Geometry.Net - Scientists: Cantor Georg

Georg Cantor
Georg Cantor Seite aus einem deutschsprachigen OnlinePhilosophenlexikon. Der deutsche Mathematiker Georg Cantor gilt als Begründer der Mengenlehre.
http://www.philosophenlexikon.de/cantor.htm

Extractions: Ebbinghaus - Ewald ... Geschichte der Philosophie Diskussion PhilTalk Philosophieforen Andere Lexika PhilLex -Lexikon der Philosophie Lexikon der griechischen Mythologie PhiloThek Bibliothek der Klassiker Zeitschriftenlesesaal Nachschlagewerke Allgemeine Information ... Dokumentenlieferdienste Spiele Philosophisches Galgenraten PhilSearch.de Shops PhiloShop PhiloShirt Service Kontakt Impressum eMail Diagonalverfahren , das inzwischen zu einem wichtigen Beweisprinzip in vielen Gebieten der Mathematik geworden ist. Eine 1895 von Cantor entdeckte und 1897 von Burali-Forti Antinomie , heute Burali-Forti's Antinomie Seine Theorie bezeichnete Cantor selbst als philosophische , d. h. als eine metaphysische powered by Uwe Wiedemann
WIEM: Cantor Georg
cantor georg (18451918), matematyk niemiecki, profesor uniwersytetu w Halle, twórca teorii mnogoci, sformuowa pojcie mocy zbioru, wykaza
http://www.encyklopedia.pl/wiem/0031c9.html

Extractions: poka¿ powi±zane Cantor Georg (1845-1918), matematyk niemiecki, profesor uniwersytetu w Halle, twórca teorii mnogo¶ci , sformu³owa³ pojêcie mocy zbioru , wykaza³ nieprzeliczalno¶æ zbioru liczb rzeczywistych , wprowadzi³ pojêcie punktu skupienia. Powi±zania Moc zbioru liczb naturalnych Matematyka Kronecker Leopold Topologia ... do góry Encyklopedia zosta³a opracowana na podstawie Popularnej Encyklopedii Powszechnej Wydawnictwa Fogra
Georg Cantor
Georg Cantor. 19th Century Philosophy at Erratic Impact's PhilosophyResearch Base. Cantor resources include Georg Cantor 1845 1918.
http://www.erraticimpact.com/~19thcentury/html/cantor.htm

Extractions: Click here for History of Mathematics Books ... Georg Ferdinand Ludwig Philipp Cantor Biography This fairly detailed Georg Cantor biography is from the School of Mathematics and Statistics at the University of St Andrews, Scotland . This is the home of the MacTutor History of Math Archives Excerpt: ...While at Berlin Cantor became much involved with the Mathematical Society being president of the Society during 1864-65. He was also part of a small group of young mathematicians who met weekly in a wine house. After receiving his doctorate in 1867, Cantor taught at a girl's school in Berlin. Then, in 1868, he joined the Schellbach Seminar for mathematics teachers. During this time he worked on his habilitation and, immediately after being appointed to Halle in 1869, he presented his thesis, again on number theory, and received his habilitation...
WIEM: Cantor Georg
(encyklopedia.pl)Category World Polska Leksykon Encyklopedia encyklopedia.pl Ccantor georg (18451918), matematyk niemiecki, profesor uniwersytetu w Halle,twórca teorii mnogosci, sformulowal pojecie mocy zbioru, wykazal
http://wiem.onet.pl/wiem/0031c9.html

Extractions: poka¿ powi±zane Cantor Georg (1845-1918), matematyk niemiecki, profesor uniwersytetu w Halle, twórca teorii mnogo¶ci , sformu³owa³ pojêcie mocy zbioru , wykaza³ nieprzeliczalno¶æ zbioru liczb rzeczywistych , wprowadzi³ pojêcie punktu skupienia. Powi±zania Moc zbioru liczb naturalnych Matematyka Kronecker Leopold Topologia ... do góry Encyklopedia zosta³a opracowana na podstawie Popularnej Encyklopedii Powszechnej Wydawnictwa Fogra
Cantor Georg Ferdinand Ludwig Philipp From FOLDOC
cantor georg Ferdinand Ludwig Philipp. Recommended Reading Georg Cantor, Contributionsto the Founding of the Theory of Transfinite Numbers, tr.
http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Cantor Georg Ferdinand Ludwig Phi
Xrefer - Search Results - Georg Cantor
cantor georg 1845 1918. cantor georg 1845 1918 Russianborn German mathematician.Cantor's work on numbers laid the cantor georg 1845 1918.
http://www.xrefer.com/results.jsp?shelf=&term=Georg Cantor
Georg Cantor - Wikipedia
Other languages Deutsch Esperanto. Georg Cantor. From Wikipedia,the free encyclopedia. Georg Ferdinand Ludwig Philipp Cantor was
http://www.wikipedia.org/wiki/Georg_Cantor

Extractions: Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Other languages: Deutsch Esperanto From Wikipedia, the free encyclopedia. Georg Ferdinand Ludwig Philipp Cantor March 3 January 6 ) was a German mathematician who is best known 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 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
Georg Cantor
Georg Cantor. 18451918.
http://dbeveridge.web.wesleyan.edu/wescourses/2001f/chem160/01/Who's Who/georg_c

Extractions: Home Science Humanities Cantor ... Mendel Biography Photo Gallery Links to Outside Sources German mathematician who founded set theory and developed precise notion of infinity. He also introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another. born March 3 age 11, family moved from St. Petersburg to Germany graduated from Realschule in Darmstadt with outstanding report (esp. trigonometry) entered the University of Zurich transferred to University of Berlin to study math under Weierstrass received doctorate, assistant professor at the backwater University of Halle (girl's school) joined Schellbach Seminar for mathematics teachers presented his thesis, again on number theory, and received his habilitation solved the problem proving uniqueness of the representation of a function as a trigonometric series begins friendship with Dedekind, published paper in which defined irrational numbers in terms of convergent sequences of rational numbers, promoted to Extraordinary Professor at Halle proved rational numbers countable with one-to-one correspondence and algebraic numbers were countable published paper that "almost all" numbers are transcendental by proving real numbers were not countable, one-to-one correspondence appears for the first time
GeorgCantor
Georg Cantor. 2/24/99. Click here to start. Table of Contents. Georg Cantor. GeorgCantor early life. Georg Cantor - education. Georg Cantor - early work.
http://www.hsu.edu/faculty/worthf/mathematicians/Cantor/
GEORG CANTOR
GEORG CANTOR (1845 1918) Georg Ferdinand Ludwig Philip Cantor was bornin St. Georg Cantor is famous for his work in developing set theory.
http://www.engr.iupui.edu/~orr/webpages/cpt120/mathbios/gcant.htm

Extractions: GEORG CANTOR Georg Ferdinand Ludwig Philip Cantor was born in St. Petersburg, Russia in 1845. His parents were of Danish decent and he moved with them to Frankfurt, Germany in 1856. His father was a Jew who was converted to Protestantism and his mother was born a Catholic. Georg was a very religious Christian and had a deep interest in medieval theology which became very influential in his motivation to investigate the Infinite. His father suggested that Georg become an engineer, but Georg decided to concentrate on philosophy, physics and mathematics. He studied at Zurich, Gotingen and Berlin and received his doctorate from Berlin in 1869. Georg taught at the University of Halle from 1869 until 1905. He died in a mental hospital in Halle in 1918. Georg Cantor is famous for his work in developing set theory. He published his first work in 1874 on set theory. This work was very controversial because it differed radically from the mathematics of that time. Today the idea of sets is widely accepted and used by almost every branch of mathematics. Cantor worked with both infinite and finite sets. He suggested that the word infinite had two meanings. The first is a magnitude which increases beyond any indicated limit. Cantor called this the
Georg Cantor - Wikipedia
Translate this page Georg Cantor. Georg Cantor (1845 - 1918), deutscher Mathematiker, gilt als Begründerder Mengenlehre und lieferte wichtige Beiträge zur modernen Mathematik.
http://de.wikipedia.org/wiki/Georg_Cantor

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Georg Ferdinand Ludwig Philipp Cantor
Georg Ferdinand Ludwig Philipp Cantor. Click here to see a picture. Georg Cantor;Microsoft Encarta 96 Encyclopedia; Funk Wagnalls New Encyclopedia (vol. 5, pg.
http://www.andrews.edu/~calkins/math/biograph/199899/biocanto.htm

Extractions: Back to the Table of Contents In this report: Early Life, Family Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. Georg had a very diverse background; his father was a Danish Jewish merchant that had converted to Protestantism, and his mother was a Danish Roman Catholic. The Cantor family stayed in Russia until 1856, when his father became deathly ill. At this point, the family moved to Frankfurt, Germany because it had a more acceptable environment. All of the Cantor children showed an early talent in mathematics, including Georg. His father saw this ability and tried to push his son into the field of engineering. In one of his letters, he told his son that his entire family and God Himself were expecting him to become a "shining star" as an engineer. Georg wasn't thrilled about this idea, but he lacked the assertiveness to stand up to his father. After several years of training, though, he became so tired of his father that he became demoralized enough to beg his father to become a mathematician. Finally, just before entering college, his father let him study mathematics.
Georg Cantor
Georg Cantor. (18451918). Georg Cantor was born in St. Petersburg,Russia, in 1845 where his father had a successful business.
http://www.scholars.nus.edu.sg/writing/ccwp10/benny/cantor.htm

Extractions: Georg Cantor Georg Cantor was born in St. Petersburg, Russia, in 1845 where his father had a successful business. As a young student, Cantor displayed an interest and aptitude for Mathematics and continued to pursue this interest when he started his university studies in Zurich. When his father passed away, Cantor moved to Germany and finished his studies at the University of Berlin. In 1869, he received a professorship at the University of Halle where he worked for the rest of his life. Cantor published his first paper on the theory of sets in 1874 that drew a lot of criticisms from his peers. They had problems accepting the notion of sets, which differed entirely from their own works. Some of his own teachers even attacked his work as theological and not mathematical. Often, the criticisms and attacks degraded to personal attacks at him. Thus, as a result of this prolonged abuse, Cantor suffered a mental breakdown and was subsequently admitted to a mental hospital at the age of 40. Although he recovered from that episode and continued to improve on his theories, he was to suffer from a series of breakdowns for the rest of his life. He died a sad and disappointed man in a mental clinic in 1918, at the age of 74. Cantors set theory opened up a whole new world of Mathematics. Before the arrival of set theory, mathematicians were contended with the state of Mathematics. They believed that everything in Mathematics had been discovered. That was why they resisted Cantors work. It was too radical and abstract for them to comprehend. However, set theory slowly gained acceptance over the years and is now regarded as the fundamental principle behind mathematical logic. It contributed greatly in the two fields of statistics and symbolic logic, founded by
Georg Ferdinand Ludwig Philipp Cantor
Georg Ferdinand Ludwig Philipp Cantor 18451918 After early education athome from a private tutor, Georg Cantor attended primary school in St.
http://www.stetson.edu/~efriedma/periodictable/html/Ca.html

Extractions: After early education at home from a private tutor, Georg Cantor attended primary school in St. Petersburg, then in 1856 when he was 11 years old his family moved to Germany. His teachers gave him outstanding reports, which mentioned in particular his exceptional skills in mathematics, in particular trigonometry. He entered the Polytechnic of Zurich in 1862. 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, a fellow student. Cantor attended lectures by Weierstrass, Kummer and Kronecker. While at Berlin, Cantor became much involved with the Mathematical Society being president of the Society during 1864-65. He was also part of a small group of young mathematicians who met weekly in a wine house. After receiving his doctorate in 1867 in number theory, Cantor taught at a girl's school in Berlin. Then, in 1868, he joined the Schellbach Seminar for mathematics teachers in Halle. There the direction of Cantor's research turned away from number theory and towards analysis. This was due to Heine, one of his senior colleagues, who challenged Cantor to prove the open problem on the uniqueness of representation of a function as a trigonometric series. Cantor solved the problem in 1870. He published further papers between 1870 and 1872 dealing with trigonometric series. Cantor was promoted to Extraordinary Professor in 1872, and in that year he began a friendship with Dedekind. Cantor published a paper on trigonometric series in 1872 in which he defined what are now known as "Dedekind cuts". In 1873, Cantor proved the rational numbers and the algebraic numbers are countable and that the real numbers were not countable. He published this in a paper in 1874, and it is in this paper that the idea of a one-to-one correspondence appears for the first time, albeit indirectly.
Georg Cantor - Wikipedia
Wersja angielska. Georg Cantor. Z Wikipedii, wolnej encyklopedii. GeorgFerdinand Ludwig Philipp Cantor byl niemieckim matematykiem.
http://pl.wikipedia.org/wiki/Georg_Cantor

Extractions: Strona gÅ³wna Ostatnie zmiany Edytuj Historia strony Strony specjalne Zmiana moich preferencji Obserwowane Ostatnio zmienione PrzesyÅanie plik³w Lista obrazk³w i multimedi³w Zarejestrowani uÅ¼ytkownicy Statystyka Losowa strona Porzucone artykuÅy Porzucone pliki Najpopularniejsze Najbardziej potrzebne Najkr³tsze NajdÅuÅ¼sze Nowoutworzone Wszystkie Zablokowane adresy IP Prosta administracja KsiÄÅ¼ki Wersja do druku Dyskusja Wersja: angielska Z Wikipedii, wolnej encyklopedii. Georg Ferdinand Ludwig Philipp Cantor byÅ niemieckim matematykiem . UrodziÅ siÄ 3 marca 1845 roku w Sankt Petersburgu. ZmarÅ 6 czerwca 1918 roku w sanatorium w Halle. Jego najwiÄkszym wkÅadem w rozw³j matematyki byÅo stworzenie podwalin teorii mnogoÅci i koncepcji liczb pozaskoÅczonych. Cantor odkryÅ, Å¼e zbiory nieskoÅczone mogÄ byÄ r³Å¼nej wielkoÅci - w szczeg³lnoÅci pokazaÅ za pomocÄ rozumowania przekÄtniowego , Å¼e zbi³r liczb naturalnych nie jest r³wnoliczny ze zbiorem liczb rzeczywistych Cantor przez dÅugi czas staraÅ siÄ udowodniÄ hipotezÄ continuum (jak siÄ okazaÅo w latach 50. - jego wysiÅki nie mogÅy przynieÅÄ zadowalajÄcego go rezultatu). DÅugie lata cierpiaÅ na ciÄÅ¼kie depresje (parokrotnie byÅ z tego powodu hospitalizowany). Pod koniec Å¼ycia zajmowaÅ siÄ r³wnieÅ¼
Georg CANTOR - Vikipedio
Georg CANTOR. El Vikipedio, la libera enciklopedio. Sciencisto GeorgCANTOR. Georg Ferdinand Ludwig Philipp Cantor Kantor estis
http://eo.wikipedia.org/wiki/Georg_CANTOR

Extractions: Presebla versio El Vikipedio, la libera enciklopedio. Sciencisto > Georg CANTOR Georg Ferdinand Ludwig Philipp Cantor [Kantor] estis germana matematikisto , naskiÄinta je la 3-a de marto en Peterburgo Rusio , kaj mortinta je la 6-a de januaro en Halle , Germanio. Li estas plej konata por krei la arteorion kaj la koncepto de transfiniaj nombroj Li rekonis, ke nefiniaj aroj povas havi malsimilajn grandecojn, kaj li distingis entre la kompteblaj kaj la nekompteblaj aroj kaj li pruvis ke la aro de Äiuj racionalaj nombroj Q estas komptebla sed la aroj de realaj nombroj R estas nekomptebla kaj do Äi estas pli granda. La pruvo uzas lia fama 'diagonala argumento'. AntaÅ , li jam malkovris multajn paradoksojn en elementa teorio de aroj. En la dua duono de sia vivo li je suferis multaj depresioj , kiuj malfaciligis lian laborkapablon kaj igis lin iri ofte al malsanulejo. Li publikigis pri literaturo kaj religio , kaj evoluis sian koncepton de la Absoluta Nefinio , kiun li komparis kun Dio . Li malricxigxis dum la Unua Mondmilito kaj mortis en frenezulejo en La nova matematiko de Cantor ne estis facile akceptita dum lia vivo. La moderna matematiko tute akceptas la verkon de Cantor kaj agnoskas Äian grandegan gravecon.
Georg Cantor
Georg Cantor. GeorgCantor was one of the most stupefyingly originalthinkers in all of mathematical history. He placed the study
http://c2.com/cgi/wiki?GeorgCantor
Editions Jacques Gabay - Georg CANTOR
Translate this page Georg CANTOR. Georg CANTOR. 1845 - 1918. Au catalogue des Editions JacquesGabay CANTOR Sur les fondements de la théorie des ensembles
http://www.gabay.com/sources/Liste_Bio.asp?NP=CANTOR Georg
Georg Cantor - Acapedia - Free Knowledge, For All
Friends of Acapedia Georg Cantor. From Wikipedia, the free encyclopedia.Georg Ferdinand Ludwig Philipp Cantor was a German mathematician
http://acapedia.org/aca/Georg_Cantor
10.5. Cantor, Georg (1845-1918)
Brief biography from the Real Analysis website.Category Science Math History People cantor, georg10.5. cantor, georg (18451918). IRA. georg cantor put forth the modern theoryon infinite sets that revolutionized almost every mathematics field.
http://www.shu.edu/projects/reals/history/cantor.html

Extractions: 10.5. Cantor, Georg (1845-1918) IRA 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."

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