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Topic: Ernest Zermelo

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	WhoWasThere reply
		Ernest Vessiot was 85 this year and would die in a further 2 years.
		Ernest William Barnes was 76 this year and would die in a further 3 years.
		Ernest Esclangon was 74 this year and would die in a further 4 years.
	www-history.mcs.st-and.ac.uk /history/cgi-bin/mathyear.cgi?YEAR=1950 (7914 words)

	1908 in science (Site not responding. Last check: 2007-09-03)
		A 40,000-year-old Neanderthal boy skeleton is found at Le Moustier in southwest France.
		Hans Geiger and Ernest Rutherford invent the Geiger counter
		Ernest Rutherford is awarded the Nobel Prize for Chemistry
	bopedia.com /en/wikipedia/1/19/1908_in_science.html (155 words)

	History of Kinetic Theory
		1896, Ludwig Boltzmann: Boltzmann refutes Poincare and Zermelo.
		1896, Ernest Zermelo: Zermelo replies to Boltzmann's refutation, and reasserts that kinetic theory contradicts Poincare's recurrence theorem.
		Basically Zermelo correctly asserts that Boltzmann's argument is not on firm mathematical while his argument is, but goes on to incorrectly assert that it follows that Boltzmann is wrong.
	www.math.umd.edu /~lvrmr/History (2064 words)

	[No title]
		This system is one that was devised largely by Ernest Zermelo, and so it is often called Zermelo-Fraenkel set theory (ZF) or sometimes just set theory.
		The core of Zermelo's solution to Russell's paradox is that set theory does not have an unlimited comprehension principle for sets.
		Instead Zermelo's set theory introduced a modified form of the comprehension principle, called the subset axioms, which allows us to construct the required sets, to show that the required sets exist, without deriving a contradiction.
	www.arts.yorku.ca /phil/pelham/phil3100/lec/RussellandPeano.doc (1320 words)

	Bibliography of Philosophical Materials Pertaining to Mathematics and Proof (Site not responding. Last check: 2007-09-03)
		Hilbert's search for new rules of inference in his proof theory, Gödel's search for new axioms and Zermelo's infinitary logic are presented as attempts to overcome this gap.
		The use of simile or analogy is frequently adopted by mathematicians in their attempt to explain features of mathematical knowledge to the general public.
		Proposing social constructivism as a novel philosophy of mathematics, this book is inspired by current work on sociology of knowledge and social studies of science.
	fcis.oise.utoronto.ca /~ghanna/philosophyabstracts.html (16270 words)

	BLACK-BODY PROBLEMATIC: GENESIS AND STRUCTURE
		Another objection to the H-Theorem came in 1896 from Ernest Zermelo, Planck’s assistant in Berlin, who developed what has since been known as the ‘recurrence paradox’.
		Applying a mathematical theorem published by Poincare five years ago, Zermelo argued that any mechanical system confined in a finite region of space would after a sufficiently long time ultimately return to its initial configuration.
		However, Planck disagreed with Zermelo’s contention that the entropy law as a natural law is really incompatible with every mechanical interpretation of nature.
	theoryandscience.icaap.org /content/vol003.001/roy.html (5927 words)

	Robin Shakal
		The response to the paradox that is generally accepted in today’s world was developed by Ernest Zermelo and modified by Abraham Fraenkel.
		Zermelo’s approach was like Cantor’s, in that he used an axiomatic approach (the formal term is axiomatizaion of set theory).
		Fraenkel took Zermelo’s theory and fine-tuned to the approach we generally use today.
	math.ups.edu /~bryans/Current/Journal_Spring_1999/RShakal_300_s99.html (987 words)

	PoME no 3
		The breadth and depth of disagreement on the most fundamental issues between individuals who on the face of it might be expected to see eye to eye on the bases, if not more, of their common subject of interest is a continual source of fascination to me.
		Paul Ernest's remarks, which I very much enjoyed reading, are a case in point.
		Therefore I interpret a social philosophy of mathematics as Paul Ernest describes it, as inevitably flawed by its deliberate avoidance of vast amounts of data about 'the activity and products of persons', and its reliance on very selective use of data.
	www.people.ex.ac.uk /PErnest/pome/pome3.htm (6154 words)

	Bloomsbury.com - Research centre
		A number is a set; a group is a set; and anything that mathematics can effectively talk about should be a set or a collection of sets.
		Today, the concept of a set has been given a more rigorous definition, mainly by the axiomatization of set theory by Ernest, Zermelo (1871-1953) and Adolf Abraham, Fraenkel (1891-1965).
		Sets, in this view, are any classes which can be proved to be sets using the axioms.
	www.bloomsbury.com /ARC/detail.asp?EntryID=102874&bid=2 (336 words)

	Save $2.59! Save Â£0.68! Axiomatic Set Theory
		If you do not object to the preceding sentence, then read on.
		Axiomatic Set Theory (AST) lays down the axioms of the now-canonical set theory due to Zermelo, Fraenkel (and Skolem), called ZFC.
		The axiom schema that is used explicitly in the book is the "axiom schema of separation" due to Ernst Zermelo, which he formulated in order to make precise the notion of a statement as being "definite".
	www.hackcraft.net /bookref/?urn:isbn:0486616304 (1718 words)

	Practical Foundations of Mathematics
		Edited by Ernst Zermelo; reprinted by Olms, Hildeshaim, 1962.
		Poincaré, Russell, Zermelo et Peano: Textes de la Discussion (1906-1912) sur les Fondements des Mathématiques: des Antinomies à la Prédicativité.
		Zermelo's Axiom of Choice: its Origins, Development, and Influence.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/bib.html (3006 words)

	Main Game Page
		Ernest Zermelo proved his theorem at the turn of the century, but it wasn't until after WW2 that efforts began in earnest (but see the paper by Schwalbe and Walker listed
		Gale and Stewart's generalization of Zermelo's theorem, which we discuss a bit in succeeding pages, beginning here.
		The other current was representation of quantifiers by games, an approach to the analysis of natural languages pioneered and popularized by
	www.math.usf.edu /~mccolm/RGintro.html (1080 words)

	ernest fraenkel - ResearchIndex document query (Site not responding. Last check: 2007-09-03)
		up for either Zermelo's Axiom of Separation or Fraenkel's Axiom Schema of Replacement, which implies
		Zermelo's Axiom of Separation was replaced by Fraenkel's Axiom Schema of Replacement, which implies the
		About 75 years ago, Zermelo and Fraenkel gave set theory its current axiomatic
	citeseer.ist.psu.edu /cis?q=Ernest+Fraenkel (602 words)

	Some observations about Hilbert
		In a lecture in 1929, Hilbert explicitly added the completeness of arithmetic as a challenge to future mathematicians.
		One of the junior professor at Gottingen, Ernest Zermelo, pointed out to Hilbert in 1904, independently and in parallel with Russell, a paradox of set theory: "The set of all sets that are not members of themselves." This raised grave doubts about set theory as it existed then.
		Hilbert was adamently opposed to the position of an earlier mathematician named Kronecker who had insisted that only constructive mathematics was appropriate.
	www.oswego.edu /~delancey/309_DIR/LLT_LECTURES/Hilbert.html (1525 words)

	[No title] (Site not responding. Last check: 2007-09-03)
		Finally, Cournot’s justification for his solution had some unattractive underlying assumptions that ended up convincing economists that although Cournot had the right answer, he did not have the right logic to justify his answer.
		SHAPE \* MERGEFORMAT Von Neumann and Morgenstern: two-player zero-sum games Mathematicians such as James Waldegrave (in 1713), Ernest Zermelo (in 1913), Emile Borel (in 1921-27), and John von Neumann (in 1928) had begun to look at decision-making in parlor games—such as poker, tic-tac-toe, and chess—as the subject of serious mathematical analysis.
		However, it was not until Oskar Morgenstern, an economist, collaborated with von Neumann to write The Theory of Games and Economic Behavior in 1944 that the problem of rational behavior by interdependent players began to be seen as central to economics.
	www.phoenix.liu.edu /~uroy/eco54/LecNotes/games.doc (2110 words)

	New Page 1
		Set theory solves the problem of infinity rather simply by introducing an axiom of infinity which Ernest Zermelo formulated as: <$Epile {{down 30 font 2 symbol $} above {italic X}} ~(~ 0 ~symbol
		The axiom uses a generation rule established by recursive definitions, hence no pretense was made that an infinite set can be generated outside theory, as Dedekind attempted to do.
		Zermelo introduces such an infinite set by a simple fiat, indicating how new elements can be derived from those already in X; but the existence of such an infinite set is ascertained from the outset.
	www.asa3.org /asa/PSCF/1993/PSCF9-93Drozdek.html.ori (2483 words)

	The M.E.B. Library Math Section - Logic (Site not responding. Last check: 2007-09-03)
		Cavaillès, Jean Remarques sur la Formation de la Théorie Abstraite des Ensembles, II, Dedekind Les Axiomatisations (Zermelo, Fraenkel, Von Neumann) Actualités Scientifique et Industrielles, 607, Le Progrès de L'Esprit, VII, Hermann and C
		A Theory of Sets Pure and Applied Mathematics, Number XVIII, Academic Press, New York, 1965.
		Nagel, Ernest and Newman, James R. Gödel's Proof New York University Press, 1958.
	www.sfu.ca /~mbarnes/mathlibrarylogic.htm (622 words)

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