extent: 1 online resource (xi, 203 pages), illustrations
• Subjects: 511.3/22; Set theory; Infinite; Logic, Symbolic and mathematical; MATHEMATICS -- General; Infinite; Logic, Symbolic and mathematical; Set theory; Electronic books
• Languages: English
• ISBNs: 9781439865507; 1439865507
• Related ISBNs: 9781568814667; 1568814666
• Notes: Note: Includes bibliographical references (page 183188) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.