1. Continuum Hypothesis - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/continuum_hypothesis . Categories Forcing Independence results Basic concepts in infinite set theory http://en.wikipedia.org/wiki/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 , about the possible sizes of infinite sets . Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he gave two proofs that the cardinality of the set of integers is strictly smaller than that of the set of real numbers . His proofs, however, give no indication of the extent to which the cardinality of the natural numbers is less than that of the real numbers. Cantor proposed the continuum hypothesis as a possible solution to this question. It states: There is no set whose size is strictly between that of the integers and that of the real numbers. In light of Cantor's theorem that the sizes of these sets cannot be equal, this hypothesis states that the set of real numbers has minimal possible cardinality which is greater than the cardinality of the set of integers. The name of the hypothesis comes from the term the continuum for the real numbers.

2. Continuum Hypothesis In 1874 Georg Cantor discovered that there is more than one level of infinity. The lowest level is called countable infinity; higher levels are known as http://www.daviddarling.info/encyclopedia/C/continuum_hypothesis.html

MATHEMATICS A B C ... CONTACT entire Web this site continuum hypothesis In 1874 Georg Cantor discovered that there is more than one level of infinity . The lowest level is called countable infinity ; higher levels are known as uncountable infinities . The natural numbers are an example of a countably infinite set and the real numbers are an example of an uncountably infinite set. The continuum hypothesis (CH), put forward by Cantor in 1877, says that the number of real numbers is the next level of infinity above countable infinity. It is called the continuum hypothesis because the real numbers are used to represent a linear continuum. Let c be the cardinality of (i.e., number of points in) a continuum, aleph -null, be the cardinality of any countably infinite set, and aleph-one be the next level of infinity above aleph-null. CH is equivalent to saying that there is no cardinal number between aleph-null and c , and that c = aleph-one. CH has been, and continues to be, one of the most hotly pursued problems in mathematics. Related category MATHEMATICS Also on this site: Encyclopedia of History BACK TO TOP var site="s13space1234"

3. Continuum Hypothesis - Wikipedia Retrieved from http//nostalgia.wikipedia.org/wiki/continuum_hypothesis . This page was last modified 2055, 22 August 2001. Content is available under GNU http://nostalgia.wikipedia.org/wiki/Continuum_hypothesis

Continuum hypothesis 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 continuum hypothesis is the hypothesis that there is no set whose cardinality is strictly between that of the integers and that of the real numbers . The real numbers have also been called "the continuum", hence the name.

4. Continuum Hypothesis - Indopedia, The Indological Knowledgebase Retrieved from http//www.indopedia.org/continuum_hypothesis.html . This page has been accessed 2357 times. This page was last modified 1615, http://www.indopedia.org/Continuum_hypothesis.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch Categories Set theory Conjectures ... Wikipedia Article Continuum hypothesis ज्ञानकोश: - The Indological Knowledgebase 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 aleph-null 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 Contents showTocToggle("show","hide") 1 The size of a set 2 Investigating the continuum hypothesis 3 Impossibility of proof and disproof 4 The generalized continuum hypothesis ... edit The size of a set To state the hypothesis formally, we need a definition: we say that two sets

5. Ontinuum Hypothesis http//nostalgia.wikipedia.org/wiki/continuum_hypothesis. continuum hypothesis http//www.factindex.com/c/co/continuum_hypothesis.html http://fastestproxy.com/Continuum_hypothesis

6. Continuum Hypothesis - Wikipedia Continuum hypothesis. In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. Georg Cantor introduced the http://facetroughgemstones.com/wikipedia/co/Continuum_hypothesis.html

Office Supplies Buy Posters A-Z Products Website Advertising ... 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 (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 The real numbers have also been called the continuum , hence the name. 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. If a set S was found that disproved the continuum hypothesis, it would be impossible to make a one-to-one correspondence between

7. Jakarta Lucene Example - Intranet Server Search Application en/c/o/n/continuum_hypothesis The continuum hypothesis postulates that the cardinality of the continuum is equal to which is regular. (bookrags (Web Site) http://keywen.com/1.jsp?query=continuum

8. Anti Philosophy [Archive] - JREF Forum It is thought to be good case of Godel, however http//en.wikipedia. org/wiki/continuum_hypothesis Arguments_for_and_against_CH http://forums.randi.org/archive/index.php/t-103259.html

JREF Forum General Topics Religion and Philosophy PDA View Full Version : Anti philosophy Pages : becomingagodo 10th January 2008, 01:05 PM Philosophy is stupid, I mean really stupid. First off semantics are pointless, I mean really pointless. Philosophy has no system of proof, so you can't say anything in it. Contrast that with science and mathematics, where you can say something. That the point it shallow, structureless. A pointless semantic battle. Even, then trivial. When do you read great philosophical works on Quantum Mechanics? never. Why? because science has surpassed philosophy. Even, then mathematics is the worse place for philosophers. Godel, Godel proves that things are unknowable. Godel proves that mathematics has limits. Godel proves logic is a failure. Lots of people say Godel, which refers to his incompleteness theorems. The sad thing is that Godel theorem doesn't really say that. Even then it debatable if it says anything beyond the branch of mathematics called logic. A good example is the continum hypothesis. It is thought to be good case of Godel, however http://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH it would be a big jump to say it is unprovable.

9. 2006-05-18 Wikipedia/Bellingham_railway_station Bellingham Railway continuum_hypothesis. name. GNU_Free_Documentation_License. name. CategoryCardinal_numbers. cat. CategorySet_theory. cat 1.0 3.061964 8.576805 74.783106 http://www.alvis.info/alvis_docs/wp_18052006/182.xml.gz

10. Continuum Hypothesis - Conservapedia Retrieved from http//www.conservapedia.com/continuum_hypothesis . Category Set theory. Views. Article; talk page; Edit; History. Personal tools http://www.conservapedia.com/Continuum_hypothesis

Continuum hypothesis From Conservapedia Jump to: navigation search The Continuum hypothesis is a conjecture by Georg Cantor which states that there is no set with cardinality greater than all the natural numbers but less than the cardinality of the real numbers (Continuum). The cardinality of such a set would be denoted by the Hebrew letter . Cantor died without knowing the answer to his conjecture. Kurt Godel and Paul Cohen has since shown that the Continuum hypothesis is undecidable in Zermelo-Fraenkel Set Theory. Retrieved from " http://www.conservapedia.com/Continuum_hypothesis Category Set theory Views Article talk page Edit History Personal tools Log in / create account master control Main Page Educational Index Debate Topics Recent changes ... Random page Help Help Index Desk Statistics Conservapedia Commandments Supreme Court Course Info and Enrollment Supreme Court Project Lectures Search edit console What links here Related changes Upload file Special pages ... Permanent link This page was last modified 20:34, 9 March 2008. This page has been accessed 403 times. About Conservapedia

11. Continuum Hypothesis - http//chr.wikigadugi.org/wiki/continuum_hypothesis . Forcing Independence results Basic concepts in infinite set http://chr.wikigadugi.org/wiki/Continuum_hypothesis

12. Continuum Hypothesis | English | Dictionary & Translation By Babylon continuum hypothesis. Dictionary terms for continuum hypothesis in English, English definition for continuum hypothesis, Thesaurus and Translations of http://www.babylon.com/definition/continuum_hypothesis/English

continuum hypothesis Define continuum hypothesis Translate continuum hypothesis continuum hypothesis in Chinese continuum hypothesis in French continuum hypothesis in Italian continuum hypothesis in Spanish ... Download this dictionary Continuum hypothesis In mathematics , the continuum hypothesis (abbreviated CH) is a hypothesis , advanced by Georg Cantor , about the possible sizes of infinite sets . Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he gave two proofs that cardinality of the set of integers is strictly smaller than that of the set of real numbers . His proofs, however, give no indication of the extent to which the cardinality of the natural numbers is less than that of the real numbers. Cantor proposed the continuum hypothesis as a possible solution to this question. It states:There is no set whose size is strictly between that of the integers and that of the real numbers. In light of Cantor's theorem that the sizes of these sets cannot be equal, this hypothesis states that the set of real numbers has minimal possible cardinality. The name of the hypothesis comes from the term the continuum for the real numbers.

13. Wiki Continuum Hypothesis Wiki Continuum hypothesis. Contents 1. As the first Hilbert problem 2. The size of a set 3. Impossibility of proof and disproof (in ZFC) http://wapedia.mobi/en/Continuum_hypothesis

Wiki: Continuum hypothesis Contents: 1. As the first Hilbert problem 2. The size of a set 3. Impossibility of proof and disproof (in ZFC) 4. Arguments for and against CH ... 7. References This article is about a hypothesis in set theory. For the assumption in fluid mechanics, see fluid mechanics Home Licensing Wapedia: For Wikipedia on mobile phones

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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 Continuum hypothesis A Wisdom Archive on Continuum hypothesis Continuum hypothesis A selection of articles related to Continuum hypothesis More material related to Continuum Hypothesis can be found here: Index of Articles related to Continuum Hypothesis Continuum hypothesis Page 2 ARTICLES RELATED TO Continuum hypothesis Continuum hypothesis: Encyclopedia - 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: ... Including: Continuum hypothesis - The size of a set Continuum hypothesis - Impossibility of proof and disproof Continuum hypothesis - Arguments pro and con Continuum hypothesis - The generalized continuum hypothesis Read more here: Continuum hypothesis: Encyclopedia II - Continuum hypothesis - The size of a set See also:

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19. Upto11.net - Wikipedia Article For 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 http://www.upto11.net/generic_wiki.php?q=continuum_hypothesis

20. Sizes Of Infinity Text - Physics Forums Library The continuum hypothesis is undecidable. http//en.wikipedia. org/wiki/continuum_hypothesis Impossibility_of_proof_and_disproof http://www.physicsforums.com/archive/index.php/t-127156.html

Physics Help and Math Help - Physics Forums Science Education PDA View Full Version : sizes of infinity EvLer So we talked about this in class but there's nothing in the textbook. Basically I want to make sure I get this: then there are only 2 sizes of infinity: inifinitely countable and infinitely uncountable. Right? Another question I have is this: can someone give an example when Cantor's diagonalization is applied to countable sets and how it works out.... thanks There are an infinite number of "sizes" of infinity. For example the power set of any set is of strictly greater cardinality, even if the original set is uncountable. Cantor's diagonalization is used only to show that sets are NOT countable. On a countable set you wouldn't be able to find a suitable diagonal not included in the listing. For example if you try the integers, any such diagonalization would be an "infinite digit" integer which doesn't exist. On the rational numbers written as decimals, such a diagonal would be nonrepeating. (Can you prove it directly?) EvLer but what about if the prof on exam asks: is this (whatever) set countable or uncountable.

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