21. Ernst Zermelo - Wikipedia Fra Wikipedia, den frie encyklopædi. Ernst Zermelo formulerede i 1908 et aksiomsystemfor mængdelæren som er hovedparten af ZermeloFraenkels aksiomer. http://da.wikipedia.org/wiki/Ernst_Zermelo

Ernst Zermelo Fra Wikipedia, den frie encyklop¦di Ernst Zermelo formulerede i 1908 et aksiomsystem for m¦ngdel¦ren som er hovedparten af Zermelo-Fraenkels aksiomer Denne artikel er kun p¥begyndt Du kan hj¦lpe Wikipedia ved at tilf¸je mere Eller give denne artikel en bedre beskrivelse Hentet fra " http://da.wikipedia.org/wiki/Ernst_Zermelo Kategorier Artikelstump Matematikere Views Artikel Diskussion Redig©r Historik Personlige v¦rkt¸jer Opret en konto eller log p¥ Navigation Forside Forside for skribenter Aktuelle begivenheder Seneste ¦ndringer ... Donation S¸g V¦rkt¸jer Hvad henviser hertil Relaterede ¦ndringer L¦g en fil op Specielle sider ... Permanent link Andre sprog Deutsch English Espa±ol Fran§ais ... Polski Denne side blev senest ¦ndret den 8. aug 2005 kl. 17:15. Indholdet er udgivet under GNU Free Documentation License Om Wikipedia Forbehold

22. Ernst_Zermelo Translate this page Zermelo, Ernst {{Personendaten NAME=Zermelo, Ernst Friedrich Ferdinand,ALTERNATIVNAMEN=, KURZBESCHREIBUNG=deutscher Mathematiker, GEBURTSDATUM=27. http://www.kraeuter-und-gewuerze.de/Ernst_Zermelo

Suche: Hauptseite '''Ernst Friedrich Ferdinand Zermelo''' (* 27. Juli in Berlin 21. Mai in Freiburg im Breisgau ) war ein deutscher Mathematiker Zermelo besuchte das ''Luisenst¤dtische Gymnasium'' in Berlin bis zum Abitur Er studierte Mathematik Physik und Philosophie an den Universit¤t en von Berlin, Halle (Saale) und Freiburg Er promovierte und wurde f¼r seine Doktorarbeit von der Universit¤t Berlin ausgezeichnet. Dort studierte er unter Max Planck Hydrodynamik ging Zermelo nach G¶ttingen , damals das Weltzentrum der Mathematik. bekam Zermelo den Lehrstuhl f¼r Mathematik an der Universit¤t Z¼rich , den er wieder aufgab. 1919 bewies er, dass endliche Spiele wie Schach (es gibt gewisse Spielabbruchbedingungen, so dass kein Schachspiel unendlich lange dauern kann) eine eindeutige L¶sung besitzen. Das heiŸt entweder WeiŸ gewinnt oder Schwarz oder das Spiel endet remis. Dieses Ergebnis war eines der ersten in der Spieltheorie Er arbeitete ab ehrenhalber in Freiburg im Breisgau, gab diese Arbeit als Protest gegen Hitler wieder auf. Nach dem

23. Ernst Zermelo - Wikipédia Ernst Zermelo (teljes nevén Ernst Friedrich Ferdinand Zermelo) (Berlin 1871.július 27. Freiburg im Breisgau 1953. május 21.) német matematikus. http://hu.wikipedia.org/wiki/Ernst_Zermelo

A Wikimedia a seg­ts©gedet k©ri gyűjtőkamp¡ny oldalon tal¡lsz. Ernst Zermelo A Wikip©di¡b³l, a szabad lexikonb³l. Ernst Zermelo (teljes nev©n Ernst Friedrich Ferdinand Zermelo Berlin jºlius 27 Freiburg im Breisgau m¡jus 21 .) n©met matematikus. Doktori disszert¡ci³j¡t 1894-ben ­rta, vari¡ci³sz¡m­t¡sb³l. Ezut¡n fizik¡val kezdett foglalkozni, 1894-1897 k¶z¶tt Max Planck asszisztense volt. 1896-ban publik¡lta Poincar© rekurrencia-t©tel©nek bizony­t¡s¡t ©s pol©mi¡ba keveredett Boltzmann -nal, mivel r¡mutatott, hogy a t©tel ellentmond Boltzmann elm©let©nek. 1897-ben G¶tting¡ba k¶lt¶z¶tt, habilit¡ci³s ©rtekez©s©t 1899-ben, hidrodinamik¡b³l nyºjtotta be. Hilbert hat¡s¡ra a matematika megalapoz¡s¡val, halmazelm©elettel kezdett foglalkozni. Felfedezte a k©sőbb Russell-paradoxon n©ven ismertt© v¡lt antin³mi¡t. 1904 augusztus¡ban Kőnig Gyula balsikerű kis©rlet©nek hat¡s¡ra a j³lrendezhetős©ggel kezdett foglalkozni. Szeptember 24-©n igazolta a j³lrendez©si t©telt : minden halmaz j³lrendezhető. Ebben a bizony­t¡sban mondta ki elősz¶r a

24. Zermelo zermelo in 1908 was the first to attempt an axiomatisation of set theory. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Zermelo.html

Ernst Friedrich Ferdinand Zermelo Born: 27 July 1871 in Berlin, Germany Died: 21 May 1953 in Freiburg im Breisgau, Germany Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Ernst Zermelo Gymnasium in Berlin and he graduated from the gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities and indeed that is precisely what Zermelo did. His studies were undertaken at three universities, namely Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius , Lazarus, Fuchs Planck Schmidt Schwarz and Edmund Husserl. This was an impressive collection of inspiring lecturers and Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation Untersuchungen zur Variationsrechnung which followed the Weierstrass approach to the calculus of variations . In this thesis he [1]:- ... extended Weierstrass 's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves.

25. Ernst Friedrich Ferdinand Zermelo Describes educational background and motivation towards working on set theory and the continuum hypothesis. Page lists other major contributions made by this person. http://www.stetson.edu/~efriedma/periodictable/html/Zr.html

Ernst Friedrich Ferdinand Zermelo Ernst Zermelo's father was a college professor, so Zermelo was brought up in a family where academic pursuits were encouraged. He graduated from gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities, and that is what Zermelo did. He studied at Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius, Lazarus, Fuchs, Planck, Schmidt, and Schwarz. Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation on the calculus of variations. In this thesis he extended Weierstrass's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves. After the award of his doctorate, Zermelo remained at the University of Berlin where he was appointed assistant to Planck who held the chair of theoretical physics there. At this stage Zermelo's work was turning more towards areas of applied mathematics and, under Planck's guidance, he began to work for his habilitation thesis studying hydrodynamics.

26. Zermelo Biography from the MacTutor History of Mathematics archive. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Zermelo.html

Ernst Friedrich Ferdinand Zermelo Born: 27 July 1871 in Berlin, Germany Died: 21 May 1953 in Freiburg im Breisgau, Germany Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Ernst Zermelo Gymnasium in Berlin and he graduated from the gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities and indeed that is precisely what Zermelo did. His studies were undertaken at three universities, namely Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius , Lazarus, Fuchs Planck Schmidt Schwarz and Edmund Husserl. This was an impressive collection of inspiring lecturers and Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation Untersuchungen zur Variationsrechnung which followed the Weierstrass approach to the calculus of variations . In this thesis he [1]:- ... extended Weierstrass 's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves.

27. Zermelo Portraits Portraits of ernst zermelo. The URL of this page is, © Copyright information.http//wwwhistory.mcs.st-andrews.ac.uk/history/PictDisplay/zermelo.html. http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Zermelo.html

Ernst Zermelo JOC/EFR August 2005 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Zermelo.html

28. Zermelo, Ernst Friedrich Ferdinand zermelo, ernst Friedrich Ferdinand (18711953) zermelo was born in Berlinand studied at Halle and Freiburg. In 1905 he became professor at Göttingen, http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/Z/Zermelo/1.html

Zermelo, Ernst Friedrich Ferdinand German mathematician who made important contributions to the development of set theory, particularly in developing the axiomatic set theory that now bears his name. In 1904 Zermelo defined the axiom of choice, the use of which had previously been unrecognized in mathematical reasoning. The first formulations of axioms for set theory - an axiom system for German mathematician Georg Cantor' s theory of sets - were made by Zermelo in 1908.

29. Zermelo Biography (18711953). http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Zermelo.html

Ernst Friedrich Ferdinand Zermelo Born: 27 July 1871 in Berlin, Germany Died: 21 May 1953 in Freiburg im Breisgau, Germany Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Ernst Zermelo Gymnasium in Berlin and he graduated from the gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities and indeed that is precisely what Zermelo did. His studies were undertaken at three universities, namely Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius , Lazarus, Fuchs Planck Schmidt Schwarz and Edmund Husserl. This was an impressive collection of inspiring lecturers and Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation Untersuchungen zur Variationsrechnung which followed the Weierstrass approach to the calculus of variations . In this thesis he [1]:- ... extended Weierstrass 's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves.

30. Zermelo, Ernst (1871-1956) -- From Eric Weisstein's World Of Scientific Biograph zermelo, ernst (18711956). German mathematician who formulated zermelo s Axiomof Choice (the axiom of choice. , which states that given any set of http://scienceworld.wolfram.com/biography/Zermelo.html

Branch of Science Mathematicians Nationality German Zermelo, Ernst (1871-1956) German mathematician who formulated Zermelo's Axiom of Choice (the "axiom of choice.", which states that given any set of mutually exclusive nonempty sets, the exists at least one set that contains exactly one element in common with each of the nonempty sets. Additional biographies: MacTutor (St. Andrews)

31. Zermelo - Ernst Friedrich Ferdinand From FOLDOC zermelo ernst Friedrich Ferdinand. biography, history of philosophy Germanmathematician (1871-1953) who developed the first systematic axiomatization http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Zermelo - Ernst Friedrich Ferdina

32. Zermelo Fraenkel Set Theory From FOLDOC Nearby terms Zeno of Citium « Zeno of Elea « zermelo ernst Friedrich Ferdinand «zermelo Fraenkel set theory » zermelo set theory » zombie. http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Zermelo Fraenkel set theory

33. Allmath.com - Math Site For Kids! Home Of Flashcards, Math zermelo, ernst Friedrich Ferdinand. tsairmeloh. (18711953). Mathematician,born in Berlin. He studied at Berlin, Halle, and Freiburg universities, http://www.allmath.com/biosearch.php?QMeth=ID&ID=35509

34. Zermelo-Fraenkel-Mengenlehre - Wikipedia Translate this page Die zermelo-Fraenkel-Mengenlehre ist eine verbreitete Axiomatisierung der Mengenlehre . und ist nach ernst zermelo und Abraham Fraenkel benannt. http://de.wikipedia.org/wiki/Zermelo-Fraenkel-Mengenlehre

Es ist geschafft - unser Spendenziel von 200.000$ ist erreicht . Herzlichen Dank an alle Spender. Zermelo-Fraenkel-Mengenlehre aus Wikipedia, der freien Enzyklop¤die Die Zermelo-Fraenkel-Mengenlehre ist eine verbreitete Axiomatisierung der Mengenlehre . Sie baut auf den Axiomen einer Pr¤dikatenlogik erster Stufe und zus¤tzlichen mengentheoretischen Axiomen auf, und ist nach Ernst Zermelo und Abraham Fraenkel benannt. Sie ist heute Grundlage fast aller Zweige der Mathematik. Dieses Axiomensystem ist das Ergebnis einer Arbeit von Thoralf Skolem , die auf Arbeiten von Abraham Fraenkel aus dem gleichen Jahr basiert, welche wiederum auf dem Axiomensystem aufbaut, das Ernst Zermelo aufgestellt hatte ( Zermelo-Mengenlehre Ohne Auswahlaxiom wird diese Mengenlehre meist mit ZF abgek¼rzt, mit Auswahlaxiom k¼rzt man es mit ZFC ab (engl. Zermelo-Fraenkel + Choice Die Axiome der Zermelo-Fraenkel-Mengenlehre sind Aussagen der Pr¤dikatenlogik . Es gibt unendlich viele Axiome, denn es werden Axiomenschemata verwendet, das heiŸt ein Ausdruck, der zu jedem Pr¤dikat mit bestimmten Eigenschaften ein Axiom angibt. Extensionalit¤tsaxiom Zwei Mengen sind genau dann gleich, wenn sie dieselben Elemente enthalten

35. Biographies Index Zeng Guofan To Zermelo, Ernst Friedrich Ferdinand Biographies of people living and dead of all nations. http://www.allbiographies.com/biographies-ZengGuofan-ErnstFriedrichFerdinandZerm

search biography names match all words match any words use wildcards browse biographies get a new biography browse by name browse by year online dictionary allmath.com math for students travel deals hotel rooms browse by name Zeng Guofan to Zermelo, Ernst Friedrich Ferdinand Zeng Guofan Zenger, John Peter Zeno of Citium Zeno of Elea ... Z browse by year 2700 - 691 BC 690 - 531 BC 530 - 481 BC 480 - 391 BC ... Allsites LLC

36. Biography Of Zermelo, Ernst Friedrich Ferdinand Biographies of people living and dead of all nations. http://www.allbiographies.com/biography-ErnstFriedrichFerdinandZermelo-35509.htm

search biography names match all words match any words use wildcards browse biographies get a new biography browse by name browse by year online dictionary allmath.com math for students travel deals hotel rooms biography classifications major works cross references biography name: Zermelo, Ernst Friedrich Ferdinand pronunciation: tsair meloh] sex: male lived: biography: browse by name A B C D ... Z browse by year 2700 - 691 BC 690 - 531 BC 530 - 481 BC 480 - 391 BC ... Allsites LLC

37. The Mathematics Genealogy Project - Update Data For Ernst Zermelo If you have Mathematics Subject Classifications to submit for an entire group ofindividuals (for instance all those that worked under a particular advisor) http://www.genealogy.math.ndsu.nodak.edu/html/php/submit-update.php?id=46828

38. PlanetMath: Zermelo-Fraenkel Axioms ernst zermelo and Abraham Fraenkel proposed the following axioms as a foundationfor what is now called zermeloFraenkel set theory, or ZF. http://planetmath.org/encyclopedia/ZermeloFraenkelAxioms.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Zermelo-Fraenkel axioms (Axiom) Ernst Zermelo and Abraham Fraenkel proposed the following axioms as a foundation for what is now called Zermelo-Fraenkel set theory, or ZF. If this set of axioms are accepted along with the Axiom of Choice , it is often denoted ZFC. Equality of sets : If and are sets, and iff , then Pair set : If and are sets, then there is a set containing only and Union over a set : If is a set, then there exists a set that contains every element of each Axiom of power set : If is a set, then there exists a set with the property that iff any element is also in Replacement axiom : Let be some formula . If, for all , there is exactly one such that is true, then for any set

39. Zermelo Set Theory -- Facts, Info, And Encyclopedia Article zermelo, ernst. Untersuchungen über die Grundlagen der Mengenlehre I .Mathematische Annalen, 65 261281, 1908. English translation, Investigations in http://www.absoluteastronomy.com/encyclopedia/z/ze/zermelo_set_theory.htm

Zermelo set theory [Categories: Set theory] Zermelo set theory , as set out in an important paper in 1908 by (Click link for more info and facts about Ernst Zermelo) Ernst Zermelo , is the ancestor of modern (The branch of pure mathematics that deals with the nature and relations of sets) set theory . It bears certain differences to its descendants, which are not always understood, and are frequently misquoted. This article sets out the original axioms, with the original text (translated into English) and original numbering. The axioms of Zermelo set theory AXIOM I. (Click link for more info and facts about Axiom of extensionality) Axiom of extensionality Axiom der Bestimmtheit ) "If every element of a set M is also an element of N and vice versa ... then M N . Briefly, every set is determined by its elements". AXIOM II. Axiom of elementary sets ( Axiom der Elementarmengen a is any object of the domain, there exists a set containing a and only a as element. If a and b are any two objects of the domain, there always exists a set containing as elements a and b but no object x distinct from them both." See Axiom of pairs.

40. Zermelo-Fraenkel Set Theory -- Facts, Info, And Encyclopedia Article The zermeloFraenkel axioms of set theory (ZF) are the standard ((logic) a by (Click link for more info and facts about ernst zermelo) ernst zermelo in http://www.absoluteastronomy.com/encyclopedia/z/ze/zermelo-fraenkel_set_theory1.

Zermelo-Fraenkel set theory [Categories: Set theory] The Zermelo-Fraenkel axioms of set theory (ZF) are the standard ((logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident) axiom s of (Click link for more info and facts about axiomatic set theory) axiomatic set theory on which, together with the (Click link for more info and facts about axiom of choice) axiom of choice , all of ordinary (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics is based in modern formulations. When the axiom of choice is included, the resulting system is ZFC The axioms are the result of work by (Click link for more info and facts about Thoralf Skolem) Thoralf Skolem in 1922, based on earlier work by (Click link for more info and facts about Abraham Fraenkel) Abraham Fraenkel in the same year, which was based on the axiom system put forth by (Click link for more info and facts about Ernst Zermelo) Ernst Zermelo in 1908 ( (Click link for more info and facts about Zermelo set theory) Zermelo set theory The axiom system is written in (Click link for more info and facts about first-order logic) first-order logic ; it has an (Click link for more info and facts about infinite) infinite number of axioms because an (Click link for more info and facts about axiom schema) axiom schema is used. An alternative

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