41. Continuum Hypothesis - Sajun.org Translate this page link=http//carriukwzsva.com/carriukwzsva/link, http//iivpjdlnpdot.com/ . http//sajun.org/index.php/continuum_hypothesis http://sajun.org/index.php/Continuum_hypothesis

42. Continuum_hypothesis - By SriLankaDOT.com Sri Lanka Dot .Com provides you any thing your are looking for, We also maintain classified, Sri Lanka news, Sri Lanka picture gallery. http://www.livesrilanka.net/wiki-Continuum_hypothesis

Sri Lanka Entertainment and Information Portal Home Sri Lanka Photos Sri Lanka Tube Sri Lanka News ... Food Recipes Members Login User ID Password Register Forgot password? Important Links India Tube Videos Property Sri Lanka Bollywood Cinema Online Bali Hotels ... Sri Lanka Hotels Mycities Network Continuum hypothesis Continuum hypothesis Continuum hypothesis From Wikipedia, the free encyclopedia Jump to: navigation search This article is about a hypothesis in set theory. For the assumption in fluid mechanics, see fluid mechanics In mathematics , the continuum hypothesis (abbreviated CH ) is a hypothesis , advanced by Georg Cantor in 1877, about the possible sizes of infinite sets . It states: There is no set whose cardinality is strictly between that of the integers and that of the real numbers. Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's twenty-three problems presented in the year 1900. The contributions of Kurt G枚del in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo鈥揊raenkel set theory , the standard foundation of modern mathematics, provided ZF set theory is consistent The name of the hypothesis comes from the term the continuum for the real numbers.

43. Continuum Hypothesis In English - Dictionary And Translation Continuum hypothesis. Dictionary terms for Continuum hypothesis in English, English definition for Continuum hypothesis, Thesaurus and Translations of Continuum hypothesis to http://www.babylon.com/definition/Continuum_hypothesis/English

44. 连续统假设_百度百科 Translate this page 2010 5 16 continuum hypothesis CH http//en.wikipedia.org/wiki/continuum_hypothesis http://baike.baidu.com/view/150466.htm

连续统假设（continuum hypothesis），数学上关于连续统势的假设。 常记作CH。 　　2000多年来，人们一直认为任意两个无穷集都一样大。直到1891年，G.康托尔证明：任何一个集合的 　　1938年，K.哥德尔证明了CH对ZFC公理系统（见 )是协调的，1963年，P.J.科恩证明CH对ZFC公理系统是独立的，是不可能判定真假的。这样，在ZFC公理系统中，CH是不可能判定真假的。这是60年代 还把无穷基数按照从小到大的次序排列为s╲s0，s╲s1，…s╲sa……其中a为任意序数，康托尔猜想，2s╲s0=s╲s1。这就是著名的连续统假设（简记CH）。一般来说，对任意序数a，断定2s╲sa=s╲sa+1成立，就称为广义连续统假设（简记GCH）。在ZF中，CH和选择公理（简记AC）是互相独立的，但是由GCH可以推出AC。ZF加上可构造性公理(简记V=L)就可以推出GCH，当然也能推出CH和AC。 http://en.wikipedia.org/wiki/Continuum_hypothesis http://en.wikipedia.org/wiki/Continuum_hypothesis nslog.set("ext-reference",1); nslog.set("module-tag",1); 百科ROBOT IQ都被注册了 mcgrandymcz

45. Cardinality Of All Cardinalities - Mathematics - Stack Exchange If (CH)en.wikipedia.org/wiki/continuum_hypothesis is false (i.e. not accepted as an axiom it is neither provable nor disprovable in set http://math.stackexchange.com/questions/1467/cardinality-of-all-cardinalities

46. The Natural Order Hypothesis Feb 24, 2010 Learning Spanish The Natural Order Hypothesis. Views 0 Downloads 0. continuum_hypothesis. Views 19 Downloads 1 http://www.docstoc.com/docs/26444928/The-Natural-Order-Hypothesis

47. Moti Gitik | Facebook Translate this page /li li The a href= http//en.wikipedia.org/wiki/continuum_hypothesis class= wikipedia GCH /a holds below and 2 = +2. http://id-id.facebook.com/pages/Moti-Gitik/111124515605511?v=info&viewas=0

48. Continuum_Hypothesis - By SriLankaDOT.com Sri Lanka Dot .Com provides you any thing your are looking for, We also maintain classified, Sri Lanka news, Sri Lanka picture gallery. http://www.srilankadot.com/wiki-Continuum_Hypothesis

Sri Lanka Entertainment and Information Portal Home Sri Lanka Photos Sri Lanka Tube Sri Lanka News ... Food Recipes Members Login User ID Password Register Forgot password? Important Links India Tube Videos Property Sri Lanka Bollywood Cinema Online Bali Hotels ... Sri Lanka Hotels Mycities Network Continuum Hypothesis Continuum Hypothesis Continuum hypothesis From Wikipedia, the free encyclopedia 聽聽(Redirected from Continuum Hypothesis Jump to: navigation search This article is about a hypothesis in set theory. For the assumption in fluid mechanics, see fluid mechanics In mathematics , the continuum hypothesis (abbreviated CH ) is a hypothesis , advanced by Georg Cantor in 1877, about the possible sizes of infinite sets . It states: There is no set whose cardinality is strictly between that of the integers and that of the real numbers. Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's twenty-three problems presented in the year 1900. The contributions of Kurt G枚del in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo鈥揊raenkel set theory , the standard foundation of modern mathematics, provided ZF set theory is consistent The name of the hypothesis comes from the term the continuum for the real numbers.

49. Hip贸tesis De La Serie Continua Translate this page En matem醫icas, hip髏esis de la serie continua (abreviado CH) es a hip髏esis, avanzado cerca Cantor de Georg, sobre los tama駉s posibles de infinito http://www.worldlingo.com/ma/enwiki/es/Continuum_hypothesis

Archivo multi-idioma Accionado por WorldLingo Hip贸tesis de la serie continua P谩gina principal 脥ndice multiling眉e del archivo Elija su lengua: English Italiano Deutsch Nederlands ... Svenska var addthis_pub="anacolta"; Hip贸tesis de la serie continua Este art铆culo est谩 sobre una hip贸tesis en teor铆a determinada. Para la asunci贸n en los mec谩nicos fl煤idos, vea mec谩nicos fl煤idos En matem谩ticas hip贸tesis de la serie continua (abreviado CH ) es a hip贸tesis , avanzado cerca Cantor de Georg , sobre los tama帽os posibles de infinito sistemas . El Cantor introdujo el concepto de cardinality comparar los tama帽os de sistemas infinitos, y lo dio a dos pruebas esas el cardinality del sistema de n煤meros enteros es terminantemente m谩s peque帽o que el del sistema de n煤meros verdaderos . Sus pruebas, sin embargo, no dan ninguna indicaci贸n del grado a el cual el cardinality de los n煤meros naturales es menos que el de los n煤meros verdaderos. El Cantor propuso la hip贸tesis de la serie continua como soluci贸n posible a esta pregunta. Indica: No hay sistema que tama帽o est谩 terminantemente entre el de los n煤meros enteros y el de los n煤meros verdaderos.

50. Infinite Ink: The Continuum Hypothesis By Nancy McGough History, mathematics, metamathematics, and philosophy of Cantor s Continuum Hypothesis. http://www.ii.com/math/ch/

mathematics T HE C ONTINUUM H YPOTHESIS By Nancy McGough nm noadsplease.ii.com Overview 1.1 What is the Continuum Hypothesis? 1.2 Current Status of CH Alternate Overview Assumptions, Style, and Terminology 2.1 Assumptions 2.1.1 Audience Assumptions 2.1.2 Mathematical Assumptions 2.2 Style 2.3 Terminology 2.3.1 The Word "continuum" 2.3.2 Ordered Sets 2.3.3 More Terms and Notation Mathematics of the Continuum and CH 3.1 Sizes of Sets: Cardinal Numbers aleph c aleph 3.1.2 CH and GCH 3.1.3 Sample Cardinalities 3.2 Ordering Sets: Ordinal Numbers 3.3 Analysis of the Continuum 3.3.1 Decomposing the Reals 3.3.2 Characterizing the Reals 3.3.3 Characterizing Continuity 3.4 What ZFC Does and Does Not Tell Us About c Metamathematics and CH 4.1 Consistency, Completeness, and Compactness of ... 4.1.1 a Logical System 4.1.2 an Axiomatic Theory 4.2 Models of ... 4.2.1 Real Numbers 4.2.2 Set Theory 4.2.2.1 Inner Models 4.2.2.2 Forcing and Outer Models 4.3 Adding Axioms to Zermelo Fraenkel Set Theory 4.3.1 Axioms that Imply CH or GCH 4.3.1.1 Explicitly Adding CH or GCH 4.3.1.2 V=L: Shrinking the Set Theoretic Universe

51. Continuum Hypothesis - Article And Reference From OnPedia.com In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. http://www.onpedia.com/encyclopedia/continuum-hypothesis

Continuum Hypothesis In mathematics , the continuum hypothesis is a hypothesis about the possible sizes of infinite sets Georg Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he showed that the set of integers is strictly smaller than the set of real numbers . The continuum hypothesis states the following: There is no set whose size is strictly between that of the integers and that of the real numbers. Or mathematically speaking, noting that the cardinality for the integers is aleph-null ") and the cardinality of the real numbers is , the continuum hypothesis says: The real numbers have also been called the continuum , hence the name. There is also a generalization of the continuum hypothesis called the generalized continuum hypothesis The size of a set To state the hypothesis formally, we need a definition: we say that two sets S and T have the same cardinality or cardinal number if there exists a bijection . Intuitively, this means that it is possible to "pair off" elements of S with elements of T in such a fashion that every element of S is paired off with exactly one element of T integers or rational numbers , things are more complicated to show. Consider the set of all rational numbers. One might naively suppose that there are more rational numbers than integers, and fewer rational numbers than real numbers, thus disproving the continuum hypothesis. However, it turns out that the rational numbers can be placed in one-to-one correspondence with the integers, and therefore the set of rational numbers is the same size as the set of integers: they are both

52. Continuum Hypothesis -- From Wolfram MathWorld The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the small infinite set of integers aleph_0 and the large http://mathworld.wolfram.com/ContinuumHypothesis.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations Continuum Hypothesis The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers and the "large" infinite set of real numbers (the " continuum "). Symbolically, the continuum hypothesis is that . Problem 1a of Hilbert's problems asks if the continuum hypothesis is true. contradiction would arise if the continuum hypothesis were added to conventional Zermelo-Fraenkel set theory . However, using a technique called forcing , Paul Cohen (1963, 1964) proved that no contradiction would arise if the negation of the continuum hypothesis was added to set theory set theory being used, and is therefore undecidable (assuming the Zermelo-Fraenkel axioms together with the axiom of choice Conway and Guy (1996, p. 282) recount a generalized version of the continuum hypothesis originally due to Hausdorff in 1908 which is also undecidable : is for every ? The continuum hypothesis follows from generalized continuum hypothesis, so

53. Ernst Friedrich Ferdinand Zermelo Describes educational background and motivation towards working on set theory and the continuum hypothesis. Page lists other major contributions made by this person. http://www.stetson.edu/~efriedma/periodictable/html/Zr.html

Ernst Friedrich Ferdinand Zermelo Ernst Zermelo's father was a college professor, so Zermelo was brought up in a family where academic pursuits were encouraged. He graduated from gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities, and that is what Zermelo did. He studied at Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius, Lazarus, Fuchs, Planck, Schmidt, and Schwarz. Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation on the calculus of variations. In this thesis he extended Weierstrass's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves. After the award of his doctorate, Zermelo remained at the University of Berlin where he was appointed assistant to Planck who held the chair of theoretical physics there. At this stage Zermelo's work was turning more towards areas of applied mathematics and, under Planck's guidance, he began to work for his habilitation thesis studying hydrodynamics.

54. Continuum Hypothesis: Definition From Answers.com The conjecture that every infinite subset of the real numbers can be put into oneto-one correspondence with either the set of positive integers or the entire set of real numbers. http://www.answers.com/topic/continuum-hypothesis

55. PlanetMath: Continuum Hypothesis The continuum hypothesis states that there is no cardinal number $\kappa$ such that $\aleph_0 \kappa 2^{\aleph_0}$ An equivalent statement is that $\aleph_1 =2^{\aleph_0}$ http://planetmath.org/encyclopedia/CH.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclop忙dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About continuum hypothesis (Axiom) The continuum hypothesis states that there is no cardinal number such that An equivalent statement is that It is known to be independent of the axioms of ZFC The continuum hypothesis can also be stated as: there is no subset of the real numbers which has cardinality strictly between that of the reals and that of the integers . It is from this that the name comes, since the set of real numbers is also known as the continuum. "continuum hypothesis" is owned by rspuzio full author list owner history view preamble ... get metadata View style: jsMath HTML HTML with images page images TeX source See Also: axiom of choice Zermelo-Fraenkel axioms generalized continuum hypothesis Other names: CH Also defines: continuum Log in to rate this entry.

56. Conference In Honor Of D. A. Martin S 60th Birthday Held in coordination with the Mathematical Sciences Research Institute workshop on The Continuum Hypothesis. University of California, Berkeley, CA, USA; 2728 May 2001. http://www.math.berkeley.edu/~steel/martin.html

Conference in Honor of D. A. Martin's 60th Birthday May 27 - 28, 2001 The University of California, Berkeley Organizers: Stephen Jackson , University of North Texas, Denton, jackson@jove.acs.unt.edu John R. Steel , University of California, Berkeley, steel@math.berkeley.edu W. Hugh Woodin , University of California, Berkeley, woodin@math.berkeley.edu Presented under the auspices of the The University of California and in coordination with the Mathematical Sciences Research Institure workshop The Continuum Hypothesis The conference focused on topics close to Martin's work. Here is the meeting schedule, with copies of the speakers' presentations, as available. May 27, morning 8:45-9:30 : Coffee, etc. in 1015 Evans 9:30-10:30 : Theodore Slaman, University of California, Berkeley, ``High'' is definable in the partial order of the Turing degrees of the recursively enumerable sets, abstract and slides of talk 10:30-11:00 : Coffee, etc. in 1015 11:00-12:00 : Stephen Jackson, University of North Texas, A survey of the inductive analysis of L(R) assuming determinacy slides of talk 12:00-2:00 : Lunch May 27, afternoon

57. The Continuum Hypothesis The Continuum Hypothesis. Cesare Brazza History of Mathematics Rutgers, Spring 2000 Infinity is up on trial (Bob Dylan, Visions of Johanna, cited in In the Light of Logic), pg. 28 http://www.math.rutgers.edu/~cherlin/History/Papers2000/brazza.html

The Continuum Hypothesis Cesare Brazza History of Mathematics Rutgers, Spring 2000 "Infinity is up on trial..." (Bob Dylan, Visions of Johanna , cited in In the Light of Logic ), pg. 28. These five words suffice to summarize the essence of Cantor's work. Cantor was tormented by opposition throughout his career. After conceiving and then proving his theorems on infinite sets, Cantor struggled against the negative reactions of his peers. It was not until the end of his lifetime that Cantor received the recognition he deserved. Cantor, a devout Christian, always held to his beliefs because to him, they came directly from G-d. "Where G-d was concerned, it was impossible to entertain hypotheses. There were no alternatives to be considered" (p. 238, Georg Cantor ). Georg Ferdinand Ludwig Philipp Cantor contributed greatly not only to discrete mathematics, but to every science based in mathematics. "Whatever the disappointments Cantor was to suffer, his transfinite set theory represented a revolution in the history of mathematics. Not a revolution in the sense of returning to ear lier starting points, but more a revolution in the sense of overthrowing older, established prejudices against the infinite in any actual, completed form." (Pg. 118, Georg Cantor). With his theory of sets and his introduction of the concept of infinite nu mbers, Cantor broke through the barriers of previous generations, and has allowed for the further exploration of areas that were previously unattainable.

58. MSRI - The Continuum Hypothesis A workshop featuring a number of lectures surveying the current insights into the continuum problem and its variations. MSRI, Berkeley, CA, USA; 29 May 1 June 2001. http://www.msri.org/calendar/workshops/WorkshopInfo/94/show_workshop

Sign In Home Scientific Programs ... Federal Support For Scientists Programs Workshops Workshops Home All Upcoming Workshops ... Workshops Search for Events By Title or Description: After: Before: Main Participants Wiki Discussions The Continuum Hypothesis May 29, 2001 to June 1, 2001 Hugh Woodin and John Steel Tags: Continuum Continuum Hypothesis The Continuum Hypothesis The Continuum Hypothesis The Continuum Hypothesis The Continuum Hypothesis Hypothesis The Continuum Hypothesis The Continuum Hypothesis The Continuum Hypothesis The Continuum Hypothesis The workshop will feature a number of lectures surveying the current insights into the continuum problem and its variations. Group Photo Group Photo (larger version) Register Registration: Please register by the deadline of Fri, Jun 01 2001 if possible. Funding: Please see Travel funding rules Important: Airline travel reimbursement restrictions If you are applying for funding , the funding deadline is Fri, Jun 01 2001 Lodging information Visa information Directions to MSRI Schedule Tuesday, May 29, 2001

59. Continuum Hypothesis (mathematics) -- Britannica Online Encyclopedia continuum hypothesis (mathematics), statement of set theory that the set of real numbers (the continuum) is in a sense as small as it can be. In 1873 the German mathematician Georg http://www.britannica.com/EBchecked/topic/135171/continuum-hypothesis

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. continuum-hypothesis My Britannica CREATE MY continuum hy... NEW ARTICLE ... SAVE continuum hypothesis Table of Contents: continuum hypothesis Article Article Related Articles Related Articles External Web sites External Web sites Citations Article Related Articles External Web sites Citations Primary Contributor: Herbert Enderton ARTICLE from the continuum hypothesis statement of set theory that the set of real number s (the continuum) is in a sense as small as it can be. In 1873 the German mathematician Georg Cantor infinity than the counting numbers infinite sets according to the number of its elements, or its

60. The Continuum Hypothesis, Part II, Volume 48, Number 7 A UGUST 2001 N OTICES OF THE AMS 681 The Continuum Hypothesis, Part II W. Hugh Woodin Introduction In the first part of this article, I identified the corr ect axioms for the http://www.ams.org/notices/200107/fea-woodin.pdf

Page 3     41-60 of 95    Back | 1  | 2  | 3  | 4  | 5  | Next 20