Geometry.Net - the online learning center
Home  - Theorems_And_Conjectures - Axiom Of Choice
e99.com Bookstore
  
Images 
Newsgroups
Page 1     1-20 of 90    1  | 2  | 3  | 4  | 5  | Next 20

         Axiom Of Choice:     more books (56)
  1. The Axiom of Choice by Thomas J. Jech, 2008-07-24
  2. Zermelo's axiom of choice: Its origins, development, and influence (Studies in the history of mathematics and physical sciences 8) by Gregory H. Moore, 1982-11-17
  3. Axiom of Choice (Lecture Notes in Mathematics) (Volume 0) by Horst Herrlich, 2006-07-06
  4. The Axiom of Choice (Studies in Logic Series) by John L Bell, 2009-11-23
  5. Equivalents of the Axiom of Choice II (Studies in Logic and the Foundations of Mathematics) by Herman Rubin, 1985-07
  6. Consequences of the Axiom of Choice (Mathematical Surveys and Monographs) by Paul Howard, 1998-06-30
  7. Equivalents of the axiom of choice (Studies in logic and the foundations of mathematics) by Herman Rubin, 1963
  8. Freyds Models for the Independence of the Axiom of Choice (Memoirs of the American Mathematical Society) by Andreas Blass, 1989-06
  9. Axiom of Choice; Axiom of Choice, Zorn's Lemma, Well-Ordering Theorem, Tychonoff's Theorem, Hausdorff Maximal Principle, König's Lemma
  10. Persian Classical Music Groups: Mastan Ensemble, the Kamkars, Afsaneh Ballet, Chemirani Ensemble, Lian Ensemble, Axiom of Choice
  11. Constructible Universe: Mathematics, Kurt Gödel, Inner model, Zermelo?Fraenkel settheory, Set theory, Axiom of choice, Continuum hypothesis,Consistency, ... of constructibility, Statementstrue in L
  12. Iranian Musical Groups: Mastan Ensemble, the Kamkars, Kahtmayan, Niyaz, Vas, Vaspooher, Quark Kent, Axiom of Choice, Masters of Persian Music
  13. the consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory by Kurt Gödel, 1940
  14. Leśniewski's ontology extended with the axiom of choice by James George Kowalski, 1975

1. Axiom Of Choice - Wikipedia, The Free Encyclopedia
Consequences of the Axiom of Choice, based on the book by Paul Howard and Jean Rubin. Retrieved from http//en.wikipedia.org/wiki/axiom_of_choice
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 . Intuitively speaking, the axiom of choice says that given any collection of bins, each containing at least one object, exactly one object can be selected 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. It was formulated in 1904 by Ernst Zermelo While it was originally controversial, it is now used without reservation by most mathematicians. However, there are schools of mathematical thought, primarily within set theory, that either reject the axiom of choice or investigate consequences of axioms inconsistent with AC.
Contents
edit Statement
A choice function is a function f , defined on a collection X of nonempty sets, such that for every set

2. Axiom_of_choice - ESnips Search
Tags axiom_of_choice ,hypothesis_of_continuum ,quantum_information ,continuum ,continuity. + Add to Quicklist. Axiom Of Choice Vàleh.wma in Dreamer.
http://www.esnips.com/_t_/axiom_of_choice
/*********************************************** * DHTML Window Widget- © Dynamic Drive (www.dynamicdrive.com) * This notice must stay intact for legal use. * Visit http://www.dynamicdrive.com/ for full source code ***********************************************/ Let your content take you places Upload and share files, photos, videos, anything! Get 5GB free storage Search: Communities Karaoke DJs Photography ... People Sort By: Relevancy Recency All Files Folders Images Videos ... For Sale eSnips Oasis Results axiom_of_choice Oasis Visit the axiom_of_choice Oasis! eSnips Oasis 4 file(s) found for Bolzano_continuum.pdf in Bolzano on continuum Болцано за континуума By vasildinev on Jan. 23 2008 7 View(s) Tags: continuum continuity + Add to Quicklist Axiom Of Choice- V leh.wma in Dreamer.. By MixMasterE on Sep. 13 2007

3. MP3Shitter
00axiom_of_choice-unfolding-2003-back-bla.jpg 00-axiom_of_choice-unfolding-2003-bla.m3u 00-axiom_of_choice-unfolding-2003-bla.nfo
http://www.mp3shitter.com/info/id27875.html
Search track names Axiom_of_Choice-Unfolding-2003-BLA Genre Ethnic Year Group BLA Size 10 files / 68 MB 00-axiom_of_choice-unfolding-2003-back-bla.jpg 00-axiom_of_choice-unfolding-2003-bla.m3u 00-axiom_of_choice-unfolding-2003-bla.nfo 00-axiom_of_choice-unfolding-2003-bla.sfv 00-axiom_of_choice-unfolding-2003-front-bla.jpg 01-axiom_of_choice-mystics_and_fools-bla.np3 02-axiom_of_choice-evanescent-bla.np3 03-axiom_of_choice-parting_ways_with_the_soul-bla.np3 04-axiom_of_choice-turquoise_land-bla.np3 05-axiom_of_choice-through_the_shadows_(part_1)-bla.np3 06-axiom_of_choice-through_the_shadows_(part_2)-bla.np3 07-axiom_of_choice-elixir-bla.np3 08-axiom_of_choice-ancient_sky-bla.np3 09-axiom_of_choice-color_of_dreams-bla.np3 10-axiom_of_choice-messenger_of_time-bla.np3

4. Index Of /AXIOM_OF_CHOICE
Index of /axiom_of_choice. Parent Directory; 1994_BEYOND_DENIAL/
http://www.smartdevelopers.com/AXIOM_OF_CHOICE/

5. Axiom Of Choice - Wikipedia
Retrieved from http//nostalgia.wikipedia.org/wiki/axiom_of_choice . This page was last modified 0440, 15 January 2005. Content is available under GNU
http://nostalgia.wikipedia.org/wiki/Axiom_of_choice
Axiom of choice
From Wikipedia HomePage Recent changes View source Page history ... Log in Special pages Double redirects Broken redirects Disambiguation pages Log in Preferences My watchlist Recent changes Upload file File list Gallery of new files User list Statistics Random page Orphaned pages Uncategorized pages Uncategorized categories Uncategorized files Uncategorized templates Unused categories Unused files Wanted pages Wanted categories Most linked to pages Most linked to categories Most linked-to templates Pages with the most categories Most linked to files Pages with the most revisions Pages with the fewest revisions Short pages Long pages New pages Oldest pages Dead-end pages Protected pages Protected titles All pages Prefix index List of blocked IP addresses and usernames User contributions What links here Book sources Categories Export pages Version System messages Logs MIME search Search for duplicate files List redirects Unused templates Random redirect Pages without language links File path Search List of Wikimedia wikis Expand templates CategoryTree Gadgets Parser diff test Cross-namespace links Wikimedia Board of Trustees election Search web links
Printable version

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:

6. Axiom Of Choice : ISOUND.COM™
iSound Site www.isound.com/axiom_of_choice. Sounds Like. Genres. Featured Album. Unfolding Released 2002. Mp3s. Albums. Click on one of the albums below
http://www.isound.com/axiom_of_choice
Artists Albums Songs
Listener Artist
Genres +Alternative +Indie/Punk +Hard/Metal +Classic Rock +Pop-Rock +Other Rock +Rap/Hip Hop +Electronic +Dance +Blues Location +Blues Style +Traditional Jazz +Non-Trad Jazz +Trad. Country +Modern Country +World/Misc... Death´s a bitch by Sick Of Sue
42 Listeners
Axiom of Choice
Add to Profile Advertisement
This artist has not uploaded any music.
Stats
iSound Site: www.isound.com/axiom_of_choice
Sounds Like Genres:
Featured Album Unfolding
Released: 2002 Albums Click on one of the albums below for more info. Unfolding Released: 2002 Niya Yesh Released: 2000 Axiom Of Choice - Beyond Denial Released: 1996 Ringtones Photos Shows Embed these shows on your other sites (myspace, blogs etc...): Biography Artist Forum Interact with other fans of Axiom of Choice. Start a new discussion now! Blog SITE MAP TERMS PRIVACY ADVERTISE ... CONTACT iSOUND

7. Axiom Of Choice - Conservapedia
Retrieved from http//www.conservapedia.com/axiom_of_choice . Categories Articles with unsourced statements Set theory Mathematics
http://www.conservapedia.com/Axiom_of_Choice
Axiom of Choice
From Conservapedia
Jump to: navigation search The Axiom of Choice AC is an axiom of Zermelo-Fraenkel set theory holding that:
given any collection of sets, however large, we can pick one element from each set in the collection.
In layman's terms, the Axiom of Choice is "For every nonempty set there is a choice function." Or, "We can choose one element from every element of a nonempty set of disjoint sets and this process by which we choose these sets will set up a new set." 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.
Yet another helpful explanation of the Axiom of Choice is this:
If you have a collection of sets C (which may potentially contain an uncountably large number of sets), then there exists a set H, called the choice set, which contains precisely one element from each (non-empty) set in C. H is called the "choice set" because you are essentially going through each set in C and choosing one element from it. One feature of the Axiom of Choice is that H is simply assumed to exist; there is no algorithm given which might tell you how to construct an example of H.
Contents
edit Use of the Axiom of Choice

8. Axiom Of Choice
An axiom in set theory that is one of the most controversial axioms in mathematics; it was formulated in 1904 by the German mathematician Ernst Zermelo
http://www.daviddarling.info/encyclopedia/A/axiom_of_choice.html
MATHEMATICS A B C ... 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 well-ordering principle , to the statement that for any two cardinal numbers m and n , then m n or m n or m n , and to Tychonoff's theorem (the product of any collection of compact spaces in topology is compact). Other results hinge upon it, such as the assertion that every infinite set has a denumerable subset. Yet AC was strongly attacked when it was first suggested, and still makes some mathematicians uneasy. The central issue is what it means to choose something from the sets in question and what it means for the choosing function to exist. This problem is brought into sharp focus when

9. BibSonomy::user::a_olympia::Axiom_of_Choice
Webapplikation des Fachgebiets Wissensverarbeitung, Universität Kassel.
http://www.bibsonomy.org/user/a_olympia/Axiom_of_Choice
BibSonomy user
tag user group author concept BibTeX key search:all search:a_olympia cssdropdown.startchrome("path"); A blue social bookmark and publication sharing system. tags relations groups popular ... about username: password: myFriends myRelations mySearch myPDF ... register cssdropdown.startchrome("upper_menu"); cssdropdown.startchrome("lower_menu");
bookmarks
  • Prologue Chapter 1: The Prehistory of the Axiom of Choice Introduction The Origins of the Assumption The Boundary between the Finite and the Infinite to Zermelo math mathematik on 2006-10-02 15:49:42.0
publications
Showing 10 items per page. Show items per page. tags BibSonomy is offered by the Knowledge and Data Engineering Group of the University of Kassel, Germany. Contact: webmaster at bibsonomy.org init(0, 0, 0, "a_olympia", "", "", "BibSonomy");

10. Axiom Of Choice - Indopedia, The Indological Knowledgebase
Retrieved from http//www.indopedia.org/axiom_of_choice.html . This page has been accessed 2998 times. This page was last modified 1743,
http://www.indopedia.org/Axiom_of_choice.html
Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch
Categories
Set theory
Printable version
... Wikipedia Article
Axiom of choice
ज्ञानकोश: - The Indological Knowledgebase
In mathematics , the axiom of choice is an axiom of 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 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

11. Furyfanzine.com Search
URL=http//mp3tube.info/axiom_of_choice/axiom_of_choiceAncient_Sky.html?1503282Axiom Of Choice - Ancient Sky (700 8.01Mb 16 .
http://www.furyfanzine.com/forum/search.php?search_author=Gothik&sid=b19ce26a7a9

12. Axiom Of Choice - English Dictionary
english to english dictionary containing references.
http://www.online-dictionary.biz/english/vocabulary/reference/axiom_of_choice.as
var language=0; var from='english'; var to='english';
Online Dictionary
Chinese to English English to Chinese ... French to English German to English to Japanese Italian to English Japanese to English to German Latin to English Russian to English ... Swedish to English
If you can't find the translation you need, try our free translation
Axiom Of Choice - English Dictionary
1. Axiom of Choice
A
B C D ... Z
All content on this website is property of LocalTranslation unless stated otherwise.
document.getElementById("generationTime").innerHTML='('+(0.52)+' seconds)'; document.getElementById("generationTime").innerHTML='('+(0.52)+' seconds)';

13. Axiom Of Choice - Wikipedia
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
http://facetroughgemstones.com/wikipedia/ax/Axiom_of_choice.html
Office Supplies Buy Posters A-Z Products Website Advertising ...
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
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. Here the axiom of choice is not needed, you can simply use the rules of formal logic.
2. Let

14. Boxed (Quarter Life Crisis)
link rel= next href= http//earthlingsoft.net/ssp/blog/2004/03/axiom_of_choice title= Axiom of Choice ! eeeeek JavaScript.
http://earthlingsoft.net/ssp/blog/2004/03/boxed
Quarter Life Crisis
The world according to Sven-S. Porst
Main Hall of Best Knowledge available as a book!
[Pre-order with amazon in the USA UK or Germany
Boxed
269 words And that was that. Two mostly fun years in one of the nicest flats. Our building March 08, 2004, 3:22
Add your comment
Remember me You can use to emphasise Markdown offers. Please note that I have to approve your comment before it appears on the site. I will not approve any commercial, vastly off-topic, tasteless or otherwise meaningless comments. Main
Comments on
Commercialism
Shop in my amazon stores with music, books and films mentioned on the site: .com .uk .de
Photos
Categories
Me
This page
People

15. Jakarta Lucene Example - Intranet Server Search Application
The consistency of the axiom_of_choice and of the generalized continuum hypothesis. en/a/x/i/axiom_of_choice Kurt G odel, The consistency of the
http://keywen.com/1.jsp?query=continuum

16. Discrete Mathematics/Axiom Of Choice - Wikibooks, Collection Of Open-content Tex
is the identity (trivial) map. Lemma Every set can be wellordered. Retrieved from http//en.wikibooks.org/wiki/Discrete_mathematics/axiom_of_choice
http://en.wikibooks.org/wiki/Discrete_mathematics/Axiom_of_choice
Discrete mathematics/Axiom of choice
From Wikibooks, the open-content textbooks collection
Discrete mathematics Jump to: navigation search Axiom of choice If is a surjective map, then there exists a map such that is the identity (trivial) map. Lemma: Every set can be well-ordered. Retrieved from " http://en.wikibooks.org/wiki/Discrete_mathematics/Axiom_of_choice Subject Discrete mathematics (book) Views Personal tools Navigation Community Search Toolbox

17. Axiom Of Choice - Wiktionary
Retrieved from http//en.wiktionary.org/wiki/axiom_of_choice . Categories English nouns Set theory Mathematics Logic
http://en.wiktionary.org/wiki/axiom_of_choice
axiom of choice
From Wiktionary
Jump to: navigation search
edit English
Wikipedia has an article on: Axiom of choice Wikipedia
edit Noun
Singular
axiom of choice Plural
uncountable
axiom of choice uncountable
  • set theory The assumption that the direct product of any nonempty family of nonempty sets , is nonempty
  • edit Translations
    Retrieved from " http://en.wiktionary.org/wiki/axiom_of_choice Categories English nouns Set theory ... Logic Views Personal tools Navigation Search Toolbox In other languages

    18. Axiom Of Choice - Interaction-Design.org: A Site About HCI, Usability, UI Design
    URL http//www.interactiondesign.org/dictionary/axiom_of_choice.html. Advertise here.. © Site Copyright/IP Policy Privacy Changelog
    http://www.interaction-design.org/dictionary/axiom_of_choice.html
    About Contact Site map References ... Dictionary Axiom Of Choice
    Axiom Of Choice
    e.g. " user interface"
    Sorry, no results in the dictionary
    If you think you may be able to help us correct this error, please click here to contact the administrator
    Page information
    Page maintainer: The Editorial Team Database provider: The DICT Development Group (dict.org)
    Date created: Not available Date last modified: Not available URL: http://www.interaction-design.org/dictionary/axiom_of_choice.html
    Advertise here..
    Privacy Changelog
    How to help
    ... RSS

    19. Compile With -DP_VERBOSE=1 For Verbose Output. */ /* Compile With
    unrecognized %token sval unsigned_integer %token sval upper_word %token sval AC %token sval AXIOM %token sval axiom_of_choice %token sval
    http://www.soe.ucsc.edu/~avg/TPTPparser/FO/syntaxBNF-1.y
    #include #include AMPERSAND %token CNF %token COLON %token COMMA %token CREATOR %token DDOLLAR %token DESCRIPTION %token EQUALS %token EXCLAMATION %token FOF %token IF %token IFF %token IMPLIES %token INCLUDE %token INFERENCE %token INTRODUCED %token IQUOTE %token LBRKT %token LPAREN %token MINUS %token NAMPERSAND %token NEQUALS %token NIFF %token NVLINE %token PERIOD %token PLUS %token QUESTION %token RBRKT %token REFUTATION %token RPAREN %token STAR %token STATUS %token THEORY %token TILDE %token TOK_FALSE %token TOK_FILE %token TOK_TRUE %token VLINE %token atomic_system_word %token comment %token distinct_object %token lower_word %token real %token signed_integer %token single_quoted %token system_comment %token unrecognized %token unsigned_integer %token upper_word %token AC %token AXIOM %token AXIOM_OF_CHOICE %token CAX %token CEQ %token CONJECTURE %token CSA %token CSB %token CSM %token CSP %token CSR %token CTH %token DEFINITION %token EQUALITY %token EQV %token HYPOTHESIS %token LEMMA %token LEMMA_CONJECTURE %token NEGATED_CONJECTURE %token NOC %token PLAIN %token SAB %token SAM %token SAP %token SAR %token SAT %token TAC %token TAU %token TAUTOLOGY %token THEOREM %token THM %token UNC %token UNKNOWN %token $ = P_BUILD("fof_annotated", P_TOKEN("FOF ", $

    20. Dick/maths/dictionary On Thu Feb 21 143040 PST 2008
    axiom_of_choice logic_30_Sets; axiom_of_choice logic_5_Maps; Axioms intro_logic; axioms math.syntax; AXIOMS_OF_SETS_OF_STRINGS.
    http://www.csci.csusb.edu/dick/maths/dictionary.html

    Page 1     1-20 of 90    1  | 2  | 3  | 4  | 5  | Next 20

    free hit counter