Table of Contents
115 relations: Absolute value, Additive inverse, Alfred Pringsheim, Algebraic structure, American Mathematical Society, Arity, Associative property, Automorphism group, Benjamin Peirce, Bijection, Binary relation, Cambridge University Press, Cartesian product, Category (mathematics), Category of sets, Category theory, Cayley's theorem, Chain rule, Clone (algebra), Cobweb plot, Codomain, Combinatory logic, Commutative property, Composition of relations, Composition ring, Converse relation, CRC Press, Cubic function, Dagger category, David Ellerman, De Rham curve, Derivative, Domain of a function, Dynamical system, Existential quantification, Exponentiation, Faà di Bruno's formula, Flow (mathematics), Fractal, Function (mathematics), Function application, Function composition (computer science), Functional decomposition, Functional square root, Generating set of a group, Group action, Group theory, Hans Heinrich Bürmann, Higher-order function, Homomorphism, ... Expand index (65 more) »
- Binary operations
Absolute value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign.
See Function composition and Absolute value
Additive inverse
In mathematics, the additive inverse of a number (sometimes called the opposite of) is the number that, when added to, yields zero.
See Function composition and Additive inverse
Alfred Pringsheim
Alfred Pringsheim (2 September 1850 – 25 June 1941) was a German mathematician and patron of the arts.
See Function composition and Alfred Pringsheim
Algebraic structure
In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy.
See Function composition and Algebraic structure
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
See Function composition and American Mathematical Society
Arity
In logic, mathematics, and computer science, arity is the number of arguments or operands taken by a function, operation or relation.
See Function composition and Arity
Associative property
In mathematics, the associative property is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result.
See Function composition and Associative property
Automorphism group
In mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms.
See Function composition and Automorphism group
Benjamin Peirce
Benjamin Peirce (April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years.
See Function composition and Benjamin Peirce
Bijection
A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the first set (the domain) is mapped to exactly one element of the second set (the codomain). Function composition and bijection are Basic concepts in set theory and functions and mappings.
See Function composition and Bijection
Binary relation
In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain.
See Function composition and Binary relation
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge.
See Function composition and Cambridge University Press
Cartesian product
In mathematics, specifically set theory, the Cartesian product of two sets and, denoted, is the set of all ordered pairs where is in and is in.
See Function composition and Cartesian product
Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows".
See Function composition and Category (mathematics)
Category of sets
In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets. Function composition and category of sets are Basic concepts in set theory.
See Function composition and Category of sets
Category theory
Category theory is a general theory of mathematical structures and their relations. Function composition and Category theory are functions and mappings.
See Function composition and Category theory
Cayley's theorem
In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group is isomorphic to a subgroup of a symmetric group.
See Function composition and Cayley's theorem
Chain rule
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions and in terms of the derivatives of and.
See Function composition and Chain rule
Clone (algebra)
In universal algebra, a clone is a set C of finitary operations on a set A such that.
See Function composition and Clone (algebra)
Cobweb plot
A cobweb plot, known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the logistic map.
See Function composition and Cobweb plot
Codomain
In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall. Function composition and codomain are Basic concepts in set theory and functions and mappings.
See Function composition and Codomain
Combinatory logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic.
See Function composition and Combinatory logic
Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
See Function composition and Commutative property
Composition of relations
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication, and its result is called a relative product. Function composition and composition of relations are binary operations.
See Function composition and Composition of relations
Composition ring
In mathematics, a composition ring, introduced in, is a commutative ring (R, 0, +, −, ·), possibly without an identity 1 (see non-unital ring), together with an operation such that, for any three elements f,g,h\in R one has.
See Function composition and Composition ring
Converse relation
In mathematics, the converse of a binary relation is the relation that occurs when the order of the elements is switched in the relation.
See Function composition and Converse relation
CRC Press
The CRC Press, LLC is an American publishing group that specializes in producing technical books.
See Function composition and CRC Press
Cubic function
In mathematics, a cubic function is a function of the form f(x).
See Function composition and Cubic function
Dagger category
In category theory, a branch of mathematics, a dagger category (also called involutive category or category with involution) is a category equipped with a certain structure called dagger or involution.
See Function composition and Dagger category
David Ellerman
David Patterson Ellerman (born 14 March 1943) is a philosopher and author who works in the fields of economics and political economy, social theory and philosophy, quantum mechanics, and in mathematics.
See Function composition and David Ellerman
De Rham curve
In mathematics, a de Rham curve is a continuous fractal curve obtained as the image of the Cantor space, or, equivalently, from the base-two expansion of the real numbers in the unit interval.
See Function composition and De Rham curve
Derivative
The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input. Function composition and derivative are functions and mappings.
See Function composition and Derivative
Domain of a function
In mathematics, the domain of a function is the set of inputs accepted by the function. Function composition and domain of a function are Basic concepts in set theory and functions and mappings.
See Function composition and Domain of a function
Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve.
See Function composition and Dynamical system
Existential quantification
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".
See Function composition and Existential quantification
Exponentiation
In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Function composition and exponentiation are binary operations.
See Function composition and Exponentiation
Faà di Bruno's formula
Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives.
See Function composition and Faà di Bruno's formula
Flow (mathematics)
In mathematics, a flow formalizes the idea of the motion of particles in a fluid.
See Function composition and Flow (mathematics)
Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension.
See Function composition and Fractal
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of. Function composition and function (mathematics) are Basic concepts in set theory and functions and mappings.
See Function composition and Function (mathematics)
Function application
In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. Function composition and function application are functions and mappings.
See Function composition and Function application
Function composition (computer science)
In computer science, function composition is an act or mechanism to combine simple functions to build more complicated ones.
See Function composition and Function composition (computer science)
Functional decomposition
In engineering, functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts. Function composition and functional decomposition are functions and mappings.
See Function composition and Functional decomposition
Functional square root
In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition.
See Function composition and Functional square root
Generating set of a group
In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.
See Function composition and Generating set of a group
Group action
In mathematics, many sets of transformations form a group under function composition; for example, the rotations around a point in the plane.
See Function composition and Group action
Group theory
In abstract algebra, group theory studies the algebraic structures known as groups.
See Function composition and Group theory
Hans Heinrich Bürmann
Hans Heinrich Bürmann (died 21 June 1817, in Mannheim) was a German mathematician and teacher.
See Function composition and Hans Heinrich Bürmann
Higher-order function
In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following.
See Function composition and Higher-order function
Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).
See Function composition and Homomorphism
Inclusion map
In mathematics, if A is a subset of B, then the inclusion map is the function \iota that sends each element x of A to x, treated as an element of B: \iota: A\rightarrow B, \qquad \iota(x). Function composition and inclusion map are Basic concepts in set theory and functions and mappings.
See Function composition and Inclusion map
Infinite compositions of analytic functions
In mathematics, infinite compositions of analytic functions (ICAF) offer alternative formulations of analytic continued fractions, series, products and other infinite expansions, and the theory evolving from such compositions may shed light on the convergence/divergence of these expansions.
See Function composition and Infinite compositions of analytic functions
Infinite set
In set theory, an infinite set is a set that is not a finite set.
See Function composition and Infinite set
Injective function
In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies. Function composition and injective function are Basic concepts in set theory and functions and mappings.
See Function composition and Injective function
Interval (mathematics)
In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".
See Function composition and Interval (mathematics)
Inverse function
In mathematics, the inverse function of a function (also called the inverse of) is a function that undoes the operation of. Function composition and inverse function are Basic concepts in set theory.
See Function composition and Inverse function
Inverse semigroup
In group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in the sense that and, i.e. a regular semigroup in which every element has a unique inverse.
See Function composition and Inverse semigroup
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping.
See Function composition and Isomorphism
Iterated function
In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. Function composition and iterated function are functions and mappings.
See Function composition and Iterated function
John Herschel
Sir John Frederick William Herschel, 1st Baronet (7 March 1792 – 11 May 1871) was an English polymath active as a mathematician, astronomer, chemist, inventor and experimental photographer who invented the blueprint and did botanical work.
See Function composition and John Herschel
Jules Molk
Jules Molk (8 December 1857 in Strasbourg, France – 7 May 1914 in Nancy) was a French mathematician who worked on elliptic functions.
See Function composition and Jules Molk
Lambda calculus
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.
See Function composition and Lambda calculus
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices.
See Function composition and Linear algebra
Logical conjunction
In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction.
See Function composition and Logical conjunction
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Function composition and Mathematics
Mathematics, Form and Function
Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane.
See Function composition and Mathematics, Form and Function
Matrix (mathematics)
In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
See Function composition and Matrix (mathematics)
Matrix multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices.
See Function composition and Matrix multiplication
Medial magma
In abstract algebra, a medial magma or medial groupoid is a magma or groupoid (that is, a set with a binary operation) that satisfies the identity or more simply, for all,, and, using the convention that juxtaposition denotes the same operation but has higher precedence.
See Function composition and Medial magma
Monoid
In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element.
See Function composition and Monoid
Morphism
In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures, functions from a set to another set, and continuous functions between topological spaces.
See Function composition and Morphism
Natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.
See Function composition and Natural number
Nth root
In mathematics, an th root of a number is a number (the root) which, when raised to the power of the positive integer, yields: r^n.
See Function composition and Nth root
Open Court Publishing Company
The Open Court Publishing Company is a publisher with offices in Chicago and LaSalle, Illinois.
See Function composition and Open Court Publishing Company
Operation (mathematics)
In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value.
See Function composition and Operation (mathematics)
Operator (mathematics)
In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes required to be the same space).
See Function composition and Operator (mathematics)
Operator theory
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators.
See Function composition and Operator theory
Partial function
In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to. Function composition and partial function are functions and mappings.
See Function composition and Partial function
Permutation
In mathematics, a permutation of a set can mean one of two different things.
See Function composition and Permutation
Philosophical Transactions of the Royal Society
Philosophical Transactions of the Royal Society is a scientific journal published by the Royal Society.
See Function composition and Philosophical Transactions of the Royal Society
Pointwise
In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function f. An important class of pointwise concepts are the pointwise operations, that is, operations defined on functions by applying the operations to function values separately for each point in the domain of definition.
See Function composition and Pointwise
Polish notation
Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation (RPN), in which operators follow their operands.
See Function composition and Polish notation
Prentice Hall
Prentice Hall was a major American educational publisher.
See Function composition and Prentice Hall
Primitive recursive function
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop). Function composition and primitive recursive function are functions and mappings.
See Function composition and Primitive recursive function
Programming language
A programming language is a system of notation for writing computer programs.
See Function composition and Programming language
Projection (set theory)
In set theory, a projection is one of two closely related types of functions or operations, namely. Function composition and projection (set theory) are Basic concepts in set theory.
See Function composition and Projection (set theory)
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
See Function composition and Real number
Regular semigroup
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such that.
See Function composition and Regular semigroup
Restriction (mathematics)
In mathematics, the restriction of a function f is a new function, denoted f\vert_A or f, obtained by choosing a smaller domain A for the original function f. The function f is then said to extend f\vert_A.
See Function composition and Restriction (mathematics)
Reuben Goodstein
Reuben Louis Goodstein (15 December 1912 – 8 March 1985) was an English mathematician with a strong interest in the philosophy and teaching of mathematics.
See Function composition and Reuben Goodstein
Reverse Polish notation
Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands.
See Function composition and Reverse Polish notation
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist.
See Function composition and Ring (mathematics)
Row and column vectors
In linear algebra, a column vector with elements is an m \times 1 matrix consisting of a single column of entries, for example, \boldsymbol.
See Function composition and Row and column vectors
Rowman & Littlefield
Rowman & Littlefield Publishing Group is an American independent academic publishing company founded in 1949.
See Function composition and Rowman & Littlefield
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences.
See Function composition and Royal Society
Rudy Rucker
Rudolf von Bitter Rucker (born March 22, 1946) is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk literary movement.
See Function composition and Rudy Rucker
Saunders Mac Lane
Saunders Mac Lane (August 4, 1909 – April 14, 2005), born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg.
See Function composition and Saunders Mac Lane
Schröder's equation
Schröder's equation, named after Ernst Schröder, is a functional equation with one independent variable: given the function, find the function such that Schröder's equation is an eigenvalue equation for the composition operator that sends a function to.
See Function composition and Schröder's equation
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.
See Function composition and Set theory
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
See Function composition and Springer Science+Business Media
Subset
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). Function composition and subset are Basic concepts in set theory.
See Function composition and Subset
Surjective function
In mathematics, a surjective function (also known as surjection, or onto function) is a function such that, for every element of the function's codomain, there exists one element in the function's domain such that. Function composition and surjective function are Basic concepts in set theory and functions and mappings.
See Function composition and Surjective function
Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
See Function composition and Symmetric group
Tetration
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation.
See Function composition and Tetration
TeX
TeX (see below), stylized within the system as, is a typesetting program which was designed and written by computer scientist and Stanford University professor Donald Knuth and first released in 1978.
See Function composition and TeX
Transformation (function)
In mathematics, a transformation or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e.. Function composition and transformation (function) are functions and mappings.
See Function composition and Transformation (function)
Transformation semigroup
In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under function composition.
See Function composition and Transformation semigroup
Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
See Function composition and Trigonometric functions
Trigonometry
Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
See Function composition and Trigonometry
Tuple
In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. Function composition and tuple are Basic concepts in set theory.
See Function composition and Tuple
Uniform convergence
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence.
See Function composition and Uniform convergence
University of California, Riverside
The University of California, Riverside (UCR or UC Riverside) is a public land-grant research university in Riverside, California.
See Function composition and University of California, Riverside
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.
See Function composition and Wiley (publisher)
Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-sized) interactive programmes called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.
See Function composition and Wolfram Demonstrations Project
Z notation
The Z notation is a formal specification language used for describing and modelling computing systems.
See Function composition and Z notation
See also
Binary operations
- Absorbing element
- Barrel shifter
- Binary operation
- Blaschke sum
- Cap product
- Circular convolution
- Commutator
- Composition of relations
- Courant bracket
- Cup product
- DE-9IM
- Demonic composition
- Elvis operator
- Exponentiation
- Ext functor
- Function composition
- Icosian calculus
- Identity element
- Inverse element
- Iterated binary operation
- Join and meet
- Light's associativity test
- Logic alphabet
- Logical connectives
- Logical consequence
- Lulu smoothing
- Magma (algebra)
- Mean operation
- Minkowski addition
- Modular multiplicative inverse
- Null coalescing operator
- Operations on numbers
- Relational operator
- Tor functor
- Wreath product
References
Also known as Compose (mathematics), Composite Function, Composition (functions), Composition function, Composition of functions, Composition of maps, Compound functions, Functional composition, Functional power, Generalized composite, Generalized composition, Ring operator, .