61. Axiom Of Choice And Something I Find To Not Be Logical - Physics Help And Math H Reload this Page axiom of choice and something I find to not be logical. User Name, Remember Me? Password, http://www.physicsforums.com/showthread.php?t=23458

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Physics Help and Math Help - Physics Forums Mathematics View Thread : Axiom of Choice and something I find to not be logical Axiom of Choice and something I find to not be logical Ed Quanta I heard something along the lines of when you accept the axiom of choice as true, you can then prove using some abstract set theory that by dividing a sphere, you can divide it and then put it together so that it is bigger than it originally was Is the math behind this proof difficult? And is this true? Register Now! Free! Talk Science! quartodeciman http://www.kuro5hin.org/story/2003/5/23/134430/275 search "Banach-Tarski" for more stuff. http://www.ams.org/new-in-math/mathdigest/200112-choice.html Register Now! Free! Talk Science! Hurkyl IIRC, the proof uses surgery theory. One of the main things to emphasize about the construction is that its intermediate steps involve sets that are not measurable. All of the clever work is done with sets for which you cannot define volume, so there isn't any reason to expect that you have the original volume when you're done. And, incidentally, the big point about the construction is that it only uses five pieces. It's a trivial exercise to prove that you can rearrange all of the points in one sphere to form two spheres of the same size, if you do it one point at a time.

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66. Powell's Books - Consistency Of The Axiom Of Choice And Of The Generalized Conti Consistency of the axiom of choice and of the Generalized ContinuumHypothesis with the Axioms of Set Theory by Kurt Gödel. Available at Beaverton, Technical. http://www.powells.com/cgi-bin/biblio?inkey=4-0691079277-0

67. Axiom Of Choice By Julio Gonzalez Cabillon axiom of choice by Julio Gonzalez Cabillon. reply to this message post a message on a new topic Back to mathhistory-list Subject http://mathforum.org/epigone/math-history-list/nayglingthun

Axiom of Choice by Julio Gonzalez Cabillon reply to this message post a message on a new topic Back to math-history-list Subject: Axiom of Choice Author: jgc@adinet.com.uy Date: The Math Forum

68. Axiom Of Choice By Mike Mirarchi axiom of choice by Mike Mirarchi. reply to this message post a message on a new topic Back to alt.math.undergrad Subject Axiom of http://mathforum.org/epigone/alt.math.undergrad/dilbrumphox

Axiom of Choice by Mike Mirarchi reply to this message post a message on a new topic Back to alt.math.undergrad Subject: Axiom of Choice Author: mike@condor.sccs.swarthmore.edu Organization: Swarthmore College Date: 20 Jan 1997 21:51:06 GMT I'm an undergraduate writing a paper on the axiom of choice. I was wondering if anyone could point me to results which are weird or counterintuitive consequences of the axiom (apart from the Banach-Tarski paradox). Any suggestions would be greatly appreciated. Mike Mirarchi mike@sccs.swarthmore.edu The Math Forum

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76. Zermelo Theorem And Axiom Of Choice Association of Mizar Users. Zermelo Theorem and axiom of choice. Grzegorz Bancerek Warsaw University, Bialystok. Summary. The article is http://mizar.uwb.edu.pl/JFM/Vol1/wellord2.html

Journal of Formalized Mathematics Volume 1, 1989 University of Bialystok Association of Mizar Users Zermelo Theorem and Axiom of Choice Grzegorz Bancerek Warsaw University, Bialystok Summary. The article is continuation of [ ] and [ ], and the goal of it is show that Zermelo theorem (every set has a relation which well orders it - proposition (26)) and axiom of choice (for every non-empty family of non-empty and separate sets there is set which has exactly one common element with arbitrary family member - proposition (27)) are true. It is result of the Tarski's axiom A introduced in [ ] and repeated in [ ]. Inclusion as a settheoretical binary relation is introduced, the correspondence of well ordering relations to ordinal numbers is shown, and basic properties of equinumerosity are presented. Some facts are based on [ MML Identifier: The terminology and notation used in this paper have been introduced in the following articles [ Contents (PDF format) Bibliography 1] Grzegorz Bancerek. The ordinal numbers Journal of Formalized Mathematics 2] Grzegorz Bancerek. The well ordering relations Journal of Formalized Mathematics 3] Czeslaw Bylinski.

77. Re: Axiom Of Choice & QM Re axiom of choice QM. Subject I ve gotten into some tussles with mathematicians on the axiom of choice and physics. Anyway Although http://www.lns.cornell.edu/spr/2000-01/msg0020712.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Subject From Date : 04 Jan 2000 00:00:00 GMT Approved : spr@rosencrantz.stcloudstate.edu (sci.physics.research) Newsgroups : sci.physics.research Organization : (none) References Follow-Ups From: toby@ugcs.caltech.edu (Toby Bartels) From: Prev by Date: Re: Measurement and Observers Next by Date: Re: gravitational wave detection Prev by thread: ADMINISTRIVIA: Welcome to sci.physics.research! Next by thread: Index(es): Date Thread

78. Re: Axiom Of Choice & QM Index Re axiom of choice QM. Subject critiqued. Traditionally the axiom of choice is needed for infinite sets, agreed. However http://www.lns.cornell.edu/spr/2000-01/msg0020753.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Subject From Date : 06 Jan 2000 00:00:00 GMT Approved : spr@rosencrantz.stcloudstate.edu (sci.physics.research) Newsgroups : sci.physics.research Organization : Clef Digital Systems Ltd References 3871CAB8.E2C80A91@ecologic.net 3871CAB8.E2C80A91@ecologic.net Follow-Ups From: From: toby@ugcs.caltech.edu (Toby Bartels) References From: Prev by Date: Re: C*-algebras Next by Date: Re: Measurement and Observers Prev by thread: Next by thread: Index(es): Date Thread

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Support Ink 19 click our sponsors' links! ( Advertising Info Search Contest Win Counting Crows Stuff! August 2000 Ink Spots Live Ink ... Bonfire Madigan x-Reference Axiom Of Choice Axiom Of Choice Niya Yesh Narada World Recorded in Iran, India, and the U.S., Niya Yesh ("gnosis" in Greek) is dedicated to "those contemplative moments in life that make everything worthwhile." The album more than lives up to its dedication; it is deeply peaceful, restful, and meditative, though it has its moments of cascading danceable rhythms as well. Building on the core of Loga Ramin Torkian's classical Persian and flamenco guitar and unique quarter-tone guitar and Mamak Khadem's richly expressive Persian vocals, Axiom Of Choice extends its reach on Niya Yesh to encompass the sounds of many cultures, from Middle Eastern ney and kamancheh fiddle to the more familiar cello and accordion. Overall, the feel is mostly classical, in the Western sense, though the intricate drum rhythms and other percussion cast a definite Eastern accent over many tracks. I especially enjoyed "Prelude," with its lovely guitar and cello duet, joined for the last part of the track by hand drums and shakers. The nine-minute-plus "Calling," with its underlying drone, mournful kamancheh, and very gentle female vocals, feels a lot like a deeply moving lament until a skirling drone and swift-tattooed hand drum beats spin the track into a dance-frenzy, ending with Khadem's wild siren song. But probably my favorite track is "Raindrops," which begins almost like a lullaby with quiet solo guitar, joined soon by Khadem's exquisitely pure and vulnerable voice in an elegantly simple arrangement that evokes the calming sound of endless raindrops falling outside the window, chased down the panes by the high and sweet tones of the kamancheh.

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