The real numbers: an introduction to set theory and analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2013
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783319015767 9783319015774 |
| DOI: | 10.1007/978-3-319-01577-4 |
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Datensatz im Suchindex
| _version_ | 1804151619179249664 |
|---|---|
| adam_text | THE REAL NUMBERS
/ STILLWELL, JOHN
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
THE FUNDAMENTAL QUESTIONS
FROM DISCRETE TO CONTINUOUS
INFINITE SETS
FUNCTIONS AND LIMITS
OPEN SETS AND CONTINUITY
ORDINALS
THE AXIOM OF CHOICE
BOREL SETS
MEASURE THEORY
REFLECTIONS
BIBLIOGRAPHY
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
THE REAL NUMBERS
/ STILLWELL, JOHN
: 2013
ABSTRACT / INHALTSTEXT
WHILE MOST TEXTS ON REAL ANALYSIS ARE CONTENT TO ASSUME THE REAL
NUMBERS, OR TO TREAT THEM ONLY BRIEFLY, THIS TEXT MAKES A SERIOUS STUDY
OF THE REAL NUMBER SYSTEM AND THE ISSUES IT BRINGS TO LIGHT. ANALYSIS
NEEDS THE REAL NUMBERS TO MODEL THE LINE, AND TO SUPPORT THE CONCEPTS OF
CONTINUITY AND MEASURE. BUT THESE SEEMINGLY SIMPLE REQUIREMENTS LEAD TO
DEEP ISSUES OF SET THEORY—UNCOUNTABILITY, THE AXIOM OF CHOICE, AND
LARGE CARDINALS. IN FACT, VIRTUALLY ALL THE CONCEPTS OF INFINITE SET
THEORY ARE NEEDED FOR A PROPER UNDERSTANDING OF THE REAL NUMBERS, AND
HENCE OF ANALYSIS ITSELF. BY FOCUSING ON THE SET-THEORETIC ASPECTS OF
ANALYSIS, THIS TEXT MAKES THE BEST OF TWO WORLDS: IT COMBINES A
DOWN-TO-EARTH INTRODUCTION TO SET THEORY WITH AN EXPOSITION OF THE
ESSENCE OF ANALYSIS—THE STUDY OF INFINITE PROCESSES ON THE REAL
NUMBERS. IT IS INTENDED FOR SENIOR UNDERGRADUATES, BUT IT WILL ALSO BE
ATTRACTIVE TO GRADUATE STUDENTS AND PROFESSIONAL MATHEMATICIANS WHO,
UNTIL NOW, HAVE BEEN CONTENT TO ASSUME THE REAL NUMBERS. ITS
PREREQUISITES ARE CALCULUS AND BASIC MATHEMATICS. MATHEMATICAL HISTORY
IS WOVEN INTO THE TEXT, EXPLAINING HOW THE CONCEPTS OF REAL NUMBER AND
INFINITY DEVELOPED TO MEET THE NEEDS OF ANALYSIS FROM ANCIENT TIMES TO
THE LATE TWENTIETH CENTURY. THIS RICH PRESENTATION OF HISTORY, ALONG
WITH A BACKGROUND OF PROOFS, EXAMPLES, EXERCISES, AND EXPLANATORY
REMARKS, WILL HELP MOTIVATE THE READER. THE MATERIAL COVERED INCLUDES
CLASSIC TOPICS FROM BOTH SET THEORY AND REAL ANALYSIS COURSES, SUCH AS
COUNTABLE AND UNCOUNTABLE SETS, COUNTABLE ORDINALS, THE CONTINUUM
PROBLEM, THE CANTOR–SCHROEDER–BERNSTEIN THEOREM, CONTINUOUS
FUNCTIONS, UNIFORM CONVERGENCE, ZORN S LEMMA, BOREL SETS, BAIRE
FUNCTIONS, LEBESGUE MEASURE, AND RIEMANN INTEGRABLE FUNCTIONS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Stillwell, John 1942- |
| author_GND | (DE-588)128427264 |
| author_facet | Stillwell, John 1942- |
| author_role | aut |
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| ctrlnum | (OCoLC)862241998 (DE-599)DNB1042999090 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Medizin |
| doi_str_mv | 10.1007/978-3-319-01577-4 |
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| spelling | Stillwell, John 1942- Verfasser (DE-588)128427264 aut The real numbers an introduction to set theory and analysis John Stillwell Cham [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Undergraduate texts in mathematics https://doi.org/10.1007/978-3-319-01577-4 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026924067&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026924067&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Stillwell, John 1942- The real numbers an introduction to set theory and analysis |
| title | The real numbers an introduction to set theory and analysis |
| title_auth | The real numbers an introduction to set theory and analysis |
| title_exact_search | The real numbers an introduction to set theory and analysis |
| title_full | The real numbers an introduction to set theory and analysis John Stillwell |
| title_fullStr | The real numbers an introduction to set theory and analysis John Stillwell |
| title_full_unstemmed | The real numbers an introduction to set theory and analysis John Stillwell |
| title_short | The real numbers |
| title_sort | the real numbers an introduction to set theory and analysis |
| title_sub | an introduction to set theory and analysis |
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