DOSEN PROFIL LENGKAP

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...

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

A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of...

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...

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

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...

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

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...

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

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

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...

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

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

{\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...

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

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...

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...

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

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 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 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...

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:...

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...

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

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...

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...

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

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 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...

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...

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...

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...

{\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...

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...

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...

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

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

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...

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

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...

{\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 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...

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...

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

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...

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

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

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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

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...

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...

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...

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...

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...

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

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

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

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...

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

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...

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...

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...

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

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

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

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

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

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

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

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

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...

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

to as "finite intervals" or "finite regions". However, they do not typically have a finite number of elements, and while they all have finite volume,...

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...

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...

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...

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 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...

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...

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

{\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...

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...

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

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

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...

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

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

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...

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

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

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

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

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

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...

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...

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

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...

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...

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...

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...

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...

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

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

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

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...

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

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...

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)...

\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....

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...

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...

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...

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...

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

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

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...

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

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...

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

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...

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

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

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...

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

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...

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...

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

{\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...

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

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...

of analysis called the Finite Element Method. The complex problems are solved by dividing a surface into a large but still finite number of elements and...

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...

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

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...

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...

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...

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

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

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

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...

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

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...

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

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...

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...

\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...

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

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

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...

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...

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...

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

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

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...

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...

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...

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...

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

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...

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

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...

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...

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

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

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...

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...

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...

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...

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...

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

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

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

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

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...

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...

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...

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...

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

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...

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...

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

(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...

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

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

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...

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...

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...

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...

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...

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

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

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

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)...

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

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

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...

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

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...

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...

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...

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...

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...

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...

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...

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 mathematics, the Conway polynomial Cp,n for the finite field Fpn is a particular irreducible polynomial of degree n over Fp that can be used to define...

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,...

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...

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

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

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

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...

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...

Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced...

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...

{\displaystyle S} is compact, that is, every open cover of S {\displaystyle S} has a finite subcover S {\displaystyle S} is closed and bounded. The theorem is sometimes...

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...

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

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

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...

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)...

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...

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...

states that certain dynamical systems will, after a sufficiently long but finite time, almost certainly return to a state arbitrarily close to their initial...

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...

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...

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...

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...

such is a finite reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups...

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...

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...

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

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...

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

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

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

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

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

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...

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...

generalization of the London–van der Waals force and includes retardation due to the finite speed of light. The fundamental principles leading to the London–van der...

coding. In the tabled ANS (tANS) variant, this is achieved by constructing a finite-state machine to operate on a large alphabet without using multiplication...

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...

 · 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...

_{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...

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...

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...

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...

transform (DFT) is a discrete version of the Fourier transform that converts a finite sequence of numbers into another sequence of the same length, representing...

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...

is finitely presentable if and only if it is a finitely presented group, i.e. if it has a presentation with finitely many generators and finitely many...

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...

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

→ 2 ∗ {\displaystyle U:2^{*}\to 2^{*}} be a computable function mapping finite binary strings to binary strings. It is a universal function if, and only...

\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 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...

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...

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...

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...

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

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

arbitrary state space. However, many applications of Markov chains employ finite or countably infinite state spaces, which have a more straightforward statistical...

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

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...

Deterministic finite automaton (DFA) Also called a finite-state machine. All real computing devices in existence today can be modeled as a finite-state machine...

all but finitely many integers n p {\displaystyle n_{\mathfrak {p}}} are zero. Thus the group of fractional ideals records, for each finite place of...

Suppose X and Y are σ-finite measure spaces and suppose that X × Y is given the product measure (which is unique as X and Y are σ-finite). Fubini's theorem...

In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs...

of functions. In particular, the finite symmetric group S n {\displaystyle \mathrm {S} _{n}} defined over a finite set of n {\displaystyle n} symbols...

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

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...

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

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...

4), the projective special linear group of 3-dimensional space over the finite field with 4 elements (Dixon & Mortimer 1996, pp. 192–205). This group,...

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...

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...

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...

(finite sequences of symbols). The Kleene star operator on an alphabet V generates the set V* of all finite-length strings over V, that is, finite sequences...

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

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

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...

two-dimensional finite CW-complexes. (When only triangular faces are used, they are two-dimensional finite simplicial complexes.) In general, for any finite CW-complex...

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

Strand7 is a Finite Element Analysis (FEA) software product developed by the company with the same name. The Strand computer software was first developed...

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

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

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...

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

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...

directed preorder or a filtered set) is a preordered set in which every finite subset has an upper bound. In other words, it is a non-empty preordered...

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...

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...

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...

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...

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 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...

the ring is a finite field, the Dickson polynomials, which are closely related to the Chebyshev polynomials, provide examples. Over a finite field, every...

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...

decomposition might not have finite volume geometric structures. (For example, the mapping torus of an Anosov map of a torus has a finite volume solv structure...

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...

a finite-dimensional subspace. This can be done by a finite element method, a finite difference method, or (particularly in engineering) a finite volume...

function. However, in infinite systems, the total energy is no longer a finite number and cannot be used in the traditional construction of the probability...

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

modelled by the empty set. When speaking of the sum of the elements of a finite set, one is inevitably led to the convention that the sum of the elements...

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...

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...

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...

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...

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

September 2018. "Accelerated Finite Element Analysis". FiniteNow. 29 July 2025. Retrieved 6 August 2025. "Accelerating Finite‑Element Structural Elastic...

phase. The finite SSH chain can behave as a topological insulator, depending on the boundary conditions at the edges of the chain. For the finite chain, there...

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...

duality, gives rise to an algebra, but not in general the other way. In finite dimensions, this duality goes in both directions (see below). Coalgebras...

Verb phrases generally are divided among two types: finite, of which the head of the phrase is a finite verb; and nonfinite, where the head is a nonfinite...

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...

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...

In the calculus of finite differences, the indefinite sum (or antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle \Delta...

Hadamard factorization theorem asserts that every entire function with finite order can be represented as a product involving its zeroes and an exponential...

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

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...

the task of determining whether or not the formula is a tautology is a finite and mechanical one: one needs only to evaluate the truth value of the formula...

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...

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

category (or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order-preserving maps. It is used...

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...

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...

is a theorem that guarantees that a suitably "consistent" collection of finite-dimensional distributions will define a stochastic process. It is credited...

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...

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...

with no last element, and where each individual result is finite and is achieved in a finite number of steps. This type of process occurs in mathematics...

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

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 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...

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

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

their speed is measured. For long distances and sensitive measurements, the finite speed of light has noticeable effects. Much starlight viewed on Earth is...

empty. Interval finite poset. A partially ordered set P is interval finite if every interval of the form {x in P | x ≤ a} is a finite set. Inverse. See...

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, ∩...

algebraically closed fields, in the classification of Weyl groups and other finite reflection groups, and in other contexts. Various properties of the Dynkin...

is finite in the past.[clarification needed] The philosophy of Aristotle, expressed in such works as his Physics, held that although space was finite, with...

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...

hyperorthogonal group is an archaic name for the unitary group, especially over finite fields. Since the determinant of a unitary matrix is a complex number with...

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...

In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences...

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

asserts that every ideal of a polynomial ring over a field has a finite generating set (a finite basis in Hilbert's terminology). In modern algebra, rings whose...

that if an ideal I in a commutative ring R is contained in a union of finitely many prime ideals Pi's, then it is contained in Pi for some i. There are...

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...

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...

two-dimensional Euclidean plane and three-dimensional space to spaces of any finite or infinite dimension. A Hilbert space is an abstract vector space, and...

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...

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...

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

In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections:...

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

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

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...

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...

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...

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...

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

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...

In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently...

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...

group G2(q) is the points of the algebraic group G2 over the finite field Fq. These finite groups were first introduced by Leonard Eugene Dickson in Dickson...

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

pairs of elements need to have a supremum and an infimum. Every non-empty finite lattice is complete, but infinite lattices may be incomplete. Complete lattices...

formulation, to a discrete problem by applying linear constraints determined by finite sets of basis functions. They are named after the Soviet mathematician Boris...

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

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...

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...

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

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...

non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata...

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...

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}...

function for which the integral of the square of the absolute value is finite. Thus, square-integrability on the real line ( − ∞ , + ∞ ) {\displaystyle...

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...

looking for evidence to support the proposal that our universe might be finite in size due to its having a nontrivial topology. Other work includes black...

difference is in fact a vector space over the field with 2 elements Z2. If X is finite, then the singletons form a basis of this vector space, and its dimension...

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...

on permutation representations. Other than a few marked exceptions, only finite groups will be considered in this article. We will also restrict ourselves...

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...

randomness of each keystroke, the monkey would almost surely type every possible finite text an infinite number of times. The theorem can be generalized to state...

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

two copies of the cyclic group of order 2 by the Fundamental Theorem of Finitely Generated Abelian Groups. It was named Vierergruppe (German: [ˈfiːʁɐˌɡʁʊpə]...

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...

numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers...

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

In finite group theory, a mathematical discipline, the Gilman–Griess theorem, proved by Robert H. Gilman and Robert L. Griess, classifies the finite simple...

{\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 +...

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...

December 1948) is an American mathematician specializing in the theory of finite groups. Solomon studied as an undergraduate at Queens College and received...

defining a probability distribution over sparse binary matrices with a finite number of rows and an infinite number of columns. This distribution is suitable...

Harada (原田 耕一郎, Harada Kōichirō) is a Japanese mathematician working on finite group theory. Harada first came to the United States in 1968, as a student...

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...

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

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...

Ado's theorem is a theorem characterizing finite-dimensional Lie algebras. Ado's theorem states that every finite-dimensional Lie algebra L over a field...

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...

of the weighted average. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the...

space. The integers modulo 2 form the finite field F 2 {\displaystyle \mathbb {F} _{2}} , the smallest finite field. It has two elements, usually denoted...

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

to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum. While the series itself diverges...

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

consisting only of scalar operators. A finite von Neumann algebra is one which is the direct integral of finite factors (meaning the von Neumann algebra...

arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set A of integers, at least one of the sets A + A and A · A (the sets of...

different kinds of finite automata. The classical result in the area is that simulating an n {\displaystyle n} -state nondeterministic finite automaton by a...

field is a special type of algebra, one that is isomorphic to a finite product of finite separable field extensions. An étale algebra is a special sort...

in a finite amount of time. Informally, it means that if the answer to a problem instance is 'yes', then there is some procedure that takes finite time...

quasi-isometry invariant of finitely generated groups. As shown by Guoliang Yu, finitely generated groups of finite homotopy type with finite asymptotic dimension...

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

curved surfaces like spheres, cylinders, and cones, which can be infinite or finite. Some two-dimensional mathematical spaces are not used to represent physical...

there is a positive number δ {\displaystyle \delta } such that whenever a finite sequence of pairwise disjoint sub-intervals ( x k , y k ) {\displaystyle...

the potential outcomes: if God does not exist, the believer incurs only finite losses, potentially sacrificing certain pleasures and luxuries; if God does...

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

reflection. Rectangular potential barrier Finite potential well Infinite potential well Delta potential barrier Finite potential barrier The transmission coefficient...

that every finite separable extension is a simple extension. For a field of characteristic 0 such as the rationals, this means all finite extensions are...

In the theory of computation, a Moore machine is a finite-state machine whose current output values are determined only by its current state. This is in...

IP set is a set of natural numbers which contains all finite sums of some infinite set. The finite sums of a set D of natural numbers are all those numbers...

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...

his Ph.D. from Princeton University in 1996 with a dissertation titled Finite Honda Systems And Supersingular Elliptic Curves. He was also featured as...

speech. Each verb lexeme has a collection of finite and non-finite forms in its conjugation scheme. Finite forms depend on grammatical tense and person/number...

mechanics. Bathe is considered to be one of the pioneers in the field of finite element analysis and its applications. He was born in Berlin as a second...

Grigorchuk group is a finitely generated group constructed by Rostislav Grigorchuk that provided the first example of a finitely generated group of intermediate...

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...

morphological finite forms); the rest only have non-finite forms, which can enter into a wide variety of compound tense structures (consisting of a non-finite verb...

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

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

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...

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

constraint logic programming is that of finite domains. Values of variables are in this case taken from a finite domain, often that of integer numbers....

mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s by Walter...

prime. The integers modulo 3 form the finite field F 3 {\displaystyle \mathbb {F} _{3}} , the smallest finite field of odd characteristic. In algebraic...

on 7 April 2017. A reviewer of Sputnikmusic commented "For all we know inFinite may very well be Deep Purple’s final stand and for what is worth, it cannot...

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...

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

group theory, the Stallings theorem about ends of groups states that a finitely generated group G {\displaystyle G} has more than one end if and only if...

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...

symbols are parts of the vocabulary under a formal grammar. Vocabulary is a finite, nonempty set of symbols. Terminal symbols are symbols that cannot be replaced...

For instance, a lattice is a partially ordered set in which all nonempty finite subsets have both a supremum and an infimum, and a complete lattice is a...

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...

discrete group of isometries (a Kleinian group). Hyperbolic 3-manifolds of finite volume have a particular importance in 3-dimensional topology as follows...

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...

σ-ring generated by R, and this extension is unique if the pre-measure is σ-finite. Consequently, any pre-measure on a ring containing all intervals of real...

Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by...

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...

paper "Finite Automata and Their Decision Problems". Soon, using nondeterministic automata, they were able to re-prove Kleene's result that finite state...

In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order...

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...

is in SLn. Let G {\displaystyle G} be a group, and V {\displaystyle V} a finite-dimensional vector space over a field k {\displaystyle k} (which in classical...

planar electrode. If the thickness of the diffusion layer is known, the finite-length Warburg element is defined as: Z O = 1 Y 0 tanh ⁡ ( B j ω ) {\displaystyle...

The following list in mathematics contains the finite groups of small order up to group isomorphism. For n = 1, 2, … the number of nonisomorphic groups...

variety or an orbifold, while still allowing mild stacky phenomena such as finite stabilizer groups. More precisely, a stack F {\displaystyle F} over schemes...

In computer science, the complexity function of a word or string (a finite or infinite sequence of symbols from some alphabet) is the function that counts...

include: The number of equivalence classes is finite or infinite; The number of equivalence classes equals the (finite) natural number n; All equivalence classes...

normed space but the converse is not true. For example, the set of the finite sequences of real numbers can be normed with the Euclidean norm, but it...

model if and only if every finite subset has a model, or in other words that an inconsistent set of formulas must have a finite inconsistent subset. The...

elements are usually called algebraic integers. The algebraic integers in a finite extension field k of the rationals Q form a subring of k, called the ring...

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

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

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...

property if all finitely generated free modules over R have a well-defined rank. In the case of fields, the IBN property is the fact that finite-dimensional...

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...

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

can be described by a finite set of (unknown) parameters. In contrast, nonparametric statistics does not assume explicit (finite-parametric) mathematical...

directed graphs. They differ from finite-state automata in several ways: The set of states is not necessarily finite, or even countable. The set of transitions...

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

computer hardware and software In particular, a finite-state automaton, an automaton limited to a finite state space Automatons (film), a 2006 film Automaton...

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

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)...

the topology of subgroups of finite index. A finite G-set is then a finite set X on which G acts through a quotient finite cyclic group, so that it is...

presentation of any language in the class, the learner will produce only a finite number of wrong representations, and then stick with the correct representation...

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...

bounds. Therefore, a set of real numbers is bounded if it is contained in a finite interval. A subset S of a metric space (M, d) is bounded if there exists...

equality) and finitely many logical symbols, only finitely many axioms are needed to build the classes satisfying them. This is why NBG is finitely axiomatizable...

statistically independent samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges...

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 input (the plaintext). The meaning of "format" varies. Typically only finite sets of characters are used; numeric, alphabetic or alphanumeric. For example:...

Hermes2D (Higher-order modular finite element system) is a C++/Python library of algorithms for rapid development of adaptive hp-FEM solvers. hp-FEM is...

meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator...

set A {\displaystyle A} of finite measure, E ∩ A {\displaystyle E\cap A} is measurable. σ {\displaystyle \sigma } -finite measures and measures arising...

time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable...