Categories: Mathematical lists | Lemmas In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... In mathematics, Borels lemma is an important result about partial differential equations named after Émile Borel. ... In mathematics, a partial differential equation (PDE) is an equation relating the partial derivatives of an unknown function of several variables. ... In probability theory, the Borel_Cantelli lemma is a theorem about sequences of events. ... Burnsides lemma, sometimes also called Burnsides counting theorem, Pólyas formula, the Cauchy-Frobenius lemma or the Orbit-Counting Theorem, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects. ... In mathematics, the butterfly lemma or Zassenhaus lemma is a technical result on the lattice of subgroups of a group. ... In mathematics, under various anti-large cardinal assumptions, one can prove the existence of the canonical inner model, called the Core Model, that is, in a sense, maximal and approximates the structure of V. A covering lemma asserts that under the particular anti-large cardinal assumption, the Core Model exists... In mathematical logic, the diagonalization lemma states that for any well formed formula with a free variable x, there is a sentence ψ such that where [ψ] is the Gödel number for ψ. ... In mathematics, Dicksons lemma is a finiteness statement applying to n-tuples of natural numbers. ... Euclids lemma is a generalisation of Proposition 30 of Book VII of Euclids Elements. ... Fatous 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. ... Jump to: navigation, search A function f(x) is subadditive if for all x and y in the domain of f. ... The Fitting lemma, named after the mathematician Hans Fitting, is a basic statement in abstract algebra. ... In mathematics, especially homological algebra and other applications of Abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams. ... The fixed-point lemma for normal functions is a basic result in axiomatic set theory; it states that any normal function has arbitrarily large fixed points and can often be used to construct ordinal numbers with interesting properties. ... In mathematics, particularly in set theory, Fodors lemma states the following: If is a regular, uncountable cardinal, is a stationary subset of , and is regressive on (that is, for any ) then there is some and some stationary such that for any . ... In mathematics, there is more than one Gauss lemma; all are named after Carl Friedrich Gauss. ... In mathematics, Grönwalls lemma states the following. ... A differential form is a mathematical concept in the fields of multivariate calculus, differential topology and tensors. ... Double-counting is a term used to refer not simply to a math problem, but to a conceptual problem in social accounting practice, when the attempt is made to estimate the new value added by Gross Output, or the value of total investments. ... In mathematics, Hensels lemma, named after Kurt Hensel, is a generic name for analogues for p-adic fields of the Newton method for solving equations. ... In mathematics, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. ... In mathematics, Itōs lemma is used in stochastic calculus to find the differential of a function of a particular type of stochastic process. ... There is also a theorem of set theory called Königs theorem. ... In topology, Lebesgues number lemma states If the metric space X is compact and an open cover of X is given, then there exists a number δ > 0 such that every subset of X of diameter < δ is contained in some member of the cover. ... In statistics, if a large number of events are all independent of one another, than there is still a positive (possibly small) probability that none of the events will occur. ... In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematics, Nakayamas Lemma is an important technical lemma in commutative algebra and algebraic geometry. ... In statistics, the Neyman-Pearson lemma states that when doing a hypothesis test between two point hypotheses H0: θ=θ0 and H1: θ=θ1, then the likelihood-ratio test which rejects H0 in favour of H1 when is the most powerful test of size α. ... In mathematics, the nine lemma is a statement about commutative diagrams and exact sequences valid in any abelian category, as well as in the category of groups. ... Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. ... In abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. ... In cryptanalysis, the piling-up lemma is a principle used in linear cryptanalysis to construct linear approximations to the action of block ciphers. ... In mathematics, both in vector calculus and in differential topology, the concepts of closed form and exact form are defined for differential forms, by the equations dα = 0 for a given form α to be a closed form, and α = dβ for an exact form, with α given and β unknown. ... A differential form is a mathematical concept in the fields of multivariate calculus, differential topology and tensors. ... In the theory of formal languages, a pumping lemma states that any language of a given class can be pumped and still belong to that class. ... In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ... In axiomatic set theory, a discipline within mathematics, the Rasiowa-Sikorski lemma is one of the most fundamental facts used in the technique of forcing in axiomatic set theory. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Sards lemma, also known as Sards theorem or the Morse-Sard theorem, is a result of mathematical analysis characterising the image of the critical points of a smooth function F from one Euclidean space to another as having Lebesgue measure 0 (and so small, in a definite sense). ... Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... For non-mathematical singularity theories, see singularity. ... In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). ... Schreiers subgroup lemma is a theorem in group theory used in the Schreier-Sims algorithm and also for finding a presentation of a subgroup. ... In mathematics, especially homological algebra and other applications of Abelian category theory, the short five lemma is a special case of the five lemma. ... Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. ... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... 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. ... Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. ... In combinatorial mathematics, Sperners lemma states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors. ... Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria. ... In mathematics, and more specifically in homological algebra, the splitting lemma states that the following statements regarding the below short exact sequence in any abelian category (with similar results if the objects are non-abelian groups) are equivalent: there exists a map t: B → A such that tq is the... Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. ... Steins lemma, named in honor of Charles Stein, may be characterized as a theorem of probability theory that is of interest primarily because of its application to statistical inference -- in particular, its application to James-Stein estimation and empirical Bayes methods. ... Probability theory is the mathematical study of probability. ... In mathematics, Szemerédis regularity lemma states that for every and every positive integer there is an integer such that every graph with vertices has an ε-regular partition into classes, Categories: Mathematics stubs | Graph theory | Lemmas ... A diagram of a graph with 6 vertices and 7 edges. ... In mathematics, the Ultrafilter Lemma states that every filter is a subset of some ultrafilter, i. ... Urysohns lemma in topology states that if X is a normal topological space and A and B are disjoint closed subsets of X, then there exists a continuous function from X into the unit interval [0, 1], f : X → [0, 1], such that f(a) = 0 for all a... In mathematics, a Lie algebra is an algebraic structure whose main use lies in studying geometric objects such as Lie groups and differentiable manifolds. ... In mathematics, the Yoneda lemma in category theory is an abstract result on functors of the type morphisms into a fixed object. ... Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... In mathematics, the butterfly lemma or Zassenhaus lemma is a technical result on the lattice of subgroups of a group. ... Group theory is that branch of mathematics concerned with the study of groups. ... Zorns lemma, also known as the Kuratowski-Zorn lemma, is a theorem of set theory that states: Every partially ordered set in which every chain (i. ...