Georg Cantor : : His Mathematics and Philosophy of the Infinite / / Joseph Warren Dauben.
One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrup...
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Dauben, Joseph Warren, author. aut http://id.loc.gov/vocabulary/relators/aut Georg Cantor : His Mathematics and Philosophy of the Infinite / Joseph Warren Dauben. Princeton, NJ : Princeton University Press, [2020] ©1991 1 online resource (424 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Acknowledgments -- Contents -- Introduction -- CHAPTER 1. Preludes in Analysis -- CHAPTER 2. The Origins of Cantorian Set Theory: Trigonometric Series, Real Numbers, and Derived Sets -- CHAPTER 3. Denumerability and Dimension -- CHAPTER 4. Cantor's Early Theory of Point Sets -- CHAPTER 5. The Mathematics of Cantor's Grundlagen -- CHAPTER 6. Cantor's Philosophy of the Infinite -- CHAPTER 7. From the Grundlagen to the Beitrdge, 1883-1895 -- CHAPTER 8. The Beiträge, Part I: The Study of Simply-Ordered Sets -- CHAPTER 9. The Beiträge, Part II: The Study of Weil-Ordered Sets -- CHAPTER 10. The Foundations and Philosophy of Cantorian Set Theory -- CHAPTER 11. The Paradoxes and Problems of Post-Cantorian Set Theory -- CHAPTER 12. Epilogue: The Significance of Cantor's Personality -- Appendixes -- Notes -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Infinite. Set theory History. Transfinite numbers History. SCIENCE / History. bisacsh Aristotle. Arithmetic. Berlin, Germany. Borchardt, C. W. Catholic church. Consistency. Continuity. Derived Set(s). Diagonal method. Epistemology. Equivalence. Finitism. Fourier series. Goldscheider, F. Grattan-Guinness, I. Hermite, C. Jeiler, I. Joseph of Arimathea. Kerry, B. Kronecker, L. Limit points. Logic. Mathematics. Neo-Thomism. Order types. Paradoxes. Point sets. Power(s). Quaternions. Schoenflies, A. Set theory. Subsets. Theologians. Transfinite numbers. Trigonemetric series. Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 https://doi.org/10.1515/9780691214207?locatt=mode:legacy https://www.degruyter.com/isbn/9780691214207 Cover https://www.degruyter.com/cover/covers/9780691214207.jpg |
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English |
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Dauben, Joseph Warren, Dauben, Joseph Warren, |
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Dauben, Joseph Warren, Dauben, Joseph Warren, Georg Cantor : His Mathematics and Philosophy of the Infinite / Frontmatter -- Acknowledgments -- Contents -- Introduction -- CHAPTER 1. Preludes in Analysis -- CHAPTER 2. The Origins of Cantorian Set Theory: Trigonometric Series, Real Numbers, and Derived Sets -- CHAPTER 3. Denumerability and Dimension -- CHAPTER 4. Cantor's Early Theory of Point Sets -- CHAPTER 5. The Mathematics of Cantor's Grundlagen -- CHAPTER 6. Cantor's Philosophy of the Infinite -- CHAPTER 7. From the Grundlagen to the Beitrdge, 1883-1895 -- CHAPTER 8. The Beiträge, Part I: The Study of Simply-Ordered Sets -- CHAPTER 9. The Beiträge, Part II: The Study of Weil-Ordered Sets -- CHAPTER 10. The Foundations and Philosophy of Cantorian Set Theory -- CHAPTER 11. The Paradoxes and Problems of Post-Cantorian Set Theory -- CHAPTER 12. Epilogue: The Significance of Cantor's Personality -- Appendixes -- Notes -- Bibliography -- Index |
author_facet |
Dauben, Joseph Warren, Dauben, Joseph Warren, |
author_variant |
j w d jw jwd j w d jw jwd |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Dauben, Joseph Warren, |
title |
Georg Cantor : His Mathematics and Philosophy of the Infinite / |
title_sub |
His Mathematics and Philosophy of the Infinite / |
title_full |
Georg Cantor : His Mathematics and Philosophy of the Infinite / Joseph Warren Dauben. |
title_fullStr |
Georg Cantor : His Mathematics and Philosophy of the Infinite / Joseph Warren Dauben. |
title_full_unstemmed |
Georg Cantor : His Mathematics and Philosophy of the Infinite / Joseph Warren Dauben. |
title_auth |
Georg Cantor : His Mathematics and Philosophy of the Infinite / |
title_alt |
Frontmatter -- Acknowledgments -- Contents -- Introduction -- CHAPTER 1. Preludes in Analysis -- CHAPTER 2. The Origins of Cantorian Set Theory: Trigonometric Series, Real Numbers, and Derived Sets -- CHAPTER 3. Denumerability and Dimension -- CHAPTER 4. Cantor's Early Theory of Point Sets -- CHAPTER 5. The Mathematics of Cantor's Grundlagen -- CHAPTER 6. Cantor's Philosophy of the Infinite -- CHAPTER 7. From the Grundlagen to the Beitrdge, 1883-1895 -- CHAPTER 8. The Beiträge, Part I: The Study of Simply-Ordered Sets -- CHAPTER 9. The Beiträge, Part II: The Study of Weil-Ordered Sets -- CHAPTER 10. The Foundations and Philosophy of Cantorian Set Theory -- CHAPTER 11. The Paradoxes and Problems of Post-Cantorian Set Theory -- CHAPTER 12. Epilogue: The Significance of Cantor's Personality -- Appendixes -- Notes -- Bibliography -- Index |
title_new |
Georg Cantor : |
title_sort |
georg cantor : his mathematics and philosophy of the infinite / |
publisher |
Princeton University Press, |
publishDate |
2020 |
physical |
1 online resource (424 p.) |
contents |
Frontmatter -- Acknowledgments -- Contents -- Introduction -- CHAPTER 1. Preludes in Analysis -- CHAPTER 2. The Origins of Cantorian Set Theory: Trigonometric Series, Real Numbers, and Derived Sets -- CHAPTER 3. Denumerability and Dimension -- CHAPTER 4. Cantor's Early Theory of Point Sets -- CHAPTER 5. The Mathematics of Cantor's Grundlagen -- CHAPTER 6. Cantor's Philosophy of the Infinite -- CHAPTER 7. From the Grundlagen to the Beitrdge, 1883-1895 -- CHAPTER 8. The Beiträge, Part I: The Study of Simply-Ordered Sets -- CHAPTER 9. The Beiträge, Part II: The Study of Weil-Ordered Sets -- CHAPTER 10. The Foundations and Philosophy of Cantorian Set Theory -- CHAPTER 11. The Paradoxes and Problems of Post-Cantorian Set Theory -- CHAPTER 12. Epilogue: The Significance of Cantor's Personality -- Appendixes -- Notes -- Bibliography -- Index |
isbn |
9780691214207 9783110442496 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA248 |
callnumber-sort |
QA 3248 D27 41990 |
url |
https://doi.org/10.1515/9780691214207?locatt=mode:legacy https://www.degruyter.com/isbn/9780691214207 https://www.degruyter.com/cover/covers/9780691214207.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
511 - General principles of mathematics |
dewey-full |
511.3/22/09 |
dewey-sort |
3511.3 222 19 |
dewey-raw |
511.3/22/09 |
dewey-search |
511.3/22/09 |
doi_str_mv |
10.1515/9780691214207?locatt=mode:legacy |
oclc_num |
1198929706 |
work_keys_str_mv |
AT daubenjosephwarren georgcantorhismathematicsandphilosophyoftheinfinite |
status_str |
n |
ids_txt_mv |
(DE-B1597)554811 (OCoLC)1198929706 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
Georg Cantor : His Mathematics and Philosophy of the Infinite / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
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1770176322425847808 |
fullrecord |
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