A brief history of analysis with emphasis on philosophy, concepts, and numbers, including Weierstraß' real numbers
Preface / The Invention of the Mathematical Formula / Numbers, Line Segments, Points—But No Curved Lines / Lines and Variables / Indivisible: An Old Notion (Or, What Is the Continuum Made of?) / Do Infinite Numbers Exist?—An Unresolved Dispute Between Leibniz and Johann Bernoulli / Johann Bernoulli’...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Cham, Switzerland
Birkhäuser
2022
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| Schlagworte: | |
| Online Zugang: | zbMATH |
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Tag hinzufügen | Zusammenfassung: | Preface / The Invention of the Mathematical Formula / Numbers, Line Segments, Points—But No Curved Lines / Lines and Variables / Indivisible: An Old Notion (Or, What Is the Continuum Made of?) / Do Infinite Numbers Exist?—An Unresolved Dispute Between Leibniz and Johann Bernoulli / Johann Bernoulli’s Rules for Differentials—What Does “Equal” Mean? / Euler and the Absolute Reign of Formal Calculation / Emphases in Algebraic Analysis After Euler / Bolzano: The Republican Revolutionary of Analysis / Cauchy: The Bourgeois Revolutionary as Activist of the Restoration / The Interregnum: Analysis on Swampy Ground / Weierstraß: The Last Effort Towards a Substancial Analysis / Analysis’ Detachment from Reality—and the Introduction of the Actual Infinite into the Foundations of Mathematics / Analysis with or Without Paradoxes? |
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| Beschreibung: | xxiii, 254 Seiten Illustrationen, Diagramme |
| ISBN: | 9783031006494 978-3-031-00649-4 |