41. Julius Wilhelm Richard Dedekind - Wikipedia NL Julius Wilhelm richard dedekind. (Doorverwezen vanaf dedekind). Julius Wilhelmrichard dedekind (18311916). Duitser, wiskundige. Leerling van Gauss. http://nl.wikipedia.org/wiki/Dedekind

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42. Julius Wilhelm Richard Dedekind - Wikipedia NL Andere talen English. Julius Wilhelm richard dedekind. Julius Wilhelmrichard dedekind (18311916). Duitser, wiskundige. Leerling van Gauss. http://nl.wikipedia.org/wiki/Julius_Wilhelm_Richard_Dedekind

Hoofdpagina Recente wijzigingen Pagina bewerken Voorgeschiedenis Speciale pagina's Mijn gebruikersvoorkeuren instellen Mijn volglijst tonen Recent bijgewerkte pagina's tonen Afbeeldingen uploaden Lijst ge-uploade afbeeldingen tonen Geregistreerde gebruikers tonen Statistieken tonen Ga naar een willekeurig artikel Niet-gelinkte artikels tonen Niet-gelinkte afbeeldingen tonen Populaire artikels tonen Meest gewenste artikels tonen Korte artikels tonen Lange artikels tonen Nieuwe artikels tonen Taallinks Alle paginatitels tonen Geblokkeerde IP-adressen tonen Onderhoudspagina Boekhandels Printer-vriendelijke versie Overleg Aanmelden Help Andere talen: English Julius Wilhelm Richard Dedekind Julius Wilhelm Richard Dedekind Duitser, wiskundige Leerling van Gauss Formuleerde een moderne theorie (gebaseerd op de verzamelingenleer ) voor het invoeren van de irrationale getallen Schreef Stetigkeit und Irrationalzahlen (1872) en Was sind und was sollen die Zahlen Pagina bewerken Voorgeschiedenis Referenties Volg links Andere talen: English Hoofdpagina Over Wikipedia Recente wijzigingen Deze pagina werd 114 maal bekeken en is voor het laatst gewijzigd op 16 oct 2002 12:08. Alle tekst op deze pagina valt onder de GNU FDL Hoofdpagina Recente wijzigingen Willekeurig artikel ... Pagina bewerken Overlegpagina Voorgeschiedenis Referenties Volg links Speciale pagina's ... Foutenrapportage

43. Dedekind, (Julius Wilhelm) Richard dedekind, (Julius Wilhelm) richard (18311916). German mathematicianwho made contributions to number theory. In 1872 he introduced http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/D/Dedekind/1.htm

Dedekind, (Julius Wilhelm) Richard German mathematician who made contributions to number theory. In 1872 he introduced the Dedekind cut (which divides a line of infinite length representing all real numbers) to define irrational numbers in terms of pairs of sequences of rational numbers. In 1858 he succeeded in producing a purely arithmetic definition of continuity and an exact formulation of the concept of the irrational number. This led to the Dedekind cut, explained in his book Stetigkeit und irrationale Zahlen 1872. In Was sind und was sollen die Zahlen? 1888 he devised axioms that formally and exactly represented the logical concept of whole numbers. The factorization of algebraic numbers and the theory of the ideal, which he described 1879-94, was fundamental to modern algebra; and he introduced the concept of dual groups, a precursor of lattice theory.

44. Dedekind, Julius Wilhelm Richard dedekind, Julius Wilhelm richard 18311916, German mathematician. dedekind,Julius Wilhelm richard. 1831-1916, German mathematician. http://www.slider.com/enc/15000/Dedekind_Julius_Wilhelm_Richard.htm

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45. À¹¼wª÷¡£Dedekind, Julius Wilhelm Richard, 1831-1916¡¤ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.edp.ust.hk/math/history/3/3_135.htm

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46. DEDEKIND Translate this page dedekind Julius Wilhelm richard (1831-1916). Matemático alemás nacidoy fallecido en Braunschweig. Empezó su carrera en ciencias http://almez.pntic.mec.es/~agos0000/Dedekind.html

DEDEKIND Julius Wilhelm Richard (1831-1916)

47. Dedekind, Julius Wilhelm Richard encyclopediaEncyclopedia dedekind, Julius Wilhelm richard, yOOl'yoosvil'helm rikh'ärt dA'dukint Pronunciation Key. dedekind, Julius http://www.infoplease.com/ce6/people/A0814946.html

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48. Dedekind Cuts dedekind cuts. The first construction of the Real numbers from the Rationalsis due to the German mathematician richard dedekind (1831 1916). http://www.gap-system.org/~john/analysis/Lectures/A3.html

MT2002 Analysis Previous page (Some Early History of Set Theory) Contents Next page (Farey sequences) Dedekind cuts The first construction of the Real numbers from the Rationals is due to the German mathematician Richard Dedekind (1831 - 1916). He developed the idea first in 1858 though he did not publish it until 1872. This is what he wrote at the beginning of the article. He defined a real number to be a pair ( L R ) of sets of rationals which have the following properties. Every rational is in exactly one of the sets Every rational in L R Such a pair is called a Dedekind cut Schnitt in German). You can think of it as defining a real number which is the least upper bound of the "Left-hand set" L and also the greatest lower bound of the "right-hand set" R . If the cut defines a rational number then this may be in either of the two sets. It is rather a rather long (and tedious) task to define the arithmetic operations and order relation on such cuts and to verify that they do then satisfy the axioms for the Reals including even the Completeness Axiom. Richard Dedekind , along with Bernhard Riemann was the last research student of Gauss . His arithmetisation of analysis was his most important contribution to mathematics, but was not enthusiastically received by leading mathematicians of his day, notably

49. Philosophical Dictionary: Decision-Deontology dedekind, JW richard (18311916). German mathematician Recommended Readingrichard dedekind, Essays on the Theory of Numbers , tr. by Wooster http://www.philosophypages.com/dy/d2.htm

Philosophy Pages F A Q Dictionary ... Locke decision procedure An algorithm by means of which to establish, in a finite number of steps, whether a statement form is tautologous or whether an argument form is valid . Drawing Venn diagrams provides a decision procedure for a modern interpretation of categorical logic , and truth-tables give a decision procedure for the propositional calculus , but there is no decision procedure for quantification theory Also see OCP on decidability and decision procedures OCDL , and noesis deconstruction Interpretive method that denies the priority or privilege of any single reading of a text (even if guided by the intentions of its author) and tries to show that the text is incoherent because its own key terms can be understood only in relation to their suppressed opposites. Deconstructionists like Derrida seek to uncover the internal conflicts that tend to undermine (or at least to "decenter") the putative significance of any text. In ordinary language, for example, someone who says, "If I may be perfectly candid for a moment, . . ." ambiguity in the very notions of honesty and truth Recommended Reading: Deconstruction in a Nutshell: A Conversation With Jacques Derrida at Amazon.com

50. µ¥µ¥Å²Æ®(Julius Wilhelm Richard Dedekind 1831¡­1916) The summary for this Korean page contains characters that cannot be correctly displayed in this language/character set. http://math.kyungwon.ac.kr/menu_add/mather/mather4.htm

µ¥µ¥Å²Æ®(Julius Wilhelm Richard Dedekind 1831¡­1916)

51. Historia Matematica Mailing List Archive: Re: [HM] Richard Dedekind Re HM richard dedekind. David Wilkins (dwilkins@maths.tcd.ie)Wed, 09 Sep 1998 160106 +0100 http://sunsite.utk.edu/math_archives/.http/hypermail/historia/sep98/0041.html

Re: [HM] Richard Dedekind David Wilkins dwilkins@maths.tcd.ie Wed, 09 Sep 1998 16:01:06 +0100 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Luis Carlos Arboleda: "[HM] Frechet on Leibniz" Previous message: Julio Gonzalez Cabillon: "Re: [HM] It fascinated Leibniz" A paper on Dedekind that I came across recently is David Charles McCarty, `The Mysteries of Richard Dedekind' in Jaakko Hintikka (ed.): From Dedekind to Go"del, Essays on the Development of the Foundations of Mathematics, 53 - 96 1995, Kluwer Academic Publishers. ISBN 0-7923-3484-1 Next message: Luis Carlos Arboleda: "[HM] Frechet on Leibniz" Previous message: Julio Gonzalez Cabillon: "Re: [HM] It fascinated Leibniz"

52. Historia Matematica Mailing List Archive: Re: [HM] Richard Dedekind Re HM richard dedekind. Julio Ann. der Naturphil., 7, 1908 PEB Jourdain, richard dedekind in The Monist 26, pp. 415427, 1916 http://sunsite.utk.edu/math_archives/.http/hypermail/historia/sep98/0006.html

Re: [HM] Richard Dedekind Julio Gonzalez Cabillon jgc@adinet.com.uy Wed, 02 Sep 1998 01:18:31 -0300 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Julio Gonzalez Cabillon: "Re: [HM] integral around a closed path symbol" Previous message: Samuel S. Kutler: "[HM] Heath's translations" Everdell@aol.com Logic_, vol. 3, no. 3, pp. 207-214, June 1993. In this article, Jourdain provides both technical and philosophical analysis of Dedekind's famous papers "Stetigkeit und irrationale Zahlen" (1872) and "Was sind und was sollen die Zahlen?" (1887/88). JGC Next message: Julio Gonzalez Cabillon: "Re: [HM] integral around a closed path symbol" Previous message: Samuel S. Kutler: "[HM] Heath's translations"

53. Www.iper1.com - Julius Wilhelm Richard Dedekind Julius Wilhelm richard dedekind. Julius Wilhelm richard dedekind Johan BartholdJongkind Frank Wedekind a b c d e f g h i j k l m n o p q r s t u v w x y z http://www.iper1.com/rime/index.asp?cerca=Julius Wilhelm Richard Dedekind

54. Richard Dedekind Translate this page Julius Wilhelm richard dedekind (1831 bis 1916). dedekind wurde am6. Oktober 1831 in Braunschweig geboren. Sein Vater war Professor http://homepages.compuserve.de/thweidenfeller/mathematiker/dedekind.html

Julius Wilhelm Richard Dedekind (1831 bis 1916) Dedekind wurde am 6. Oktober 1831 in Braunschweig geboren. Sein Vater war Professor am Collegium Carolinum in Braunscheig, und seine Mutter war die Tochter eines Professors am Collegium Carolinum. Er war das jüngste von vier Kindern. Die meiste seiner Zeit lebte er mit seiner Schwester, die, wie auch er, unverheiratet blieb. Er besuchte ab sieben die Martino-Catharineum Schule in Braunschweig, welche zu dieser Zeit eine gute Ausbildung ermöglichte. Dort interessierte sich Dedekind zuerst für Physik und Chemie, entdeckte aber bald sein Interesse für die Mathematik. Im Jahre 1848 besuchte er mit 16 das Collegium Carolinum, das ein Lehranstalt zwischen Gymnasium und Universität darstellte. Dort erwarb Dedekind sein Basiswissen über Differential- und Integralrechnung, analytische Geometrie und über die Grundlagen der Analysis. Im Frühling 1850 immatrikulierte er in Göttingen mit einen guten Grundwissen über Mathematik. Zu dieser Zeit war Göttingen eher eine Enttäuschung für Studenten der Mathematik. Erst einige Zeit später erlangte diese Universität eine führende Rolle im Bereich der mathematischen Forschung. Das mathematische Institut von Göttingen

55. Logician's Year 12 Feb, Herbrand, Jean, (* 1908). dedekind, richard, (+ 1916). 13 Feb, Lukasiewicz,Jan, (+ 1956). 5 Oct, Bolzano, Bernard, (* 1781). 6 Oct, dedekind, richard, (* 1831). http://www.volny.cz/logici/vyroci/english.html

The Logician's Year January February March April ... December January 5 Jan Kleene, Stephen Cole 6 Jan Cantor, Georg 12 Jan Hintikka, Jaakko 14 Jan Carroll, Lewis Tarski, Alfred Gödel, Kurt 19 Jan Ramsey, Frank Plumpton 23 Jan Hilbert, David 26 Jan Kleene, Stephen Cole 27 Jan Carroll, Lewis February 2 Feb Russell, Bertrand Artur William 3 Feb Lewis, Clarence Irving 6 Feb Arnauld, Antoine 8 Feb von Neumann, Johannes 11 Feb Post, Emil Leon 12 Feb Herbrand, Jean Dedekind, Richard 13 Feb £ukasiewicz, Jan 14 Feb Hilbert, David 15 Feb Whitehead, Alfred North 16 Feb Nicod, Jean 17 Feb Fraenkel, Adolf Abraham 22 Feb Ramsey, Frank Plumpton 27 Feb Brouwer, Luitzgen Egbertus Jan March 3 Mar Cantor, Georg 5 Mar Barwise, Jon 6 Mar Davidson, Donald 7 Mar Montague, Richard 18 Mar de Morgan, Augustus Carnap Rudolf 23 Mar Skolem, Thoralf 24 Mar Lorenzen, Paul 25 Mar Ackermann, Wilhelm April 2 Apr Vaught, Robert Lawson 4 Apr Venn, John Vaught, Robert Lawson 12 Apr Lewis, Clarence Irving 19 Apr Peirce, Charles Sanders 20 Apr Peano, Giuseppe 21 Apr Post, Emil Leon 26 Apr Wittgenstein, Ludwig 28 Apr Gödel, Kurt

56. Logikùv Rok Translate this page 12. 2. Herbrand, Jean, (* 1908). dedekind, richard, (+ 1916). 13. Bolzano, Bernard,(* 1781). 6. 10. dedekind, richard, (* 1831). Prior, Arthur Norman, (+ 1969). 14.10. http://www.volny.cz/logici/vyroci/

Logikùv rok Leden Únor Bøezen Duben ... Prosinec Leden Kleene, Stephen Cole Cantor, Georg Hintikka, Jaakko Carroll, Lewis Tarski, Alfred Gödel, Kurt Ramsey, Frank Plumpton Hilbert, David Kleene, Stephen Cole Carroll, Lewis Únor Russell, Bertrand Artur William Lewis, Clarence Irving Arnauld, Antoine von Neumann, Johannes Post, Emil Leon Herbrand, Jean Dedekind, Richard £ukasiewicz, Jan Hilbert, David Whitehead, Alfred North Nicod, Jean Fraenkel, Adolf Abraham Ramsey, Frank Plumpton Brouwer, Luitzgen Egbertus Jan Bøezen Cantor, Georg Barwise, Jon Davidson, Donald Montague, Richard de Morgan, Augustus Carnap Rudolf Skolem, Thoralf Lorenzen, Paul Ackermann, Wilhelm Duben Vaught, Robert Lawson Venn, John Vaught, Robert Lawson Lewis, Clarence Irving Peirce, Charles Sanders Peano, Giuseppe Post, Emil Leon Wittgenstein, Ludwig Gödel, Kurt Wittgenstein, Ludwig Kvìten Löwenheim, Leopold Heyting, Arend Wang, Hao Russell, Bertrand Arthur William Wang, Hao Zermelo, Ernst Skolem, Thoralf Èerven Turing, Alan Mathison Church, Alonzo von Wright, Georg Henrik Turing, Alan Mathison Quine, Willard Van Orman

57. Dedekind, Julius Wilhelm Richard encyclopediaEncyclopedia dedekind, Julius Wilhelm richard, yOOl'yoosvil'helm rikh'ärt dA'dukint Pronunciation Key. dedekind, Julius http://www.factmonster.com/ce6/people/A0814946.html

58. 100 Marathon Club Deutschland richard dedekind Marathon am 06.10.2002. dedekind, richard,deutscher Mathematiker, * 6. 10. 1831 Braunschweig, Ý 12. http://www.100marathon-club.de/Rueckblick02/er061002.htm

100 Marathon Club Deutschland Ergebnisse "Richard Dedekind Marathon" am 06.10.2002 Pl.Ges. Name Vorname Ort Verein Nat. Jg. AK Zeit Pl. AK Wieneke Peter Hamfelde 100 Marathon Club GER Hottas Christian Hamburg 100 Marathon Club GER Gehrke Lothar Hamburg 100 Marathon Club GER 4 / 1.F Eichner Sigrid Berlin 100 Marathon Club GER "Richard Dedekind Marathon" am Peter Wieneke vor Christian Hottas Lothar Gehrke (26:15 min hinter Christian). Bei dem Frauen siegte Sigrid Eichner im wahrsten Sinne "konkurrenzlos". Christian Hottas (C) by 100 Marathon Club Deutschland e. V.

59. Essays On The Theory Of Numbers By Richard Dedekind, Wooster W. Beman (Translato Buy Essays on the Theory of Numbers by richard dedekind, Wooster W.Beman (Translator) (Paperback June 2001) here at low prices. http://www.rbookshop.com/mathematics/n/Number_Theory/Essays_on_the_Theory_of_Num

AMAZON.COM Search All Products Electronics Books Classical Music DVD Kitchen Popular Music Software Toys VHS Video Video Games Enter keywords: Related Stores Math Videos Math Software Computers and Accessories Toys and Games More Stores Ray Ban Store Sporting Goods Store Electronics Store Electronics Store ... Toy Store NOTICE : All prices, availability, and specifications are subject to verification by their respective retailers. Privacy Policy info@rbookshop.com Last Modified : 3-28-2003 Essays on the Theory of Numbers Home Mathematics Books Number Theory Essays on the Theory of Numbers by Richard Dedekind, Wooster W. Beman (Translator) (Paperback - June 2001) List Price: $7.95 At Amazon on 3-28-2003. Features Paperback: ; Dimensions (in inches): 0.26 x 7.98 x 5.37 Publisher: Dover Pubns; (June 2001) ISBN: 0486210103 Reader Reviews 3 of 3 people found the following review helpful: An interesting pair of historical essays, July 23, 2001 Reviewer: A reader from Brooklyn, NY United States Essays on the Theory of Numbers Available from Amazon Price: $7.95

60. Galerie: Dedekind Translate this page richard dedekind. richard dedekind's Vater war Professor am CollegiumCarolinum in Braunschweig, wo seine Mutter ebenfalls arbeitete. http://www.klemensneumann.de/demorgan/dedekind.html

Richard Dedekind Geboren am 6. Oktober 1831 in Braunschweig, Deutschland Gestorben am 12. Februar 1916 in Braunschweig, Deutschland Richard Dedekind's Vater war Professor am Collegium Carolinum in Braunschweig, wo seine Mutter ebenfalls arbeitete. Richard kam als jüngstes von vier Kindern auf die Welt. Er heiratete nie und lebte später mit einer seiner Schwestern zusammen. Ab sieben Jahren besuchte er eine Braunschweiger Schule, ohne sich sonderlich für Mathematik zu interessieren. Dort wurde er besonders in Physik und Chemie unterrichtet. Jedoch wurde Dedekind immer unzufriedener mit der seiner Meinung nach unpräzisen logischen Struktur der Physik und wandte sich der Mathematik zu. 1848 wechselte der Sechszehnjährige aufs Collegium Carolinum und studierte grundlegende Mathematik. Im Jahre 1850 studierte er dann an der Universität von Göttingen und machte dort mit Zahlentheorie Bekanntschaft machte. Begeistern konnte ihn experimentelle Physik bei Weber sowie später ein Mathematik-Kurs bei Gauß. Unter Gauß schrieb er auch seine Doktorarbeit über die Theorie Eulerscher Integrale. Sein Doktorat wurde ihm 1852 verliehen. Jedoch fehlte ihm Wissen im Bereich höherer Mathematik, wie er selbst und sein Freund Riemann merkten. Dedekind verbrachte daher weitere zwei Jahre mit dem Studium der Mathematik.

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