Sci.math FAQ: The Continuum Hypothesis Subject sci.math FAQ The continuum hypothesis; From alopezo@neumann.uwaterloo.ca (AlexLopez-Ortiz); Date Fri, 17 Nov 1995 171559 GMT http://www.uni-giessen.de/faq/archiv/sci-math-faq.ac.continuumhyp/msg00000.html
Extractions: Index Subject : sci.math FAQ: The Continuum Hypothesis From alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Date : Fri, 17 Nov 1995 17:15:59 GMT Newsgroups sci.math sci.answers news.answers Sender news@undergrad.math.uwaterloo.ca (news spool owner) Summary : Part 28 of many, New version, Index: Index sci-math-faq.ac.continuumhyp
Extractions: var GLB_RIS='http://www.economicexpert.com';var GLB_RIR='/cincshared/external';var GLB_MMS='http://www.economicexpert.com';var GLB_MIR='/site/image';GLB_MML='/'; document.write(''); document.write(''); document.write(''); document.write(''); A1('s',':','html'); Non User A B C ... First Prev [ 1 Next Last In mathematics , the continuum hypothesis is a hypothesis about the possible sizes of infinite set s. Georg Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he showed that the set of integer s is strictly smaller than the set of real number s. 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 for 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 To state the hypothesis formally, we need a definition: we say that two sets
Extractions: Normal Nonmetrizable Moore Space from Continuum Hypothesis or Nonexistence of Inner Models with Measurable Cardinals William G. Fleissner Assuming the continuum hypothesis, a normal nonmetrizable Moore space is constructed. This answers a question raised by F. B. Jones in 1931, using an axiom well known at that time. For the construction, a consequence of the continuum hypothesis that also follows from the nonexistence of an inner model with a measurable cardinal is used. Hence, it is shown that to prove the consistency of the statement that all normal Moore spaces are metrizable one must assume the consistency of the statement that measurable cardinals exist.
Continuum Hypothesis There is also a generalization of the continuum hypothesis called the generalized If a set S was found that disproved the continuum hypothesis, http://www.teachersparadise.com/ency/en/wikipedia/c/co/continuum_hypothesis.html
Extractions: Free Teacher Resources First Time Visitors Gift Certificates Education Directory ... Edit this page 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 (naively: whole numbers) is strictly smaller than the set of real numbers (naively: infinite decimals) 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 for 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 , which is described at the end of this article. Table of contents showTocToggle("show","hide")
Continuum Hypothesis A community for everyone interested in science and technology, with science links,forums, news, headlines, quizzes, and reviews. http://www.hypography.com/info.cfm?id=17391
Encyclopaedia Britannica Entry unsolved problems) concerning the truth of the continuum hypothesis.Georg Cantor s continuum hypothesis states that there is no cardinal number between http://www.aam314.vzz.net/EB/Cohen.html
Extractions: Born: April 2, 1934, Long Branch, N.J., U.S. American mathematician who was awarded the Fields Medal in 1966 for his proof of the independence of the continuum hypothesis from the other axioms of set theory. Cohen attended the University of Chicago (M.S., 1954; Ph.D., 1958). He held appointments at the University of Rochester, N.Y. (1957-58), and the Massachusetts Institute of Technology (1958-59) before joining the Institute for Advanced Study, Princeton, N.J. (1959-61). In 1961 he moved to Stanford University in California. Cohen was awarded the Fields Medal at the International Congress of Mathematicians in Moscow in 1966. Cohen solved a problem (first on David Hilbert's influential 1900 list of important unsolved problems) concerning the truth of the continuum hypothesis. Georg Cantor's continuum hypothesis states that there is no cardinal number between and 2 . In 1940 Kurt Gdel had shown that, if one accepts the Zermelo-Fraenkel system of axioms for set theory, then the continuum hypothesis is not disprovable. Cohen, in 1963, showed that it is not provable under these hypotheses and hence is independent of the other axioms. To do this he introduced a new technique known as forcing, a technique that has since had significant applications throughout set theory. The question still remains whether, with some axiom system for set theory, the continuum hypothesis is true. Alonzo Church, in his comments to the Congress in Moscow, suggested that the "Gdel-Cohen results and subsequent extensions of them have the consequence that there is not one set theory but many, with the difference arising in connection with a problem which intuition still seems to tell us must ?really' have only one true solution." After proving his startling result about the continuum hypothesis, Cohen returned to research in analysis.
Extractions: The Continuum hypothesis reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference : snapshots of Wikipedia from wikipedia.org) 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 for 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 , which is described at the end of this article. Table of contents showTocToggle("show","hide")
Program On Computation Prospects Of Infinity - IMS Cantor s continuum hypothesis states that there is no set whose size falls betweenthose of the natural numbers and of the real numbers. http://www.ims.nus.edu.sg/Programs/infinity/
Extractions: (20 Jun - 15 Aug 2005) Organizing Committee Confirmed Visitors Overview Activities ... Membership Application Organizing Committee Confirmed Visitors Overview This two-month program on Computational Prospects of Infinity will focus on recent developments in Set Theory and Recursion Theory, which are two main branches of mathematical logic. Topics for Set Theory will include topics related to Cantor's Continuum Hypothesis (CH), with special attention paid to the importance of the
Encyclopedia: Continuum Hypothesis The continuum hypothesis states the following Mathematics is the study of There is also a generalization of the continuum hypothesis called the http://www.nationmaster.com/encyclopedia/Continuum-hypothesis
Extractions: Related Articles People who viewed "Continuum hypothesis" also viewed: Divides Mojo (sauce) Block error Mundus (Devil May Cry) ... Infinite What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates List of Bugs Bunny cartoons List of Brisbane suburbs Liquid dancing Linda Crockett ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Updated 57 days 11 hours 2 minutes ago. Other descriptions of 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: Mathematics is the study of quantity, structure, space and change. ... A hypothesis (= assumption in ancient Greek) is a proposed explanation for a phenomenon. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ...
