03401nam a22005535i 4500 978-3-662-70057-0 DE-He213 20251030114606.0 cr nn 008mamaa 241206s2024 gw | s |||| 0|eng d 9783662700570 978-3-662-70057-0 10.1007/978-3-662-70057-0 doi QA21-27 PBX bicssc MAT015000 bisacsh PBX thema Müller-Stach, Stefan. author. aut http://id.loc.gov/vocabulary/relators/aut 83735 Richard Dedekind [electronic resource] : What Are and What Should the Numbers Be? Continuity and Irrational Numbers / by Stefan Müller-Stach. 1st ed. 2024. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2024. X, 236 p. 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Classic Texts in the Sciences, 2365-9971 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. 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. Mathematics. 65523 History. Number theory. Set theory. History of Mathematical Sciences. 66197 Number Theory. Set Theory. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783662700563 Printed edition: 9783662700587 Printed edition: 9783662700594 Classic Texts in the Sciences, 2365-9971 88625 https://doi.org/10.1007/978-3-662-70057-0 ZDB-2-SMA ZDB-2-SXMS 65533 65533