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Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function
Function_(mathematics)
Expression which is not assigned an interpretation
In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system
Undefined_(mathematics)
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some
List of mathematical functions
List_of_mathematical_functions
Function whose actual domain of definition may be smaller than its apparent domain
In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that
Partial_function
Generalization of the concept from statistical mechanics
normalized to one. The normalization for the potential function is the Jacobian for the appropriate mathematical space: it is 1 for ordinary probabilities, and
Partition function (mathematics)
Partition_function_(mathematics)
Generalization of the indicator function for classical sets in fuzzy logic
In mathematics, the membership function of a fuzzy set is a generalization of the indicator function for classical sets. In fuzzy logic, it represents
Membership function (mathematics)
Membership_function_(mathematics)
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Operation on mathematical functions
In mathematics, the composition operator ∘ {\displaystyle \circ } takes two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new
Function_composition
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Hyperbolic analogues of trigonometric functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just
Hyperbolic_functions
Functions of an angle
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate
Trigonometric_functions
Mathematical function such that every output has at least one input
In mathematics, a surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's
Surjective_function
Branch of mathematics
Mathematical analysis is the branch of mathematics that studies functions, spaces, and operators through methods of approximation and convergence. It
Mathematical_analysis
Function that is continuous everywhere but differentiable nowhere
In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass function (nowhere-differentiable function)
Weierstrass_function_(nowhere-differentiable_function)
Mathematical function, denoted exp(x) or e^x
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is
Exponential_function
C standard library header file
C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions. Different
C_mathematical_functions
Symbol representing a mathematical object
had a big influence on mathematics ever since. Originally, the term variable was used primarily for the argument of a function, in which case its value
Variable_(mathematics)
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
Book on philosophy of mathematics
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
Mathematics, Form and Function
Mathematics,_Form_and_Function
Linear map or polynomial function of degree one
In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose
Linear_function
Branch of mathematics studying functions of a complex variable
known as the theory of functions of a complex variable, is the branch of mathematical analysis that studies complex-valued functions of one or more complex
Complex_analysis
Function equal to cos x + i sin x
In mathematics, cis is a function defined by cis x = cos x + i sin x, where cos is the cosine function, i is the imaginary unit and sin is the sine function
Cis_(mathematics)
Product of numbers from 1 to n
probability theory, and computer science. Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th
Factorial
Input to a mathematical function
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example
Argument_of_a_function
Generalized mathematical function
In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in
Multivalued_function
Function that returns its argument unchanged
In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the
Identity_function
Simpler variant of the Riemann zeta function
In mathematics, the Riemann xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation
Riemann_xi_function
Field of knowledge
Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical
Mathematics
Counterintuitive mathematical object
those in related sciences) very frequently speak of whether a mathematical object—a function, a set, a space of one sort or another—is "well-behaved". While
Pathological_(mathematics)
Topics referred to by the same term
Handbook of Mathematical Functions may refer to: NBS Handbook of Mathematical Functions (with Formulas, Graphs, and Mathematical Tables) a.k.a. Abramowitz
Handbook of mathematical functions
Handbook_of_mathematical_functions
Collection of mathematical objects
space, lines, other geometric shapes, variables, functions, or even other sets. Sets cannot be mathematically defined, since they form a primitive notion.
Set_(mathematics)
Degree of differentiability of a function or map
In mathematical analysis, the smoothness describes the number of times a function can be differentiated without producing discontinuities. The smoothness
Smoothness
Conjecture on zeros of the zeta function
problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics In mathematics
Riemann_hypothesis
Fundamental trigonometric functions
In mathematics, sine and cosine are trigonometric functions. The sine and cosine of an acute angle are defined in the context of a right triangle: the
Sine_and_cosine
Function in thermodynamics and statistical physics
partition functions can be defined for different circumstances; see partition function (mathematics) for generalizations. The partition function has many
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Arithmetic function
Liouville Function". Tokyo Journal of Mathematics. 3 (1): 187–189. doi:10.3836/tjm/1270216093. MR 0584557. Weisstein, Eric W. "Liouville Function". MathWorld
Liouville_function
Generalized function whose value is zero everywhere except at zero
In mathematical analysis, the Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized
Dirac_delta_function
Study of mathematical algorithms for optimization problems
interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically
Mathematical_optimization
Point where function's value is zero
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f {\displaystyle f} , is a member x {\displaystyle
Zero_of_a_function
Linear combination of indicator functions of real intervals
In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of
Step_function
Type of mathematical function
In mathematics, a constant function is a function whose (output) value is the same for every input value. As a real-valued function of a real-valued argument
Constant_function
1964 mathematical reference work edited by M. Abramowitz and I. Stegun
Technology (NIST). Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. A digital successor to the Handbook
Abramowitz_and_Stegun
Branch of mathematics
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis. Originally called
Calculus
Divergent sum of positive unit fractions
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: ∑ i = 1 ∞ 1 i = 1 1 + 1 2 + 1 3 + 1 4 + 1 5
Harmonic_series_(mathematics)
Representation of a mathematical function
In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle
Graph_of_a_function
Mathematical functions having established names and notations
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis
Special_functions
Target set of a mathematical function
In mathematics, a codomain or set of destination of a function is a set into which all of the outputs of the function are constrained to fall. It is the
Codomain
Complex-differentiable (mathematical) function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood
Holomorphic_function
Arithmetic operation
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no universal notation for tetration, though
Tetration
Topics referred to by the same term
Function (language), a way of achieving an aim using language Function (mathematics), a relation that associates an input to a single output Function
Function
Function with a repeating pattern
illustrated through both common, everyday examples and more formal mathematical functions. Functions that map real numbers to real numbers can display periodicity
Periodic_function
Mathematical function
In mathematics, the reciprocal gamma function is the function f ( z ) = 1 Γ ( z ) , {\displaystyle f(z)={\frac {1}{\Gamma (z)}},} where Γ(z) denotes the
Reciprocal_gamma_function
Types of mappings in mathematics
In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the
Functional_(mathematics)
Mathematical function
In mathematics, an algebraic function is a function that satisfies a polynomial equation. Thus an equation of the following form holds: a n ( x ) f ( x
Algebraic_function
Mathematical function with no sudden changes
In mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies
Continuous_function
Extension of the factorial function
\ln(x)} or log e ( x ) {\displaystyle \log _{e}(x)} . In mathematics, the gamma function, denoted by Γ {\displaystyle \Gamma } (capital Greek letter
Gamma_function
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Process of repeating items in a self-similar way
logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition
Recursion
One-to-one correspondence
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the
Bijection
Sequence of program instructions invokable by other software
Event (computing) – Computing state associated with a point in time Function (mathematics) – Association of one output to each input Functional programming –
Function (computer programming)
Function_(computer_programming)
Function, homomorphism, or morphism
In mathematics, a map or mapping is synonymous to a function, though various branches add further nuances to differentiate them. The terms may have originated
Map_(mathematics)
Symbolic description of a mathematical object
In mathematics, an expression is an arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can
Expression_(mathematics)
Inputs for which a function's value is non-zero
In mathematics, the support of a real-valued function f {\displaystyle f} is the subset of the function's domain consisting of those elements that are
Support_(mathematics)
Analytic function that does not satisfy a polynomial equation
In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the
Transcendental_function
Type of function in mathematics
In mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex
Analytic_function
Function returning minus 1, zero or plus 1
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether
Sign_function
Analytic function in mathematics
In mathematics, the Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ {\displaystyle \zeta } (zeta), is
Riemann_zeta_function
Study of discrete mathematical structures
continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes
Discrete_mathematics
Amount of variation between extrema
In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme
Oscillation_(mathematics)
Inverse functions of sin, cos, tan, etc.
In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions
Inverse trigonometric functions
Inverse_trigonometric_functions
Function defined by multiple sub-functions
In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose
Piecewise_function
Continued Fractions for Special Functions. Springer. p. 182. ISBN 978-1-4020-6948-2. Cajori, Florian (1991). A History of Mathematics (5th ed.). AMS Bookstore
List of mathematical constants
List_of_mathematical_constants
Base of natural logarithms
The number e is a mathematical constant that is the base of the natural logarithm and exponential function. It is approximately equal to 2.718281828459045235360287471352
E_(mathematical_constant)
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Mathematical function, inverse of an exponential function
exponentiation extends to other mathematical structures as well. However, in general settings, the logarithm tends to be a multi-valued function. For example, the complex
Logarithm
Basic notion of sameness in mathematics
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical
Equality_(mathematics)
Subfield of mathematics
definitions of addition and multiplication from the successor function and mathematical induction. In the mid-19th century, flaws in Euclid's axioms for
Mathematical_logic
Symbols for constants, special functions
are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Real function with secant line between points above the graph itself
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or
Convex_function
mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics
Lists_of_mathematics_topics
Function that takes one or more functions as an input or that outputs a function
In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as
Higher-order_function
Number of arguments required by a function
In logic, mathematics, and computer science, arity (/ˈærɪti/ ) is the number of arguments or operands taken by a function, operation or relation. In mathematics
Arity
Basic framework of mathematics
17th century. This new area of mathematics involved new methods of reasoning and new basic concepts (continuous functions, derivatives, limits) that were
Foundations_of_mathematics
Topics referred to by the same term
integer function, INT Arithmetic function, a term for some functions of an integer variable Integer Function (mathematics) Integer (computer science) This
Integer_function
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/), denoted by sinc(x), is defined as either sinc ( x ) = sin x x {\displaystyle
Sinc_function
Mathematical function characterizing set membership
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all
Indicator_function
Mathematical-logic system
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Kind of mathematical function
In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves
Measurable_function
Function that is its own inverse
In mathematics, an involution, involutory function, or self-inverse function is a function f that is its own inverse, f(f(x)) = x for all x in the domain
Involution_(mathematics)
formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex;
Mathematical_object
Measure of the shape of a function
In mathematics, moments of a function are certain quantitative measures related to the shape of the function's graph. For example, in physics, if the
Moment_(mathematics)
Function with a smaller domain
In mathematics, the restriction of a function f {\displaystyle f} is a new function, denoted f | A {\displaystyle f\vert _{A}} or f ↾ A , {\displaystyle
Restriction_(mathematics)
Special function defined by an integral
In mathematics, the exponential integral Ei {\displaystyle \operatorname {Ei} } is a special function on the complex plane. It is defined as one particular
Exponential_integral
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
Functions such that f(–x) equals f(x) or –f(x)
In mathematics, an even function is a real function such that f ( − x ) = f ( x ) {\displaystyle f(-x)=f(x)} for every x {\displaystyle x} in its domain
Even_and_odd_functions
Mathematical function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}
Gaussian_function
Operation in calculus
comprehensive mathematical framework that both Leibniz and Newton developed. Given the name infinitesimal calculus, it allowed for precise analysis of functions with
Integral
Function returning one of only two values
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1
Boolean_function
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