Geometry.Net - Scientists: Cantor Georg

Cantor
Biography of georg cantor (18451918) from the MacTutor History of Mathematics Archive.Category Science Math History People cantor, georg georg cantor's father, georg Waldemar cantor, was a successful merchant, workingas a wholesaling agent in St Petersburg, then later as a broker in the St
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html

Extractions: Georg Cantor After early education at home from a private tutor, Cantor attended primary school in St Petersburg, then in 1856 when he was eleven years old the family moved to Germany. However, Cantor [21]:- ... remembered his early years in Russia with great nostalgia and never felt at ease in Germany, although he lived there for the rest of his life and seemingly never wrote in the Russian language, which he must have known. Cantor's father had poor health and the move to Germany was to find a warmer climate than the harsh winters of St Petersburg. At first they lived in Wiesbaden, where Cantor attended the Gymnasium ... a shining star in the engineering firmament. However, in 1862 Cantor had sought his father's permission to study mathematics at university and he was overjoyed when eventually his father consented. His studies at Zurich, however, were cut short by the death of his father in June 1863. Cantor moved to the University of Berlin where he became friends with Herman Schwarz who was a fellow student. Cantor attended lectures by
Georg Cantor
Complete bibliography of cantor's writings.
http://www.dean.usma.edu/math/people/rickey/hm/cantor.htm

Extractions: Georg Cantor (1845-1918) This is intended to be a complete list of the publications of Georg Cantor as well as translations of those works. It is followed by works which contain his correspondence and by a list of some of the most valuable English language historical books and papers dealing with Cantor and his work. Corrections and suggestions would be most welcome. Send email to fred-rickey@usma.edu De aequationibus secundi gradus indeterminatis.
Cantor
Features a biography of the mathematician best known for creating set theory and for his discovery of the transfinite numbers. georg cantor's father, georg Waldemar cantor, was a successful merchant, working as a wholesaling agent in St Petersburg,
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html

Extractions: Georg Cantor After early education at home from a private tutor, Cantor attended primary school in St Petersburg, then in 1856 when he was eleven years old the family moved to Germany. However, Cantor [21]:- ... remembered his early years in Russia with great nostalgia and never felt at ease in Germany, although he lived there for the rest of his life and seemingly never wrote in the Russian language, which he must have known. Cantor's father had poor health and the move to Germany was to find a warmer climate than the harsh winters of St Petersburg. At first they lived in Wiesbaden, where Cantor attended the Gymnasium ... a shining star in the engineering firmament. However, in 1862 Cantor had sought his father's permission to study mathematics at university and he was overjoyed when eventually his father consented. His studies at Zurich, however, were cut short by the death of his father in June 1863. Cantor moved to the University of Berlin where he became friends with Herman Schwarz who was a fellow student. Cantor attended lectures by
References For Cantor
References for georg cantor. Books JW Dauben, georg cantor His Mathematicsand Philosophy of the Infinite (Cambridge, Mass, 1979; reprinted 1990).
http://www-gap.dcs.st-and.ac.uk/~history/References/Cantor.html

Extractions: J W Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite (Cambridge, Mass, 1979; reprinted 1990). P E Johnson, A history of set theory (Boston, Mass., 1972). A Kertesz, Georg Cantor, 1845-1918 : Schopfer der Mengenlehre, Acta historica leopoldina H Meschkowski, Georg Cantor : Leben, Werk und Wirkung (Mannheim, 1983). Briefweschsel Cantor-Dedekind (Paris, 1937). W Purkert and H J Ilgauds, Georg Cantor (Leipzig, 1985). W Purkert and H J Ilgauds, Georg Cantor 1845-1918 (Basel, 1987). K Richter, Cantor, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983). A Schoenflies, Georg Cantor (Magdeburg, 1928). D Stander, Makers of modern mathematics : Georg Cantor Articles:
CantorNetwork - Aktuelles
Diese Netzwerk versteht sich als Kommunikationsplattform im Internet f¼r Sch¼ler, Ehemalige, Lehrer und andere Personen die sich mit dem Gymnasium vebrunden f¼hlen. Mit Forum und einer Datenbank.
http://www.cantor-netzwerk.de
Georg-Cantor-Gymnasiums
http://www.gym-cantor.bildung-lsa.de/
Cantor, Georg (1845-1918) -- From Eric Weisstein's World Of Scientific Biography
cantor, georg (18451918), Dauben, J. W. georg cantor His Mathematics and Philosophyof the Infinite. Princeton, NJ Princeton University Press, 1990.
http://scienceworld.wolfram.com/biography/CantorGeorg.html

Extractions: German mathematician who built a hierarchy of infinite sets according to their cardinal number By one-to-one pairing, he showed that the set of real numbers has a higher cardinal number than does the set of rational fractions However, he found every class of algebraic numbers has the same cardinal number as the integers. Such considerations led to his Mengenlehre (theory of assemblages) and Manningfaltigkeitslehre (theory of manifolds). He also invented the Cantor set Cantor's highly original views were vigorously opposed by his contemporaries, especially Kronecker . The attacks contributed to the nervous breakdowns he suffered throughout the final 33 years of his life. Cantor died in a mental institution. Kronecker
GCG
georgcantor-Gymnasium. Gymnasium mit mathematisch-naturwissenschaftlichem Schwerpunkt. Willkommen auf der Homepage des georg-cantor-Gymnasiums
http://www.cantor-gymnasium.de/
Cantor, Georg
http://euler.ciens.ucv.ve/matematicos/cantor.html

Extractions: Cantor, Georg Georg Ferdinand Ludwig Philipp Cantor, nacido en Mar. 3, 1845, muerto en Ene. 6, 1918, era un matemático ruso-alemán mejor conocido como el creador de la TEORIA CONJUNTISTA y por su descubrimiento de los números transfinitos. También adelantó el estudio de las series trigonométricas, fue el primero en probar la no numerabilidad de los números reales, y hizo contribuciones significantes a la teoría de la dimensión. Cantor recibió su doctorado en 1867 y aceptó una posición en la Universidad de Halle en 1869, donde permaneció. Estrechamente relacionado al trabajo de Cantor en la teoría de los conjuntos transfinitos estuvo su definición del continuo como un conexo, conjunto perfecto. Nunca dudó de su absoluta confianza en su trabajo, pero seguidamente del descubrimiento de las paradojas de la teoría de conjuntos, el dejó la teoría de los conjuntos transfinitos a matemáticos más jóvenes tales como David HILBERT, Bertrand RUSSELL, y Ernst Zermelo. Autor: J. W. Dauben
Cantor, Georg
cantor, georg. Author JW Dauben Bibliography Dauben, JW, georg cantor HisMathematics and Philosophy of the Infinite (1978; repr. 1990). Homepage,
http://euler.ciens.ucv.ve/English/mathematics/cantor.html

Extractions: Cantor, Georg Georg Ferdinand Ludwig Philipp Cantor, b. Mar. 3, 1845, d. Jan. 6, 1918, was a Russian-born German mathematician best known as the creator of SET THEORY and for his discovery of the transfinite numbers. He also advanced the study of trigonometric series, was the first to prove the nondenumerability of the real numbers, and made significant contributions to dimension theory. Cantor received his doctorate in 1867 and accepted a position at the University of Halle in 1869, where he remained. Closely related to Cantor's work in transfinite set theory was his definition of the continuum as a connected, perfect set. He never doubted the absolute truth of his work, but following the discovery of the paradoxes of set theory, he left the defense of transfinite set theory to younger mathematicians such as David HILBERT, Bertrand RUSSELL, and Ernst Zermelo. Author: J. W. Dauben
Cantor, Georg (1845-1918)
cantor, georg (18451918). georg cantor put forth the modern theory oninfinite sets that revolutionized almost every mathematics field.
http://pirate.shu.edu/projects/reals/history/cantor.html

Extractions: Click here for pronunciation Georg Cantor put forth the modern theory on infinite sets that revolutionized almost every mathematics field. However, his new ideas also created many dissenters and made him one of the most assailed mathematicians in history. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. Georg's background was very diverse. His father was a Danish Jewish merchant that had converted to Protestantism while his mother was a Danish Roman Catholic. The family stayed in Russia for eleven years until the father's ailing health forced them to move to the more acceptable environment of Frankfurt, Germany, the country Georg would call home for the rest of his life. All the Cantor children displayed an early artistic talent with Georg excelling in mathematics. His father, the eternal pragmatic, saw this gift and tried to push his son into the more profitable but less challenging field of engineering. In one of his letters, he pressed upon his son that his entire family and God Himself were expecting him to become a "shining star" as an engineer. Georg was not at all happy about this idea but he lacked the assertiveness to stand up to his father and relented. However, after several years of training, he became so fed up with the idea that he mustered up the courage to beg his father to become a mathematician. Finally, just before entering college, his father let Georg study mathematics. The son accepted his decision with the same submission that he had before, thanking his father for the fact that he would not "displease him."
Cantor, Georg. The Columbia Encyclopedia, Sixth Edition. 2001
The Columbia Encyclopedia, Sixth Edition. 2001. cantor, georg. (g ´ôrkh kän´tôr)(KEY) , 18451918, German mathematician, b. St. Petersburg.
http://www.bartleby.com/65/ca/Cantor-G.html

Extractions: Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. Cantor, Georg
Cantor, Georg Ferdinand Ludwig Philipp
cantor, georg Ferdinand Ludwig Philipp .
http://episte.math.ntu.edu.tw/people/p_cantor/

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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

Extractions: 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.
Cantor, Georg
encyclopediaEncyclopedia cantor, georg, gA'ôrkh kän'tôr PronunciationKey. cantor, georg , 18451918, German mathematician, b. St. Petersburg.
http://www.factmonster.com/ce6/people/A0810251.html
Cantor, Georg
cantor, georg (18451918) cantor was born in Russia. He attended schoolin Wiesbaden and Darmstadt in Germany, where he first became
http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib

Extractions: Cantor, Georg (18451918) Cantor was born in Russia. He attended school in Wiesbaden and Darmstadt in Germany, where he first became interested in mathematics. In 1862 he began his university studies in Zurich and then went to University of Berlin in 1863, where he studied with Karl Weierstrass Cantors early research on series and real numbers shows Weierstrasss influence, although in Berlin he also studied with Kummer and Kronecker. In 1869 Cantor obtained a teaching position at the University of Halle, soon becoming an associate professor and, in 1879, full professor. His chief contributions to mathematics were in the subjects of analysis and set theory. When Cantor first published his paper on the theory of sets in 1874, it was very controversial because it was innovative and completely differed from current mathematical thinking. His work was ridiculed by many of his contemporaries. Among the critics was his former instructor Kronecker. Unfortunately, Cantor suffered a series of breakdowns and eventually died in a mental institution. Today, we know that much of the foundation of modern mathematics rests directly on Cantors work.
Glossary Of People: Ca
Sec. of SWP till his death in August 1974. Further Reading JamesCannon Archive. cantor, georg (1845 1918). German mathematician
http://www.marxists.org/glossary/people/c/a.htm

Extractions: MIA Encyclopedia of Marxism : Glossary of People French utopian author of Voyage en Icarie Cafiero, Carlo (1846-1892) Italian Anarchist, published a condensed version of Capital in Italian. Cannon, James P. (1890-1974) US Socialist Workers Party January 1938. Participated in bitter factional struggle in 1940 against Burnham and Schachtman's "petit-bourgeois opposition", the subject of Trotsky's In Defence of Marxism; Jailed 1944-45 for opposition to war; National Sec. of SWP till his death in August 1974. Further Reading: James Cannon Archive Cantor, Georg (1845 - 1918) German mathematician who founded modern Set Theory and introduced the concept of transfinite numbers, indefinitely large but distinct from one another. Cantor wrote little of a philosophical nature, but his startling achievements in fundamental investigations of mathematics stimulated the deeper enquiry into the epistemological foundations of mathematics which had a profound influence on Western thought during the first three decades of the twentieth century. Of prosperous and cultured Danish-born parents, Cantor's talent for mathematics was observed when he was only 14 and by the age of 18 he was studying under the great mathematicians Karl Weierstrass and Leopold Kronecker, and by 1867 had published a doctoral thesis on one of Gauss's famous unsolved problems. Cantor then joined the University of Halle, where he remained for the rest of his life.
Cantor, Georg (1845-1918)
Translate this page cantor, georg (1845-1918). georg Ferdinand Ludwig Philipp cantor pôsadiante a teoria moderna sobre os jogos infinitos que revolucionaram
http://www.cinei.hpg.ig.com.br/cantor.htm

Extractions: Georg Ferdinand Ludwig Philipp Cantor pôs adiante a teoria moderna sobre os jogos infinitos que revolucionaram quase todos os campos da matemática. Entretanto, suas idéias novas também criaram-lhe muitas divergências e fizerem-no um dos matemáticos mais perseguidos da história. Cantor nasceu em St. Petersburg, Rússia, em 3 de março de 1845. Seu pai era um comerciante judeu dinamarquês que se converteu ao Protestantismo e sua mãe era dinamarquesa e Católica. Mudaram-se mais tarde para a Alemanha.Em 1862, Georg Cantor entrou na universidade de Zurique para transferir somente o ano seguinte à universidade de Berlim após a morte do seu pai. Em Berlim estudou matemática, filosofia e física. Lá estudou com alguns dos maiores matemáticos da includindo Kronecker e Weierstrass. Após ter recebido seu doutorado em 1867 e com dificuldade para encontrar um bom emprego acabou aceitando uma posição como professor assistente. Em 1874, casou e teve eventualmente seis filhos. Entretanto, com suas novas idéias ganharamu também inimigos numerosos. Muitos matemáticos apenas não aceitavam suas idéias. Um de seus maiores críticos, Leopold Kronecker, que usando seu prestígio como professor da universidade de Berlim, fêz tudo que pode para suprimir as idéias de Cantor e arruinar sua vida. Entre outras coisas, atrasou ou suprimiu completamente Cantor e as publicações dos seus seguidores, com ataques pessoais escritos e verbais, atrapalhando a ambição da vida de Cantor de ganhar uma posição na prestigiosa universidade de Berlim.
Georg Cantor (1845-1918)
author home author list georg cantor (18451918) Bibliography Links Translations between biology and sociology - formalism a
http://homepages.which.net/~gk.sherman/eaaaaabb.htm
Cantor, Georg
cantor, georg (18451918). German mathematician who followed his work on numbertheory and trigonometry by considering the foundations of mathematics.
http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/C/Cantor/1.html

Extractions: German mathematician who followed his work on number theory and trigonometry by considering the foundations of mathematics. He defined real numbers and produced a treatment of irrational numbers using a series of transfinite numbers. Cantor's set theory has been used in the development of topology and real function theory. Investigating sets of the points of convergence of the Fourier series (which enables functions to be represented by trigonometric series), Cantor derived the theory of sets that is the basis of modern mathematical analysis. His work contains many definitions and theorems in topology. For the theory of sets, he had to arrive at a definition of infinity, and also therefore consider the transfinite; for this he used the ancient term 'continuum'. He showed that within the infinite there are countable sets and there are sets having the power of a continuum, and proved that for every set there is another set of a higher power.

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