How To Use Theorem In A Sentence
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However, Ulam did make a fundamental contribution in proposing the antipodal map theorem.
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According to the theorem, any triangle inscribed in a semicircle is a right triangle, as is shown in the following diagram:
The Medieval Problem of Universals
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The story of Fermat's Last Theorem, the centuries spent trying to find a proof and Professor - now Sir - Andrew Wiles's final victory, is recounted in a book by Simon Singh , a physicist and author also famous for his battle to change the libel laws after he was sued for calling pseudoscientific medical treatments "bogus" .
Telegraph.co.uk - Telegraph online, Daily Telegraph and Sunday Telegraph
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It then follows from the Menelaus theorem, that every three such points are collinear provided all or two of the bisectors are external.
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Theorem In any triangle, the midpoints of the sides, the feet of the altitudes, and the midpoints of the segments from the orthocenter to the vertices lie on a circle.
Recently Uploaded Slideshows
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Saccheri then studied the hypothesis of the acute angle and derived many theorems of non-Euclidean geometry without realising what he was doing.
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In 1826 he generalised his theorem to a hyperboloid of revolution, rather than a cone.
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Re: official quant thread for CAT 2009Re: official quant thread for CAT 2009hey puys can u give me the rough idea of a multinomial theoremRe: official quant thread for CAT 2009Re: official quant thread for CAT 2009
Undefined
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He left topologists a treasure-trove of theorems and techniques and left the University of Texas Mathematics Department with a goal and thirteen years of good progress toward it.
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A theorem is proved that delineates criteria for the radii of the annulus of the zeros in the complex plane of the generating function for factorial moments as it applies to high-energy charged-hadron multiproduction.
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An idea of Koopman on the possibilities of treating problems of classical mechanics by means of operators on a function space stimulated him to give the first mathematically rigorous proof of an ergodic theorem.
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Using comparison theorem and some properties of the matrix norm and the matrix measure, the paper provides several stability conditions for single and symmetric composite uncertain delay systems.
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Sally wasn’t the person Mariah would have picked for her daughter’s friend, but watching Lindsay apply the Thomas theorem, matching an opponent’s wit and endurance often resulted in a desired friendship, was ethnomethodology, a theory Mariah respected, because instead of accepting a perceived reality as already being out there, it showed that you could create and live your own reality.
The Owl and Moon Cafe
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To verify the properties of the concurrent and reactive systems based on the theorem proving approach, an axiomatization is formulized for the first order projection temporal logic (FPTL).
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This includes many surprising analogues to results in commutative algebra theory, such as the Serre splitting theorem on the existence of free summands and the theorem of Bass on the cancellation of free summands.
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Book One discusses his laws of motion then proceeds to a series of propositions, theorems and problems.
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The interval of the time lag is identical of each lane controlled and when the input is a random sign, we can adopt quadratic function of optimum control and separation theorem.
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The interval of the time lag is identical of each lane controlled and when the input is a random sign, we can adopt quadratic function of optimum control and separation theorem.
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They contain impulsive wave components, and therefore do not satisfy the conditions of Tipler's theorem.
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The concepts of viability and invariance about complex stochastic system are introduced, theorems of viability and invariance are proposed and proved to characterize rational decision.
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The theorem holds in spherical and elliptic geometry.
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I also read about a new play that explored mathematical theorems.
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We learn how the dynamics of addition and subtraction are linked to multiplication and division, and eventually to theorems of algebra.
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In a series of articles, beginning in 1934, Péter developed various deep theorems about primitive recursive functions, most of them with an explicit algorithmic content.
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This ‘index theorem’ had antecedents in algebraic geometry and led to important new links between differential geometry, topology and analysis.
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In his talk, he gave an outline of some of Thompson's work, beginning with the odd order theorem of Feit and Thompson.
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Maybe we can think of story where it turns out that Burt is actually an AI that arose out of a theorem prover.
A Gut Check Moment for SFWA « Whatever
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Economic theories have been axiomatized, and articles and books of economics are full of theorems.
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Hi Nitin - heh - actually my "mathematical" theorem was just a joke, authentic-sounding mathematical babble.
Toward a unified theory of social networks
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Tarski's theorem on the undefinability of the truth predicate shows that, given certain general assumptions, the resources of the metalanguage or metatheory must go beyond the resources of the object-language.
Axiomatic Theories of Truth
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Hume notes that we cannot imagine or conceive of the negations of typical mathematical theorems, but this seems to be a weak hold on the necessity of mathematics.
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- uniform hypergraph and you want a monochromatic complete subhypergraph with one has the usual finite Ramsey theorem for graphs, and although getting good asymptotics for is a major open problem in combinatorics, at least the general type of function is known: the growth is exponential in the general type of the function is no longer known.
Gowers's Weblog
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By pulling these observations together with some mathematical syntax, a theorem is formed relating to the expansion of binomial terms.
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There is a theorem proved by Kurt Godel in 1931, which is the Incompleteness Theorem for mathematics.
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It was thenceforth no longer a question of whether this or that theorem was true, but whether it was useful to capital or harmful, expedient or inexpedient, in accordance with police regulations or contrary to them.
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He pretended to show how an uneducated slave boy could be led to prove Pythagoras' theorem for doubling the square.
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It is also important to stress that a few years later (1938) an analog of the diagonalization lemma (the so-called second recursion theorem) was discovered by Kleene and was soon to become a basic tool in the foundations of recursion theory and computability theory.
Paradoxes and Contemporary Logic
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One can do this by basing the material on the Cox-Ross-Rubinstein theorem and the like, approximating the Black-Scholes model with discrete-time binomial trees.
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In the modern world Pythagoras is best remembered for the mathematical theorem that he is said to have created - the one about the square on the hypotenuse of a right-angled triangle.
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Norman decided to shift his field from gap and density theorems to non-linear differential equations, both ordinary and partial.
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One of the results on which al-Karaji uses this form of induction comes from his work on the binomial theorem, the binomial coefficients and the Pascal triangle.
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Euclid and Archimedes utilized two important techniques to prove theorems from their axioms: reductio ad absurdum arguments, and a method of exhaustion.
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As a corollary to this theorem Higman proved the existence of a universal finitely presented group containing every finitely presented group as a subgroup.
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A maximum value theorem and a minimal value theorem of a canonical correlation variable in the context of a unitarily invariant norm were derived.
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However, Cutkosky was able to provide an alternate method of detecting primes for a hypergraph in any dimension, relying on different structures than those used in the two-dimensional theorem.
Columbia Missourian: Latest Articles
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Of these laws the summation theorems have a counterpart in the control analysis of oscillatory systems.
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The theorem states that the posterior probability is proportional to the prior probability multiplied by the likelihood.
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Mean Value Theorem. Go over Homework 3.
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This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form, and obtain an integrate inequality and a rigidity theorem.
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Of course we have modernised the notation, for example subscript notation was not used in Parseval's time, and we have also corrected his theorem for he omitted the first 2 on the left hand side.
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And quite frequently I state a number of definitions and ask students to formulate some theorems using them.
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Book One discusses his laws of motion then proceeds to a series of propositions, theorems and problems.
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The work is a survey of Kerala mathematics and, very unusually for an Indian mathematical text, it contains proofs of the theorems and gives derivations of the rules it contains.
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The pitfall trap or the nearest pit for turtles at the fence was also recorded in order to calculate a minimum straight-line travel distance from the release point using the Pythagorean theorem.
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There is a wealth of information in the binomial theorem that we have yet to exploit.
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I had not known about the halting problem, the number [Omega], or Lucas's curious theorem connecting the parity of binomial coefficients and the binary system.
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Using the heat theorem discovered by you it has now become possible on the one hand to calculate from the heat evolution during chemical reactions and the specific heats, the chemical affinity and the maximum possible output of energy during chemical reactions, and on the other hand to calculate the equilibrium in reactions not yet studied.
Nobel Prize in Chemistry 1920 - Presentation Speech
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The fuzzy linear programming duality theory has been also studied in this article; the related theorems corresponding to the duality theorems in classical linear programming were proposed and proved.
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Students in math know that the essence of the subject lies in theorems and proofs.
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This follows from formal theorems in metamathematics as well as from the history of science.
Smart Mobs » Blog Archive » The Peer-Production/Wisdom of Crowds Debate contd.
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Other topics in the large range of applied mathematics topics which he studied were existence theorems and asymptotic expansions.
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I find that farm work clears the mind, and the vineyard is a great place to prove theorems.
Daniel L. McFadden - Autobiography
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Bearing in mind all these subjective states and experiences, including the whole range of so-called mediumship, the _theorem_ of the Masters and adepts of all ages may be made exceeding plain.
The New Avatar and The Destiny of the Soul The Findings of Natural Science Reduced to Practical Studies in Psychology
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In fact he is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities.
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In this paper, the conception of the standard well ordered set is introduced and ten theorems of the standard well ordered set has been proved.
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He studied primitive permutation groups and proved a finiteness theorem.
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He introduced and developed two fundamental methods, which could be briefly described as ‘the bilinear form technique’ and ‘the mean value theorem’.
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Largely under the impetus of the odd order theorem, there was an awakening interest in finite group theory.
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Reiter 1980 provides a fixpoint definition of the extensions of such a theory, and develops the theoretical groundwork for the approach, proving a number of the basic theorems.
Logic and Artificial Intelligence
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This is an algebraic expression of the disjunctive normal form theorem of sentential logic.
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He proved a major theorem concerning the measure-preserving property of Hamiltonian dynamics.
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And based on this conclusion, Darboux theorem on open interval is also given.
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The reason for this is something called the equipartition theorem in statistical mechanics.
Another Antimatter Supernova Discovered | Universe Today
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Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.
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Ideally the definitions would generate all the concepts from clear and distinct ideas, and the proofs would generate all the theorems from self-evident truths.
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Given this, the Löwenheim-Skolem theorems show that the notions of countability and uncountability will in fact vary as we move from model to model.
Skolem's Paradox
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There are similar but more complicated theorems for uncountable first-order languages; some of these can be paraphrased as omitting types theorems for infinitary languages.
First-order Model Theory
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If the problem is difficult enough, a theorem like this can be a significant achievement.
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In this work he gave what Thomson considered the first proof of the Waterston-Maxwell equipartition theorem.
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Do you think you'll be able to solve this problem or theorem -- or whatever it's called?
GOING OUT
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I am not sure how the equipartition theorem comes into this picture.
Dark Matter: Still Dark.
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Again it is a theorem of intuitionistic arithmetic that every natural number is either prime or composite.
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Moreover, in GEM the generalized Product principle (P. 16Ï) is also derivable as a theorem, with ˜Ï™ as weak as the requirement of mutual overlap, and we can introduce a corresponding functor as follows:
Wild Dreams Of Reality, 3
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Tarski's theorem on the undefinability of the truth predicate shows that a definition of such a predicate requires resources that go beyond those of the formal language for which truth is going to be defined.
Axiomatic Theories of Truth
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But why would you pass up free education that could take you places somewhere someday, even though we will never use the algebra theorems ever?
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For the most part these chapters do computations with specific examples, establishing canonical forms and other structure theorems for certain classes of groups.
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It discusses Milnor's theorem, which shows that the total curvature of a knot is at least 4p.
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Zermelo introduces axioms of set theory, explicitly formulates AC and uses it to prove the well-ordering theorem, thereby raising a storm of controversy.
The Axiom of Choice
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We wish to expound in detail some of the many proofs of this theorem.
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“Since all theorems of applied mathematics are deducible from the subsystem [of physical interpretation of the field of rational numbers] ¦ it is only this subsystem which is verified by the interpretations.” (1978, vol. I, p. 423) So we cannot empirically confirm any claims that are properly about real or complex numbers, so we cannot empirically confirm their consistency.
Hans Reichenbach
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Temperature in the equipartition theorem is related to energy
Telekinesis and Quantum Field Theory
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It assumes that the phenomenon is something that you can put in a lab, measure, quantify, and repeat exhaustively as much as needed in order to elaborate a theory or enunciate a theorem.
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Before the Coase Theorem, the prevailing view in economics was government intervention in the form of taxes on externalities, forcing the polluter to internalize costs borne by others.
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Of course, an analysis of the notion of finitism cannot be presented as a theorem.
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Since Euclid's axiomatic formulation of geometry mathematicians had been trying to prove his fifth postulate as a theorem deduced from the other four axioms.
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The items in boldface indicate that the students were handed sets of axioms and theorems.
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His work on topology, in particular on characteristic classes, cobordism theory and the Thom transversality theorem led to his being awarded a Fields medal in 1958.
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On the monodromy theorem for isolated hypersurface singularities.
RegEM « Climate Audit
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Unfortunately, it's the only theorem I remember from school. That may be why it took me two goes to get my maths O level.
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By using a universal method a new existence theorem of solution for a generalized equilibrium problem in topological vector space is obtained.
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And indeed one can show that there is no single choice of antiderivative for which the Fundamental Theorem will always work.
Wolfram Blog : Mathematica and the Fundamental Theorem of Calculus
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Certainly the theorems which Galileo had proved on the centres of gravity of solids, and left in Rome, were discussed in this correspondence.
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The theorem thus implies existence of the total of 18 equilateral triangles.
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Additionally, the well—known four colour problem and elementary geometry theorem—proving problem have been discussed.
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In standard metamathematics, an important role for a thorough understanding of the second incompleteness theorem has been played by Löb's theorem (Löb 1955).
Paradoxes and Contemporary Logic
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For the customary morality, that which education and opinion have consecrated, is the only one which presents itself to the mind with the feeling of being _in itself_ obligatory; and when a person is asked to believe that this morality _derives_ its obligation from some general principle round which custom has not thrown the same halo, the assertion is to him a paradox; the supposed corollaries seem to have a more binding force than the original theorem; the superstructure seems to stand better without, than with, what is represented as its foundation.
Utilitarianism
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You might even stumble upon a theorem or two in your researches.
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Although Riemann had given a proof of the theorem that any simply connected region of the plane can be mapped conformally onto a disc, his proof involved using the Dirichlet problem.
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Twenty years earlier Gordan had proved the finite basis theorem for binary forms using a highly computational approach.
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According to the field matching theorem, the transmission equation and scatter matrix expressions of the coaxial extractor system with support post are educed in this paper.
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After analyzing several theory models of inductive reasoning, we use the Bayes Theorem to prove the premise probability principle, and integrate this theory with human mental process.
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OK, so basically you can apply Green's theorem for a region that has several boundary curves. You just have to be careful that the outer boundary must go counterclockwise.
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In 1965 I read about Penrose's theorem that any body undergoing gravitational collapse must eventually form a singularity.
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We show that nonexistence theorems for continuous surjections between continua and related results extend to almost continuous functions.
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Hahn was a pioneer in set theory and functional analysis and is best remembered for the Hahn - Banach theorem.
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Demonstrations of general theorems; contracted method of division and of finding the highest common divisor of polynominals; theory of indices and radicals; discussion of equations; mathematical infinity, infinitesimals and indeterminate quantities; summation and interpolation of series; theory of logarithms; binomial, multinomial and exponential theorems; theory of probabilities general theory and solution of equations of the higher orders; symbolical representation and properties of numbers; different systems of notation, etc., constituting the philosophy of Arithmetic.
A Catalogue of the Officers and Students of The Furman University, for 1860-'61
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Given this, the Löwenheim-Skolem theorems show that the notions of countability and uncountability will in fact vary as we move from model to model.
Skolem's Paradox
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Protothetic is an absolute propositional calculus in the sense that the principle of bivalence is its theorem.
Lvov-Warsaw School
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We can find the length of the other side of the triangle, the diagonal AT, by using Pythagoras' Theorem.
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This work continues the tradition of mathematical experiment to help discover patterns, suggest conjectures, and develop new theorems.
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In a nutshell, it asks for the simplest proof of any theorem.
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Thus, if you write card (N) = µ 0 (read: aleph sub zero), his theorems justified calling the cardinality of the “second number class” µ 1.
The Early Development of Set Theory
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This theorem shows that if a cone is intersected by a plane in a conic, then the foci of the conic are the points where this plane is touched by the spheres inscribed in the cone.
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No mathematical theorem could require the number of pages these fellows were taking!
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The movie tosses mathematical theories and theorems in the audience's direction, but explains them simply and lucidly; no one is going to become lost or bored.
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The code uses so called Bayesian networks, a combination of statistical principles, including Bayes Theorem, hence the name.
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Since Euclid's axiomatic formulation of geometry mathematicians had been trying to prove his fifth postulate as a theorem deduced from the other four axioms.
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Even if Ockham's semantics, as well as his theory of mental language governed by a trans-idiomatic mental grammar transforming the theorems of terminist logic into a theory of thought processes (William of Ockham, Summa log., 1974, 11ff), [46] was by no means undisputed, and came under severe criticism by his opponents as well as no less severe modifications by his ˜followers™.
Medieval Semiotics
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In addition, fixed point theorems and section theorems, maximal element theorems and the existence theorems of equilibrium for abstract economies can also be discussed.
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I do research in computer science, in the formal semantics of programming languages, and it looks like my subfield is on the verge of a phase change -- I think that very soon paper proofs of theorems will stop being acceptable for publication; we will have to submit formal, machine-checked proofs.
Memetic Suicide, Bryan Caplan | EconLog | Library of Economics and Liberty
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In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups.
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; Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f (2), Re f (3), and Re f (4); and the positivity of the real part of a linear functional on a subspace of C (X).
AvaxHome RSS:
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A deeper characterization of a helix is that it is the unique curve in 3-space for which the ratio of curvature to torsion is a constant, a result known as Lancret's Theorem.
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This is called Zeckendorf's theorem, and the subsequence of Fibonacci numbers which add up to a given integer is called its Zeckendorf representation.
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A few of his principal articles are: "Mémoire sur la théorie des axes conjugués et des moments d'inertie des corps", enunciating the principle sometimes called Binet's Theorem (Journ. de l'Ec. pol.,
The Catholic Encyclopedia, Volume 2: Assizes-Browne
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Given this algebraic conception of axiomatization, then, Skolem appeals to the Löwenheim-Skolem theorems to argue that the axioms of set theory lack the resources to pin down the notion of uncountability.
Skolem's Paradox
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And where a theorem may present some problem, he may always look down to the numerical examples for help.
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The virtue of this conception is that it explains how two or more people can be said to be thinking of the same abstract object, such as the number ˜two,™ and how various properties, such as the Pythagorean Theorem, can be said to follow logically from the idea of a right triangle.
Malebranche's Theory of Ideas and Vision in God
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Fermat subsequently died, leaving mathematicians to search for 350 years for a proof of the theorem.
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The fan theorem is, in fact, a corollary of the bar theorem; combined with the continuity principle, which is not classically valid, it yields the continuity theorem.
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But these laws and theorems are not just abstract mathematics.
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The method is an application of the weak transversality theorem used in catastrophe theory.
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Furthermore, we prove some theorems about the inversion of functor structures.
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There are many reasons why certain theorems are not named after their discoverer but after a later rediscoverer.
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Theorem 2 extends the application of Theorem 10.17 applied in Mathematics Analysis which is adopted as the textbook by East China Normal University and proves its converse proposition untenable.
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IN bivious theorems, [138] and Janus-faced doctrines, let virtuous considerations state the determination.
Christian Morals
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He has a theorem named after him which concerns the intersection of surfaces.
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The cusp catastrophe model is established by means of the upper bound theorem of plastic limit theory for analyzing the stability of slope.
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This theorem was also proved by Felix Bernstein and independently by E Schröder.
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The Unit Theorem implies that this map has the roots of unity as kernel and maps '' U '' to a lattice of full rank in a hyperplane.
Citizendium, the Citizens' Compendium - Recent changes [en]
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In 1964 John Bell, an Irish theoretical physicist, published a theorem that seemed to prove the argument for non-locality.
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He discovered characterisations of topological mappings of the Cartesian plane and a number of fixed point theorems.
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The third part of the work is on summands with a common distribution function and includes discussion of principal limit theorems and convergence to the normal law.
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After all, it's still a theorem that set-theoretic notions like countability and uncountability come out relative on the algebraic conception.
Skolem's Paradox
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The spectral theorem for unitary matrices allows each of these matrices to be diagonalised; as is abelian, the matrices commute and so one can simultaneously diagonalise these matrices.
What's new
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In mechanics Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and solids.
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The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.
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This paper makes studies of researched proposition on Pythagorean theorem an Projection theorem.
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Because, when you state it fully, the theorem requires that the antiderivative that is going to be subtracted be continuous throughout the interval.
Wolfram Blog : Mathematica and the Fundamental Theorem of Calculus
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The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.
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Although less than the full Shimura - Taniyama conjecture, this result does imply that the elliptic curve given above is modular, thereby proving Fermat's Last Theorem.
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A generalization of Morley's theorem would be an appropriate contribution to the coming centennial anniversary of the discovery of this wonderful result.
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From these beginnings he moved to prove a number of limit theorems, now known as the Szegö limit theorem, the strong Szegö limit theorem and Szegö's orthogonal polynomials and on the unit circle.
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A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss Bonnet theorem.
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Many valuable conclusions can be reached by adopting inframarginal analysis, introducing transaction efficiency, and conducting new analysis of Heckscher-Ohlin factor endowment theorem.
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Existence theorem for optimal portfolio is provided.
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Based on the continuity theorem of the air mass variation in the slide guide, dynamic motion equations of the multi-throttle air-lubricated hydrostatic slide guide are also built.
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In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.
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Using multiple integral to prove a generalization of Pythagoras theorem and to calculate the Moivre integral.
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This theorem gave, as a corollary, the complete structure of all finite projective geometries.
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In modern Fourier analysis, theorems are usually less important than the techniques developed to prove them.
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The validity of simulating star map is verified by using the angle-distance of stars and projection theorem.
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So far as experience goes, such a thing has no more real existence than a line without breadth; and hence an atomic theory based upon such an assumption may be as true ideally as any of the theorems of Euclid, but it can give only an approximatively true account of the actual universe.
The Unseen World, and Other Essays
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Cotes discovered an important theorem on the nth roots of unity, anticipated the method of least squares and discovered a method of integrating rational fractions with binomial denominators.
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We math majors could write term papers on cotangent bundles and prove the Bolzano Weirstrass theorem, but we don't know jack about T tests or chi-square.
Undefined
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This theorem reveals that there exist undecidable propositions in a consistent formal system.
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This theorem, also called the infinitude of primes theorem, was proved by Euclid in Proposition IX.20 of the Elements.
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Smith also extended Gauss's theorem on real quadratic forms to complex quadratic forms.
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Now, both the original Asymmetric Propeller and Napoleon's theorem start with three equilateral triangles and discover the fourth one by construction.
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Nicolas Bourbaki, who never existed, is named in the Bourbaki-Witt theorem, used in computability theory and domain theory.
The Volokh Conspiracy » People’s Names in Computing
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It happened when he came across a theorem which stated that points in the plane could be specified with a single coordinate.
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As Craig noted at the time, his interpolation theorem gives a neat proof of Evert Beth's definability theorem, which runs as follows.
First-order Model Theory
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The limitation result of Gödel's theorem is closely related to another limitation result known as the undecidability of the halting problem.
Self-Reference
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This gave powerful results such as a purely algebraic proof of the Riemann Roch theorem.
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Bonnet used Codazzi's formulas to prove the existence theorem in the theory of surfaces.
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Like other valid theorems, this is a truism, but it is not useless, for it helps in organising the argument.
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Nash and I proved the same theorem, or, rather, two theorems very close to each other.
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Certainly the theorems which Galileo had proved on the centres of gravity of solids, and left in Rome, were discussed in this correspondence.
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Thus they visit the classic marginal-value theorem and its graphical solution by constructing a tangent to the mean gain curve.
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He developed a quantitative relationship for the strength of a magnetic field in relation to an electric current (known as Ampère's theorem) and studied the process of iron magnetization.
Ampère, André Marie
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the theorem falls out nicely
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One of the principles I have always fallen back on when the world seems really depressing is something I came up with while daydreaming in a graduate statistics class in 1975 which I call Kelley's Theorem of Human Nature.
Lions and Tigers and Bears, Oh My!
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He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant T_p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures.
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Using the witten index for a supersymmetric field theory, we proved the Gauss - Bonnet - Chern theorem.
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The paper gives a proof of the intermediate value theorem with Bolzano's new approach and in the work he defined what is now called a Cauchy sequence.
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Pythagorean theorem
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In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.
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The upper bound and lower bound theorem of classical plasticity theory and corresponding FEM is applied to analyze the bearing capacity of gravity dam for judging the stability of the dam.
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Consider, for example, the Pythagorean theorem that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
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But he also says that the proof of the indefinability theorem can be adapted to show that, in general, one cannot define a truth predicate "if the order of the metalanguage is at most equal to that of the language itself
Alfred Tarski
