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Topic: Axiom

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List of axioms

Postulate

Axiomatic system

Propositional calculus

Axiomatic set theory

Axiomatization

Logic

Peano axioms

Fifth postulate

Intuitionistic logic

Natural deduction

Mathematics

Mathematical logic

Mathematical proof

Axiom computer algebra system

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	Axiom schema of specification - Wikipedia, the free encyclopedia
		In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom schema of specification, or axiom schema of separation, or axiom schema of restricted comprehension, is a schema of axioms in Zermelo-Fraenkel set theory.
		The axiom schema of specification is characteristic of systems of axiomatic set theory related to the usual set theory ZFC, but does not usually appear in radically different systems of alternative set theory.
		Most of the other Zermelo-Fraenkel axioms (but not the axiom of extensionality or the axiom of regularity) then became necessary to serve as an additional replacement for the axiom schema of comprehension; each of these axioms states that a certain set exists, and defines that set by giving a predicate for its members to satisfy.
	en.wikipedia.org /wiki/Axiom_schema_of_specification (1005 words)

	Axiom - Wikipedia, the free encyclopedia
		In mathematics, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results.
		Reasoning about two different structures, for example the natural numbers and the integers, may involve the same logical axioms; the non-logical axioms aim to capture what is special about a particular structure (or set of structures, such as groups).
		The axioms are referred to as "4 + 1" because for nearly two millennia the fifth (parallel) postulate ("through a point outside a line there is exactly one parallel") was suspected of being derivable from the first four.
	en.wikipedia.org /wiki/Axiom (1603 words)

	PlanetMath: axiom
		Axioms and postulates are the basic assumptions underlying a given body of deductive knowledge.
		In the modern understanding, a set of axioms is any collection of formally stated assertions from which other formally stated assertions follow by the application of certain well-defined rules.
		A set of axioms should be consistent; it should be impossible to derive a contradiction from the axiom.
	planetmath.org /encyclopedia/Axiom.html (1184 words)

	Axiom Automotive Technologies Online - Terms of Use
		Axiom offers its Products and Services to individuals and legal entities who participate in the aftermarket transmission repair or rebuilding business who utilize or who could utilize Axiom’s Products and Services and who are in a position to recommend or order the procurement of such Products and Services.
		Axiom may suspend or terminate eligibility if it determines, in its discretion, that a User has engaged in fraudulent or improper activity in connection with the utilization of Axiom’s Services or the purchase of its Products.
		Axiom’s failure to act with respect to a breach by You or others does not waive the right to act with respect to subsequent or similar breaches.
	www.axiom.com /atc/site/locations/locations.aspx (3863 words)

	Axiom, 3D abstract strategy game - Invented by Michael Seal
		Axiom is a unique 3D boardgame invented by Michael Seal in 1988.
		The fun and indeed the depth of Axiom is soon realised as you enter and travel through this third dimension.
		Axiom is currently out of production and due to be republished in 2003.
	www.lumicube.com /pages/axiom.html (517 words)

	Axiom (Site not responding. Last check: 2007-09-19)
		A true axiom can not be refuted because the act of trying to refute it requires that very axiom as a premise.
		The term "axiom" has been abused in many different ways, so it is important to distinguish the proper definition from the others.
		In this sense, "axiom" was used to mean a postulate which one was sure was true.
	www.importanceofphilosophy.com /Metaphysics_Axiom.html (263 words)

	DevMaster.net - Axiom - Engine Details
		Because Axiom is licensed under the LGPL, it can be used by commercial and open-source software developers alike and because it is a SourceForge.net project, you have easy access to a wealth of services such as access to the code base via CVS and web-browsing, feature requests, and bug-tracking.
		Axiom has not received as much use as it deserves as it classifies itself as in an “alpha” status.
		Axiom (C#) is a port of the Ogre3D rendering engine (C++), it's user base is smaller, but with the increased performance of the managed.net languages from Microsoft, it is a good bet on productivity.
	www.devmaster.net /engines/engine_details.php?id=81 (2612 words)

	Axiom (Site not responding. Last check: 2007-09-19)
		The goal of Axiom is to place one of your sceptres on the same cube as one of your opponents sceptres.
		Axiom sets are of good quality and rugged enough to stand up to many playings and even a bit of travel.
		Axiom is produced by Seventh Seal, 3 Denmark Terrace, Brighton, BN1 3AN, England and distributed on the continent by Dewar Ltd., Postfach 1223, 77802 Bhl/Baden, Germany.
	www.gamecabinet.com /reviews/Axiom.html (805 words)

	Axiom (Site not responding. Last check: 2007-09-19)
		As the word axiom is understood in mathematics, an axiom is not a proposition that is self-evident.
		For example, in some rings, the operation of multiplication is commutative, and in some it isn't; those rings in which it is are said to satisfy the "axiom of commutativity of multiplication." Another name for an axiom is postulate.
		An axiom is an elementary basis for a formal logic system that together with the rules of inference define a logic.
	www.websign.sk /ax/Axiom.html (657 words)

	Axiom Capital, Albany NY 12207 \| Company Profile \| Personnel
		Charles M. Cronin, founder of Axiom Capital, is a former bank president with an insider's understanding of the lending industry.
		He provides Axiom with personal experience and insight as a developer/borrower, and has been involved in all phases of acquiring, negotiating and closing many forms of financing transactions.
		Prior to joining Axiom, he spent 18 years managing real estate and securities portfolios of up to $200 and $400 million, respectively as CFO of an upstate New York real estate company.
	www.axiom-capital.com /personnel.htm (954 words)

	YFCNI.ORG - WELCOME
		Axiom is the Creative Arts Team of Youth for Christ Northern.
		The AIM of Axiom is to provide teachers in schools with a resource to assist them in the vital role they play.
		Working within the Northern Ireland curriculum, Axiom can enhance and complement the existing programme of study in schools and by using their creative abilities communicate effectively with other young people on issues that are relevant and important in their lives today.
	www.yfcni.org /axiom (442 words)

	DivmodAxiom - Divmod - Trac
		Axiom is an object database, or alternatively, an object-relational mapper.
		Axiom provides a full interface to the database, which strongly suggests that you do not write any SQL of your own.
		Writing your own SQL is still possible, however, and Axiom does have several methods which return fragments of generated schema if you wish to use them in your own queries.
	divmod.org /trac/wiki/DivmodAxiom (222 words)

	Axiom Resource Management, Inc.
		Axiom Resource Management, Inc. announced a major contract to provide far-reaching support to the Department of Health and Human Services and other federal government agencies.
		Axiom Resource Management, Inc. announced that one of its employees is scheduled to present lectures on Leadership at the United States Military Academy at West Point.
		Axiom Resource Management, Inc. released a summary of its business activities for the year 2002 today showing the company continued its recent phenomenal growth, winning 38 new contracts worth an aggregate $55 million.
	www.axiom-rm.com /news/news_press_2003.htm (1016 words)

	GoodSound! "Equipment" Archives
		Axiom, as it turns out, is one of the larger Canadian speaker manufacturers.
		The Axiom Millennia M3Ti measures 13.5"H x 8.5"W x 8.5"D. The speaker represents a nominal 8-ohm load, with an optimistically overstated sensitivity of 93dB that's probably closer to 89dB.
		Axiom's OEM history partially explains their high value operation.
	www.goodsound.com /equipment/axiom_m3ti.htm (1712 words)

	java.net: Introducing AXIOM: The Axis Object Model
		AXIOM is the object model for Apache Axis 2, the next generation of the Apache web services engine.
		AXIOM is different from existing XML object models in various ways, the major one being the way it incrementally builds the memory model of an incoming XML source.
		AXIOM itself does not contain a parser and it depends on StAX for input and output.
	today.java.net /pub/a/today/2005/05/10/axiom.html (1969 words)

	axiom from FOLDOC (Site not responding. Last check: 2007-09-19)
		A formula containing variables of the metalanguage which becomes an axiom when its variables are instantiated to wffs of the formal language.
		An axiom that is a logically valid wff of the language of the system.
		An axiom that is not a logically valid wff of the language of the system (but is a closed wff).
	www.swif.uniba.it /lei/foldop/foldoc.cgi?axiom (109 words)

	Axiom Photo Design :: A commercial art studio located in Davis, California (Site not responding. Last check: 2007-09-19)
		Axiom invites you to visit the Michel-Novelozo Gallery of Photography, located on the ground-floor of our building at the corner of 4th and E St. in downtown Davis.
		Axiom is a commercial art studio in Davis, California.
		Since 1992, Axiom has earned trust in numerous industries including publishing, advertising, marketing, public relations and art.
	www.axiomphoto.com (166 words)

	Axiom Publishing (Site not responding. Last check: 2007-09-19)
		Axiom Publishing is an Australian book publisher with 30 years experience in both distribution and publishing of book titles.
		Axiom is well on the way to publishing its wish list of 75 individual titles for the year 2005/6.
		Axiom welcomes interest from International publishers or significant retail groups for rights in countries so far not agreed on.
	www.axiompublishers.com.au (183 words)

	Spectroscopy \| Infrared Spectroscopy \| IR Spectroscopy \| Axiom Analytical (Site not responding. Last check: 2007-09-19)
		With over 25 patents and 15 years experience, Axiom Analytical provides the chemical and pharmaceutical industries with robust and time tested sampling equipment required to meet the wide ranging and rapidly changing demands of spectroscopic analysis.
		Only Axiom provides the complete set of solutions necessary to take you from the laboratory, through the plant and on to full scale on-line manufacturing..
		Axiom provides application development and custom system integration services to both the spectroscopic instrument....
	www.goaxiom.com (274 words)

	AXIOM (Site not responding. Last check: 2007-09-19)
		AXIOM is a wonderful combination of the ObjectOriented Programming paradigm and Algebraic Structure.
		AXIOM itself, through the fact that the company marketing it, NAG, has a successful relationship with engineering computing users, has a chance of eventually becoming a mass-market CAS.
		Axiom 2.0 was installed at UWA Maths in Dec 94, but the licence was not renewed in 96.
	www.maths.uwa.edu.au /~keady/GKAXIOM.html (474 words)

	About "Axiom (Encarta Encyclopedia 2000)" (Site not responding. Last check: 2007-09-19)
		Axiom, in logic and mathematics, a basic principle that is assumed to be true without proof.
		The use of axioms in mathematics stems from the ancient Greeks, most probably during the 5th century BC, and represents the beginnings of pure mathematics as it is known today...
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /library/view/17265.html (61 words)

	MathAction and Axiom FrontPage
		Axiom is a general purpose system for doing mathematics by computer.
		Axiom has a strongly-typed high-level programming language for expressing abstract mathematical concepts.
		The Axiom Foundation is our means to promote the development and maintenance of the open source version of Axiom through the dispersement of donations and royalties from Axiom Gear to support Axiom-related projects and through the Award Of Bounties.
	wiki.axiom-developer.org (168 words)

	NAG Symbolic Software
		For further information about the status of Aldor, the AXIOM extension language, and its compiler, please visit www.aldor.org.
		For the most powerful symbolic solver system, particularly if you are also seeking to use high quality numerical software, we strongly recommend that you visit www.maplesoft.com, the web site of Maplesoft, developers of the Maple system.
		Maple, like AXIOM, is an advanced and comprehensive system for solving a wide range of symbolic and symbolic-numeric problems.
	www.nag.co.uk /symbolic_software.asp (160 words)

	Welcome To Axiom Online
		Axiom Automotive Technologies is the world’s largest supplier of OEM and aftermarket replacement parts to transmission professionals.
		Axiom is the industry leader in the availability, quality and distribution of transmission products.
		Customers of Axiom may use the Parts Numbers for purposes of placing orders with Axiom, or otherwise operating their business, but no permission is granted to any customer or other individual or entity to make use of the Part Numbers to compete with Axiom in any way.
	www.axiom.com (299 words)

	Debian -- axiom
		Axiom is useful for research and development of mathematical algorithms.
		Axiom has been in development since 1973 and was sold as a commercial product.
		Efforts are underway to extend this software to (a) develop a better user interface (b) make it useful as a teaching tool (c) develop an algebra server protocol (d) integrate additional mathematics (e) rebuild the algebra in a literate programming style (f) integrate logic programming (g) develop an Axiom Journal with refereed submissions.
	packages.debian.org /unstable/math/axiom.html (293 words)

	AXIOM
		AXIOM's entrance on the contemporary Jazz scene presents a truly unique fusion of Latin, Funk, and Jazz styles united in both concept and presentation.
		AXIOM has been appearing at some of Southern California's premier Jazz clubs and performing in concerts with recording artists such as Lee Ritenour, The Rippingtons, Kirk Whalum, and Billy Childs, among many others.
		AXIOM, founded by guitarist Peter Templer and drummer Phil Templer, also includes the outstanding musicianship of Brian Mastalski on Electric Bass and Chapman Stick, Alan Palmer on Tenor/Alto Sax and Electronic Wind Synthesizer and Jared Stewart on Keyboards.
	www.axiomjazz.com (135 words)

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