Richard Dedekind

• Verfasst von: Müller-Stach, Stefan [VerfasserIn]
• Titel: Richard Dedekind
• Titelzusatz: What Are and What Should the Numbers Be? Continuity and Irrational Numbers
• Verf.angabe: by Stefan Müller-Stach
• Ausgabe: 1st ed. 2024.
• Verlagsort: Berlin, Heidelberg
• Verlagsort: Berlin, Heidelberg
• Verlag: Springer Berlin Heidelberg
• Verlag: Imprint: Springer
• E-Jahr: 2024
• Jahr: 2024.
• Jahr: 2024.
• Umfang: 1 Online-Ressource(X, 236 p. 2 illus. in color.)
• Gesamttitel/Reihe: Classic Texts in the Sciences
• ISBN: 978-3-662-70057-0
• DOI: doi:10.1007/978-3-662-70057-0
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Müller-Stach, Stefan, 1962 - : Richard Dedekind. - [Basel] : Birkhäuser, 2024. - x, 236 Seiten
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• K10plus-PPN: 1911776908
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Preface -- 1. Historical Introduction -- 2. Dedekind’s Investigations into the Concept of Number -- 3. Reprint of Dedekind’s Books -- 4. Explanation of the Texts in Today’s Language -- 5. Reception History -- 6. Impact and Positions of Research -- A Dedekind’s Publications -- B The Letter to Keferstein from February 27, 1890 -- Bibliography -- Name and Subject Index.

Abstract

The two works titled "What are Numbers and What Should They Be?" (1888) and "Continuity and Irrational Numbers" (1872) are Dedekind's contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind's achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today. This volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind's pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann. Researchers and students alike will find this work a valuable reference in the history of mathematics.