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Articles Archives Start page News Contact Community General Newsletter Contact information Site map Most recommended Search the site Archive Photo Archive Video Archive Articles Archive More ... Wisdom Archive Body Mind and Soul Faith and Belief God and Religion ... Yoga Positions Site map 2 Site map Axiom of choice A Wisdom Archive on Axiom of choice Axiom of choice A selection of articles related to Axiom of choice More material related to Axiom Of Choice can be found here: Index of Articles related to Axiom Of Choice Axiom of choice Page 2 ARTICLES RELATED TO Axiom of choice Axiom of choice: Encyclopedia II - List of axioms - Axiom of choice With the Zermelo-Frankel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable List of axioms - Equivalents of AC. Hausdorff maximality theorem Well-ordering principle Zorn's lemma List of axioms - Weaker than AC. Axiom of countable choice Axiom of dependent choice Boolean prime ideal theorem Axiom of uniformization List of axioms - Alternates incompatible with AC See also: List of axioms List of axioms - Zermelo-Frankel axioms List of axioms - Axiom of choice List of axioms - Equivalents of AC ... List of axioms - Other axioms Read more here: Axiom of choice: Encyclopedia - Axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory. It was formulated in 1904 by Ernst Zermelo. While it was originally controversial, it is now used without embarrassment by most mathematicians. However, there are still schools of mathematical thought, primarily within set theory, that either reject the axiom of choice, or even investigate consequences of axioms inconsistent with AC. Intuitively speaking, AC says that given a collection of bins, each containing at least one object, then exactly one ob ...

83. SingaporeMoms - Parenting Encyclopedia - Axiom Of Choice Ask our Moms, Share my experience, Share my photos. Pregnancy Calendar, Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10 http://singaporemoms.com/parenting/Axiom_of_choice

Ask our Moms Share my experience Share my photos Pregnancy Calendar Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 Week 12 Week 13 Week 14 Week 15 Week 16 Week 17 Week 18 Week 19 Week 20 Week 21 Week 22 Week 23 Week 24 Week 25 Week 26 Week 27 Week 28 Week 29 Week 30 Week 31 Week 32 Week 33 Week 34 Week 35 Week 36 Week 37 Week 38 Week 39 Week 40 Browse the Encyclopedia Search Parenting Encyclopedia 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

84. Axiom Of Choice | Definition | Information | Explanation | Review | WikiCity.com 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 http://www.wikicity.com/wikipedia/a/ax/axiom_of_choice.html

Debts and Credits Myspace Proxy Boracay Beach Bikini Babes internet advertising ... Alphabetical index 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.

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Abaara topic: Axiom of choice ABAARA Home About Abaara Tools Contact us Abaara topic: Axiom of choice Categories Business Travel Small Business Computing Personal life ... eLeaP is a secure, easy to use, web-based training platform e-Learning Systems, LMS, LCMS and easy elearning management systems Visit eL eaPsoftware.com Web Packages Level37 Web Design Package $59.95 Let our Professional Designers Host Build and Maintain your website Visit www.level37.com Newsletter eLeaP eLearning Management Systems LMS LCMS Systems. Online training made easy. Free trial now. Axiom of choice 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.

90. Lingua Franca - November 2001| Hypothesis: Single-Egg Theory University Business UB Daily UB Exec Arts Letters Daily Academic Partners. Volume 11, No. 8—November 2001 Table of contents for this issue HYPOTHESES http://linguafranca.mirror.theinfo.org/print/0111/hypothesis.html

University Business UB Daily UB Exec Academic Partners ... Table of contents for this issue HYPOTHESES A Matter Of Choice Can a mathematical idea have political import? By Jim Holt THE LITERARY THEORIST JULIA KRISTEVA has written that "the functioning of poetic meaning obeys the principles designated by the axiom of choice." Alan Sokal, in his famous send-up of postmodern theory, "Transgressing the Boundaries," suggested that the axiom of choice had something to do with the abortion-rights movement and the feminist agenda for equality. Later, in the book Fashionable Nonsense , Sokal and his co-author, Jean Bricmont, correctively declared that the axiom of choice "has no political implications whatsoever." What is this much-invoked thing called the axiom of choice? Is it really devoid of political significance, as Sokal and Bricmont claim? Or could it turn out to pack an ideological punch beyond the imagination of even the most wild-eyed Left Bank postmodern theorist? socks and you want to select one sock from each pair. Since socks in a pair, unlike shoes, are identical, there is no rule for defining a set that consists of precisely one sock from each pair. The choice for each pair would have to be arbitrary; and since there are infinitely many pairs, that means an infinite number of arbitrary choices. Here is where the axiom of choice comes to the rescue. It allows one to assume the existence of such a "choice set," even though there is no rule for constructing it. The axiom of choice caused fierce controversy when it was first framed by the German logician Ernst Zermelo in 1904. Anti-choicers scoffed at the idea of a mathematical object existing by fiat. Pro-choicers countered by insisting that the axiom was self-evidently true and that it was crucial for mathematics and for science itself. Zermelo pointed out that many vocal anti-choicers had unwittingly been using the axiom of choice in their work before he explicitly formulated it.

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