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010   $a9783662700570$b(electronic bk.)
010   $z9783662700563
024 7 $a10.1007/978-3-662-70057-0
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035   $a(DE-He213)978-3-662-70057-0
035   $a(EXLCZ)9936841096600041
100   $a20241206d2024      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aRichard Dedekind $eWhat Are and What Should the Numbers Be? Continuity and Irrational Numbers /$fby Stefan Müller-Stach
205   $a1st ed. 2024.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2024.
215   $a1 online resource (244 pages)
225 1 $aClassic Texts in the Sciences,$x2365-9971
311 08$aPrint version: Müller-Stach, Stefan Richard Dedekind Berlin, Heidelberg : Springer Berlin / Heidelberg,c2025 9783662700563 
327   $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.
330   $aThe two works titled "What are Numbers and What Should They Be?" (1888) and "Continuity and Irrational Numbers" (1872) are Dedekind's contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind's achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today. This volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind's pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann. Researchers and students alike will find this work a valuable reference in the history of mathematics.
410  0$aClassic Texts in the Sciences,$x2365-9971
606   $aMathematics
606   $aHistory
606   $aNumber theory
606   $aSet theory
606   $aHistory of Mathematical Sciences
606   $aNumber Theory
606   $aSet Theory
615  0$aMathematics.
615  0$aHistory.
615  0$aNumber theory.
615  0$aSet theory.
615 14$aHistory of Mathematical Sciences.
615 24$aNumber Theory.
615 24$aSet Theory.
676   $a510.9
700   $aMüller-Stach$b Stefan$0149978
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9910917200303321
996   $aRichard Dedekind$94302444
997   $aUNINA