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020 _a9783662700570
_9978-3-662-70057-0
024 7 _a10.1007/978-3-662-70057-0
_2doi
050 4 _aQA21-27
072 7 _aPBX
_2bicssc
072 7 _aMAT015000
_2bisacsh
072 7 _aPBX
_2thema
100 1 _aMüller-Stach, Stefan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_983735
245 1 0 _aRichard Dedekind
_h[electronic resource] :
_bWhat Are and What Should the Numbers Be? Continuity and Irrational Numbers /
_cby Stefan Müller-Stach.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aX, 236 p. 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aClassic Texts in the Sciences,
_x2365-9971
505 0 _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.
520 _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.
650 0 _aMathematics.
_965523
650 0 _aHistory.
650 0 _aNumber theory.
650 0 _aSet theory.
650 1 4 _aHistory of Mathematical Sciences.
_966197
650 2 4 _aNumber Theory.
650 2 4 _aSet Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662700563
776 0 8 _iPrinted edition:
_z9783662700587
776 0 8 _iPrinted edition:
_z9783662700594
830 0 _aClassic Texts in the Sciences,
_x2365-9971
_988625
856 4 0 _uhttps://doi.org/10.1007/978-3-662-70057-0
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c65533
_d65533