92 relations: Absolute value, Additive inverse, Algebraic structure, Arity, Associative property, Bijection, Binary relation, 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, Concentration, Converse relation, Cubic function, Dagger category, 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), Function of several real variables, Functional decomposition, Functional square root, Generating set of a group, Group action, Group theory, Higher-order function, Homomorphism, Inclusion map, Infinite compositions of analytic functions, Infinite set, Injective function, Interval (mathematics), Inverse function, ..., Inverse semigroup, Isomorphism, Iterated function, Lambda calculus, Linear algebra, Logical conjunction, Mathematics, Matrix (mathematics), Matrix multiplication, Medial magma, Monoid, Morphism, Natural number, Operation (mathematics), Operator (mathematics), Operator theory, Partial function, Permutation, Pointwise, Polish notation, Primitive recursive function, Programming language, Projection (set theory), Real number, Regular semigroup, Restriction (mathematics), Reverse Polish notation, Ring (mathematics), Row and column vectors, Schröder's equation, Subset, Surjective function, Symmetric group, TeX, Transformation (function), Transformation semigroup, Trigonometric functions, Trigonometry, Tuple, Uniform convergence, Wolfram Demonstrations Project, Z notation. Expand index (42 more) »

## Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

New!!: Function composition and Absolute value · See more »

## Additive inverse

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

New!!: Function composition and Additive inverse · See more »

## Algebraic structure

In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.

New!!: Function composition and Algebraic structure · See more »

## Arity

In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.

New!!: Function composition and Arity · See more »

## Associative property

In mathematics, the associative property is a property of some binary operations.

New!!: Function composition and Associative property · See more »

## Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

New!!: Function composition and Bijection · See more »

## Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

New!!: Function composition and Binary relation · See more »

## Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

New!!: Function composition and Cartesian product · See more »

## Category (mathematics)

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.

New!!: Function composition and Category (mathematics) · See more »

## Category of sets

In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets.

New!!: Function composition and Category of sets · See more »

## Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

New!!: Function composition and Category theory · See more »

## Cayley's theorem

In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. This can be understood as an example of the group action of G on the elements of G. A permutation of a set G is any bijective function taking G onto G; and the set of all such functions forms a group under function composition, called the symmetric group on G, and written as Sym(G).

New!!: Function composition and Cayley's theorem · See more »

## Chain rule

In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.

New!!: Function composition and Chain rule · See more »

## Clone (algebra)

In universal algebra, a clone is a set C of finitary operations on a set A such that.

New!!: Function composition and Clone (algebra) · See more »

## Cobweb plot

A cobweb plot, 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.

New!!: Function composition and Cobweb plot · See more »

## Codomain

In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.

New!!: Function composition and Codomain · See more »

## Combinatory logic

Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic.

New!!: Function composition and Combinatory logic · See more »

## Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

New!!: Function composition and Commutative property · See more »

## Composition of relations

In the mathematics of binary relations, the composition relations is a concept of forming a new relation from two given relations R and S. The composition of relations is called relative multiplication in the calculus of relations.

New!!: Function composition and Composition of relations · See more »

## 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.

New!!: Function composition and Composition ring · See more »

## Concentration

In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture.

New!!: Function composition and Concentration · See more »

## Converse relation

In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation.

New!!: Function composition and Converse relation · See more »

## Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

New!!: Function composition and Cubic function · See more »

## Dagger category

In mathematics, a dagger category (also called involutive category or category with involution) is a category equipped with a certain structure called dagger or involution.

New!!: Function composition and Dagger category · See more »

## De Rham curve

In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham.

New!!: Function composition and De Rham curve · See more »

## Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

New!!: Function composition and Derivative · See more »

## Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

New!!: Function composition and Domain of a function · See more »

## Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

New!!: Function composition and Dynamical system · See more »

## 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".

New!!: Function composition and Existential quantification · See more »

## Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

New!!: Function composition and Exponentiation · See more »

## Faà di Bruno's formula

Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after, though he was not the first to state or prove the formula.

New!!: Function composition and Faà di Bruno's formula · See more »

## Flow (mathematics)

In mathematics, a flow formalizes the idea of the motion of particles in a fluid.

New!!: Function composition and Flow (mathematics) · See more »

## Fractal

In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.

New!!: Function composition and Fractal · See more »

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

New!!: Function composition and Function (mathematics) · See more »

## 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.

New!!: Function composition and Function application · See more »

## Function composition (computer science)

In computer science, function composition (not to be confused with object composition) is an act or mechanism to combine simple functions to build more complicated ones.

New!!: Function composition and Function composition (computer science) · See more »

## Function of several real variables

In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables.

New!!: Function composition and Function of several real variables · See more »

## Functional decomposition

In mathematics, 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 by function composition.

New!!: Function composition and Functional decomposition · See more »

## 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.

New!!: Function composition and Functional square root · See more »

## Generating set of a group

In abstract algebra, a generating set of a group is a subset such that every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.

New!!: Function composition and Generating set of a group · See more »

## Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

New!!: Function composition and Group action · See more »

## Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

New!!: Function composition and Group theory · See more »

## Higher-order function

In mathematics and computer science, a higher-order function (also functional, functional form or functor) is a function that does at least one of the following.

New!!: Function composition and Higher-order function · See more »

## 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).

New!!: Function composition and Homomorphism · See more »

## Inclusion map

In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element, x, of A to x, treated as an element of B: A "hooked arrow" is sometimes used in place of the function arrow above to denote an inclusion map; thus: \iota: A\hookrightarrow B. (On the other hand, this notation is sometimes reserved for embeddings.) This and other analogous injective functions from substructures are sometimes called natural injections.

New!!: Function composition and Inclusion map · See more »

## 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.

New!!: Function composition and Infinite compositions of analytic functions · See more »

## Infinite set

In set theory, an infinite set is a set that is not a finite set.

New!!: Function composition and Infinite set · See more »

## Injective function

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.

New!!: Function composition and Injective function · See more »

## Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

New!!: Function composition and Interval (mathematics) · See more »

## Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

New!!: Function composition and Inverse function · See more »

## 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 x.

New!!: Function composition and Inverse semigroup · See more »

## Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

New!!: Function composition and Isomorphism · See more »

## Iterated function

In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.

New!!: Function composition and Iterated function · See more »

## 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.

New!!: Function composition and Lambda calculus · See more »

## Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

New!!: Function composition and Linear algebra · See more »

## Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

New!!: Function composition and Logical conjunction · See more »

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Function composition and Mathematics · See more »

## Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

New!!: Function composition and Matrix (mathematics) · See more »

## Matrix multiplication

In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.

New!!: Function composition and Matrix multiplication · See more »

## Medial magma

In abstract algebra, a medial magma, or medial groupoid, is a set with a binary operation which satisfies the identity using the convention that juxtaposition denotes the same operation but has higher precedence.

New!!: Function composition and Medial magma · See more »

## Monoid

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

New!!: Function composition and Monoid · See more »

## Morphism

In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.

New!!: Function composition and Morphism · See more »

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

New!!: Function composition and Natural number · See more »

## Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

New!!: Function composition and Operation (mathematics) · See more »

## Operator (mathematics)

In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space.

New!!: Function composition and Operator (mathematics) · See more »

## Operator theory

In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators.

New!!: Function composition and Operator theory · See more »

## Partial function

In mathematics, a partial function from X to Y (written as or) is a function, for some subset X ′ of X.

New!!: Function composition and Partial function · See more »

## Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

New!!: Function composition and Permutation · See more »

## 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 — operations defined on functions by applying the operations to function values separately for each point in the domain of definition.

New!!: Function composition and Pointwise · See more »

## 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 reverse Polish notation (RPN) in which operators follow their operands.

New!!: Function composition and Polish notation · See more »

## Primitive recursive function

In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive).

New!!: Function composition and Primitive recursive function · See more »

## Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

New!!: Function composition and Programming language · See more »

## Projection (set theory)

In set theory, a projection is one of two closely related types of functions or operations, namely.

New!!: Function composition and Projection (set theory) · See more »

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

New!!: Function composition and Real number · See more »

## Regular semigroup

In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a, there exists an element x such that axa.

New!!: Function composition and Regular semigroup · See more »

## Restriction (mathematics)

In mathematics, the restriction of a function f is a new function f\vert_A obtained by choosing a smaller domain A for the original function f. The notation f is also used.

New!!: Function composition and Restriction (mathematics) · See more »

## Reverse Polish notation

Reverse Polish notation (RPN), also known as Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to Polish notation (PN), in which operators precede their operands.

New!!: Function composition and Reverse Polish notation · See more »

## Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

New!!: Function composition and Ring (mathematics) · See more »

## Row and column vectors

In linear algebra, a column vector or column matrix is an m × 1 matrix, that is, a matrix consisting of a single column of m elements, Similarly, a row vector or row matrix is a 1 × m matrix, that is, a matrix consisting of a single row of m elements Throughout, boldface is used for the row and column vectors.

New!!: Function composition and Row and column vectors · See more »

## 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, which sends a function to.

New!!: Function composition and Schröder's equation · See more »

## Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

New!!: Function composition and Subset · See more »

## Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).

New!!: Function composition and Surjective function · See more »

## 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.

New!!: Function composition and Symmetric group · See more »

## TeX

TeX (see below), stylized within the system as TeX, is a typesetting system (or "formatting system") designed and mostly written by Donald Knuth and released in 1978.

New!!: Function composition and TeX · See more »

## Transformation (function)

In mathematics, particularly in semigroup theory, a transformation is a function f that maps a set X to itself, i.e..

New!!: Function composition and Transformation (function) · See more »

## Transformation semigroup

In algebra, a transformation semigroup (or composition semigroup) is a collection of functions from a set to itself that is closed under function composition.

New!!: Function composition and Transformation semigroup · See more »

## Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

New!!: Function composition and Trigonometric functions · See more »

## Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

New!!: Function composition and Trigonometry · See more »

## Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

New!!: Function composition and Tuple · See more »

## Uniform convergence

In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.

New!!: Function composition and Uniform convergence · See more »

## Wolfram Demonstrations Project

The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.

New!!: Function composition and Wolfram Demonstrations Project · See more »

## Z notation

The Z notation is a formal specification language used for describing and modelling computing systems.

New!!: Function composition and Z notation · See more »

## Redirects here:

Compose (mathematics), Composite Function, Composite function, Composition (functions), Composition (mathematics), Composition function, Composition of functions, Composition of maps, Compound functions, Functional composition, Functional power, Generalized composite, Generalized composition, Ring operator, ∘.

## References

[1] https://en.wikipedia.org/wiki/Function_composition