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Topic: Ernst Zermelo

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Zermelo set theory

Well ordering theorem

University of Berlin

University of Freiburg

Mathematics

David Hilbert

International Congress of Mathematicians

William Burnside

Georg Cantor

Hermann Weyl

Carl Gustav Jakob Jacobi

Aleksandr Danilovich Aleksandrov

Felix Hausdorff

Freiburg im Breisgau

Berlin

	Ernst Zermelo - Wikipedia, the free encyclopedia
		Zermelo remained at the University of Berlin where he was appointed assistant to Planck and under his guidance began to study hydrodynamics.
		Zermelo began to work on the problems of set theory and in 1902 published his first work concerning the addition of transfinite cardinals.
		At the end of World War II Zermelo requested that he be reinstated to his honorary position in Freiburg and indeed he was reinstated to the post in 1946.
	en.wikipedia.org /wiki/Ernst_Zermelo (489 words)

	Zermelo set theory - Wikipedia, the free encyclopedia
		Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory.
		Zermelo is of course referring to the "Russell antinomy".
		Zermelo's paper is notable for what may be the first mention of Cantor's theorem explicitly and by name.
	en.wikipedia.org /wiki/Zermelo_set_theory (986 words)

	Ernst Zermelo - Wikipedia
		Zermelo besuchte das Luisenstädtische Gymnasium in Berlin bis zum Abitur 1889.
		1897 ging Zermelo nach Göttingen, damals das Weltzentrum der Mathematik.
		1910 bekam Zermelo den Lehrstuhl für Mathematik an der Universität Zürich, den er 1916 wieder aufgab.
	de.wikipedia.org /wiki/Ernst_Zermelo (167 words)

	Ernst Zermelo -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		Ernst Friedrich Ferdinand Zermelo (July 27, 1871 – May 21, 1953) was a (A person of German nationality) German (A person skilled in mathematics) mathematician and (A specialist in philosophy) philosopher.
		Zermelo was born in (Capital of Germany located in eastern Germany) Berlin, (A republic in central Europe; split into East German and West Germany after World War II and reunited in 1990) Germany.
		Zermelo remained at the University of Berlin where he was appointed assistant to (German physicist whose explanation of flbody radiation in the context of quantized energy emissions initiated quantum theory (1858-1947)) Planck and under his guidance began to study (Study of fluids in motion) hydrodynamics.
	www.absoluteastronomy.com /encyclopedia/E/Er/Ernst_Zermelo.htm (603 words)

	Ernst Zermelo - Wikipedia
		Zermelo permaneció en la Universidad of Berlín, donde fue nombrado ayudante de Planck y bajo su guía comenzó a estudiar hidrodinámica.
		Zermelo comenzó a trabajar en los problemas de teoría de conjuntos y en 1902 publicó su primer trabajo sobre la adición de cardinales transfinitos.
		En 1905, Zermelo comenzó a axiomatizar la teoría de conjuntos; en 1908, publicó sus resultados a pesar de haber fallado en probar la consistencia de su sistema axiomático.
	es.wikipedia.org /wiki/Zermelo (498 words)

	Zermelo (Site not responding. Last check: 2007-11-05)
		Zermelo began to work on the problems of set theory, in particular taking up Hilbert's idea to head towards a resolution of the problem of the continuum hypothesis.
		Although Zermelo certainly gained fame for his proof of the well ordering property, set theory at this time was in the rather unusual position that many mathematicians rejected the type of proofs that Zermelo had discovered.
		Zermelo made other fundamental contributions to axiomatic set theory which were partly a consequence of the criticism of his first major contribution to the subject and partly because set theory began to become an important research topic at Göttingen.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Zermelo.html (1366 words)

	Ernst Zermelo (Site not responding. Last check: 2007-11-05)
		Zermelo remained at the University of where he was appointed assistant to Planck and under his guidance began to hydrodynamics.
		Zermelo began to work on the problems set theory and in 1902 published his first work concerning the of transfinite cardinals.
		In 1905 Zermelo began to axiomatize set theory; 1908 he published his results despite his to prove the consistency of his axiomatic See the article on Zermelo set theory for an outline of this paper with the original axioms with the original
	www.freeglossary.com /Zermelo (773 words)

	zermelo (Site not responding. Last check: 2007-11-05)
		Ernst Friedrich Ferdinand Zermelo (July 27, 1871 - May 21, 1953) was a German mathematician.
		In 1897, Zermelo went to Göttingen, at that time the leading centre for mathematical research in the world, where he completed his thesis in 1899.
		In 1904, he succeeded in taking the first step suggested by Hilbert towards the continuum hypothesis when he the well-ordering theorem (every set can be well ordered).
	www.yourencyclopedia.net /Zermelo.html (498 words)

	Kids.net.au - Encyclopedia Ernst Zermelo -
		In 1908, Zermelo succeeded to produce a proof that found a much wider acceptance.
		It should be noted that, in 1922, Fraenkel[?] and Skolem[?] independently improved Zermelo's axiom system.
		Zermelo died on 21 May 1953 in Freiburg im Breisgau, Germany.
	www.kids.net.au /encyclopedia-wiki/ze/Zermelo (471 words)

	Zermelo, Ernst Friedrich Ferdinand (Site not responding. Last check: 2007-11-05)
		Zermelo was born in Berlin and studied at Halle and Freiburg.
		In 1900 Zermelo provided an ingenious proof to the well-ordering theorem, which states that every set can be well ordered (that is, can be arranged in a series in which each subclass - not being null - has a first term).
		In 1904 Zermelo defined the axiom of choice, the use of which had previously been unrecognized in mathematical reasoning.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/Z/Zermelo/1.html (220 words)

	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.
		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.
		Zermelo's reaction to these criticisms was to try to prove the well ordering property with a proof that would find more widespread acceptance, and this he succeeded in doing in 1908.
	www.stetson.edu /~efriedma/periodictable/html/Zr.html (773 words)

	Ernst Friedrich Ferdinand Zermelo Biography / Biography of Ernst Friedrich Ferdinand Zermelo World of Mathematics ...
		Zermelo was born in Berlin, Germany on July 27, 1871.
		Later that year, Zermelo published the results of his efforts to axiomize set theory despite his failure to prove that the seven axioms were consistent.
		Zermelo, who was beginning to suffer from poor health, left the University of Gôttingen in 1910 to take up the chair of mathematics at the University of Zurich in Switzerland.
	www.bookrags.com /biography-ernst-friedrich-ferdinand-zermelo-wom (525 words)

	The Factasia Glossary - Z (Site not responding. Last check: 2007-11-05)
		The first axiomatisation of set theory published by Ernst Zermelo in 1908 [Zermelo08] in response to the antinomies found in informal set theory by Russell and others.
		Zermelo's system includes the axiom of choice, but the letter "Z" is now normally used to refer to his system with the axiom of choice omitted.
		Zermelo-Fraenkel set theory, an axiomatisation of set theory consisting of Zermelo set theory (see above) strengthened with the axiom of replacement, due to Abraham Fraenkel, the effect of which is to ensure that any collection of sets which can be shown to be no greater in size than an existing set is itself a set.
	www.rbjones.com /rbjpub/philos/glossary/z.htm (197 words)

	Ernst Zermelo (Site not responding. Last check: 2007-11-05)
		In 1908 Ernst Zermelo expanded upon Russell's paradox...
		And we know that Ernst Zermelo (1908) was working on it before the completion of Principia...
		Zermelo's axiom of choice: Its origins, development, and influence (Studies in the history of mathematics and physical s...
	enciclopedia.cc /Ernst_Zermelo (253 words)

	Ernst Zermelo (Site not responding. Last check: 2007-11-05)
		Zermelo seguía siendo en la universidad de Berlín en donde lo designaron ayudante a Planck y bajo su dirección comenzó a estudiar la hidrodinámica.
		Zermelo comenzó a trabajar en los problemas de la teoría determinada y en 1902 publicó su primer trabajo referente a la adición de los cardenales del transfinite.
		En 1905, Zermelo comenzó axiomatize teoría determinada; en 1908, él publicó sus resultados a pesar de su falla de probar la consistencia de su sistema axiomático.
	www.yotor.net /wiki/es/er/Ernst%20Zermelo.htm (536 words)

	Fundamentals (Site not responding. Last check: 2007-11-05)
		Zermelo considered Chess to be a potentially infinite game, but took it that if such a game occurred, it would be a draw.
		Zermelo considers the class of two-person games without chance, where players have strictly opposing interests and where only a finite number of positions are possible.
		Zermelo responded with a correct proof of his statement, using methods similar to those employed by König.
	www-groups.dcs.st-and.ac.uk /~history/Projects/MacQuarrie/Chapters/Ch4.html (1986 words)

	Citations: Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels - Zermelo (ResearchIndex)
		Zermelo, Uber eine Anwendung der Mengenlehre auf die Theorie des Schachpiels, in Proc.
		Zermelo, Uber eine anwendung der Mengenlehre auf die Theorie des Schachspiels, in: E.W. Hobson and A.E.H. Love (editors), Proceedings of the Fifth International Congress of Mathematicians, Vol.
		Zermelo, E. Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels", Proceedings of the Fifth International Congress of Mathematicians, Vol II, pp.501-504.
	citeseer.ist.psu.edu /context/34082/0 (1438 words)

	Citations: Untersuchungen uber die Grundlagen der Mengenlehre - Zermelo (ResearchIndex)
		The attitude adopted in his axiomatic development of set theory is that it is not necessary to know what sets are and the things that are its elements, nor what the membership relation means [49, see page 288, paragraph 1] Zermelo instead postulated a domain of abstract objects and....
		....equivalent, but Zermelo argued that AC is evident in a way that WO is not.
		Zermelo "Untersuchungen uber die Grundlagen der Mengenlehre I ", Mathemathische Annalen 65 (1908) pp.
	citeseer.ist.psu.edu /context/429709/0 (991 words)

	What is Ernst Zermelo? : Abaara fun facts and uncommon knowledge (Site not responding. Last check: 2007-11-05)
		Zermelo remained at the University of Berlin where he was appointed assistant to Planck and under his guidance began to study
		Göttingen, at that time the leading centre for mathematical research in the world, where he completed his thesis in 1899.
		World War II Zermelo requested that he be reinstated to his honorary position in Freiburg and indeed he was reinstated to the post in 1946.
	www.abaara.com /pac/Ernst_Zermelo (421 words)

	Directory - Science: Math: Logic and Foundations: History: People: Zermelo, Ernst
		Ernst Zermelo (1871-1953) made significant early contributions to set theory.
		Ernst Zermelo · cached · Biography from the MacTutor History of Mathematics archive.
		Ernst Friedrich Ferdinand Zermelo · cached · Describes educational background and motivation towards working on set theory and the continuum hypothesis.
	www.incywincy.com /default?p=899272 (75 words)

	Practical Foundations of Mathematics
		The subsequent work sought to formalise them in terms of a notion of membership in which any entity in the universe may serve either as an element or as a set, and where it is legitimate to ask of any two entities whether one bears this relation to the other.
		Why Zermelo made the choice he did between ordered and unordered pairs is perhaps worthy of historical study, though it seems unlikely that it actually occurred to him that he was making any significant decision at all.
		After Zermelo, more axioms were added to set theory in an endeavour to formulate the strongest system that would remain consistent, in which everything anyone could possibly want would be provable, and the model would be unique.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/s22.html (3278 words)

	Zermelo (Site not responding. Last check: 2007-11-05)
		Zermelo is the premiere Windows application for running table tennis tournaments.
		If you use Zermelo to run a tournament that you do not submit to Ratings Central, then the cost to use Zermelo is $20 per tournament.
		Enclosed is $20 for the use of Zermelo for the Univ. of California, Berkeley, Associated Student Union Center tournament.
	www.midy.com /~djmarcus/Zermelo.html (723 words)

	Ed Mares’s Web Page (Site not responding. Last check: 2007-11-05)
		Zermelo was one of the founders of modern set theory, having provided it with an early axiomatisation.
		Zermelo was also responsible for the first explicit formulation of the axiom of choice and for the discovery of large cardinals.
		Zermelo even discovered Russell’s paradox four years before Russell (at least according to Hilbert).
	www.vuw.ac.nz /phil/ed.html (1016 words)

	Ernst Zermelo
		Er graduierte 1894 und wurde für seine Doktorarbeit von Universität Berlin ausgezeichnet.
		1910 bekam Zermelo den Lehrstuhl für Mathematik der Universität Zürich den er 1916 wieder aufgab.
		Er arbeitete ab 1926 ehrenhalber in Freiburg im Breisgau gab Arbeit als Protest gegen Hitler wieder auf.
	www.uni-protokolle.de /Lexikon/Ernst_Zermelo.html (128 words)

	References for Zermelo (Site not responding. Last check: 2007-11-05)
		G Heinzmann (ed.), Poincare, Russell, Zermelo et Peano : textes de la discussion (1906-1912) sur les fondements des mathématiques : des antinomies a la predicativite (Paris, 1986).
		G H Moore, Zermelo's axiom of choice : its origins, development, and influence (New York, 1982).
		G H Moore, Ernst Zermelo, A E Harward, and the axiomatization of set theory, Historia Mathematica 3 (2) (1976), 206-209.
	www-history.mcs.st-andrews.ac.uk /history/References/Zermelo.html (82 words)

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