61. MSN Encarta - Cantor, Georg Sign in above. cantor, georg. cantor, georg (18451918), German mathematician, born in Saint Petersburg. Find more about cantor, georg from, http://encarta.msn.com/encyclopedia_761575007/Cantor_Georg.html

MSN Home My MSN Hotmail Shopping ... Money Web Search: logoImg('http://sc.msn.com'); Encarta Subscriber Sign In Help Home ... Upgrade to Encarta Premium Search Encarta Subscription Article MSN Encarta Premium: Get this article, plus 60,000 other articles, an interactive atlas, dictionaries, thesaurus, articles from 100 leading magazines, homework tools, daily math help and more for $4.95/month or $29.95/year (plus applicable taxes.) Learn more. This article is exclusively available for MSN Encarta Premium Subscribers. Already a subscriber? Sign in above. Cantor, Georg Cantor, Georg (1845-1918), German mathematician, born in Saint Petersburg. He taught at the University of Halle and was professor there after 1872.... Related Items influence of Bernhard Bolzano set theory 4 items Multimedia Selected Web Links Georg Ferdinand Ludwig Philipp Cantor [MacTutor] 1 item Want more Encarta? Become a subscriber today and gain access to: Daily Math Help Literature Guides Researcher Tools Paper-Writing Guides 60,000 + articles Interactive Atlas Magazine Center Find more about Cantor, Georg

62. Lexikon - Georg Cantor Definition Erklärung Bedeutung Translate this page georg cantor. Definition, Bedeutung, Erklärung im Lexikon. Artikel auf Englisch georg cantor. georg cantor (* 3. März 1845 http://www.net-lexikon.de/Georg-Cantor.html

Suche: Info Mitglied werden A B ... Impressum Beta 0.71 powered by: akademie.de Wikipedia PHP PostgreSQL ... englischen Lexikon Google News zum Stichwort Georg Cantor Definition, Bedeutung, Erkl¤rung im Lexikon Artikel auf Englisch: Georg Cantor Georg Cantor 3. M¤rz in Sankt Petersburg 6. Januar in Halle (Saale) ) war ein deutscher Mathematiker Er studierte in Darmstadt Z¼rich G¶ttingen und promovierte in Berlin . Zu seinen Lehrern z¤hlten Karl Weierstrass Ernst Eduard Kummer und Leopold Kronecker . Sp¤ter arbeitete er in Halle. Cantor gilt als Begr¼nder der Mengenlehre und lieferte wichtige Beitr¤ge zur modernen Mathematik . Auf ihn geht folgende Definition ¼ber Mengen zur¼ck: Eine Menge ist eine Zusammenfassung bestimmter, wohlunterschiedlicher Dinge unserer Anschauung oder unseres Denkens, welche Elemente der Menge genannt werden, zu einem Ganzen. Siehe auch Cantor-Diagonalisierung Cantor-Staub Literatur Amir D.Aczel: Die Natur der Unendlichkeit - Mathematik, Kabbala und das Geheimnis des Aleph, Verlag Rowohlt, Reinbek bei Hamburg, Oktober 2002, ISBN 3499613581 , Titel bei Amazon.de

63. MSN Encarta - Cantor, Georg Translate this page cantor, georg. cantor, georg (1845-1918), mathématicien allemand fondateur de la théorie des ensembles. Médias. Plus de résultats pour cantor, georg, http://fr.encarta.msn.com/encyclopedia_761575007/Cantor_Georg.html

Accueil MSN Mon MSN Hotmail Rechercher ... S'abonner   Encarta Premium Rechercher Article accessible sur abonnement MSN Encarta Premium : Acc©dez   30 000 articles encyclop©diques avec plus de 12 000 illustrations, un atlas mondial interactif, un guide du Web et une palette compl¨te de ressources et d'outils ©ducatifs. 34,99 € par an (service d’acc¨s   Internet non compris). En savoir plus. Cet article n'est accessible que si vous ªtes abonn©   MSN Encarta Premium. Dans ce cas, connectez-vous en cliquant sur le lien Aller sur MSN Encarta Premium (ci-dessus). Cantor, Georg Cantor, Georg (1845-1918), math©maticien allemand fondateur de la th©orie des ensembles. M©dias Encarta vous int©resse ? Abonnez-vous d¨s maintenant et b©n©ficiez de : Plus de 30 000 articles 2 000 analyses d'oeuvre Plus de 12 000 m©dias (dont des extraits sonores, des vid©os et des m©dias interactifs) Un atlas mondial interactif Une palette compl¨te de ressources et d'outils ©ducatifs Un guide du Web Plus de r©sultats pour Cantor, Georg

64. Smart Computing Encyclopedia Smart Computing ® Encyclopedia. cantor, georg. See georg cantor. Copyright Legal Information Privacy Policy Site Map Contact Us Need Site Help? http://www.smartcomputing.com/editorial/dictionary/detail.asp?guid=&searchtype=1

65. Georg Cantor Page georg cantor(18451918). History of Mathematics. Changing LINKS. My georg cantor paper for a grade in Math 461(Now almost completeupdated on May 2, 2002) http://www.geocities.com/CollegePark/Union/3461/cantor.htm

Georg Cantor(1845-1918) History of Mathematics Changing LINKS My Georg Cantor paper for a grade in Math 461 (Now almost completeupdated on May 2, 2002) Born: March 3, 1845 in St Petersburg, Russia Died: January 6, 1918 in Halle, Germany Full Name is: Georg Ferdinand Ludwig Philipp Cantor Georg was educated early in his life by private tutoring He went to primary school while in St. Petersburgh, Russia. In 1856 his family moved to Germany for a warmer climate, due to his father's poor health Cantor's father wanted him to be an Engineer, but Georg was interested in Mathematics In 1873 Cantor proved the rational numbers are countable,they can be put into a 1-1 correspondence with the natural numbers. He showed that the algebraic numbers, the numbers which are roots of polynomial equations with integer coefficients, were countable. Cantor is famous for proving that the real numbers are not countable. A transcendental number is an irrational number that is not a root of any polynomial equation having integer coefficients. Cantor showed that almost all numbers are transcendental by proving the real numbers were not countable while proving that the algebraic numbers were countable.

66. Skolavpohode.cz cantor, georg Ferdinand Ludwig Philipp (18451918) Nemecký matematik, který vystavel teorii nekonecných množin. Párováním http://www.skolavpohode.cz/clanek.asp?polozkaID=3465

67. Cantor-Vereinigung Halle Translate this page abgesteckt In der Tradition von mathematischer Forschung und Lehre an der Universität Halle stehend, deren berühmtester Vertreter georg cantor war, geht es http://www.mathematik.uni-halle.de/~cantorev/

G EORG - C ANTOR - V EREINIGUNG Homepage Anschrift, Telefon, ... Aktuelles Vorstand Dokumente ... Aufnahmeantrag Herzlich Willkommen auf der Homepage unserer Vereinigung! Fachbereichs , durch Studenten und Absolventen. Georg Cantor in einem Brief von 7.2.1869 an seine Schwester Sophie: "Ich sehe ... immer mehr ein, wie sehr mir ... Mathematik ans Herz gewachsen ist ... . Das Arbeiten ist und bleibt für mich der eigentliche Kern meines Lebens, und meine Wünsche erstrecken sich nur so weit, daß ich mich ... stets in solchen Lagen befinden möchte, wo ich ungehemmt diesen Beschäftigungen nachgehen und durch sie einem Kreise der menschlichen Gesellschaft nützlich werden kann." Georg Cantor, Aufnahme um 1902 geb. in St. Petersburg "De aequationibus secundi gradus indeterminatis" "De transformatione formarum ternarium quadricarum" Tod in Halle Virtuellen Museum des Fachbereiches. Wer etwa die Exponate der historischen Sammlung mathematischer Modelle des Fachbereichs anschaut , entdeckt auf vielen von ihnen ein kleines Messingschild: " ". Die Unterstützung bei der Bereitstellung dieser Modelle, die in den ersten Jahrzehnten dieses Jahrhunderts sowohl in den Lehrveranstaltungen als auch direkt in der mathematischen Forschung genutzt wurden, darf wohl noch heute als bedeutsame Hilfe der Freunde der Universität eingeschätzt werden. Es lohnt sich, die Modellsammlung mit Muße anzuschauen!

68. Porträt - Cantor Translate this page Porträt georg cantor. georg cantor wurde 1845 in St. Petersburg geboren. As er elf Jahre alt war, zog die Familie nach Deutschland http://www.zahlenjagd.at/cantor.html

Porträt: Georg Cantor Georg Cantor wurde 1845 in St. Petersburg geboren. As er elf Jahre alt war, zog die Familie nach Deutschland; dort schloß er seine Schulbildung ab, wobei er eine große Begabung für Mathematik zeigte. Cantor studierte 1862-1867 in Zürich, Göttingen und Berlin, unter anderem bei Leopold Kronecker mit dem Ihm zunächst eine freundschaftliche Beziehung hatte. Sein Traum wäre eine Stellung an der Universität Berlin gewesen, doch wurde er Professor in Halle, wo er über 40 Jahre tätig war. Cantors Arbeiten verstießen schon früh gegen alle Grundsätze Kroneckers. Seine erste Arbeit zu mengen erschien 1874. Sie war nicht-konstruktivistisch, verwendete aktuale Unendlichkeit und war grundlegend neu und innovativ. Neben mathematischen und philosophischen Studien widmente er sich auch der Literaturgeschichte. So vertiefte er sich in den alten Streit über die wahre Urheberschaft der Shakespearschen Stücke und lieferte bedeutende Beiträge zur frühen Geschichte der Mathematik in Indien. Er war damit einer der ersten, die erwogen, wie sich mathematisches Wissen von einer Kultur zur anderen ausbreiten konnte, also nicht an verschiedenen Orten unabhängig erfunden wird. In einer Arbeit aus dem Jahre 1874 bewies Cantor die Abzählbarkeit der Menge aller algebraischen Zahlen und die Nichtabzählbarkeit der Menge aller reellen Zahlen und folgerte hieraus die Existenz der transzendente Zahlen. Er benutzte dazu das noch heute nach Ihm benannte Diagonalverfahren.

69. Natural Theology > Synopsis > 16 Cantor to restore theology to the mainstream of science. georg cantor. (18451918). The natural numbers, 1, 2, 3 are infinite, since we can always add another one. http://www.naturaltheology.net/Synopsis/s16Cantor.html

Synopsis page 16: Site Map Directory Search this site Home ... Synopsis Next: page 17: Einstein Previous: page 15: Analysis Development: toc Essays: toc Glossary: toc ... Supplementary: toc ... to restore theology to the mainstream of science Georg Cantor The natural numbers, 1, 2, 3 ... are infinite, since we can always add another one. It was known in antiquity that Pythagoras' theorem implies that there are quantities that cannot be measured by the natural numbers or by the rational numbers, ratios (eg 3/5) of natural numbers. To measure such quantities, we must invent the 'irrational' or real numbers. Cantor showed that the step from natural to real numbers is not unique, but the first an endless series of steps to even bigger number spaces, which he called the transfinite numbers. Following Cantor, our theology is based on the hypothesis that the transfinite can help us to understand God. One might argue that the oldest scientific problem in the world is the relationship between discrete and continuous systems. A continuous system is something like a wheel, which moves smoothly without jumps or gaps. A discrete system is the exact opposite. Each unit of the system is separate from the others, and if one is to move, one must jump the gaps between the elements of the system. Language is a discrete system. Different words and sentences have a gap between them. Cantor found a path toward understanding the relationship between discrete and continuous systems which, through quantum mechanics, shows us how the mathematical relationship between discrete and continuous is played out in reality.

70. Cantor, Georg Ferdinand Ludwig Philipp - Gedächtnis Berlin Translate this page cantor, georg Ferdinand Ludwig Philipp. * 03.03.1845 St. Petersburg (Rußland). † 06.01.1918 Halle/Saale (Provinz Sachsen). Mathematiker. Straßen http://www.luise-berlin.de/Ehrung/c/cantor_georg_ferdinand_ludwig.htm

Cantor Georg Ferdinand Ludwig Philipp Mathematiker www.berlin-geschichte.de

71. Georg Cantor :: Online Encyclopedia :: Information Genius georg cantor. Online Encyclopedia georg Ferdinand Ludwig Philipp cantor (March 3, 1845 January 6, 1918) was a German mathematician http://www.informationgenius.com/encyclopedia/g/ge/georg_cantor.html

Quantum Physics Pampered Chef Paintball Guns Cell Phone Reviews ... Science Articles Georg Cantor Online Encyclopedia Georg Ferdinand Ludwig Philipp Cantor March 3 January 6 ) was a German mathematician who is best known as the creator of modern set theory . He is recognized by mathematicians for having extended set theory to the concept of transfinite numbers , including the cardinal and ordinal number classes. He was born in Saint Petersburg Russia , the son of a Danish merchant, George Waldemar Cantor, and a Russian musician, Maria Anna Böhm. In the family moved to Germany and he continued his education in German schools, earning his doctorate from the University of Berlin in Cantor recognized that infinite sets can have different sizes, distinguished between countable and uncountable sets and proved that the set of all rational numbers Q is countable while the set of all real numbers R is uncountable and hence strictly bigger. The proof uses his celebrated diagonal argument . In his later years, he tried in vain to prove the continuum hypothesis . By , he had discovered several paradoxes in elementary set theory.

72. MSN Encarta - Cantor, Georg Translate this page Melden Sie sich oben an. cantor, georg. cantor, georg (1845-1918), deutscher Mathematiker. cantor, georg. Möchten Sie noch mehr von Encarta? http://de.encarta.msn.com/encyclopedia_761575007/Cantor_Georg.html

MSN Home My MSN Hotmail Suche ... Upgrade auf Encarta Premium Encarta - Suche Abonnentenartikel MSN Encarta Premium: Holen Sie sich diesen Artikel, 47.000 weitere Artikel, einen interaktiven Atlas, W¶rterb¼cher und vieles mehr f¼r 29,95€/Jahr (zuz¼glich Steuern). Lernen Sie mehr. Dieser Artikel ist ausschlieŸlich f¼r Abonnenten von MSN Encarta Premium verf¼gbar. Sind Sie schon Abonennt? Melden Sie sich oben an. Cantor, Georg Cantor, Georg (1845-1918), deutscher Mathematiker. Seine Besch¤ftigung mit Fourier-Reihen f¼hrte zur Entwicklung einer Theorie der irrationalen Zahlen.... Multimedia Literaturangaben In diesen Quellen finden Sie weitere Informationen zu folgenden Themen: Cantor, Georg M¶chten Sie noch mehr von Encarta? Werden Sie noch heute Abonnent, und Sie erhalten Zugriff auf: 47.000 Artikel W¶rterb¼cher Interaktiver Atlas Lernstudio Erfahren Sie mehr ¼ber Cantor, Georg aus Andere Features aus Encarta Suchen in Encarta nach Cantor, Georg MSN Home My MSN ... Groups ©2004 Microsoft Corporation. Alle Rechte vorbehalten. TRUSTe-gepr¼fte Datenschutzbestimmungen Werbung Nutzungsbedingungen Impressum

73. No. 1484: Georg Cantor No. 1484 georg cantor. by John H. Lienhard. (Theme music). Meschkowski, H., cantor, georg. Dictionary of Scientific Biography, Vol. http://www.uh.edu/engines/epi1484.htm

No. 1484: GEORG CANTOR by John H. Lienhard Click here for audio of Episode 1484. Today, we wonder about counting to infinity. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. W hen I was in grade school, Time magazine ran an article that snatched my imagination. Someone proposed a new number called the googol a one followed by a hundred zeros. Later I learned that it wouldn't help very much in counting real objects, because there aren't that many real objects in the whole universe even atoms. But still, we've all wondered where counting ends and infinity begins. And we have good reason for asking about infinity. Every engineering student soon learns that infinity is not just the end of numbers. If we ask how real systems behave when velocity, or time, or force becomes infinite if we ask about the character of infinity we get unexpected and profoundly useful answers. Georg Cantor also wondered about infinity. He was born in Russia in 1845. He wanted to become a violinist like his mother. But his father, a worldly merchant, wouldn't have it. When he was seventeen, his father died, and Cantor went on to finish a doctorate in mathematics, in Berlin. He was only twenty-two when he did.

74. Bibliography cantor, georg, 18451918, Briefe / herausgegeben von Herbert Meschkowski und Winfried Nilson, Berlin, Springer-Verlag, 1991. cantor, georg http://www.library.cornell.edu/math/bibliography/display.cgi?start=C&

75. Georg Cantor Essays, Georg Cantor Term Papers, Research Papers On Georg Cantor Buy georg cantor essays, research papers on georg cantor, book reports, essays, georg cantor term papers, research papers, essays, book reports. http://www.essaytown.com/authors/georg_cantor_essays_papers.html

Georg Cantor Essays and Research Papers Book Reports, Term Papers, Essays, and Research Papers on Georg Cantor Research Papers, Essays, Term Papers, and Book Reports on Georg Cantor - only $26.99 each! Do you need an essay, term paper, review, thesis paper, book report, or research paper on Georg Cantortoday, tomorrow, next week, or next month? Since 1998, our Georg Cantor experts have helped students worldwide by providing the most comprehensive, lowest-priced research service on the Internet for Georg Cantor studies and coursework. If you've waited too long to formulate ideas for your Georg Cantor research paper, essay, thesis, book report, or term paper, our Georg Cantor research specialists can help you research and write any paper immediately! Over the years, our staff of professional, contracted, Georg Cantor researchers has produced thousands of undergraduate-, master-, and doctoral-level research papers, book reports, essays, and term papers on all Georg Cantor topics. Over 40,000 of our top-quality papers are available for research at only $26.99 each

76. Allmath.com - Math Site For Kids! Home Of Flashcards, Math Click Here cantor, georg (Ferdinand Ludwig Philipp). (18451918). Mathematician, born in St Petersburg, Russia. He studied at Berlin http://www.allmath.com/biosearch.php?QMeth=ID&ID=5813

77. Georg Cantor Translate this page georg Ferdinand Ludwig Philipp cantor. (1845-1918). georg cantor nasceu em S. Petersburgo, de pais que haviam emigrado da Dinamarca. http://www.mat.puc-rio.br/~inicient/biografias/georg_cantor.htm

Georg Ferdinand Ludwig Philipp Cantor Journal Alguns resultados na teoria dos conjuntos dos pontos eram tão paradoxais que o próprio Cantor uma vez, em 1877, escreveu a Dedekind. "Eu vejo isso, mas não acredito", e pediu a seu amigo que verificasse a prova. Os editores também hesitavam muito antes de aceitar seus artigos, e várias vezes a publicação de artigos de Cantor no Journal Cantor, por sua vez, escreveu uma defesa vigorosa em 1883 em seu "Fundamentos de uma teoria geral das multiplicidades", em que mantinha que "numerações definidas podem ser feitas com conjuntos infinitos tão bem quanto com finitos". Não temia cair no que chamava um "abismo de transcendentes" no entanto ocasionalmente ele se entregava a argumentos de tipo teológico. Kronecker continuou seus ataques contra Cantor e em 1884 este sofreu o primeiro dos esgotamentos nervosos que viriam a reaparecer durante os trinta e três anos restantes de sua vida. Voltar para o menu principal

78. Dauben, J.W.: Georg Cantor: His Mathematics And Philosophy Of The Infinite. of the book georg cantor His Mathematics and Philosophy of the Infinite by Dauben, JW, published by Princeton University Press....... http://pup.princeton.edu/titles/4740.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Georg Cantor: His Mathematics and Philosophy of the Infinite Joseph Warren Dauben 424 pp. Shopping Cart Reviews One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory. Review: "Historians of mathematics can only be grateful for the effort Professor Dauben has expended to create the synthesis of Cantor scholarship found in this book. But the book can, and I hope will, be read with profit by a far more extensive audience. Any student, mathematician, philosopher, theologian, or general historian with an interest in Georg Cantor and the wondrous revolution in mathematical and philosophical thought that his work did so much to precipitate will find this book of considerable interest."Thomas Hawkins

79. életrajzok: C cantor, georg Ferdinand (1845. március 3.—1918. január 6.) német matematikus. A XX. századi matematikát forradalmasító halmazelmélet megalapítója. http://www.iif.hu/~visontay/ponticulus/eletrajzok/c.html

rovatok j¡t©k arch­vum jegyzetek mutat³k kitekintő v©lem©nyek inform¡ci³k ©letrajzok magyar¡zatok forr¡sok CANTOR, Georg Ferdinand (1845. m¡rcius 3.—1918. janu¡r 6.): n©met matematikus. A XX. sz¡zadi matematik¡t forradalmas­t³ halmazelm©let megalap­t³ja. Szentp©terv¡ron sz¼letett d¡n kereskedőcsal¡db³l. A csal¡d 1856-ban Frankfurtba k¶lt¶z¶tt. Apja m©rn¶knek sz¡nta, de őt jobban ©rdekelt©k a folytonoss¡ggal ©s a v©gtelennel kapcsolatos matematikai ©s filoz³fiai probl©m¡k. V©g¼l apja megengedte, hogy matematik¡t tanuljon. Tanulm¡nyait Z¼richben kezdte, majd Berlinben folytatta. Tan¡rai KUMMER WEIERSTRASS ©s k©sőbbi ellenfele, KRONECKER voltak. Tanulm¡nyait G¶ttingenben fejezte be, ott is doktor¡lt 1867-ben. 1869-ben mag¡ntan¡ri habilit¡ci³t tett Hall©ben, ahol 1879-ben katedr¡t is kapott. Kezdetben a sz¡melm©let, a hat¡rozatlan egyenletek ©s a trigonometrikus sorok elm©lete ©rdekelt©k. Ezut¡n az anal­zis megalapoz¡s¡ba kapcsol³dott be. Megadta az irracion¡lis sz¡moknak egy, a Dedekind-szeletektől k¼l¶nb¶ző defin­ci³j¡t. 1874-ben kezdte meg halmazelm©leti vizsg¡latait. Az aktu¡lis v©gtelen l©tez©s©re alapozva kifejlesztette a transzfinit sz¡mok elm©let©t. A v©gtelenek k¶r©ben el©rt n©h¡ny eredm©nye őt mag¡t is meglepte. tl³s m³dszer©vel kapott eredm©ny©ről, amely szerint a term©szetes sz¡mok ©s a val³s sz¡mok halmaza nem ekvivalens, ­gy ­rt:

80. Georg Cantor --  Britannica Concise Encyclopedia Online Article cantor , georg Britannica Concise. , Early life and training from cantor, georg (Ferdinand Ludwig Philipp) cantor s parents were Danish. http://concise.britannica.com/ebc/article?eu=385007

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