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# Topic: Theorem

###### In the News (Wed 20 Feb 19)

 The Mathematics of Fermat's Last Theorem Theorem B is even harder still, and it is the theorem of which Andrew Wiles first claimed a proof in 1993, thus proving FLT as well. Theorem B certainly seems, to one unfamiliar with the territory, to be quite technical and abstruse. Theorem B and more general forms of the Taniyama-Shimura Conjecture can be viewed in yet another way to affirm that there is a very significant relationship between modular functions and elliptic curves. www.mbay.net /~cgd/flt/fltmain.htm   (2364 words)

 PlanetMath: lemma A lemma is a proven statement, typically named a lemma to distinguish it as a truth used as a stepping stone to a larger result rather than an important statement in and of itself. In contrast, a theorem under this format would represent a major result, and would often be named in relation to mathematicians who worked on or solved the problem in question. The Greek “Theoria” means “view, or vision" and is clearly linguistically related to the word “theatre.” The apparent relation is that a theorem is a mathematical fact which you see to be true (and can now show others!). planetmath.org /encyclopedia/Theorem.html   (337 words)

 Theorem - Wikipedia, the free encyclopedia Proving theorems is a central activity of mathematicians. A theorem has two parts, stated in a formal language – a set of assumptions, and a conclusion that can be derived from the given assumptions according to the inference rules of the formal system comprising the formal language. Informally speaking, most such theorems are not of any particular interest; 'theorem' used in this sense is a technical term indicating that a derivation exists and has none of the subjective connotations of importance as when the term is used in general mathematics. en.wikipedia.org /wiki/Theorem   (488 words)

 Arrow's impossibility theorem - Wikipedia, the free encyclopedia Arrow's theorem says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social welfare function that satisfies all these conditions at once. The Gibbard-Satterthwaite theorem, an attempt at weakening the conditions of Arrow's paradox, replaces the IIA criterion with a criterion of non-manipulability, only to reveal the same impossibility. So, what Arrow's theorem really shows is that voting is a non-trivial game, and that game theory should be used to predict the outcome of most voting mechanisms. en.wikipedia.org /wiki/Arrow's_impossibility_theorem   (1737 words)

 Bell's Theorem The same theorem can be applied to measurements of the polarisation of light, which is equivalent to measuring the spin of photon pairs. However, the fact that Quantum Mechanics correctly predicts the correlations that are experimentally observed indicates that the theory too violates at least one of the three assumptions. What is actually found [in the experimental tests of Bell's theorem] is that the behavior of the two [electrons] is correlated in a way that is rather similar to that of the two television images of the fish, as described earlier. www.upscale.utoronto.ca /GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html   (6569 words)

 Theorem Summary Since theorems were a direct result of deductive reasoning, which yields unquestionably true conclusions, they believed their theorems were undoubtedly true. A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. A theorem is often stated informally when the intended audience is believed to be able to produce the formal version from the informal one. www.bookrags.com /Theorem   (1213 words)

 What is the Last Theorem?   (Site not responding. Last check: ) Pythagoras’ Theorem is not just a nice idea, or a notion that seems to work for most right-angled triangles. It is believed that the creation and proof of the Last Theorem happened in about 1637, but it was not until after Fermat’s death in 1665 that his marginal note came to light. The Last Theorem was a source of frustration, but it also had a lighter side. www.simonsingh.net /What_is_the_Theorem.html   (792 words)

 Binomial theorem Summary The binomial theorem is a statement of the result obtained by multiplying a binomial by itself any given number of times. The binomial theorem for positive integer exponents was known by the Arabs of the thirteenth century. The theorem was generalized to fractional and negative exponents by Isaac Newton in 1664 or 1665, but his results were not actually published until 1711. www.bookrags.com /Binomial_theorem   (1384 words)

 The Pythagorean Theorem The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. According to the Pythagorean Theorem, the sum of the areas of the two red squares, squares A and B, is equal to the area of the blue square, square C. Therefore, the square on c is equal to the sum of the squares on a and b. jwilson.coe.uga.edu /EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html   (2131 words)

 Argument Principle and Rouche's Theorem Theorem 8.8, known as the argument principle, is useful in determining the number of zeros and poles that a function has. Theorem 8.10 is usually stated with the requirement that The improved theorem that we gave was discovered by Irving Glicksberg (see the American Mathematical Monthly, 83 (1976), pp. math.fullerton.edu /mathews/c2003/RoucheTheoremMod.html   (584 words)

 Proofs of the Pythagorean Theorem This theorem is one of the earliest know theorems to ancient civilizations. This theorem is talking about the area of the squares that are built on each side of the right triangle. As I stated earlier, this theorem was named after Pythagoras because he was the first to prove it. jwilson.coe.uga.edu /EMT668/EMT668.Student.Folders/HeadAngela/essay1/Pythagorean.html   (1106 words)

 Gödel's Theorem A much-abused result in mathematical logic, supposed by many authors who don't understand it to support their own favored brand of rubbish, and even subjected to surprisingly rough handling by some who really should know better. Gödel's theorem is a result about axiomatic systems, which is already a source of some confusion. Goodstein's Theorem is a result about natural numbers which is undecidable within Peano arithmetic, but provable within stronger set-theoretic systems. cscs.umich.edu /~crshalizi/notebooks/godels-theorem.html   (1269 words)

 PlanetMath: hairy ball theorem The second proof gives the hairy ball theorem as a corollary of the Poincaré-Hopf index theorem. Near a zero of a vector field, we can consider a small sphere around the zero, and restrict the vector field to that. This is version 9 of hairy ball theorem, born on 2002-12-04, modified 2006-09-15. planetmath.org /encyclopedia/HairyBallTheorem.html   (269 words)

 Computing Papers on Theorem   (Site not responding. Last check: ) Some of the principal Theorems include the existence of a universal program, the unsolvability of the halting problem (there does not exist a mechanical means of checking for infinite loops in the executions of programs), and Rice`s Theorem. The sweeping conclusion of Rice`s Theorem is the impossibility of algorithmically analyzing computer programs to determine in which cases a given property is possessed by the function computed by the program. Unfortunately, after GÂ¨del announced his famed incompleteness Theorem in o 1931 stating that it is impossible to have a formalism that can help us to reach all truths and only truths, we nally realized that we had gone a long way in ghting a battle that was impossible to win. computing.breinestorm.net /Theorem   (3065 words)

 The Long FAQ on Liberalism But if the theorem only works by identifying the right party in the first place, and then only by qualifying their property rights, then the advantages of the theorem are nil. The improved efficiency of the Coase theorem derives from the fact that either of the parties would have made only \$40,000 without buying the equipment (the fisherman by absorbing the loss, the factory by compensating them for their losses). At the heart of the theorem lies the "invariance proposition." This is the assertion that no matter who is given the property rights, the outcomes will be identical. www.huppi.com /kangaroo/L-chicoase.htm   (5987 words)

 Pythagorean Theorem To begin, the Pythagorean theorem states that the square on the hypotenuse of a right triangle has an area equal to the combined areas of the squares on the other two sides. The Pythagorean theorem was a mathematical fact that the Babylonians knew and used. With the Pythagorean theorem being such a popular topic, it is no wonder high school students study the theorem. www.ms.uky.edu /~lee/ma502/pythag/pythag.htm   (488 words)

 Fermat's last theorem It may well be that Fermat realised that his remarkable proof was wrong, however, since all his other theorems were stated and restated in challenge problems that Fermat sent to other mathematicians. In 1986 the connection was made between the Shimura-Taniyama- Weil Conjecture and Fermat's Last Theorem by Frey at Saarbrücken showing that Fermat's Last Theorem was far from being some unimportant curiosity in number theory but was in fact related to fundamental properties of space. The proof of Fermat's Last Theorem was completed in 1993 by Andrew Wiles, a British mathematician working at Princeton in the USA. www-gap.dcs.st-and.ac.uk /~history/HistTopics/Fermat's_last_theorem.html   (2143 words)

 Bayes theorem definition - Medical Dictionary definitions of popular medical terms Bayes' theorem is employed in clinical epidemiology to determine the probability of a particular disease in a group of people with a specific characteristic on the basis of the overall rate of that disease and of the likelihood of that specific characteristic in healthy and diseased individuals, respectively. A common application of Bayes' theorem is in clinical decision making where it is used to estimate the probability of a particular diagnosis given the appearance of specific signs, symptoms, or test outcomes. In technical terms, in Bayes' theorem the impact of new data on the merit of competing scientific hypotheses is compared by computing for each hypothesis the product of the antecedent plausibility and the likelihood of the current data given that particular hypothesis and rescaling them so that their total is unity. www.medterms.com /script/main/art.asp?articlekey=10301   (348 words)

 Bayes' Theorem (Stanford Encyclopedia of Philosophy) Bayes's theorem lets us use this information to compute the "direct" probability of J. Doe dying given that he or she was a senior citizen. In this guise Bayes's theorem is particularly useful for inferring causes from their effects since it is often fairly easy to discern the probability of an effect given the presence or absence of a putative cause. Though a mathematical triviality, the Theorem's central insight — that a hypothesis is supported by any body of data it renders probable — lies at the heart of all subjectivist approaches to epistemology, statistics, and inductive logic. plato.stanford.edu /entries/bayes-theorem   (7492 words)

 Math Forum: Ask Dr. Math FAQ: Pythagorean Theorem The Pythagorean theorem is used any time we have a right triangle, we know the length of two sides, and we want to find the third side. The applications that use the Pythagorean theorem include computing the distance between points on a plane; converting between polar and rectangular coordinates; computing perimeters, surface areas and volumes of various geometric shapes; and calculating maxima and minima of perimeters, or surface areas and volumes of various geometric shapes. One of the most common applications of the Pythagorean theorem is in the distance formula. mathforum.org /dr.math/faq/faq.pythagorean.html   (657 words)

 LaTeX Tips: Theorems Note that the "real" theorems (thm, cor,lem) need no explicit theoremstyle declaration, since the style appropriate for these theorems is the default. The reason for this behavior is that the theorem environment "eats up" (nearly) any space at the beginning of the theorem, so commands like \hfill or \newline or \par have no effect. Theorems quoted from the literature are often stated in a form like "Theorem A (Gauss [3])" or "Theorem A ([3, Theorem 4.6])". www.math.uiuc.edu /~hildebr/tex/theorems.html   (1490 words)

 Fermat's last theorem It may well be that Fermat realised that his remarkable proof was wrong, however, since all his other theorems were stated and restated in challenge problems that Fermat sent to other mathematicians. Sophie Germain proved Case 1 of Fermat's Last Theorem for all n less than 100 and Legendre extended her methods to all numbers less than 197. In 1986 the connection was made between the Shimura-Taniyama- Weil Conjecture and Fermat's Last Theorem by Frey at Saarbrücken showing that Fermat's Last Theorem was far from being some unimportant curiosity in number theory but was in fact related to fundamental properties of space. www-groups.dcs.st-and.ac.uk /~history/HistTopics/Fermat's_last_theorem.html   (2143 words)

 The Remainder Theorem The Remainder Theorem is useful for evaluating polynomials at a given value of This is because the tool is presented as a theorem with a proof, which you probably don't feel ready for at this stage in your studies. First off, even though the Remainder Theorem refers to the polynomial and to long division and to restating the polynomial in terms of a quotient, a divisor, and a remainder, that's not actually what you're meant to be doing. www.purplemath.com /modules/remaindr.htm   (525 words)

 theorem - Search Results - MSN Encarta Theorem, proposition or formula in mathematics or logic that is provable from a set of postulates and basic assumptions. Postulate (mathematics), statement that has not been proven but is assumed to be true. Fermat’s Last Theorem: picture of Pierre de Fermat encarta.msn.com /encnet/refpages/search.aspx?q=theorem   (160 words)

 theorem Search Results From Healthline Bayes' theorem deals with the role of new information in revising probability estimates. That one must have no outgoing edges and cannot be the start state.Eliminate all the states one by one and replace them with RE subexpressions.When all the... This is the Reynolds Transport Theorem.Reynolds Transport Theorem - proof. www.healthline.com /search?q1=theorem   (148 words)

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