61. PHILTAR - Compendium Of Philosophers/Z Zeno of Sidon (c150c70) An introduction to his life and work. zermelo,ernst Friedrich Ferdinand (1871-1953) An introduction to http://philtar.ucsm.ac.uk/compendium_of_philosophers/z/

Compendium of Philosophers Z Links to materials by and/or about over a thousand philosophers from thousands of years from all over the world from A to Z This compendium contains entries large and small, single or multiple, on hundreds of philosophers. Links vary in size from a few lines of biography to the whole of the Summa Theologica. Sometimes you are directed to a site which has further links. In that case there is no guarantee that all the further links will work, but enough work to make a visit worthwhile. This compendium does not provide links to philosophers’ own home pages. A list of them can be found here A B C ... Z Zallinger zum Thurn, Jacob Anton (1735-1813) A brief introduction from TCE Zarathustra [Zoroaster] (7th century BC) This page provides an outline of his life, with links to more detailed materials This site provides links to a number of essays introducing his teachings Zeno of Citium (342-270 BC) Zeno of Citium A useful essay on the founder of Stoicism. Zeno of Elea (5th century BC) An introduction to his life and thought from the on-line edition of Burnet’s Early Greek Philosophy An introduction to his life and work from the IEP More on Zeno’s race course The paradox of the race course. ... Zeno’s paradox of the arrow Zeno of Sidon (c150-c70) An introduction to his life and work Zermelo, Ernst Friedrich Ferdinand (1871-1953)

62. Science Timeline Translate this page Zeeman, Pieter, 1896. Zeno of Elea, 470 bce. zermelo, ernst, 1897, 1908. Zernicke,Frits, 1932. zero, 2700 bce, 250 bce, 458, first half seventh century, 1783. http://www.sciencetimeline.net/siteindex_w-z.htm

use checkboxes to select items you wish to download Select Index Letter: a b c d ... w-x-y-z Waddington, Conrad Hal, early 1930s, 1942, 1949, 1956 Wagner, Moritz, 1873 Wagoner, Robert V., 1966 Wahl, Arthur, 1941 Waksman, Selman, 1944 Walcott, Charles D., 1909 Waldeyer, Heinrich Wilhelm Gottfried, 1888, 1891 Walker, Alan, 1984 Walker, Merle F., 1964 Wallace, Alfred Russel, 335 bce, 1810, 1829, 1855, 1858, 1867, 1876, 1881, 1889 walled communities, 5500 bce, Wallis, John, 1656 Walton, Ernest T. S., 1932 Wang, An, 1953 Wankel, Felix, 1936 Warburg, Otto Heinrich, 1923, 1926, 1934, 1937 Warner, Noel L., 1959 watches, end of the fifteenth century, Waterston, Robert, 1998 Watson, James Dewey, 1953 Watson, John Broadus, 1912 Watson-Watt, Robert Alexander, 1926, 1935

63. Liste Historischer Mathematischer Dissertationen Von 1810 Bis 1933 Translate this page Promotion (Bemerkungen). 119, zermelo, ernst (1871-1953), H, Untersuchungenzur Variationsrechnung. (Schwarz, Fuchs), 6.10.1894. 130, Ziegel http://dochost.rz.hu-berlin.de/listen/histdisslist.php3?sec=Z

64. Directory :: Look.com zermelo ernst Friedrich Ferdinand zermelo (1871-1953) zermelo in 1908 was thefirst to attempt an axiomatisation of set theory al-Khwarizmi - Abu Ja'far al http://www.look.com/searchroute/directorysearch.asp?p=142472

65. Practical Foundations Of Mathematics Paul Taylor. 2.2 Sets (zermelo Type Theory). These methods of constructionwere first set out as a basis of set theory by ernst zermelo in 1908. http://www.dcs.qmul.ac.uk/~pt/Practical_Foundations/html/s22.html

Practical Foundations of Mathematics Paul Taylor Sets (Zermelo Type Theory) These methods of construction were first set out as a basis of set theory by Ernst Zermelo in 1908. 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. We shall make a distinction between elements and sets, though in such a formalism it is usual to refer to terms and types as we did in Section . We shall also modify what Zermelo did very slightly, taking the cartesian product XxY X Y cf Examples Our system conforms very closely to the way mathematical constructions have actually been formulated in the twentieth century. The claim that set theory provides the foundations of mathematics is only justified via an encoding of this system, and not directly. It is, or at least it should be, surprising that it took 60 years to arrive at an axiomatisation which is, after all, pretty much as Zermelo did it in the first place. V - 1pt. For a detailed account of the modern system and its history, see [

66. Thomas Steiner's Homepage Translate this page Mai, 19, Mai, 20, Mai, 21, Dürer, Albrecht, 1471, Mai, 21, zermelo, ernst FriedrichFerdinand, 1953. Mai, 22, Cauchy, Augustin-Louis, 1857. Mai, 23, Skolem, ThoralfAlbert, 1887, http://fsmat.htu.tuwien.ac.at/~thire/mathkal.php

Thomas Steiners Homepage Thomas Steiner's Homepage :9550 views since 10/06/02 Last modified Tue, dem 01.Oct 02 um 18:06 by Thomas Steiner optimized for Microsoft Internet Explorer 5.0 at 1024x768 resolution website hosted by Fachschaft Technische Mathemaik, TU Wien Familie Freunde Irene Thomas ... Zugriffe Mathematik - Kalender Monat Tag Mathematiker Geburtstag Sterbetag Bernulli, Johann I Newton, Isaac Cramer, Gabriel Jordan, Camille Marie Ennemont Cantor, Georg Borel, Emil Galilei, Galileo Courant, Richard Legendre, Adrien-Marie Fermat, Pierre de Robbins, Herbert Ellis Halley, Edmond Dodgson, Charles Lutwidge (Lewis Caroll) Hermite, Charles Tarski, Alfred Menger, Karl Galton, Sir Francis Watt Kantorowitsch Jordan, Camille Marie Ennemont Hilbert, David Lagrange, Joseph Louis Schwarz, Hermann Amandus Briggs, Henry Dodgson, Charles Lutwidge (Lewis Caroll) Courant, Richard Ceulen, Ludolph von Pohlke, Karl-Wilhelm Kummer, Ernst Eduard Februar Heisenberg, Werner Februar Ferrari Februar Kuratowski Februar Waerden, Bartel Leendert van der

67. Biografisk Register Translate this page 1238-98) Zagier, Don B. Zenon (ca. 490-430 f.Kr.) zermelo, ernst (1871-1953)Zeuthen, Hieronymus Georg (1839-1920) Zorn, Max (1606-93) http://www.geocities.com/CapeCanaveral/Hangar/3736/biografi.htm

Biografisk register Matematikerne er ordnet alfabetisk på bakgrunn av etternavn. Linker angir at personen har en egen artikkel her. Fødsels- og dødsår oppgis der dette har vært tilgjengelig. Abel, Niels Henrik Abu Kamil (ca. 850-930) Ackermann, Wilhelm (1896-1962) Adelard fra Bath (1075-1160) Agnesi, Maria G. (1718-99) al-Karaji (rundt 1000) al-Khwarizmi, Abu Abd-Allah Ibn Musa (ca. 790-850) Anaximander (610-547 f.Kr.) Apollonis fra Perga (ca. 262-190 f.Kr.) Appel, Kenneth Archytas fra Taras (ca. 428-350 f.Kr.) Argand, Jean Robert (1768-1822) Aristoteles (384-322 f.Kr.) Arkimedes (287-212 f.Kr.) Arnauld, Antoine (1612-94) Aryabhata (476-550) Aschbacher, Michael Babbage, Charles (1792-1871) Bachmann, Paul Gustav (1837-1920) Bacon, Francis (1561-1626) Baker, Alan (1939-) Ball, Walter W. R. (1892-1945) Banach, Stéfan (1892-1945) Banneker, Benjamin Berkeley, George (1658-1753) Bernoulli, Jacques (1654-1705) Bernoulli, Jean (1667-1748) Bernstein, Felix (1878-1956) Bertrand, Joseph Louis Francois (1822-1900) Bharati Krsna Tirthaji, Sri (1884-1960)

68. À¯¸íÇÑ ¼öÇÐÀÚ ? Chapman, Sydney (1888.1.29~1970.6.16) Church, Alonzo (1903) zermelo, ernst (1871.7.27~1953.5.21) Chebyshyov http://user.chollian.net/~jjang88/mathman/mathman.htm

69. életrajzok: Z zermelo, ernst Friedrich Ferdinand (1871. július 27.—1953. május 21.) németmatematikus. A halmazelmélet elso axiómarendszerének kidolgozója. http://www.iif.hu/~visontay/ponticulus/eletrajzok/z.html

rovatok j¡t©k arch­vum jegyzetek mutat³k kitekintő v©lem©nyek inform¡ci³k ©letrajzok magyar¡zatok forr¡sok Z‰NON (Kr. e. 450 k¶r¼l): eleai filoz³fus. Ap³ri¡i (Akhilleusz ©s a teknősb©ka; a rep¼lő ny­l stb.) nagy hat¡ssal voltak a matematikai gondolkod¡s fejlőd©s©re. ZERMELO, Ernst Friedrich Ferdinand (1871. jºlius 27.—1953. m¡jus 21.): n©met matematikus. A halmazelm©let első axi³marendszer©nek kidolgoz³ja. Berlinben sz¼letett. A g¶ttingeni ©s a z¼richi egyetem professzora volt. Axi³marendszer©t FRAENKEL t¶k©letes­tette. Nev©hez fűződik a sok vit¡t kavar³ kiv¡laszt¡si axi³ma is. A matematika sz¡mos ter¼let©n ©rt el eredm©nyeket.

70. Zermelo'nun Biyografisi Bir Alman matematikçisi olan ernst zermelo, 1891 yilinda Berlin'de dogdu. Özellikle,kümeler kuraminin gelistirilmesinde çok katkilarda bulundu. http://matematikcecom.kolayweb.com/biyografi/zermelo.htm

Zermelo (1891 - 1953) Bir Alman matematikçisi olan Ernst Zermelo, 1891 yýlýnda Berlin'de doðdu. Özellikle, kümeler kuramýnýn geliþtirilmesinde çok katkýlarda bulundu. 1904 yýlýnda Zermelo aksiyomunu veya seçme aksiyomunu ortaya attý. Bu aksiyoma göre, verilen bir kümenin her alt kümesinde, tek ve belirli bir þekilde üstünlüðü bulunan bir öðe seçmek olanaðý vardýr. Her küme iyi sýralanabilir. Ancak bazý matematikçiler bunu kabul etmiþ, bazýlarý da karþý çýkmýþtýr. Bu konudaki tartýþmalar, matematiðin modern evriminde önemli yer tutar. Ýyi sýralama, yirminci yüzyýlýn baþýnda oldukça ateþli tartýþmalara konu olmuþ ve bugün herkes tarafýndan kabul edilmiþtir. Zermelo, 1953 yýlýnda Freinburrg'da ölmüþtür. (Biyografiler genel sayfa) Ana sayfa Matematik Tarihi Ýncelenen Konular ... Ziyaretci Defteri

71. Zermelo Résumé à la théorie des Echecs (1913) du mathématicien allemand ernst zermelo. http://mamasphi.free.fr/Zermelo_resume.htm

72. The Mathematics Genealogy Project - Index Of ZE Translate this page Zerling, David, University of Pennsylvania, 1973. zermelo, ernst,Universität Berlin, 1894. Zerna, Wolfgang, Universität Hannover,1947. http://genealogy.math.ndsu.nodak.edu/html/letter.phtml?letter=ZE

73. Salvador Vera: Directorio - Algebra Translate this page zermelo - ernst Friedrich Ferdinand zermelo (1871-1953) zermelo in 1908was the first to attempt an axiomatisation of set theory. Journals (2). http://www.satd.uma.es/matap/svera/links/matnet01.html

Álgebra Restaurar marco Añade tu web Anterior Home ... Siguiente en todo el directorio Dmoz sólo en Matemáticas/Álgebra_Lineal Top Directorio Español: Matemáticas Álgebra Lineal Descripción Genéricas: Acontecimientos Aplicaciones Asociaciones Bibliotecas ... Software Específicas: Álgebra Análisis An. Numérico Cálculo ... Topología Esta categoría en otros idiomas: Inglés Álgebra abstracta - Conceptos generales de álgebra abstracta y lógica. Definiciones y teoremas. Álgebra Matricial . Programa de Álgebra Matricial perteneciente al curriculum de 2º de Bachillerato. Esta Web genera matrices para que el alumno opere con ellas on line y comprueba las respuesta del alumno. Todos los contenidos de la Web están orientados a conseguir soltura en la manipulación de matrices y determinantes usando el método de Gauss o de triangulación. Puedes descargar la Web en formato zip (302 Kb). Matrices y Determinantes - Breve tutorial sobre cálculo matricial con numerosos ejemplos y un apartado para el cálculo interactivo. Teoría de conjuntos . Teoría de conjuntos, tratada de manera elemental.

74. Epsilon And Omega rational numbers ). ( II ) The Basic Axioms of Set Theory ZFC,the AxiomSystem of ernst zermelo and Abraham Fraenkel. A naive http://www.mathematik.uni-muenchen.de/~deiser/set.html

Set Theory The mathematical study of infinity Epsilon and omega are two basic symbols in set theory, representing the membership relation and infinity. (Click on the stop button of your browser to stop the animations.) Four basic aspects of set theory Cantor's Diagonal Argument : Uncountable sets The Basic Axioms of Set Theory (ZFC) Interpretability of Mathematics inside Set Theory The Independence of the Continuum Hypothesis and extensions of ZFC ( I ) Cantor's Diagonal Argument ("Diagonalverfahren") : Uncountable Sets Now we can apply this diagonalization procedure (switching diagonal entries from to 1 and vice versa) to an infinite table which has rows and columns for every natural number. Given any sequence B(0), B(1), B(2), ..., B(n), ... of subsets of the natural numbers N we can build such a table: Fill row number n with the infinite sequence representing B(n). Now build D as before by switching the infinite diagonal of the infinite table. Again it follows that D is not represented by any row of the table, i.e., D is different from every B(n). (It is easy to see that n is an element of D if and only if n is not an element of B(n): This gives a neat definition of D, but a table as above is better for visualizing D.) We have just proven one of the most important theorems of set theory: A sequence B(0), B(1), ..., B(n), ... of subsets of

75. Russell's Paradox [Internet Encyclopedia Of Philosophy] Examines selfreferential linguistics used to describe properties and sets.Category Society Philosophy Internet Encyclopedia of Philosophy...... (First published in 1902.); zermelo, ernst. Investigations in the Foundationsof Set Theory I. In From Frege to Gödel, ed. by Jean van Heijenoort. http://www.utm.edu/research/iep/p/par-russ.htm

Russell's Paradox Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Some classes (or sets) seem to be members of themselves, while some do not. The class of all classes is itself a class, and so it seems to be in itself. The null or empty class, however, must not be a member of itself. However, suppose that we can form a class of all classes (or sets) that, like the null class, are not included in themselves. The paradox arises from asking the question of whether this class is in itself. It is if and only if it is not. The other form is a contradiction involving properties. Some properties seem to apply to themselves, while others do not. The property of being a property is itself a property, while the propery of being a cat is not itself a cat. Consider the property that something has just in case it is a property (like that of being a cat ) that does not apply to itself. Does this property apply to itself? Once again, from either assumption, the opposite follows. The paradox was named after Bertrand Russell, who discovered it in 1901. Table of Contents (Clicking on the links below will take you to that part of this article) History Possible Solutions to the Paradox of Properties Possible Solutions to the Paradox of Classes or Sets Suggested Reading History Russell's discovery came while he was working on his Principles of Mathematics . Although Russell discovered the paradox independently, there is some evidence that other mathematicians and set-theorists, including Ernst Zermelo and David Hilbert, had already been aware of the first version of the contradiction prior to Russell's discovery. Russell, however, was the first to discuss the contradiction at length in his published works, the first to attempt to formulate solutions and the first to appreciate fully its importance. An entire chapter of the

76. Collected Works Hrsg. von ernst zermelo. Nebst 1965. Added Entry zermelo, ernst, 1871ed. CALL NO QA300 C3 1960 AUTHOR Carleman, Torsten, 1892-1949. http://lib.nmsu.edu/subject/math/mbib.html

C OLLECTED W ORKS F M ATHEMATICIANS B IBLIOGRAPHY CALL NO: QA3 A14 1881 AUTHOR: Abel, Niels Henrik, 1802-1829. MAIN TITLE: OEuvres completes de Niels Henrik Abel. EDITION: Nouv. ed., publiee aux frais de l'etat norve-gien par L. Sylow PUBLISHER: Christiania [Sweden] Grondahl, 1881. LOCATION: Branson Material: 2 v. in 1. 28 cm. Contents: t. 1. Memoires publies par Abel.t. 2. Memoires posthumes d'Abel Subject: Mathematics. cm Added Entry: Sylow, Peter Ludvig Mejdel, 1832- Added Entry: Lie, Sophus, 1842-1899. CALL NO: QB3 A2 AUTHOR: Adams, John Couch, 1819-1892. MAIN TITLE: The scientific papers of John Adams Couch, edited by William Grylls Adams, with a memoir by J. W. L. Glaisher. PUBLISHER: Cambridge, University press, 1896-1900. LOCATION: Branson V.1 and V.2 Material: 2 v. front. (port.) fold. map, facsims., diagr. 30 cm. Contents: v. 1. Biographical notice, by J. W. L. Glaisher. [Original papers published by the author during his lifetime, 1844-1890, ed. by William Grylls Adams]v. 2. pt. 1. Extracts from unpublished manuscripts, ed. by Ralph Allen Simpson. pt. 2. Terrestial magnetism, ed. by William Grylls Adams. Subject: Geomagnetism.

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

Math for the people, by the people. Encyclopedia Books Papers Expositions ... Random Login create new user name: pass: forget your password? Main Menu the math Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports information Docs Classification News Legalese ... TODO List Zermelo-Fraenkel axioms (Axiom) Existence of the empty set : There exists a set with the property that there does not exist any such that 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 there exists a set with the property that iff there exists some such that is true. regularity axiom : Let be some formula. If there is some that makes true, then there is a set

78. People Click on the Image for more information about ernst zermelo zermelo is bestknown for his work on the axiom of choice and axiomatic set theory. http://ergo.ucsd.edu/~movellan/courses/245/people/Zermelo.html

Click on the Image for more information about Ernst Zermelo Zermelo is best known for his work on the axiom of choice and axiomatic set theory. After studying the set paradoxes, he made the first attempt to axiomatise set theory in 1908. He gave seven axioms : Axiom of extensionality, Axiom of elementary sets, Axiom of separation, Power set axiom, Union axiom, Axiom of choice and Axiom of infinity. Zermelo usually stated his axioms and theorems in words rather than symbols.

79. The Factasia Glossary - Z Z zermelo Set Theory The first axiomatisation of set theory published by ernst zermeloin 1908 zermelo08 in response to the antinomies found in informal set http://www.rbjones.com/rbjpub/philos/glossary/z.htm

..Z Z Zermelo Set Theory The first axiomatisation of set theory published by Ernst Zermelo in 1908 in response to the antinomies found in informal set theory by Russell and others. Intended to provide a consistent foundation for mathematics, its consistency remains unimpeached, though it has been found necessary to augment the theory with the axiom of replacement (see ZF ) to provide an adequate foundation for modern mathematics. 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. The Z specification language A language developed by Jean Raymond Abrial and others at the University of Oxford, broadly similar in strength and character to Zermelo set theory (though the etymology seems uncertain), but with a much richer syntax oriented to applications in the specification of software. ZF 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. ZFC Zermelo-Fraenkel set theory augmented by the axiom of choice.

80. Zermelo Set Theory From FOLDOC zermelo set theory. mathematics A set theory with the following set of. axioms zermeloFr nkel set theory adds the Replacement axiom. FOLDOC. 200103-16 . http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Zermelo set theory

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