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Finiteness, finitude, or being finite, is the state of being limited or having an end, and is a counter to the concept of infinity. Humans are considered...

theoretical computer science, a finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine...

English imperative). A finite transitive verb or a finite intransitive verb can function as the root of an independent clause. Finite verbs are distinguished...

Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical...

In mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically...

a finite field or Galois field (so-named in honor of Évariste Galois) is a field that has a finite number of elements. As with any field, a finite field...

In mathematics education, Finite Math is a syllabus in college and university mathematics that is independent of calculus. A course in precalculus may...

A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often...

is called geometrically finite if it has a well-behaved fundamental domain. A hyperbolic manifold is called geometrically finite if it can be described...

theory, a finite game (sometimes called a founded game or a well-founded game) is a two-player game that is assured to end after a finite number of moves...

A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line...

finite graph Locally finite group Locally finite measure Locally finite operator in linear algebra Locally finite poset Locally finite space, a topological...

A {\displaystyle A} over a ring R {\displaystyle R} is called finite if it is finitely generated as an R {\displaystyle R} -module. An R {\displaystyle...

of finite character if for each A {\displaystyle A} , A {\displaystyle A} belongs to F {\displaystyle {\mathcal {F}}} if and only if every finite subset...

Finite number may refer to: Natural number, a countable number less than infinity, being the cardinality of a finite set Real number, such as may result...

pseudo-finite field F is an infinite model of the first-order theory of finite fields. This is equivalent to the condition that F is quasi-finite (perfect...

deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state...

analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences...

{\displaystyle \sigma } -finite subset is a measurable subset which is the union of a countable number of measurable subsets of finite measure. The measure...

{\displaystyle \emptyset } ⁠) and the latter has no elements at all. A set is finite if there exists a natural number ⁠ n {\displaystyle n} ⁠ such that the first...

mathematics, a hyper-finite field is an uncountable field similar in many ways to finite fields. More precisely a field F is called hyper-finite if it is uncountable...

In algebraic geometry, a finite morphism between two affine varieties X , Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion...

In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical...

branch of mathematics, a morphism f : X → Y of schemes is quasi-finite if it is of finite type and satisfies any of the following equivalent conditions:...

In linguistics, a non-finite clause is a dependent or embedded clause that represents a state or event in the same way no matter whether it takes place...

Finite type refers to several related concepts in mathematics: Algebra of finite type, an associative algebra with finitely many generators Morphism of...

Finite topology is a mathematical concept which has several different meanings. A finite topological space is a topological space, the underlying set of...

generalized notions of volumes, an s-finite measure is a special type of measure. An s-finite measure is more general than a finite measure, but allows one to generalize...

finitely presented may refer to: finitely presented group finitely presented monoid finitely presented module finitely presented algebra finitely presented...

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination...

space X {\displaystyle X} is said to be point-finite if every point of X {\displaystyle X} lies in only finitely many members of U . {\displaystyle {\mathcal...

{\displaystyle X} is said to be locally finite if each point in the space has a neighbourhood that intersects only finitely many of the sets in the collection...

In quantum computing, quantum finite automata (QFA) or quantum state machines are a quantum analog of probabilistic automata or a Markov decision process...

In mathematics, finite-dimensional distributions are a tool in the study of measures and stochastic processes. A lot of information can be gained by studying...

particularly in abstract algebra, a ring R is said to be stably finite (or weakly finite) if, for all square matrices A and B of the same size with entries...

mathematics, a ring is said to be a Dedekind-finite ring (also called directly finite rings and Von Neumann finite rings) if ab = 1 implies ba = 1 for any...

conjecture could be carried over to the Euclidean case. Finite Field Kakeya Conjecture: Let F be a finite field, let K ⊆ Fn be a Kakeya set, i.e. for each vector...

In mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure. Let ( X , T ) {\displaystyle...

processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because...

In mathematics, the finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the...

{\displaystyle B} is called an A {\displaystyle A} -algebra of finite type if B {\displaystyle B} can be finitely generated as an A {\displaystyle A} -algebra. It is...

learning theory, a class C of languages has finite thickness if every string is contained in at most finitely many languages in C. This condition was introduced...

which every finitely generated subgroup is finite. Since the cyclic subgroups of a locally finite group are finitely generated hence finite, every element...

A finite map can be one of the following: In computer science, finite map is a synonym for an associative array. A finite map in algebraic geometry is...

In mathematics, subshifts of finite type are shift spaces defined by a finite set of forbidden words. They are used to model dynamical systems, and in...

Look up finite, finitely, or finiteness in Wiktionary, the free dictionary. Finite, or variants, may refer to: Finite set, a set whose cardinality (number...

to an arbitrary order of accuracy, it is possible to use the finite difference. A finite difference can be central, forward or backward. This table contains...

In mathematics, a quasi-finite field is a generalisation of a finite field. Standard local class field theory usually deals with complete valued fields...

The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite...

branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values. Among finite measures are probability...

hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite, and all of...

In mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space which...

games: finite and infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play. Finite games are...

used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences...

R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related...

residually finite or finitely approximable if for every element g that is not the identity in G there is a homomorphism h from G to a finite group, such...

initially subamenable graph, or equivalently a subgroup of an ultraproduct of finite-rank symmetric groups such that every two elements of the group have distance...

The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case...

these arguments to show there is an infinite hierarchy of infinities. For finite sets, cardinality recovers the usual concept of size as "number of elements...

can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deal with finite sets, particularly...

Sequences can be finite, as in these examples, or infinite, such as the sequence of positive even integers (2, 4, 6, 8, ...). The length of a finite sequence...

finite ring is a ring that has a finite number of elements. Every finite field is an example of a finite ring, and the additive part of every finite ring...

mathematical logic, a logic L has the finite model property (fmp for short) if any non-theorem of L is falsified by some finite model of L. Another way of putting...

groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. An abelian...

the fundamental theorem of finitely generated abelian groups it is therefore a finite direct sum of copies of Z and finite cyclic groups. The proof of...

between finite and non-finite clauses. A finite clause contains a structurally central finite verb, whereas the structurally central word of a non-finite clause...

In mathematics the finite Fourier transform may refer to either another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g...

is finite-dimensional if its dimension is a natural number. Otherwise, it is infinite-dimensional, and its dimension is an infinite cardinal. Finite-dimensional...

In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of...

with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine...

In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be...

a finite set. In other words, A {\displaystyle A} contains all but finitely many elements of X . {\displaystyle X.} If the complement is not finite, but...

In mathematics, the theory of finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed...

Finite part may refer to: Cauchy principal value Hadamard finite part This disambiguation page lists mathematics articles associated with the same title...

Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part...

In logic, a finite-valued logic (also finitely many-valued logic) is a propositional calculus in which truth values are discrete. Traditionally, in Aristotle's...

property of finite sets is that every cover of a finite set by subsets has a finite subcover: one may choose, for each point of the finite set, a member...

finite intersection property (FIP) if any finite subfamily of A {\displaystyle {\mathcal {A}}} has non-empty intersection. It has the strong finite intersection...

condition on subgroups (that is, every subgroup is finitely generated). Polycyclic groups are finitely presented, which makes them interesting from a computational...

of mathematics, a finite-rank operator is a bounded linear operator between Banach spaces whose range is finite-dimensional. Finite-rank operators are...

approximately finite-dimensional if it contains an increasing sequence of finite-dimensional subalgebras that is dense. One can consider Approximately finite dimensional...

into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that...

Theistic finitism, also known as finitistic theism or finite godism, is the belief in a deity that is limited. It has been proposed by some philosophers...

bijective function from A onto some proper subset B of A. A set is Dedekind-finite if it is not Dedekind-infinite (i.e., no such bijection exists). Proposed...

mathematics, a finitely generated algebra (also called an algebra of finite type) over a (commutative) ring R {\displaystyle R} , or a finitely generated R...

the finite Coxeter groups are precisely the finite Euclidean reflection groups; for example, the symmetry group of each regular polyhedron is a finite Coxeter...

In mathematics, finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) contrary to arithmetic in a field...

The Hecke algebra of a finite group is the algebra spanned by the double cosets HgH of a subgroup H of a finite group G. It is a special case of a Hecke...

refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The...

Finite completeness may refer to: Complete category, a category in which all finite limits exist Completeness (order theory)#Finite completeness, a condition...

used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set called an alphabet. A primary...

cyclic group is isomorphic to the additive group of Z, the integers. Every finite cyclic group of order n is isomorphic to the additive group of Z/nZ, the...

abelian group ( G , + ) {\displaystyle (G,+)} is called finitely generated if there exist finitely many elements x 1 , … , x s {\displaystyle x_{1},\dots...

digit occurs more frequently than any other. If a number is normal, no finite combination of digits of a given length occurs more frequently than any...

supercomputers. The simplest and the original implementation, later formalized as Finite Field Diffie–Hellman in RFC 7919, of the protocol uses the multiplicative...

In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its...

trumpet) is a type of geometric figure that has infinite surface area but finite volume. The name refers to the Christian idea that the archangel Gabriel...

multiply connected space like a 3 torus has everywhere zero curvature but is finite in extent, whereas a flat simply connected space is infinite in extent (such...

allowed. Generally, the vertex set V is taken to be finite (which implies that the edge set E is also finite). Sometimes infinite graphs are considered, but...

The finite strip method is a technique of structural analysis used for bridge and tall structure design as well and in the design of construction components...

In automata theory, an alternating finite automaton (AFA) is a nondeterministic finite automaton whose transitions are divided into existential and universal...

A finite-state transducer (FST) is a finite-state machine with two memory tapes, following the terminology for Turing machines: an input tape and an output...

interpretations (semantics). Finite model theory is a restriction of model theory to interpretations on finite structures, which have a finite universe. Since many...

or topological notions. Varieties of finite monoids, varieties of finite ordered semigroups and varieties of finite ordered monoids are defined similarly...

classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either...

it is often used for finite populations when people are interested in measuring the process that created the existing finite population (this is called...

is an instance of the schema. Axiom schemata are commonly used to give finite descriptions of theories whose axioms include infinitely many formulas....

construct a nondeterministic finite automaton (NFA), which is then made deterministic and the resulting deterministic finite automaton (DFA) is run on the...

In applied mathematics, the finite pointset method (FPM) is a general approach for the numerical solution of problems in continuum mechanics, such as the...

A finite wing is an aerodynamic wing with tips that result in trailing vortices. This is in contrast to an infinite wing. According to John D. Anderson...

generalized finite element method (GFEM), extended finite element method (XFEM), spectral finite element method (SFEM), meshfree finite element method...

The Finite Element Machine (FEM) was a late 1970s-early 1980s NASA project to build and evaluate the performance of a parallel computer for structural...

defined. V {\displaystyle V} is said to be finite-dimensional if the dimension of V {\displaystyle V} is finite, and infinite-dimensional if its dimension...

automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input. A two-way deterministic finite automaton (2DFA) is an...

In mathematics, a K-finite function is a type of generalized trigonometric polynomial. Here K is some compact group, and the generalization is from the...

for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple...

In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the...

or finite temperature field theory is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature...

correctness. The name "finite bypass" means that any process (concurrent part) of the algorithm is bypassed at most a finite number times before being...

In computer science, a communicating finite-state machine is a finite-state machine labeled with "receive" and "send" operations over some alphabet of...

a locally finite space is a topological space in which every point has a finite neighborhood, that is, a neighborhood consisting of finitely many elements...

is that of finite completeness. A category is finitely complete if all finite limits exists (i.e. limits of diagrams indexed by a finite category J)...

Geometry in affine spaces over a finite fields has also been widely studied. For example, elliptic curves over finite fields are widely used in cryptography...

one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set. The notation for...

In mathematics, the axiom of finite choice is a weak version of the axiom of choice which asserts that if ( S α ) α ∈ A {\displaystyle (S_{\alpha })_{\alpha...

be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after...

In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve...

In mathematics, there are several finiteness theorems. Ahlfors finiteness theorem Finiteness theorem for a proper morphism Compactness theorem, in mathematical...

In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic...

Farrell–Jones conjecture Finite lattice representation problem: is every finite lattice isomorphic to the congruence lattice of some finite algebra? Goncharov...

The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points. The FPM was...

the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...

system of finite groups. The idea of using a profinite group is to provide a "uniform", or "synoptic", view of an entire system of finite groups. Properties...

showing what state (or states in the case of a nondeterministic finite automaton) a finite-state machine will move to, based on the current state and other...

group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004. Since the...

infinite groups. Special cases of groups with finiteness properties are finitely generated and finitely presented groups. Given an integer n ≥ 1, a group...

between 1960 and 2004, that culminated into a complete classification of finite simple groups. Group theory has three main historical sources: number theory...

is also a cyclic group, since every non-zero integer can be written as a finite sum 1 + 1 + ... + 1 or (−1) + (−1) + ... + (−1). In fact, ⁠ Z {\displaystyle...

designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization...

can have finite length only when the module has Krull dimension zero. Modules of finite length are finitely generated modules, but most finitely generated...

In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of...

{\displaystyle f:V\to V} is called locally finite if the space V {\displaystyle V} is the union of a family of finite-dimensional f {\displaystyle f} -invariant...

projective planes, both infinite, such as the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective...

aperiodic finite-state automaton (also called a counter-free automaton) is a finite-state automaton whose transition monoid is aperiodic. A finite-state automaton...

rather than a static product. The theory of finite semiotics explains semiosis as an effect of the finite nature of the human mind that occurs as an individual...

Finite risk insurance is the term applied within the insurance industry to describe an alternative risk transfer product that is typically a multi-year...

differential equations. With numerical models, geologists can use methods, such as finite difference methods, to approximate the solutions of these equations. Numerical...

mathematics, a finite von Neumann algebra is a von Neumann algebra in which every isometry is a unitary. In other words, for an operator V in a finite von Neumann...

Finite element model updating is the process of ensuring that finite element analysis results in models that better reflect the measured data than the...

In computer science, a deterministic acyclic finite state automaton (DAFSA), is a data structure that represents a set of strings, and allows for a query...

unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton...

model if and only if it has a finite model. This question is important in the mathematical field of finite model theory. Finite satisfiability and satisfiability...

syntax, verb-second (V2) word order is a sentence structure in which the finite verb of a sentence or a clause is placed in the clause's second position...

of Kleinian groups, the Ahlfors finiteness theorem describes the quotient of the domain of discontinuity by a finitely generated Kleinian group. The theorem...

number variables to help distinguish them from natural number variables. A finite set can be enumerated by successively labeling each element with the least...

algebra and finite geometry, the list of transitive finite linear groups is an important classification of certain highly symmetric actions of finite groups...

In mathematics, rank-finiteness for fusion categories is a collection of related theorems and conjectures about structures related to fusion categories...

objects are all finite sets and whose morphisms are all functions between them. FinOrd is the category whose objects are all finite ordinal numbers and...

continuous symmetries of differential equations, in much the same way that finite groups are used in Galois theory to model the discrete symmetries of algebraic...

VOO, OBE & Be tv, Proximus, Shelter Prod, and Tint, in association with Finite Films, Northern Ireland Screen, and the UK Global Screen Fund. It received...

_{0}} : Every finite set of natural numbers has a maximum, which is also a natural number, and finite unions of finite sets are finite. An example application...

In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains...

from abelian varieties defined over number fields to ones defined over finite fields and various local fields. Since a number field is the fraction field...

The compact finite difference formulation, or Hermitian formulation, is a numerical method to compute finite difference approximations. Such approximations...

book, Finite and Infinite Games to topics of business and leadership. The book is based on Carse's distinction between two types of games: finite games...

on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking...

In a conventional finite-state machine, the transition is associated with a set of input Boolean conditions and a set of output Boolean functions. In an...

The finite potential well (also known as the finite square well) is a concept from quantum mechanics. It is an extension of the infinite potential well...

\sum _{i=m}^{n}\sum _{j=m}^{n}a_{i,j}=\sum _{i,j=m}^{n}a_{i,j}} . The term finite series is sometimes used when discussing the summation presented above....

Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis...

v t e In computation, a finite-state machine (FSM) is event driven if the transition from one state to another is triggered by an event or a message. This...

Finite Records was a private jazz record label which released about five records in the late 1970s. Drummer John Lewis is involved in three of the albums...

that if μ {\displaystyle \mu } is a nonnegative σ-finite measure, and ν {\displaystyle \nu } is a finite-valued signed or complex measure such that ν ≪ μ...

are σ-finite but not finite. The natural numbers are also σ-finite with respect to counting measure. However, the real numbers are not σ-finite with respect...

by groups of finite Morley rank (see below). A group of finite Morley rank is an abstract group G such that the formula x = x has finite Morley rank for...

some languages. Because English lacks most inflectional morphology, the finite and nonfinite forms of a verb may appear the same in a given context. In...

The finite-difference frequency-domain (FDFD) method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics...

countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations...

of G. A subgroup H of finite index in a group G (finite or infinite) always contains a normal subgroup N (of G), also of finite index. In fact, if H has...

{\displaystyle {\mathcal {O}}_{v}} be the corresponding valuation ring. The set of finite adeles of K {\displaystyle K} , denoted A K , f i n {\displaystyle \mathbb...

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence...

finite poset is a partially ordered set P such that for all x, y ∈ P, the interval [x, y] consists of finitely many elements. Given a locally finite poset...

states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory...

is finitely generated as a B {\displaystyle B} -module. See finite morphism. Finite morphisms are quasi-finite, but not all morphisms having finite fibers...

in the classification of finite semigroups is Krohn–Rhodes theory, analogous to the Jordan–Hölder decomposition for finite groups. Some other techniques...

A finite element limit analysis (FELA) uses optimisation techniques to directly compute the upper or lower bound plastic collapse load (or limit load)...

this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization...

group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or...

Finite Automata is an American dark electronic and electro industrial music group from Atlanta, Georgia. Originally formed in Pensacola, Florida in 2006...

In mathematics, a finite subdivision rule is a recursive way of dividing a polygon or other two-dimensional shape into smaller and smaller pieces. Subdivision...

theorem states that every finite division ring is a field; thus, every finite domain is a field. In other words, for finite rings, there is no distinction...

from some finite set to the first natural numbers (1, 2, 3, ...), up to the number of elements in the counted set. It results that two finite sets have...

finitely generated if S is finite and finitely related if R is finite. If both are finite it is said to be a finite presentation. A group is finitely...

The ATLAS of Finite Groups, often simply known as the ATLAS, is a group theory book by John Horton Conway, Robert Turner Curtis, Simon Phillips Norton...

has a finite number of elements if and only if F is a finite field and the vector space has a finite dimension. Thus we have Fq, the unique finite field...

sets is open (while the definition of a topology only requires this for a finite family). Equivalently, an Alexandrov topology is one whose open sets are...

mathematics, the Jordan–Schur theorem also known as Jordan's theorem on finite linear groups is a theorem in its original form due to Camille Jordan. In...

In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav V. Nori, as the main tool in the construction...

Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞ Predicate First-order list Second-order Monadic Higher-order Fixed-point...

A virtual finite-state machine (VFSM) is a finite-state machine (FSM) defined in a virtual environment. The VFSM concept provides a software specification...

have finite activity (only finitely many jumps on any finite time interval), finite variation (the sum of the absolute value of all jumps is finite on every...

group. Finitely generated group Finitely generated monoid Finitely generated abelian group Finitely generated module Finitely generated ideal Finitely generated...

{\displaystyle r} be the common ratio of a geometric progression. For a finite number of terms, the geometric sequence consists of the elements up to n...

The patch test in the finite element method is a simple indicator of the quality of a finite element, developed by Bruce Irons. The patch test uses a partial...

II-finite, III-finite, IV-finite, V-finite, VI-finite and VII-finite. I-finiteness is the same as normal finiteness. IV-finiteness is the same as Dedekind-finiteness...

In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant (so named after Victor Anatolyevich Vassiliev), is a knot invariant...

The finite Legendre transform (fLT) transforms a mathematical function defined on the finite interval into its Legendre spectrum. Conversely, the inverse...

f(x)=0} for all but a finite number of points x ∈ X , {\displaystyle x\in X,} then f {\displaystyle f} is said to have finite support. If the set X {\displaystyle...

generalized nondeterministic finite automaton (GNFA), also known as an expression automaton or a generalized nondeterministic finite state machine, is a variation...

The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method...

of a division ring is a field. It turned out that every finite domain (in particular finite division ring) is a field; in particular commutative (the...

distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations...

it is finite, the lacking digits are assumed to be 0. If all a i {\displaystyle a_{i}} are 0, the separator is also omitted, resulting in a finite sequence...

model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness)...

dynamics software — including multiphysics simulation, finite-element, finite-volume, finite difference, boundary element, riemann solver, dissipative...

condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on the characters, and without any explicit matrix...

is a linear operator that behaves, in several important respects, like a finite-dimensional operator such as a matrix. In infinite-dimensional spaces, bounded...

for Paul Gordan [another elderly mathematician], Hilbert's proof of the finiteness of the basis of the invariant system was simply not mathematics. Hilbert...

whether a given first-order sentence is a logical consequence of a given finite set of sentences, but validity in first-order theories with infinitely many...

lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular lattice without the assumption of finiteness. Geometric...

word, or more generally any finite character encoding such as ASCII or Unicode. A word over an alphabet can be any finite sequence (i.e., string) of letters...

f(c^{-})=f(c)=f(c^{+})} , as one expects for a smooth function. All the values must be finite. If c {\displaystyle c} is not a point of continuity, then a discontinuity...

A mathematical set is countable if either it is finite or it can be put in one to one correspondence with the set of natural numbers. Equivalently, a set...

substantial power savings. A finite-state machine with data path (FSMD) is a mathematical abstraction which combines a finite-state machine, which controls...

an algorithm that computes the membership of every natural number in a finite number of steps. A set is noncomputable (or undecidable) if it is not computable...

This is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed...

525–530, doi:10.1016/0021-8693(76)90235-0, ISSN 0021-8693, MR 0399193 MathWorld: Thompson group Atlas of Finite Group Representations: Thompson group...

be simply finite if it is a finite extension; this should not be confused with the fields themselves being finite fields (fields with finitely many elements)...

x y {\displaystyle xy} that has the desired property. Languages with a finite number of strings vacuously satisfy the pumping lemma by having p {\displaystyle...

probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition...

Burnside problem asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. It was posed by William...

one. There are countably infinitely many WFE's, however, each WFE has a finite number of nodes. In computer science, an expression is a syntactic entity...

as a graph whose vertices are hereditarily finite sets (finite sets whose elements are hereditarily finite) with edges representing set membership, as...

\right\}} is finite. A cover of X {\displaystyle X} is said to be point finite if every point of X {\displaystyle X} is contained in only finitely many sets...

 · 10! · ( 4! )2 · 2 · 7 · 13 · 41 · 47 · 59 · 71 ≈ 8.0802 × 1053 . The finite simple groups have been completely classified. Every such group belongs...

Prayers and Finite Experience is a book of prose and poetry by Paul Goodman. Harper & Row first published 5,000 copies of Little Prayers and Finite Experience...

approximately finite-dimensional (AF) C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality...

automata, finite tree automata (FTA) can be either a deterministic automaton or not. According to how the automaton processes the input tree, finite tree automata...

(bijection) between the elements of the two sets. The cardinality of a finite set can be identified with a natural number, which can be found simply by...

extensions and cubic extensions, respectively. A finite extension is an extension that has a finite degree. Given two extensions L / K {\displaystyle...

Jerome Schaefer, states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete...

Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed...

{\displaystyle X\subseteq M} (with parameters taken from M {\displaystyle M} ) is a finite union of intervals and points. O-minimality can be regarded as a weak form...

Maryland. Fields received his Ph.D. in 1887. His thesis, entitled Symbolic Finite Solutions and Solutions by Definite Integrals of the Equation dny/dxn =...

locally finite if every finitely generated algebra has finite cardinality, or equivalently, if every finitely generated free algebra has finite cardinality...

unique. The finitely indexed discrete sets are just the finite sets. In particular, finitely indexed subsets of ω {\displaystyle \omega } are finite. Taking...

In category theory and its applications to mathematics, a biproduct of a finite collection of objects, in a category with zero objects, is both a product...

for finite fields and their algebraic closures. That is, for any field F {\displaystyle F} that is itself finite or that is the closure of a finite field...

express languages (sets of finite strings) in them. A string w = w1···wn in a finite alphabet A can be represented by a finite structure with domain D = {1...

Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of...

over some division ring K. A finite projective space is a projective space where P is a finite set of points. In any finite projective space, each line...

monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for...

may have any cardinality ("size") and, depending on its purpose, may be finite (e.g., the alphabet of letters "a" through "z"), countable (e.g., { v 1...

mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function...

mathematics, the Ihara zeta function is a zeta function associated with a finite graph. It closely resembles the Selberg zeta function, and is used to relate...

1939. It states that every finite group is the group of symmetries of a finite undirected graph. More strongly, for any finite group G {\displaystyle G}...

some cases, a finite tree) of formulae with a specially designated conclusion. The definition of a deduction is such that it is finite and that it is...

condition. In other contexts, only chains that are finite sets are considered. In this case, one talks of a finite chain, often shortened as a chain. In this...

algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits...

S is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}. If S is a finite set with the cardinality |S| = n (i.e., the number of all elements in the...

mathematician at the University of Florida noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970, the Wolf Prize in 1992...

with functional composition as group operation. If V {\displaystyle V} has finite dimension n {\displaystyle n} , then GL ⁡ ( V ) {\displaystyle \operatorname...

theorem for finite semigroups states that every finite semigroup S {\displaystyle S} is a divisor of a finite alternating wreath product of finite simple groups...

In the mathematical classification of finite simple groups, a thin group is a finite group such that for every odd prime number p, the Sylow p-subgroups...

particular linear representation of a reductive algebraic group over a finite field or local field, or a group with a BN-pair. It is analogous to the...

of a finite group, although Frobenius remarked that the theorem followed from Cauchy's theorem on permutation groups and the fact that every finite group...

theorem.) If both X {\displaystyle X} and Y {\displaystyle Y} are finite with the same number of elements, then f : X → Y {\displaystyle f:X\to Y}...

elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set. There...

GS is affine over S if and only if G is a finite group. However, one can take a projective limit of finite constant group schemes to get profinite group...

small fragment of Zermelo set theory sufficient for the Peano axioms and finite sets; Kripke–Platek set theory, which omits the axioms of infinity, powerset...

function from the natural numbers to X. The cardinality of X is neither finite nor equal to ℵ 0 {\displaystyle \aleph _{0}} (aleph-null). The set X has...

Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods...

science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states...

mathematics, the obstruction to a finitely dominated space X being homotopy-equivalent to a finite CW-complex is its Wall finiteness obstruction w(X) which is...

instructions (i.e. a program), finite in length, for the procedure." Thus every computable function must have a finite program that completely describes...

In numerical analysis, a mixed finite element method, is a variant of the finite element method in which extra fields to be solved are introduced during...

and for each infinite cardinal κ, 2κ is the γth successor of κ, then γ is finite. For any infinite sets A and B, if there is an injection from A to B then...

number of elements, while a finite set is a set with a finite number of elements. The above examples are examples of finite sets. An example of an infinite...

efficient than volume-discretization methods (finite element method, finite difference method, finite volume method). Boundary element formulations typically...

simply primary. A finite group is a p-group if and only if its order (the number of its elements) is a power of p. Given a finite group G, the Sylow...

in a finite-dimensional K-vector space V is a finitely generated R-submodule of V that spans V; in other words, L ⊗R K = V. Let AK be a finite-dimensional...

weighted finite-state machine is a generalization of a finite-state machine in which the edges have weights, for example real numbers or integers. Finite-state...

only finite intersections, and which does not necessarily contain all complements of its sets) or a set algebra (which is closed only under finite unions...

it has the finite intersection property and X i {\displaystyle X_{i}} is compact. We note If M ′ ⊂ M {\displaystyle M'\subset M} is a finite subset, ∩...

the opposite of finite a nonfinite verb is a verb that is not capable of serving as the main verb in an independent clause a non-finite clause is a clause...

automaton in the same way that an alternating finite automaton is a generalisation of a nondeterministic finite automaton (NFA). The emptiness problem (deciding...

xn+1. An aperiodic monoid is an aperiodic semigroup which is a monoid. A finite semigroup is aperiodic if and only if it contains no nontrivial subgroups...

vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups...

number of points. If finite this number is often denoted by k. RPr: Each point is incident with the same number of lines. If finite this number is often...

only itself is a hereditary set. Hereditarily countable set Hereditarily finite set Well-founded set Kunen, Kenneth (1980). Set Theory: An Introduction...

In automata theory, a self-verifying finite automaton (SVFA) is a special kind of a nondeterministic finite automaton (NFA) with a symmetric kind of nondeterminism...

o)){\Bigr ]}} For finite-horizon POMDPs, the optimal value function is piecewise-linear and convex. It can be represented as a finite set of vectors. In...

In mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements...

in Abkhaz is finite versus non-finite. Finite verbs usually contain enough information to form a complete sentence, whereas non-finite verbs typically...

and nonconforming finite element, mixed finite element, mimetic finite difference...) inherit these convergence properties. The finite-volume method is...

reliable and efficient finite element procedures. ADINA R & D sponsored twelve bi-yearly academic conferences at M.I.T. on nonlinear finite element analysis...

only hold for a subgroup of finite index. Given a property P, the group G is said to be virtually P if there is a finite index subgroup H ≤ G {\displaystyle...

The Finite Volume Community Ocean Model (FVCOM; Formerly Finite Volume Coastal Ocean Model) is a prognostic, unstructured-grid, free-surface, 3-D primitive...

behavior of systems. State diagrams require that the system is composed of a finite number of states. Sometimes, this is indeed the case, while at other times...

button a finite number of times during a finite time. And similarly, in a finite time, the elevator can only open and close its door a finite number of...

Katz–Lang finiteness theorem, proved by Nick Katz and Serge Lang (1981), states that if X is a smooth, geometrically connected scheme of finite type over...

in New York City, New York) is an American mathematician specializing in finite group theory. Lyons received his PhD in 1970 at the University of Chicago...

three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets that can be put back together in a different...

Helsinki Finite-State Technology (HFST) is a computer programming library and set of utilities for natural language processing with finite-state automata...

Sn(T) is finite. For every natural number n, the number of formulas φ(x1, ..., xn) in n free variables, up to equivalence modulo T, is finite. The theory...

Zorn's lemma, based on the idea that a contradiction involves use of only finitely many premises. In the case of modal logics, the collection of maximal consistent...

those by Lewis Fry Richardson, in the sense that these calculations used finite differences and divided the physical space in cells. Although they failed...

the automata theory, a tagged deterministic finite automaton (TDFA) is an extension of deterministic finite automaton (DFA). In addition to solving the...

notable for our purposes are: finite difference methods, finite volume methods, finite element methods, and spectral methods. Finite difference replace the infinitesimal...

Charles Babbage. The name difference engine is derived from the method of finite differences, a way to interpolate or tabulate functions by using a small...

In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language)...

with a finite residue field: hence every local field is isomorphic (as a topological field) to the real numbers R, the complex numbers C, a finite extension...

bounded automata (LBAs) or deterministic machines with finite memory. Such a machine has finitely many possible configurations, so any deterministic program...

computation (often with a much smaller complex). The C in CW stands for "closure-finite", and the W for "weak" topology. A CW complex is constructed by taking the...

components: A finite set N of nonterminal symbols. A finite set Σ {\displaystyle \Sigma } of terminal symbols that is disjoint from N. A finite set P of production...

particular, if J is finite, then M is a finitely generated module. If I and J are finite sets, then the presentation is called a finite presentation; a module...

Principal ideal: An ideal generated by one element. Finitely generated ideal: This type of ideal is finitely generated as a module. Primitive ideal: A left...

\left(k,n\right)} -threshold scheme based on polynomial interpolation over finite fields. In such a scheme, the aim is to divide a secret S {\displaystyle...

the σ-algebra of Borel sets of a Hausdorff topological space X that is finite on all compact sets, outer regular on all Borel sets, and inner regular...

exist. For example, a poset is locally finite if every closed interval [a, b] in it is finite. Locally finite posets give rise to incidence algebras which...

Finite element exterior calculus (FEEC) is a mathematical framework that formulates finite element methods using chain complexes. Its main application...

lattice of cells). However, for any Garden of Eden there is at least one finite pattern (a subset of cells and their states, called an orphan) with the...

Holonomic functions can also be described as differentiably finite functions, also known as D-finite functions. When a power series in the variables is the...

mathematics, calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices...

where the total size reading population has been normalized to 1. A typical finite-dimensional mixture model is a hierarchical model consisting of the following...

after Emil Artin and Max Zorn, states that any finite alternative division ring is necessarily a finite field. It was first published in 1930 by Zorn,...

which have been featured in internet memes. He has released the albums Finite Form (2013), Viator (2015), Reviator (2017) Pop Food (2017), HiLo (2018)...

ordinals less than ω {\displaystyle \omega } are finite. A finite sequence of finite ordinals always has a finite maximum, so ω {\displaystyle \omega } cannot...

rational functions, algebraic function fields, algebraic number fields, finite fields, and p-adic fields are commonly used and studied in mathematics,...

for certain verb forms existing in many languages, most often used as non-finite verbs that do not show a tense. As with many linguistic concepts, there...

Group". Finite Groups—Coming of Age (Montreal, Que, 1982). Contemp. Math. Vol. 45. Providence: Amer. Math. Soc. pp. 303–313. Atlas of finite groups: maximal...

solvable group when G is a finite simple group. This result is now known to be true as a corollary of the classification of finite simple groups, although...

the pattern and the searched text are arrays of elements of an alphabet (finite set) Σ. Σ may be a human language alphabet, for example, the letters A through...

method used to construct (infinite) mathematical structures from their (finite) substructures. It is a special example of the more general concept of a...

field: A finite extension of Q {\displaystyle \mathbb {Q} } Global function field: The function field of an irreducible algebraic curve over a finite field...

choice is to take "small" to mean finite. In this case, two sets are almost disjoint if their intersection is finite, i.e. if | A ∩ B | < ∞ . {\displaystyle...

that a group subjected to certain finiteness conditions on chains of subgroups, can be uniquely written as a finite direct product of indecomposable subgroups...

group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses. In other words, if S {\displaystyle...

2\uparrow \uparrow n} elements using Knuth's up-arrow notation. So the finite stages of the cumulative hierarchy cannot physically be written down explicitly...

are therefore not algebraic and admit no faithful finite-dimensional representations. Over finite fields, the Lang–Steinberg theorem implies that H1(k...

(repetitive process) terminates with a simple fraction, the result is a finite continued fraction; if it continues indefinitely, the result is an infinite...

suitable sense) measurable and has (at least locally) a finite measure. A synonym is set of (locally) finite perimeter. Basically, a set is a Caccioppoli set...

equations can be used for finite element computations of high Reynolds number incompressible flow using equal order of finite element space (i.e. P k −...

L} preserving finite products. A model of a Lawvere theory in a category C {\displaystyle C} with finite products is a finite-product preserving...

In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric...

Retrieved 2020-05-19. Riley, Robert (1971). "Homomorphisms of Knot Groups on Finite Groups". Mathematics of Computation. 25 (115): 603–619. doi:10...

stated as follows: Given the description of an arbitrary program and a finite input, decide whether the program finishes running or will run forever....

permutation of each of its elements. A general property of finite groups implies that a finite nonempty subset of a symmetric group is a permutation group...

G {\displaystyle G} can be written in exactly one way as a product of finitely many elements of S {\displaystyle S} and their inverses (disregarding trivial...

category theory, FinVect (or FdVect) is the category whose objects are all finite-dimensional vector spaces and whose morphisms are all linear maps between...

mathematical finite group theory, the Thompson order formula, introduced by John Griggs Thompson (Held 1969, p.279), gives a formula for the order of a finite group...

of the finite element method (FEM). His 1956 article was one of the first applications of this computational method. He coined the term "finite elements"...

of Finite Projective Planes", Duke Mathematical Journal, 15: 929–940, doi:10.1215/s0012-7094-48-01581-6 Baer, Reinhold (1946), "Polarities in Finite Projective...

The finite water-content vadose zone flux method represents a one-dimensional alternative to the numerical solution of Richards' equation for simulating...

Affix grammars over a finite lattice (AGFL) is a restricted type of affix grammar in which affixes can only assume finite sets of values. It is aimed...

structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian...

with a collection of sets with a hereditary property (like finiteness in a hereditarily finite set). Some authors regard a nested set collection as a family...

concept that corresponds to size, that is, the number of elements, of a finite set) as the whole; such cases can run counter to one's initial intuition...

propositions is the smallest set of propositions satisfying these conditions. Finite subdivision rules are a geometric form of recursion, which can be used to...

the integral by approximating the region under the graph of a function by finite sums of areas of vertical rectangles. For suitable functions, including...

finitely generated. The alternating group A4 is an example of a finite solvable group that is not supersolvable. If we restrict ourselves to finitely...

a derivation of a finite length, and thus involve only a finite number of axioms. Each forcing condition can be regarded as a finite piece of information...

finite type over A and if C is finite over B, then B is of finite type over A. (Here, "of finite type" means "finitely generated algebra" and "finite"...

in the semigroup. The class of finite semigroups consists of those semigroups for which the underlying set has finite cardinality. Members of the class...

non-archimedean and has finite residue field. Let L / K {\displaystyle L/K} be a finite Galois extension of nonarchimedean local fields with finite residue fields...

function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named...

Several methods of discretization can be applied: Finite volume method Finite elements method Finite difference method We begin with the incompressible...

translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of G, was introduced by John von...

for an object to exist: The combinatorial formulation answers whether a finite collection of sets has a transversal—that is, whether an element can be...

torsion group or a periodic group is a group in which every element has finite order. The exponent of such a group, if it exists, is the least common multiple...

axiomatize ZFC using only finitely many axioms. On the other hand, von Neumann–Bernays–Gödel set theory (NBG) can be finitely axiomatized. The ontology...

positive integer k such that ak=0. Equivalent definitions exists for finite semigroup. A finite semigroup S is nilpotent if, equivalently: x 1 … x n = y 1 … y...

still involves only a finite number of indeterminates (so that its degree remains finite), and each polynomial is a still a (finite) linear combination...

In finite group theory, a branch of mathematics, a Thompson factorization, introduced by Thompson (1966), is an expression of some finite groups as a product...

discrete for solution on a digital computer with the finite element method in space and the finite difference method in time. The resulting nonlinear,...

grammars acknowledge both finite verb phrases and non-finite verb phrases while dependency grammars only acknowledge non-finite verb phrases. The split...

redirect targets Liouvillian function – Elementary functions and their finitely iterated integrals Symbolic regression – Type of regression analysis Tarski's...

closure under composition and projection of a finite number of basis functions, and thus only a finite number of defining equations are needed. Elementary...

groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra whose...

Any two vertices in G can be connected by a unique simple path. If G has finitely many vertices, say n of them, then the above statements are also equivalent...

if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural...

for some finite positive ordinal d. ℶ d − 1 ( | α + ω | + ℶ 2 ) {\displaystyle \beth _{d-1}(|\alpha +\omega |+\beth _{2})} for some finite positive ordinal...

Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology (Étale cohomology) with compact...

Earthquake Engineering Research (PEER) Center. OpenSees allows users to create finite element applications for simulating the response of structural and geotechnical...

In mathematics, Robinson arithmetic is a finitely axiomatized fragment of first-order Peano arithmetic (PA), first set out by Raphael M. Robinson in 1950...

a matrix group (that is, admitting a faithful, finite-dimensional representation over K). Any finite group is linear, because it can be realized by permutation...

Nonstandard finite difference schemes is a general set of methods in numerical analysis that gives numerical solutions to differential equations by constructing...

Lie group forms of E6 are therefore not algebraic and admit no faithful finite-dimensional representations. The compact real form of E6 as well as the...

family of sets is also called a set family or a set system. A finite family of subsets of a finite set S {\displaystyle S} is also called a hypergraph. The...

arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set A {\displaystyle A} of integers, at least one of the sets A + A {\displaystyle...

subbase is a non-empty family of sets that has the finite intersection property (i.e. all finite intersections are non-empty). Equivalently, a filter...

in which every non-zero non-unit can be written in at least one way as a finite product of irreducible elements. Atomic domains are different from unique...

then it also holds for any finite number of sets, namely, the function value on the union of k disjoint sets (where k is a finite number) equals the sum of...

Extremal Problems For Finite Sets is a mathematics book on the extremal combinatorics of finite sets and families of finite sets. It was written by Péter...

introduced by Oswald Veblen (1912), states that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if...

mathematics and logic, an operation is finitary if it has finite arity, i.e. if it has a finite number of input values. Similarly, an infinitary operation...

series that terminates with G. Equivalently, it has a central series of finite length or its lower central series terminates with {1}. Intuitively, a nilpotent...

lens, so the plane at which the image sensor is placed is said to be a finite conjugate. Within a system with relay lenses or eyepieces, there may be...

equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is an ordinary integer. An example of an infinite...

of finite measures. This is a generalization of σ-finite measures, which are the same as those that are a disjoint union of countably many finite measures...

Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy—or equivalently, the maximum amount of...

When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. More precisely...

economics, scarcity refers to the basic fact of life that there exists only a finite amount of human and nonhuman resources which the best technical knowledge...

if and only if it is regular and has a countably locally finite (that is, 𝜎-locally finite) basis. A topological space X {\displaystyle X} is called...

language is defined as a (finite or infinite) set of strings that can be described by one of the mathematical formalisms called "finite automaton", "regular...

these words depends on the context. For example, if G is a finite group, then a nontrivial finite-dimensional representation V over a field is said to be...

group is a countable locally finite group, say U, which is uniquely characterized by the following properties. Every finite group G admits a monomorphism...

-categorical for some κ ≥ | σ | {\displaystyle \kappa \geq |\sigma |} and has no finite model, then it is complete. This theorem was proved independently by Jerzy...

product is called a cartesian monoidal category. Any category with finite products (a "finite product category") can be thought of as a cartesian monoidal category...

parameters finite (and bigger than 1) while the other infinite (these cases are called semi-finite). Peter Cameron proved the non-existence of semi-finite generalized...

in the subset are incomparable. The size of the largest antichain in a finite partially ordered set is known as its width. By Dilworth's theorem, this...

conjecture) states that for any smooth projective variety X defined over a finite field, the higher algebraic K-groups vanish up to torsion: K i ( X ) ⊗ Q...

of the notion of finite words into a complete topological space. This notion allows the use of topology to study languages and finite semigroups. For example...

set is cofinite, while the union of two finite sets is finite. Intersection behaves like union with "finite" and "cofinite" interchanged. This example...

Gelfand together with Mark Naimark in the same year. The full theory of the finite-dimensional representations of the Lie algebra of the Lorentz group is deduced...

approach to minimizing functions that can be decomposed into finite sums. By exploiting the finite sum structure, variance reduction techniques are able to...

semi-infinite space. However, numerical methods like finite difference or finite element methods require a finite, truncated grid to remain computationally feasible...

such that the field extension K / Q {\displaystyle K/\mathbb {Q} } has finite degree (and hence is an algebraic field extension). Thus K {\displaystyle...

In mathematics, the Scott core theorem is a theorem about the finite presentability of fundamental groups of 3-manifolds due to G. Peter Scott, (Scott...

Fq with q elements and Nk is the number of points of V defined over the finite field extension Fqk of Fq. Making the variable transformation t = q−s, gives...

also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties...

factor of type II and also hyperfinite Hyper-finite field, an uncountable field similar in many ways to finite fields Uniformly hyperfinite algebra, a C*-algebra...

measure theory in 1919. In simple terms, it states that if a system has a finite volume (or total probability measure) and preserves that volume over time...

In mathematics, the category FdHilb has all finite-dimensional Hilbert spaces for objects and the linear transformations between them as morphisms. Whereas...

geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain...

measures the failure of commutativity for the Lie group.) Conversely, to any finite-dimensional Lie algebra over the real or complex numbers, there is a corresponding...

{\displaystyle U} is non-empty, it must contain all of its finite subsets and a subset of each finite cardinality. One can also prove immediately from the definitions...

algebra known as group theory, the diameter of a finite group is a measure of its complexity. Consider a finite group ( G , ∘ ) {\displaystyle \left(G,\circ...

NASTRAN is a finite element analysis (FEA) program that was originally developed for NASA in the late 1960s under United States government funding for...

A\colon H\to H} that acts on a Hilbert space H {\displaystyle H} and has finite Hilbert–Schmidt norm ‖ A ‖ HS 2   = def   ∑ i ∈ I ‖ A e i ‖ H 2 , {\displaystyle...

In the mathematical area of order theory, the compact elements or finite elements of a partially ordered set are those elements that cannot be subsumed...

group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a divisor of | G | {\displaystyle...

invented in order to) compare mixed characteristic situations with purely finite characteristic ones. Technical tools for making this precise are the tilting...

wealth of subgroups, in particular it shows that the group is residually finite. An important question regarding the algebraic structure of arithmetic groups...

(over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a...

of all the infinities over any finite region, we get a finite result. The infinities are not well-defined; but the finite values can be associated with...

particular, all finite integral domains are finite fields (more generally, by Wedderburn's little theorem, finite domains are finite fields). The ring...

strength of mathematical theorems utilizing the language defined as all finite types. This richer language allows for a more natural direct formalization...

In field theory, a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field. In other words, α ∈ GF(q) is called...

referred to as finitely presented objects, or objects of finite presentation, are objects in a category satisfying a certain finiteness condition. The...

finite amount of memory. So in principle, any problem that can be solved (decided) by a Turing machine can be solved by a computer that has a finite amount...

over a finite field, using only multiplication of the matrix by long, thin matrices. Such matrices are considered as vectors of tuples of finite-field...

[etal]) is a morphism of schemes that is formally étale and locally of finite presentation; the étale morphism is connected to the concept of étale covering...

In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix is a matrix that represents the...

as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and...

signature with no relation symbols is called an algebraic signature. A finite signature is a signature such that S func {\displaystyle S_{\operatorname...

the reverse process of differentiation. Infinite element method Finite difference Finite difference time domain "Indefinite Integrals: Learn Methods of...

In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician...

space in which every open cover has an open refinement that is locally finite. These spaces were introduced by Dieudonné (1944). Every compact space is...

Python for specifying finite element discretizations of differential equations in terms of finite element variational forms; FIAT (finite element automatic...

In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph...

if the centralizer of any non-identity element is an abelian subgroup. Finite CA-groups are of historical importance as an early example of the type of...

specifically finite group theory, the Gorenstein–Harada theorem, proved by Daniel Gorenstein and Koichiro Harada, classifies the finite simple groups...

Definition", a language is assumed to be a countable set of sentences, each of finite length, and constructed out of a countable set of symbols. A theory of syntax...

The earliest contributors were Max Dehn and Jakob Nielsen: Dehn proved finite generation of the group, and Nielsen gave a classification of mapping classes...

compact-finite open refinement. That is, given any open cover, we can find an open refinement with the property that every compact set meets only finitely many...

awarded her doctorate in 1974 for a dissertation on permutation groups, Finite Permutation Groups supervised by Graham Higman. Bailey's career has not...

In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element...

grammar distinguishes non-finite clauses used as above from adverbial use, adjective-like modification of nouns, and use in finite progressive (continuous)...

{\displaystyle \{a_{i}\}} of integer numbers. The sequence can be finite or infinite, resulting in a finite (or terminated) continued fraction like a 0 + 1 a 1 +...

numbers is the unique atomic model of the theory of real closed fields. Any finite model is atomic. A dense linear ordering without endpoints is atomic. Any...

certain homomorphism from an arbitrary finite or infinite group to the commutator quotient group of a subgroup of finite index. Originally, such mappings arose...

Moore matrix, introduced by E. H. Moore (1896), is a matrix defined over a finite field. When it is a square matrix, its determinant is called a Moore determinant...

known as UML statechart, is an extension of the mathematical concept of a finite automaton in computer science applications as expressed in the Unified Modeling...

can be seen as an extension of the Moore machine formalism, which is a finite state automaton where the outputs are determined by the current state alone...

called a δ-ring if it has all of the following properties: Closed under finite unions: A ∪ B ∈ R {\displaystyle A\cup B\in {\mathcal {R}}} for all A ,...

family of graphs that is closed under taking minors can be defined by a finite set of forbidden minors, in the same way that Wagner's theorem characterizes...

analysis of partial differential equations in general and finite difference method and finite element method in particular. Mitchell has authored several...

is in NP. The "no"-answer version of this problem is stated as: "given a finite set of integers, does every non-empty subset have a nonzero sum?". The verifier-based...

required) that the elastic stress–strain relation be phrased in terms of a finite strain measure that is work conjugate to the selected stress measure, i...

theorem states that a certain claim in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in Peano arithmetic, is not provable...

Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} . The theorem...

An Egyptian fraction is a finite sum of distinct unit fractions, such as 1 2 + 1 3 + 1 16 . {\displaystyle {\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{16}}...

mathematician with expertise and contributions in discrete mathematics and finite groups. Arie received his BSc, MSc, and PhD (1984) from Tel-Aviv University...

through the notion of a universal property, as done below. When V is a finite-dimensional real vector space and Q is nondegenerate, Cl(V, Q) may be identified...

theorem is trivial if the cardinal numbers mi and ni are finite and the index set I is finite. If I is empty, then the left sum is the empty sum and therefore...

division algebras are the finite-dimensional real ones (that is, algebras over the field R of real numbers that are finite-dimensional as a vector space...

NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states...

Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream...

multiplies an element, the result is 0. However, if a finite field is considered as a module over the same finite field taken as a ring, it is a vector space and...

{\displaystyle \exists } α)Φ each to be formulas of our predicate calculus. finite-state automaton Hinman, Peter (2005). Fundamentals of Mathematical Logic...

moment) is a generalization of the weighted average. Provided that it is finite, the expected value can be interpreted as the long-run average of results...

effective method for determining membership (returning a correct answer after finite, though possibly very long, time in all cases) can exist for them. Each...

X  and  Y  finite } . {\displaystyle \operatorname {cl} (X)=\bigcup \left\{\operatorname {cl} (Y):Y\subseteq X{\text{ and }}Y{\text{ finite}}\right\}.}...

In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct...

_{8}=\langle a,b\mid a^{4}=e,a^{2}=b^{2},ba=a^{-1}b\rangle .} Like many other finite groups, it can be realized as the Galois group of a certain field of algebraic...

modern probability theory; but, alternatives exist, such as the adoption of finite rather than countable additivity by Bruno de Finetti. Most introductions...

A non-renewable resource (also called a finite resource) is a natural resource that cannot be readily replaced by natural means at a pace quick enough...

which have been proved, such as the Riemann hypothesis for curves over finite fields, which was proved by André Weil. The Riemann zeta function ζ {\displaystyle...

analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions. The mathematical...

order 81 with normal commutative subgroup of order 27. Conjecture: Any finite commutative Moufang loop of period 3 can be embedded into a commutative...

equally well to other situations like particle flow. A general discontinuous finite element formulation is needed. The unsteady convection–diffusion problem...

a category algebra is an associative algebra, defined for any locally finite category and commutative ring with unity. Category algebras generalize the...

topology on a finite set is the discrete one, a finite Hausdorff topological group must necessarily be discrete. It follows that every finite subgroup of...

phrases such as "the set of all natural numbers is infinite". Just as for finite sets, the theory makes further definitions which allow us to consistently...

Spectrum of Finite Scale is a tour-only album by the band Man or Astro-man? A departure from the band's space-surf instrumentals, A Spectrum of Finite Scale...

the Finnish mathematician Bertil Qvist [de], is a statement on ovals in finite projective planes. Standard examples of ovals are non-degenerate (projective)...

In field theory, the primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element. This theorem...

filtration of the Galois group of a finite Galois extension. A special case of it when the residue fields are finite was originally proved by Helmut Hasse...

In nonstandard analysis, a branch of mathematics, a hyperfinite set or *-finite set is a type of internal set. An internal set H of internal cardinality...