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The number systems: foundations of algebra and analysis

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Main Author:	Feferman, Solomon 1928- (Author)
Format:	Book
Language:	English
Published:	Providence, RI AMS Chelsea Publ. 2003
Edition:	2. ed., Repr
Subjects:	Number theory Analysis Zahlentheorie Algebra Grundlage
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 418 S. graph. Darst.
ISBN:	0821829157

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adam_text	CONTENTS Chapteb 1.1 The mathematical method 1.2 Mathematical statements and thefr structure Logical connectives Chapter 2.1 Sets as abstractions from conditions cept of set sets 2.2 Intersection, union, and complement algebra of sets 2.3 Relations as abstractions from conditions and cartesian products Ternary (etc.) relations tion and partitions Converse and composition of functions 2.4 Isomorphism tems Chapteb 3.1 Peano systems and inductive proofs systems 3.2 Recursive definitions Multiplication of positive integers other operations 3.3 Simply ordered systems ing and the arithmetical operations 3.4 Finite and infinite sequences ucts Some special sums and products Знартев 4.1 Practical motivations mutative rings with unity 4.2 Ordered integral domains 4.3 The existence theorem tion 4.4 More general associative and commutative laws metric series; binomial expansion 4.5 The division algorithm primes integers into primes 4.6 Homomorphism phism to a Diophantine problem )haptbe 5.1 Existence and uniqueness of simple transcendental exten¬ sions derivatives 5.2 fe-fold transcendental extensions mials nomials Chapter 6.1 Algebraic motivations Melds fields 6.2 The existence theorem tients 6.3 Systems of linear equations domains 6.4 Basic properties of divisibility The division algorithm for polynomials mon divisors nomials Chapter 7.1 Algebraic motivations Upper and lower sections; continuously ordered systems Existence of continuously ordered systems lower bounds and least upper bounds 7.2 The Archimedean property ordered fields zano;Weierstrass Theorem ously ordered field 7.3 Positional notations for real numbers The exponential function 7.4 Weierstrass roots Sturm s theorem bers 7.5 Cantor s method sets Liouville s method Chapter 8.1 Characterization of the complex numbers jugates metric interpretation erties of the trigonometric functions representation; 8.2 Limits and the Bolaano-Weierstrass theorem extended Continuity extended minimum of the modulus complex algebra nomials 8.3 Roots of polynomials over a subfield subfields cubic equations On equations of higher degree Chapter 9.1 The general extension process Simple transcendental extensions sions 9.2 Linearly generated extensions; bases and dimension field extensions 9.3 Basic geometric notions plane braic equivalent of constructibility struction problems 9.4 Appendix I Some Axioms for Set Theory Appendix II The Analytical Basis of the Trigonometric Functions Bibliography Index
adam_txt	CONTENTS Chapteb 1.1 The mathematical method 1.2 Mathematical statements and thefr'structure Logical connectives Chapter 2.1 Sets as abstractions from conditions cept of set sets 2.2 Intersection, union, and complement algebra of sets 2.3 Relations as abstractions from conditions and cartesian products Ternary (etc.) relations tion and partitions Converse and composition of functions 2.4 Isomorphism tems Chapteb 3.1 Peano systems and inductive proofs systems 3.2 Recursive definitions Multiplication of positive integers other operations 3.3 Simply ordered systems ing and the arithmetical operations 3.4 Finite and infinite sequences ucts Some special sums and products Знартев 4.1 Practical motivations mutative rings with unity 4.2 Ordered integral domains 4.3 The existence theorem tion 4.4 More general associative and commutative laws metric series; binomial expansion 4.5 The division algorithm primes integers into primes 4.6 Homomorphism phism to a Diophantine problem )haptbe 5.1 Existence and uniqueness of simple transcendental exten¬ sions derivatives 5.2 fe-fold transcendental extensions mials nomials Chapter 6.1 Algebraic motivations Melds fields 6.2 The existence theorem tients 6.3 Systems of linear equations domains 6.4 Basic properties of divisibility The division algorithm for polynomials mon divisors nomials Chapter 7.1 Algebraic motivations Upper and lower sections; continuously ordered systems Existence of continuously ordered systems lower bounds and least upper bounds 7.2 The Archimedean property ordered fields zano;Weierstrass Theorem ously ordered field 7.3 Positional notations for real numbers The exponential function 7.4 Weierstrass' roots Sturm's theorem bers 7.5 Cantor's method sets Liouville's method Chapter 8.1 Characterization of the complex numbers jugates metric interpretation erties of the trigonometric functions representation; 8.2 Limits and the Bolaano-Weierstrass theorem extended Continuity extended minimum of the modulus complex algebra nomials 8.3 Roots of polynomials over a subfield subfields cubic equations On equations of higher degree Chapter 9.1 The general extension process Simple transcendental extensions sions 9.2 Linearly generated extensions; bases and dimension field extensions 9.3 Basic geometric notions plane braic equivalent of constructibility struction problems 9.4 Appendix I Some Axioms for Set Theory Appendix II The Analytical Basis of the Trigonometric Functions Bibliography Index
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spelling	Feferman, Solomon 1928- Verfasser (DE-588)128682167 aut The number systems foundations of algebra and analysis by Solomon Feferman 2. ed., Repr Providence, RI AMS Chelsea Publ. 2003 XIV, 418 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Number theory Analysis (DE-588)4001865-9 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Analysis (DE-588)4001865-9 s Grundlage (DE-588)4158388-7 s Algebra (DE-588)4001156-2 s Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014962036&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Feferman, Solomon 1928- The number systems foundations of algebra and analysis Number theory Analysis (DE-588)4001865-9 gnd Zahlentheorie (DE-588)4067277-3 gnd Algebra (DE-588)4001156-2 gnd Grundlage (DE-588)4158388-7 gnd
subject_GND	(DE-588)4001865-9 (DE-588)4067277-3 (DE-588)4001156-2 (DE-588)4158388-7
title	The number systems foundations of algebra and analysis
title_auth	The number systems foundations of algebra and analysis
title_exact_search	The number systems foundations of algebra and analysis
title_exact_search_txtP	The number systems foundations of algebra and analysis
title_full	The number systems foundations of algebra and analysis by Solomon Feferman
title_fullStr	The number systems foundations of algebra and analysis by Solomon Feferman
title_full_unstemmed	The number systems foundations of algebra and analysis by Solomon Feferman
title_short	The number systems
title_sort	the number systems foundations of algebra and analysis
title_sub	foundations of algebra and analysis
topic	Number theory Analysis (DE-588)4001865-9 gnd Zahlentheorie (DE-588)4067277-3 gnd Algebra (DE-588)4001156-2 gnd Grundlage (DE-588)4158388-7 gnd
topic_facet	Number theory Analysis Zahlentheorie Algebra Grundlage
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014962036&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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