1. Axiom Of Choice - Uncyclopedia, The Content-free Encyclopedia Apr 12, 2009 In set theory, the Axiom of Choice (aka AC) is a totally unwarranted assumption which blatantly disregards the fundamental right of sets and http://uncyclopedia.wikia.com/wiki/Axiom_of_choice

2. Axiom Of Choice - Conservapedia The Axiom of Choice (AC) in set theory states that for every set made of nonempty sets there is a function that chooses an element from http://www.conservapedia.com/Axiom_of_Choice

Axiom of Choice From Conservapedia Jump to: navigation search The Axiom of Choice AC ) in set theory states that "for every set made of nonempty sets there is a function that chooses an element from each set". This function is called a choice function This axiom is powerful because by assuming the existence of such a function, one can then manipulate the function to prove otherwise unprovable theorems. This axiom is controversial because it assumes the existence of a function without giving any hint on how it could be constructed. This axiom has been used to prove many apparently absurd results, as in the Banach-Tarski Paradox discussed below. To better understand the Axiom of Choice, consider alternative descriptions of it: The Axiom of Choice holds that: given any collection of sets , however large, we can pick one element from each set in the collection. More precisely, the Axiom of Choice states that: For every collection of nonempty sets S, there exists a function f such that f(S) is a member of S for every possible S. Mathworld explains the Axiom of Choice as follows: Given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets.

3. Axiom Of Choice - Definition In mathematics, the axiom of choice is an axiom of set theory. It was formulated about a century ago by Ernst Zermelo and has remained controversial to this http://www.wordiq.com/definition/Axiom_of_choice

Axiom of choice - Definition In mathematics , the axiom of choice is an axiom of set theory . It was formulated about a century ago by Ernst Zermelo and has remained controversial to this day. It states the following: Let X be a collection of non-empty sets . Then we can choose a member from each set in that collection. Stated more formally: There exists a function f defined on X such that for each set S in X f S ) is an element of S Another formulation of the axiom of choice (AC) states: Given any set of mutually exclusive non-empty sets, there exists at least one set that contains exactly one element in common with each of the non-empty sets. Until the late 19th century, the axiom of choice was often used implicitly. For example, a proof might have, after establishing that the set S contains only non-empty sets, said "let F(X) be one of the members of X for all X in S ." Here, the existence of the function F depends on the axiom of choice. The principle seems obvious: if there are several boxes, each containing at least one item, the axiom simply states that one can choose exactly one item from each box. Although the statement sounds straightforward, the main issue is that the axiom of choice is unnecessary when one can come up with a rule to choose items from the sets, but it becomes necessary when such a rule can either not be found or when such as rule can be proved not to exist. Thus the controversy involves what it means to choose something from these sets, and what it means for a set to

4. Axiom Of Choice The axiom of choice (AC) says simply that you can always choose one item out of each box. More formally, if S is a collection of nonempty sets, http://www.daviddarling.info/encyclopedia/A/axiom_of_choice.html

LOGIC SETS AND SET THEORY A B ... CONTACT entire Web this site axiom of choice An axiom in set theory S is a collection of non-empty sets , then there exists a set that has exactly one element in common with every set S of S . Put another way, there exists a function f with the property that, for each set S in the collection, f S ) is a member of S . Bertrand Russell summed it up neatly: "To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed. His point is that the two socks in a pair are identical in appearance, so, to pick one of them, we have to make an arbitrary choice. For shoes, we can use an explicit rule, such as "always choose the left shoe." Russell specifically mentions infinitely many pairs, because if the number is finite then AC is superfluous: we can pick one member of each pair using the definition of "nonempty" and then repeat the operation finitely many times using the rules of formal logic. AC lies at the heart of a number of important mathematical arguments and results. For example, it is equivalent to the

5. Axiom Of Choice The axiom of choice is an axiom in set theory. It was formulated about a century ago by Ernst Zermelo, and was quite controversial at the time. http://www.fact-index.com/a/ax/axiom_of_choice.html

Main Page See live article Alphabetical index Axiom of choice The axiom of choice is an axiom in set theory . It was formulated about a century ago by Ernst Zermelo , and was quite controversial at the time. It states the following: Let X be a collection of non-empty sets . Then we can choose a member from each set in that collection. Stated more formally: There exists a function f defined on X such that for each set S in X f S ) is an element of S Another formulation of the axiom of choice (AC) states: Given any set of mutually exclusive non-empty sets, there exists at least one set that contains exactly one element in common with each of the non-empty sets. It seems obvious: if you've got a bunch of boxes lying around with at least one item in each of them, the axiom simply states that you can choose one item out of each box. Where's the controversy? Well, the controversy was over what it meant to choose something from these sets. As an example, let us look at some sample sets. 1. Let X be any finite collection of non-empty sets. Then f can be stated explicitly (out of set A choose a , ...), since the number of sets is finite.

6. Axiom Of Choice - Wikipedia, The Free Encyclopedia In mathematics, the axiom of choice, or AC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of bins, http://en.wikipedia.org/wiki/Axiom_of_choice

Axiom of choice From Wikipedia, the free encyclopedia Jump to: navigation search This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band) In mathematics , the axiom of choice , or AC , is an axiom of set theory . Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if there are infinitely many bins and there is no "rule" for which object to pick from each. The axiom of choice is not required if the number of bins is finite or if such a selection "rule" is available. For example, given an infinite collection of pairs of socks, one needs AC to pick one sock out of each pair; but given an infinite collection of pairs of shoes, one shoe out of each pair can be specified even without AC, by choosing the left one. The axiom of choice was formulated in 1904 by Ernst Zermelo Although originally controversial, it is now used without reservation by most mathematicians. One motivation for this use is that a number of important mathematical results, such as

7. Axiom Of Choice In English - Dictionary And Translation Axiom of Choice. Dictionary terms for Axiom of Choice in English, English definition for Axiom of Choice, Thesaurus and Translations of Axiom of Choice to English, Chinese http://www.babylon.com/definition/Axiom_of_Choice/English

8. Axiom Of Choice - Wiktionary Aug 14, 2010 axiom of choice. Definition from Wiktionary, the free dictionary Retrieved from http//en.wiktionary.org/wiki/axiom_of_choice http://en.wiktionary.org/wiki/axiom_of_choice

axiom of choice Definition from Wiktionary, the free dictionary Jump to: navigation search edit English Wikipedia has an article on: Axiom of choice Wikipedia edit Noun axiom of choice uncountable set theory One of the axioms in axiomatic set theory , equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty. edit Translations axiom of choice Croatian: aksiom izbora hr (hr) m Czech: axiom výběru cs (cs) m Dutch: keuzeaxioma nl (nl) French: axiome du choix fr (fr) m German: Auswahlaxiom de (de) n Polish: aksjomat wyboru pl (pl) m Slovak: axióma výberu sk (sk) f Retrieved from " http://en.wiktionary.org/wiki/axiom_of_choice Categories English nouns Set theory ... Mathematics Personal tools New features Log in / create account Namespaces Entry Discussion Variants Views Read Edit History Actions Search Navigation Main Page Community portal Preferences Requested entries ... Contact us Toolbox What links here Related changes Upload file Special pages ... Permanent link In other languages Svenska This page was last modified on 14 August 2010, at 10:14. Text is available under the Creative Commons Attribution/Share-Alike License ; additional terms may apply. See

9. Online Encyclopedia And Dictionary - Axiom Of Choice In mathematics, the axiom of choice is an axiom of set theory. It was formulated in 1904 by Ernst Zermelo and has remained controversial to this day. http://fact-archive.com/encyclopedia/Axiom_of_choice

Search The Online Encyclopedia and Dictionary Encyclopedia Dictionary Quotes Categories ... Set theory Axiom of choice In mathematics , the axiom of choice is an axiom of set theory . It was formulated in 1904 by Ernst Zermelo and has remained controversial to this day. It states the following: Stated more formally: Let X be a set of non-empty sets. There exists a choice function f defined on X such that for each set S in X f S ) is an element of S Another formulation of the axiom of choice (AC) states: Given any set of mutually disjoint non-empty sets, there exists at least one set that contains exactly one element in common with each of the non-empty sets. Until the late 19th century, the axiom of choice was often used implicitly. For example, a proof might have, after establishing that the set S contains only non-empty sets, said "let F(X) be one of the members of X for all X in S ." Here, the existence of the function F depends on the axiom of choice. The axiom might seem at first glance to be obviously true and unobjectionable: if there are several boxes, each containing at least one item, the axiom simply states that one can choose exactly one item from each box. The existence of a choice function is indeed straightforward and uncontroversial when only finite sets are concerned. In fact its existence can be proven from the other axioms of set theory, without the axiom of choice. More generally, the axiom of choice is not necessary for the existence of a choice function when one can come up with a rule to choose items from the sets. However, it is necessary when such a rule cannot be found, and applicable even when such a rule can be proven not to exist. Asserting the existence of a choice function in such cases is controversial. The controversy involves what it means to

10. Bambooweb: Axiom Of Choice In mathematics, the axiom of choice is an axiom in set theory. It was formulated about a century ago by Ernst Zermelo, and wa http://www.bambooweb.com/articles/a/x/Axiom_of_choice.html

Axiom of choice In mathematics , the axiom of choice is an axiom in set theory . It was formulated about a century ago by Ernst Zermelo , and was quite controversial at the time. It states the following: Let X be a collection of non-empty sets . Then we can choose a member from each set in that collection. Stated more formally: There exists a function f defined on X such that for each set S in X f S ) is an element of S Another formulation of the axiom of choice (AC) states: Given any set of mutually exclusive non-empty sets, there exists at least one set that contains exactly one element in common with each of the non-empty sets. For many years, the axiom of choice was used implicitly. For example, a proof could use a set S that was previously demonstrated to be non-empty and claim "because S is non-empty, let a be one of the members of S ." Here, the use of a requires the axiom of choice. The principle seems obvious: if you have several boxes lying around with at least one item in each box, the axiom simply states that you can choose one item out of each of them. Although the statement sounds straightforward there's a controversy over what it means to choose something from these sets. As an example, let us look at some sample sets.

11. Axiom_of_choice's Fotolog Page - Fotolog Powered by. Google�. Log in Language Help. New to Fotolog? Create Your Page; Take a Tour Gold Camera; Gift Store; Foto Ads; Members; Groups http://www.fotolog.com/axiom_of_choice

12. Axiom Of Choice Pronunciation: How To Pronounce Axiom Of Choice In English, Axio Feb 17, 2010 Pronunciation guide Learn how to pronounce Axiom of Choice in English with native pronunciation. Axiom of Choice translation and audio http://www.forvo.com/word/axiom_of_choice/

13. Axiom Of Choice : Top Topics (The Full Wiki) The following are the current most viewed articles on Wikipedia within Wikipedia s Axiom of choice category. Think of it as a What s Hot list for Axiom of http://top-topics.thefullwiki.org/Axiom_of_choice

14. Axiom Of Choice - Academic Kids In mathematics, the axiom of choice is an axiom of set theory. It was formulated in 1904 by Ernst Zermelo. While it was originally controversial, it is now accepted and used http://www.academickids.com/encyclopedia/index.php/Axiom_of_choice

Axiom of choice From Academic Kids In mathematics , the axiom of choice is an axiom of set theory . It was formulated in by Ernst Zermelo . While it was originally controversial, it is now accepted and used casually by most mathematicians. However, there are still schools of mathematical thought, primarily within set theory, which either reject the axiom of choice, or even investigate consequences of its negation. The axiom of choice is typically abbreviated AC, or C as a suffix. Contents showTocToggle("show","hide") 1 Statement 2 Usage 3 Independence of AC 4 Weaker versions of choice ... edit Statement The axiom of choice states: Template:Axiom Stated more formally: Template:Axiom Another formulation of the axiom of choice states: Template:Axiom edit Usage Until the late 19th century, the axiom of choice was often used implicitly. For example, after having established that the set S contains only non-empty sets, a mathematician might have said "let F(X) be one of the members of X for all X in S ." In general, it is impossible to prove that F exists without the axiom of choice, but this seems to have gone unnoticed until Zermelo.

15. Math.vanderbilt.edu > Axiom Of Choice Disclaimer Galaxy is not affiliated in any way with the Axiom of Choice (math. vanderbilt.edu/~schectex/ccc/choice.html) website. http://www.galaxy.com/rvw14878-859701/Axiom_of_Choice.htm

submit a site post content Galaxy.com :: The Web's Original Searchable Directory post Galaxy Galaxy United States Canada Europe UK / Ireland ... Africa search for: in: The Directory The Web Stories Politics Sports Entertainment For Sale Personals Real Estate Services Announcements Jobs Home Science Mathematics Set Theory ... Axiom of Choice Axiom of Choice ... math.vanderbilt.edu/~schectex/ccc/choice.html Post a Review Do you have experience with or are you familiar with this website? Please post your comments / review below to share with the rest of the community. Review: Approve! Disapprove! Your Name: Email: Review: Please note, all comments are subject to review and can be removed at any time for any reason. Views and opinions expressed may not be representative of Galaxy or its owners but all effort is made to keep the site free of obscenities, illegal or otherwise malicious activity. Are you the owner of this site? You can manage your listing here Terms Privacy Help

16. Axiom Of Choice Usa Radio EN - Cineversity.TV cineversity.tv ctv online news media network cineversity groningen radio Axiom of Choice usa , Evanescent, Mystics and Fools, Panj The name of the ensemble http://www.cineversity.tv/EN/radio/usa/Axiom_of_Choice

17. Axiom Of Choice - Rapidshare Search - Rapid4search.com rapidshare.com/files/3VF_93e63c47323334df03ea/Axiom Of Choice 05 - A Walk By The Lake (Ba Shere Khaneam Abrist Az Nima Yooshij).zip http://search.ccebook.net/axiom_of_choice/page1/en

Rapidshare8 Search Skip over navigation English Français Deutsch ... Rapidshare Search-rapid4search.com Rapidshare Search Document Search Torrent search Rapidshare Bay Search Rapidshare Files Documents(PDF,DOC...) Torrent Files RSBay.com [new] Download: of about for axiom of choice . (0.05 seconds) Also Try - axiom of choice PDF axiom of choice Torrent ... Rubin-equivalents Of The Axiom Of Choice Ii-9780444877086.djvu Keywords equivalents choice axiom rubin ... foundations Description : Equivalents of the Axiom of Choice II (Studies in Logic and the Foundations of Mathematics) ifile.it Equivalents Of Axiom Of Choice Ii 0444877088.rar Keywords equivalents choice axiom mathematics ... logic Description : Equivalents of the Axiom of Choice II (Studies in Logic and the Foundations of Mathematics) ifile.it Keywords axiom logic mathematics foundations ... studies Description : Axiom,Logic,Equivalents of the Axiom of Choice (Studies in Logic and the Foundations of Mathematics) ifile.it Choice G 01.rar Keywords choice book audio radio ... collection Description : source: http://g***a.com/items/71232/choice-grenfellbbc-radio-collectionaudio-book- ifile.it

18. Axiom Of Choice : Math Jul 27, 2009 The axiom of choice (AC) is independent of the usual axiom of set theory, meaning that you can either add it as an axiom or you can add its http://www.reddit.com/r/math/comments/94z4j/axiom_of_choice/

19. Axiom Of Choice (band) - Wikipedia, The Free Encyclopedia Axiom of Choice is a southern California based world music group of Iranian migr s who perform a fusion style incorporating Persian classical music and Western classical music. http://en.wikipedia.org/wiki/Axiom_of_Choice_(band)

Axiom of Choice (band) From Wikipedia, the free encyclopedia Jump to: navigation search Axiom of Choice is a southern California USA ) based world music group of Iranian émigrés who perform a fusion style incorporating Persian classical music and Western classical music Contents History Discography References External links ... edit History Led by Loga Ramin Torkian who plays a variant of a guitar of his own invention that is fretted to play quarter tones , the band has a sound combining soaring female vocals, Middle-Eastern rhythms and melodies, and progressive Western production styles. The band was named after the mathematical concept, the Axiom of choice The melodies and rhythms of Persia 's Radif tradition are mixed with Western music. Led by Persia-born nylon-string classical guitar, quarter-tone guitar, and tarbass player and musical director Loga Ramin Torkian, the septet incorporates a global range of influences into its sound. Axiom of Choice remains rooted in the musical heritage of Torkian and fellow Persian émigrés Mamak Khadem and Pejman Hadadi . While Khadem 's singing in the Persian language retains the spirit of the past, the playing of Hadadi, one of the leading Persian percussionists living in the United States, gives the group its flavor. Hadadi—who plays

20. [lex ] Unrecognized Rule Problems - Ubuntu Forums 2 posts 1 author - Last post Jul 23, 2009 return DEFINITION;} axiom_of_choice {lexEcho( axiom_of_choice ); return axiom_of_choice;} tautology {lexEcho( tautology ); http://ubuntuforums.org/showthread.php?t=1220667

Page 1     1-20 of 99    1  | 2  | 3  | 4  | 5  | Next 20