03059nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001600165072002300181072001500204100008500219245015100304250001800455264008200473300005100555336002600606337002600632338003600658347002400694490004600718505038200764520104501146650001702191650001302208650001902221650001602240650003802256650001902294650001602313710003402329773002602363776003602389776003602425776003602461830004602497856004602543978-3-662-70057-0DE-He21320251030114606.0cr nn 008mamaa241206s2024    gw |    s    |||| 0|eng d  a97836627005707 a10.1007/978-3-662-70057-02doi 4aQA21-27 7aPBX2bicssc 7aMAT0150002bisacsh 7aPBX2thema1 aMüller-Stach, Stefan.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aRichard Dedekindh[electronic resource] :bWhat Are and What Should the Numbers Be? Continuity and Irrational Numbers /cby Stefan Müller-Stach.  a1st ed. 2024. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg :bImprint: Springer,c2024.  aX, 236 p. 2 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aClassic Texts in the Sciences,x2365-99710 aPreface -- 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.  aThe 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. 0aMathematics. 0aHistory. 0aNumber theory. 0aSet theory.14aHistory of Mathematical Sciences.24aNumber Theory.24aSet Theory.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978366270056308iPrinted edition:z978366270058708iPrinted edition:z9783662700594 0aClassic Texts in the Sciences,x2365-997140uhttps://doi.org/10.1007/978-3-662-70057-0