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# Topic: Lemma

###### In the News (Thu 21 Mar 19)

 Five lemma   (Site not responding. Last check: 2007-10-12) The five lemma can be thought of as a combination of two other theorems, the four lemmas, which are dual[?] to each other. The five lemma states that, if the rows are exact, m and p are isomorphisms, l is an epimorphism, and q is a monomorphism, then n is also an isomorphism. To perform diagram chasing, we assume that we are in a category of modules over some ring, so that we may speak of elements of the objects in the diagram and think of the morphisms of the diagram as functions (in fact, homomorphisms) acting on those elements. www.ebroadcast.com.au /lookup/encyclopedia/fi/Five_lemma.html   (606 words)

 Pumping lemma   (Site not responding. Last check: 2007-10-12) In the theory of formal languages, the pumping lemmas provide necessary conditions for languages to be regular or context-free. One can say therefore that 'pumping lemma' is a name for the application of the pigeonhole principle, in the context of a finite state machine. The proof idea for the pumping lemma is as follows: the regular language is accepted by a certain deterministic finite acceptor; every string that's longer than the number m of states of that acceptor will revisit a certain state, thereby causing a loop which can be repeated; the loop corresponds to the string y. www.ebroadcast.com.au /lookup/encyclopedia/pu/Pumping_lemma.html   (316 words)

 NationMaster - Encyclopedia: Gauss lemma In mathematics, there is more than one Gauss lemma; all are named after Carl Friedrich Gauss. In the theory of polynomials, the Gauss lemma relates the highest common factor of a product of two polynomials with integer coefficients to the corresponding hcfs of the factors. The Gauss lemma in number theory is involved in some proofs of quadratic reciprocity. www.nationmaster.com /encyclopedia/Gauss-lemma   (403 words)

 FATOU'S LEMMA : Encyclopedia Entry In mathematics, Fatou's lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of the sequence of integrals of the functions. Fatou's lemma is proved using the monotone convergence theorem, and can be used to prove the dominated convergence theorem. Fatou's lemma is particularly useful in probability theory, in establishing results about the convergence of the expectations of the elements of a sequence of random variables. www.bibleocean.com /OmniDefinition/Fatou's_lemma   (168 words)

 Alles over lemma '''Lemma''' (meervoud ''lemma's'' of ''lemmata'') is het woord waarop een bepaald begrip in een woordenboek of encyclopedie kan worden gezocht. Als zodanig is het lemma dikwijls het eerste, meestal '''vetgedrukte''' woord van de woordenboekopname of het encyclopedie-artikel. *''Lemma'' is ook de gangbare term voor een onderdeel (een kafje) van de bloem van grassen. www.ask-all.nl /lemma.html   (161 words)

 Kids.Net.Au - Encyclopedia > Ultrafilter lemma   (Site not responding. Last check: 2007-10-12) Proving the lemma from the axiom of choice is an application of Zorn's Lemma, and is fairly standard as these things go. This proof uses Zorn's Lemma, which is equivalent to the axiom of choice. The Ultrafilter Lemma cannot be proven from ZF (the Zermelo-Fraenkel axioms) alone, and it cannot be used to prove the axiom of choice, so it is properly weaker. www.kids.net.au /encyclopedia-wiki/ul/Ultrafilter_lemma   (250 words)

 Gauss lemma   (Site not responding. Last check: 2007-10-12) In mathematics, there is more than one Gauss lemma ; all are named after Carl Friedrich Gauss. In the theory of polynomial s, the Gauss lemma relates the highest common factor of a product of two polynomials with integer coefficient s to the corresponding hcfs of the factors. For any odd prime p let a be an integer that is relatively prime to p. www.serebella.com /encyclopedia/article-Gauss_lemma.html   (452 words)

 PlanetMath: Gauss's lemma II Remark: Another result with the same name is Gauss' lemma on quadratic residues. Cross-references: quadratic residues, Gauss lemma, Gauss's lemma I, reducible, field of fractions, Gauss, unit, divisible, UFD, polynomial This is version 10 of Gauss's lemma II, born on 2002-11-04, modified 2006-10-10. www.planetmath.org /encyclopedia/GaussLemmaII.html   (108 words)

 Lemma Lemma last appeared in the top thousand girl or boy names during 1891, the last year shown on the table. During the last 125 years, parents have used Lemma as a girl's name nearly 100% of the time and almost never as a boy's name. Cumulative counts and total counts shown on the above tables are slightly lower than actual counts because the name Lemma appears in the top 1,000 girl names only 116 times during the last 125 years. www.baby-girl-names.org /l/lemma.htm   (266 words)

 Definition of Snake lemma In mathematics, particularly homological algebra, the snake lemma, a statement valid in every Abelian category, is the crucial tool used to construct the long exact sequences that are ubiquitous in homological algebra and its applications, for instance in algebraic topology. The maps between the kernels and the maps between the cokernels are induced in a natural manner by the given (horizontal) maps because of the diagram's commutativity. The important statement of the lemma is that a connecting homomorphism d exists which completes the exact sequence. www.wordiq.com /definition/Snake_lemma   (551 words)

 The Dispatch - Serving the Lexington, NC - News Lemma (mathematics), a proven statement used as a stepping-stone toward the proof of another statement Lemma (linguistics), the canonical form of a word Lemma (logic), which is simultaneously a premise for a contention above it and a contention for premises below it www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=lemma   (94 words)

 Nine lemma   (Site not responding. Last check: 2007-10-12) In mathematics, the Nine Lemma is a statement about commutative diagram s and exact sequence s valid in any abelian category, as well as in the category of group s. It states: if : is a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well. The Nine Lemma can be proved by direct diagram chasing, or by applying the snake lemma (to the two bottom rows in the first case, and to the two top rows in the second case). www.serebella.com /encyclopedia/article-Nine_lemma.html   (204 words)

 Daniel Lemma - Music Downloads - Online Bio: Lemma first became known to a wider audience in 2000 when he provided the soundtrack for Josef Fares' film Jalla Jalla. But before this, Lemma had both recorded an album that was not released, and lead the bands Mo Blues and Mo Funk. Here, he was contacted by Josef Fares and agreed on writing the music for his film, and the next year Morning Train was released, produced by Lemma himself and using many of the musicians he had played with in his other bands, among them bassist Stefan Wingefors and guitarist Mats Eriksson. musicstore.connect.com /artist/345/Daniel-Lemma/12106345.html   (275 words)

 Lemma II - Memory Alpha, the Star Trek Wiki Lemma II is the location of a Federation colony. In 2368, an experimental facility was installed on the planet to create a scattering field to dissipate a soliton wave from Bilana III, a planet located about three lightyears away. After the wave had gotten out of control, it massively increased in velocity and energy level, threatening to destroy the colony and take most of Lemma II with it. www.memory-alpha.org /en/wiki/Lemma_II   (105 words)

 Title page for ETD etd-04282003-101336 The pumping lemma for regular languages and its application are among the more dicult concepts students encounter in an introductory theory of computing course. The pumping lemma is used to prove that particular languages are not regular. The pumping lemma animator will be included in an ongoing project designed to create animations and interactive tools for a complete course on theory of computing. www.montana.edu /etd/available/cogliati_0805.html   (443 words)

 Aklilu Lemma and Legesse Wolde-Yohannes - Ethiopia - 1989 Right Livelihood Award Recipient   (Site not responding. Last check: 2007-10-12) In 1964 a young Ethiopian doctor, Aklilu Lemma, discovered that suds from the fruit of a common African plant, the endod or soapberry, which African women have used as soap for centuries, act as a potent molluscicide. In the last few years, however, Lemma's and Wolde-Yohannes' persistence and the support of key scientists and donors in the West has opened the door to the necessary laboratory and field trials. Following collaboration with Lemma, the University of Toledo, USA, was granted a US patent on an endod-based molluscicide intended to control the zebra mussels which have recently invaded American lakes and caused extensive damage to water supplies. www.rightlivelihood.org /recip/lemma.htm   (527 words)

 PlanetMath: Gauss' lemma The product is nonzero, hence can be cancelled, yielding the proposition. It is possible to prove Gauss' Lemma or Proposition 2 “from scratch”, without leaning on Euler's criterion, the existence of a primitive root, or the fact that a polynomial over This is version 11 of Gauss' lemma, born on 2002-02-14, modified 2006-12-22. www.planetmath.org /encyclopedia/GaussLemma.html   (163 words)

 Zorn's lemma   (Site not responding. Last check: 2007-10-12) Lemma 2..4 (Zorn's lemon) Let X be a poset. Zorn's lemma needs no proof since this statement is equivalent to Axiom of Choice. Lemma 2..5 Every module M over a division ring D is free. www.maths.warwick.ac.uk /~rumynin/rings2002/ln/node17.html   (75 words)

 Voorwaarden   (Site not responding. Last check: 2007-10-12) De redactie kan in overleg met de auteur wijzigingen in de tekst van het lemma aanbrengen. De auteur, van wie de naam onder het lemma wordt vermeld, verklaart dat hij/zij geen auteursrecht of enig ander recht van derden schendt en dat het lemma niets bevat dat in strijd is met de wet. De auteur ontvangt voor het door hem/haar geschreven lemma eenmalig een tevoren overeengekomen onkostenvergoeding, die onmiddellijk na goedkeuring en afhandeling van het lemma zal worden uitbetaald door het genoemde Instituut voor Nederlandse Geschiedenis. www.inghist.nl /Nieuws/Actueel/Onderzoek/Projecten/DVN/voorwaardenauteurs   (238 words)

 LEMMA - Lerntheoretische Entwicklung multimedialer Anwendungen LEMMA ist ein Beratungs- und Weiterbildungssystem zur Ausbildung von Multimedia-Autoren und Multimedia-Anwendern. LEMMA gibt eine Einführung in die lerntheoretischen Grundlagen multimedialer Anwendungen und macht den Mehrwert multimedialer Lernprogramme deutlich. LEMMA ist ein Werkzeugsystem, dass dem Anwender die kreative Umsetzung lerntheoretischer Prinzipien und innovativer didaktischer Konzepte ermöglicht. www.uni-koeln.de /phil-fak/paedsem/psych/mm_prod/lemma/index.html   (295 words)

 The Short Five Lemma and the Five Lemma The short five lemma says that β is injective when α and γ are injective. The five lemma (proved below) is a generalization of the short five lemma, and this step of the proof will have to be modified. The short five lemma can be generalized to five modules, top and bottom, with 5 homomorphisms connecting corresponding modules and forming a commutative diagram. www.mathreference.com /mod-hom,5lemma.html   (744 words)

 LEMMA-INSTANCE.html -- ACL2 Version 3.0 A lemma instance denotes a formula which is either known to be a theorem or which must be proved to be a theorem before it can be used. To use a lemma instance in a particular subgoal, the theorem prover adds the formula as a hypothesis to the subgoal before the normal theorem proving heuristics are applied. 's in constraints that ``support'' the lemma to be functionally instantiated; see constraint. www.cs.utexas.edu /users/moore/acl2/v3-0/LEMMA-INSTANCE.html   (576 words)

 Corpora Nov 1999 to Dec 1999: RE: Corpora: lemma vs lexeme lemma can take to represent a `word' in all its inflected forms. In an English lemma lexicon, the lemma is given in the form points, then they are considered as belonging to one lemma. torvald.aksis.uib.no /corpora/1999-4/0038.html   (490 words)

 Diskussion:Lemma   (Site not responding. Last check: 2007-10-12) Dez 2003 (CET) Das Lemma von Zorn ist entgegen seines Namens ein Axiom. Das Lemma von Zorn z.B. heisst Lemma, weil es als Hilfssatz gebraucht wird, es ist aber nicht unwichtig ("minor theorem" auf der englischen Seite), schliesslich wird es in vielen Saetzen gebraucht. Das Lemma von Zorn ist entgegen seines Namens ein Axiom. www.wissensnetz.de /lexikon/wiki,index,goto,Diskussion:Lemma.html   (318 words)

 Re: RDF Semantics / error in RDFS entailment lemma from Pat Hayes on 2005-10-28 (www-rdf-comments@w3.org from October ... Re: RDF Semantics / error in RDFS entailment lemma from Pat Hayes on 2005-10-28 (www-rdf-comments@w3.org from October to December 2005) >In particular I discovered an error that remains >in the RDFS entailment lemma and that was missed earlier. This represents the way that OWL should have been defined as an extension of RDFS, in my view, and is a sounder basis for future work than the current OWL-DL spec. lists.w3.org /Archives/Public/www-rdf-comments/2005OctDec/0004.html   (998 words)

 The Pumping Lemma: Examples   (Site not responding. Last check: 2007-10-12) Suppose this language is context-free; then it has a context-free grammar. be the constant associated with this grammar by the Pumping Lemma. By the Pumping Lemma this must be representable as www.cs.may.ie /%7Ejpower/Courses/parsing/node41.html   (169 words)

 Lemma Daniel, Dreamers & fools 2005 Att Daniel Lemma har soul är det inget snack om. Daniel Lemma är en mästare på att skriva klassiska, organiska låtar som väver samman influenser från rhythm and blues, soul, reggae, pop, jazz, rock och gospel. Daniel Lemma slog igenom med låten "If I Used To Love You" som hördes i filmen "Jalla Jalla". www.ginza.se /Product/Product.aspx?ItemId=156439&PreviousItemId=87818&LogSectionId=-2&p=1   (203 words)

 Borel-Cantelli lemma - Definition, explanation In probability theory, the Borel-Cantelli lemma is a theorem about sequences of events. In a slightly more general form, it is also a result in measure theory. A related result, sometimes called the second Borel-Cantelli lemma, is a partial converse of the first Borel-Cantelli lemma. www.calsky.com /lexikon/en/txt/b/bo/borel_cantelli_lemma.php   (295 words)

 Hiroshi Haruki's Lemma BE = AF, and their length does not depend on the position of P on the given circle. The latter is an unintended consequence of the proof of Hiroshi Haruki's Lemma [Honsberger]: The lemma leads to elegant proofs of the Butterfly and Two Butterflies theorems. www.cut-the-knot.org /Curriculum/Geometry/Haruki.shtml   (318 words)

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