Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Georg_Cantor> ?p ?o }
- Georg_Cantor abstract "Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔr/ KAN-tor; German: [ˈɡeɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfɪlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician. He invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections. Cantor, a devout Lutheran, believed the theory had been communicated to him by God. Some Christian theologians (particularly neo-Scholastics) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously rejected.The objections to Cantor's work were occasionally fierce: Henri Poincaré referred to his ideas as a "grave disease" infecting the discipline of mathematics, and Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "scientific charlatan", a "renegade" and a "corrupter of youth." Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included in a standard mathematics curriculum. Writing decades after Cantor's death, Wittgenstein lamented that mathematics is "ridden through and through with the pernicious idioms of set theory," which he dismissed as "utter nonsense" that is "laughable" and "wrong". Cantor's recurring bouts of depression from 1884 to the end of his life have been blamed on the hostile attitude of many of his contemporaries, though some have explained these episodes as probable manifestations of a bipolar disorder.The harsh criticism has been matched by later accolades. In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics. David Hilbert defended it from its critics by declaring: "No one shall expel us from the Paradise that Cantor has created."".
- Georg_Cantor alias "Cantor, Georg".
- Georg_Cantor almaMater ETH_Zurich.
- Georg_Cantor almaMater Frederick_William_University.
- Georg_Cantor award Sylvester_Medal.
- Georg_Cantor birthDate "1845-03-03".
- Georg_Cantor birthName "Georg Ferdinand Ludwig Philipp Cantor".
- Georg_Cantor birthPlace Russia.
- Georg_Cantor birthPlace Russian_Empire.
- Georg_Cantor birthPlace Saint_Petersburg.
- Georg_Cantor birthYear "1845".
- Georg_Cantor deathDate "1918-01-06".
- Georg_Cantor deathPlace German_Empire.
- Georg_Cantor deathPlace Germany.
- Georg_Cantor deathPlace Halle,_Saxony-Anhalt.
- Georg_Cantor deathPlace Halle_(Saale).
- Georg_Cantor deathPlace Province_of_Saxony.
- Georg_Cantor deathYear "1918".
- Georg_Cantor doctoralAdvisor Ernst_Kummer.
- Georg_Cantor doctoralAdvisor Karl_Weierstrass.
- Georg_Cantor doctoralStudent Alfred_Barneck.
- Georg_Cantor field Mathematics.
- Georg_Cantor knownFor Set_theory.
- Georg_Cantor nationality Germany.
- Georg_Cantor residence German_Empire.
- Georg_Cantor residence Russian_Empire.
- Georg_Cantor thumbnail Georg_Cantor2.jpg?width=300.
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- Georg_Cantor wikiPageExternalLink set-theory.
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- Georg_Cantor wikiPageExternalLink wittgenstein-mathematics.
- Georg_Cantor wikiPageExternalLink www.cantor-gymnasium.de.
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- Georg_Cantor wikiPageRevisionID "681702938".
- Georg_Cantor wikiPageWikiLink Abraham_Fraenkel.
- Georg_Cantor wikiPageWikiLink Absolute_Infinite.
- Georg_Cantor wikiPageWikiLink Actual_infinity.
- Georg_Cantor wikiPageWikiLink Adolf_Fraenkel.
- Georg_Cantor wikiPageWikiLink Adolf_Hurwitz.
- Georg_Cantor wikiPageWikiLink Aleph_number.
- Georg_Cantor wikiPageWikiLink Alfred_Barneck.
- Georg_Cantor wikiPageWikiLink Algebra.
- Georg_Cantor wikiPageWikiLink Algebraic_number.
- Georg_Cantor wikiPageWikiLink Annals_of_Science.
- Georg_Cantor wikiPageWikiLink Aristotle.
- Georg_Cantor wikiPageWikiLink Arthur_Moritz_Schoenflies.
- Georg_Cantor wikiPageWikiLink Arthur_Moritz_Schönflies.
- Georg_Cantor wikiPageWikiLink Austria-Hungary.
- Georg_Cantor wikiPageWikiLink Austro-Hungarian.
- Georg_Cantor wikiPageWikiLink Axiom_of_choice.
- Georg_Cantor wikiPageWikiLink Axiomatic_set_theory.
- Georg_Cantor wikiPageWikiLink Back-and-forth_method.
- Georg_Cantor wikiPageWikiLink Baconian_theory.
- Georg_Cantor wikiPageWikiLink Baconian_theory_of_Shakespeare_authorship.
- Georg_Cantor wikiPageWikiLink Bernard_Bolzano.
- Georg_Cantor wikiPageWikiLink Bernhard_Riemann.
- Georg_Cantor wikiPageWikiLink Bertrand_Russell.
- Georg_Cantor wikiPageWikiLink Bijection.
- Georg_Cantor wikiPageWikiLink Bipolar_disorder.
- Georg_Cantor wikiPageWikiLink Birkhäuser.
- Georg_Cantor wikiPageWikiLink Birkhäuser_Verlag.
- Georg_Cantor wikiPageWikiLink Burali-Forti_paradox.
- Georg_Cantor wikiPageWikiLink Cantor_algebra.
- Georg_Cantor wikiPageWikiLink Cantor_cube.
- Georg_Cantor wikiPageWikiLink Cantor_function.
- Georg_Cantor wikiPageWikiLink Cantor_medal.
- Georg_Cantor wikiPageWikiLink Cantor_set.
- Georg_Cantor wikiPageWikiLink Cantor_space.
- Georg_Cantor wikiPageWikiLink Cantors_back-and-forth_method.
- Georg_Cantor wikiPageWikiLink Cantors_diagonal_argument.
- Georg_Cantor wikiPageWikiLink Cantors_first_uncountability_proof.
- Georg_Cantor wikiPageWikiLink Cantors_paradox.
- Georg_Cantor wikiPageWikiLink Cantors_theorem.
- Georg_Cantor wikiPageWikiLink Cantor–Bernstein–Schroeder_theorem.
- Georg_Cantor wikiPageWikiLink Cardinal_Johannes_Franzelin.
- Georg_Cantor wikiPageWikiLink Cardinal_arithmetic.
- Georg_Cantor wikiPageWikiLink Cardinal_number.
- Georg_Cantor wikiPageWikiLink Cardinality.
- Georg_Cantor wikiPageWikiLink Carl_Johannes_Thomae.
- Georg_Cantor wikiPageWikiLink Cartesian_product.
- Georg_Cantor wikiPageWikiLink Category:1845_births.
- Georg_Cantor wikiPageWikiLink Category:1918_deaths.
- Georg_Cantor wikiPageWikiLink Category:19th-century_German_mathematicians.
- Georg_Cantor wikiPageWikiLink Category:19th-century_German_writers.
- Georg_Cantor wikiPageWikiLink Category:19th-century_philosophers.
- Georg_Cantor wikiPageWikiLink Category:20th-century_German_mathematicians.
- Georg_Cantor wikiPageWikiLink Category:20th-century_German_writers.
- Georg_Cantor wikiPageWikiLink Category:20th-century_philosophers.
- Georg_Cantor wikiPageWikiLink Category:Baltic-German_people.