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Function from sets to numbers
mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values
Set_function
Association of one output to each input
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 and the set Y
Function_(mathematics)
Set-to-real map with diminishing returns
submodular set function (also known as a submodular function) is a set function that, informally, describes the relationship between a set of inputs and
Submodular_set_function
mathematics, a superadditive set function is a set function whose value when applied to the union of two disjoint sets is greater than or equal to the
Superadditive_set_function
subadditive set function is a set function whose value, informally, has the property that the value of function on the union of two sets is at most the
Subadditive_set_function
Mapping function
an additive set function is a function μ \mu mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum
Sigma-additive_set_function
Function whose values are sets (mathematics)
A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the
Set-valued_function
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
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
Set of the values of a function
In mathematics, the image of a function f : X → Y {\displaystyle f:X\to Y} is the set of all f ( x ) {\displaystyle f(x)} such that x {\displaystyle
Image_(mathematics)
primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather
Primitive recursive set function
Primitive_recursive_set_function
Class of mathematical functions
function is a function on a lattice that, informally, has the property of being characterized by "increasing differences." Seen from the point of set
Supermodular_function
Collection of mathematical objects
geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a "set" or "collection", because
Set_(mathematics)
Fractal sets in complex dynamics of mathematics
set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function
Julia_set
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
Point where function's value is zero
hypothesis on the codomain of the function, a level set of a function f {\displaystyle f} is the zero set of the function f − c {\displaystyle f-c} for some
Zero_of_a_function
Real function with secant line between points above the graph itself
a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph
Convex_function
Target set of a mathematical function
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 set Y in the notation
Codomain
In set theory, a continuous function is a sequence of ordinals such that the values assumed at limit stages are the limits (limit suprema and limit infima)
Continuous function (set theory)
Continuous_function_(set_theory)
Type of function in mathematics
an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at
Analytic_function
Conceptual framework used in numerical analysis of surfaces and shapes
well-behaved boundary. Below it, the red surface is the graph of a level set function φ {\displaystyle \varphi } determining this shape, and the flat blue
Level-set_method
Mathematical function such that every output has at least one input
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 codomain, there
Surjective_function
Mathematical function with convex lower level sets
quasiconvex function is a real-valued function defined on a convex subset of a real vector space, such that for any real number y, the set of points on
Quasiconvex_function
Axiomatic set theories based on the principles of mathematical constructivism
total) function. This is often because the predicate in a case-wise would-be definition may not be decidable. Adopting the standard definition of set equality
Constructive_set_theory
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computable_function
Set of functions used to represent the electronic wave function
computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method
Basis_set_(chemistry)
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
relations are true of composition of functions, such as associativity. Composition of functions on a finite set: If f = {(1, 1), (2, 3), (3, 1), (4, 2)}
Function_composition
Function that is continuous everywhere but differentiable nowhere
concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. Weierstrass's demonstration that continuity
Weierstrass_function
codomain of a function, the function does not change as a set since by definition it is just a set of ordered pairs. That is, a function does not determine
Implementation of mathematics in set theory
Implementation_of_mathematics_in_set_theory
Kind of mathematical function
mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure
Measurable_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
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
Class of mathematical function
function on an open subset D {\displaystyle D} of the complex plane is a function that is holomorphic on all of D {\displaystyle D} except for a set of
Meromorphic_function
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
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
Set of functions between two fixed sets
In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which
Function_space
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Ratio of polynomial functions
polynomial functions of x {\displaystyle x} and Q {\displaystyle Q} is not the zero function. The domain of f {\displaystyle f} is the set of all values
Rational_function
Smooth and compactly supported function
commonly used as cutoff functions, for example functions that are equal to 1 on a prescribed set and vanish outside a larger set, and as standard examples
Bump_function
Generalized mathematical function
It is a set-valued function with additional properties depending on context; though some authors do not distinguish between set-valued functions and multifunctions
Multivalued_function
Subset of a function's domain on which its value is equal
In mathematics, a level set of a real-valued function f of n real variables is a set where the function takes on a given constant value c, that is: L
Level_set
Shape containing unit line segments in all directions
bounds on a circular maximal function analogous to the Kakeya maximal function. It was conjectured that there existed sets containing a sphere around every
Kakeya_set
Topics referred to by the same term
are sets and total functions, respectively Set (abstract data type), a data type in computer science that is a collection of distinct values Set (C++)
Set
Function computable with bounded loops
§ Limitations below. The set of primitive recursive functions is known as PR in computational complexity theory. A primitive recursive function takes a fixed number
Primitive_recursive_function
Extension of the factorial function
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic
Gamma_function
exclusive possible worlds. The application of functions to value sets creates combinations of value sets from different worlds. Narrowing reduces those
Narrowing of algebraic value sets
Narrowing_of_algebraic_value_sets
One-to-one correspondence
bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the
Bijection
Constant function: has a fixed value regardless of its input. Empty function: whose domain equals the empty set. Set function: whose input is a set. Set-valued
List_of_types_of_functions
Expressing a measure as an integral of another
between two measures defined on the same measurable space. A measure is a set function that assigns a consistent magnitude to the measurable subsets of a measurable
Radon–Nikodym_theorem
In geometry, set whose intersection with every line is a single line segment
smallest convex set containing A. A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points
Convex_set
About mathematical functions
invention of set theory by Georg Cantor, eventually led to the much more general modern concept of a function as a single-valued mapping from one set to another
History of the function concept
History_of_the_function_concept
Javascript design pattern
are functions. let counter = (function () { let i = 0; return { get: function () { return i; }, set: function (val) { i = val; }, increment: function ()
Immediately invoked function expression
Immediately_invoked_function_expression
Set of elements common to all of some sets
Hall. ISBN 0-13-181629-2. Rosen, Kenneth (2007). "Basic Structures: Sets, Functions, Sequences, and Sums". Discrete Mathematics and Its Applications (Sixth ed
Intersection_(set_theory)
Generalization of mass, length, area and volume
(cf. Dirac delta function) is given by δa(S) = χS(a), where χS is the indicator function of S . {\displaystyle S.} The measure of a set is 1 if it contains
Measure_(mathematics)
Type of mathematical function
value is c = 4. The domain of this function is the set of all real numbers. The image of this function is the singleton set {4}. The independent variable x
Constant_function
Subset of a function's codomain
image of a function are the same set; such a function is called surjective or onto. For any non-surjective function f : X → Y , {\displaystyle f:X\to
Range_of_a_function
Mathematical set of all subsets of a set
indicator function or a characteristic function of a subset A of a set S with the cardinality |S| = n is a function from S to the two-element set {0, 1}
Power_set
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 {−1,1})
Boolean_function
Statistical function that defines the quantiles of a probability distribution
probability distribution's quantile function is the inverse of its cumulative distribution function. That is, the quantile function of a distribution D {\displaystyle
Quantile_function
Tasks in machine learning
training data set. The performance of the networks is then compared by evaluating the error function using an independent validation set, and the network
Training, validation, and test data sets
Training,_validation,_and_test_data_sets
Branch of mathematics that studies sets
function as a relation from one set (the domain) to another set (the range). Paul Halmos, Naive Set Theory, 1960, Springer Verlag. Thomas Jech, Set Theory
Set_theory
Mathematical function whose derivative exists
Banach states that the set of functions that have a derivative at some point is a meagre set in the space of all continuous functions. Informally, this means
Differentiable_function
Mathematical function with no sudden changes
a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies
Continuous_function
Study of mathematical algorithms for optimization problems
minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization
Mathematical_optimization
Distance from origin of tangent hyperplanes
In mathematics, the support function hA of a non-empty closed convex set A in R n {\displaystyle \mathbb {R} ^{n}} describes the (signed) distances of
Support_function
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Elementary functions and their finitely iterated integrals
Liouvillian functions comprise a set of functions including the elementary functions and their repeated integrals. Liouvillian functions can be recursively
Liouvillian_function
Function that returns its argument unchanged
X {\displaystyle X} is a set, the identity function f {\displaystyle f} on X {\displaystyle X} is defined to be a function with X {\displaystyle X} as
Identity_function
Distance from a point to the boundary of a set
the signed distance function or signed distance field (SDF) is the orthogonal distance of a given point x to the boundary of a set Ω in a metric space
Signed_distance_function
Function uniquely mapping two numbers into a single number
a pairing function is a process to uniquely encode two natural numbers into a single natural number. Any pairing function can be used in set theory to
Pairing_function
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Mathematical set that can be enumerated
countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural
Countable_set
Mathematical function whose set of values is bounded
mathematics, a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values
Bounded_function
Analytic function that does not satisfy a polynomial equation
mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable
Transcendental_function
Region with boundary of finite measure
measure. A synonym is set of (locally) finite perimeter. Basically, a set is a Caccioppoli set if its characteristic function is a function of bounded variation
Caccioppoli_set
Largest and smallest value taken by a function at a given point
maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded
Maximum_and_minimum
Maximum size of an independent set of the matroid
independent subset of S, and the rank function of the matroid maps sets of elements to their ranks. The rank function is one of the fundamental concepts
Matroid_rank
Mathematical function
Let X be a set of sets none of which are empty. Then a choice function (selector, selection) on X is a mathematical function f that is defined on X such
Choice_function
Evaluation of a function on its argument
In mathematics, function application (or evaluation) is the act of taking a function and an input from its domain to obtain the corresponding value from
Function_application
Function, homomorphism, or morphism
can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph
Map_(mathematics)
Well-quasi-ordering of finite trees
application of the theorem gives the existence of a fast-growing TREE function. TREE(3) is one of the largest simply defined finite numbers, dwarfing
Kruskal's_tree_theorem
Mathematical activation function in data analysis
set to 1) or trainable and "sigmoid" refers to the logistic function. The swish family was designed to smoothly interpolate between a linear function
Swish_function
Construct related to weighted sums and averages
elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in
Weight_function
functions. They were introduced by René-Louis Baire in 1899. A Baire set is a set whose characteristic function is a Baire function. Baire functions of
Baire_function
Multiplicative function in number theory
The Möbius function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand
Möbius_function
Function that applies a set to itself
transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include
Transformation_(function)
Comprehensive list of Magic: The Gathering card sets since its inception in 1993
similar function; however, they are always attached to a specific set or block, while compilations are free to pick and choose cards from any set. All expansion
List of Magic: The Gathering sets
List_of_Magic:_The_Gathering_sets
Indicator function of rational numbers
mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle
Dirichlet_function
Set function that is a precursor to a measure
In mathematics, a pre-measure is a set function that is, in some sense, a precursor to a bona fide measure on a given space. Indeed, one of the fundamental
Pre-measure
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
Symbol representing a mathematical concept
systems particularly mathematical logic, a function symbol is a non-logical symbol which represents a function or mapping on the domain of discourse, though
Function_symbol
Objective function of evolutionary algorithm
fitness function does not change, as in optimizing a fixed function or testing with a fixed set of test cases; and one where the fitness function is mutable
Fitness_function
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
S-shaped curve
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac
Logistic_function
Function family in complex analysis
a holomorphic function on an open set D {\displaystyle D} , then f ( z ¯ ) {\displaystyle f({\bar {z}})} is an antiholomorphic function on D ¯ {\displaystyle
Antiholomorphic_function
Function with a repeating pattern
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which are used to describe waves
Periodic_function
Mathematical logic concept
set S is the range of a partial computable function. The set S is the range of a total computable function, or empty. If S is infinite, the function can
Computably_enumerable_set
are two equivalent ways to define a cylinder set measure. One way is to define it directly as a set function on the cylindrical algebra such that certain
Cylinder_set_measure
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
SET FUNCTION
SET FUNCTION
Female
Egyptian
, an uncertain goddess.
Female
Hungarian
Hungarian form of Greek Elisabet, ERZSÉBET means "God is my oath."
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Female
Egyptian
, the wife of Osirtesen.
Female
Egyptian
, a wife and daughter of Antef.
Female
Egyptian
, second wife of Antef.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Surname or Lastname
English
English : variant spelling of See.
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Female
Egyptian
, a sister of Sekherta.
Male
English
Short form of English Stephen, STE means "crown."
Surname or Lastname
English and German
English and German : topographic name for someone who lived by the sea-shore or beside a lake, from Middle English see ‘sea’, ‘lake’ (Old English sǣ), Middle High German sē. Alternatively, the English name may denote someone who lived by a watercourse, from an Old English sēoh ‘watercourse’, ‘drain’.
Surname or Lastname
English
English : perhaps a variant of Sait, from the Old English personal name Sǣgēat (‘sea Geat’).
Female
Egyptian
, a sister of Sekherta.
Female
Egyptian
, the wife of the usurper Sipthah.
Female
Egyptian
, the mother of Fai-hor-ou-oer.
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
SET FUNCTION
SET FUNCTION
Boy/Male
English
Lives in the valley.
Boy/Male
Gujarati, Hindu, Indian, Malayalam, Marathi, Sindhi, Telugu
One who Stays in Heaven
Boy/Male
Hindu
Beautiful flower
Boy/Male
French American Italian
Born on Easter.
Boy/Male
Arabic, Muslim
Writer; Scribe
Boy/Male
Hindu, Indian, Kannada, Sanskrit, Traditional
Name of Famous Priest Called Lord Basava; Bull; Strong; Virile
Male
English
Variant spelling of English Piers, PEARCE means "rock, stone."
Boy/Male
Indian, Tamil
Lake; Love; Royal Child
Female
Polish
Short form of Polish Joasia, ASIA means "Yahweh is gracious." Compare with another form of Asia.
Boy/Male
Muslim
Cone bearing tree, Fir
SET FUNCTION
SET FUNCTION
SET FUNCTION
SET FUNCTION
SET FUNCTION
n.
Direction or course; as, the set of the wind, or of a current.
n.
That which is set, placed, or fixed.
n.
See Set, n., 2 (e) and 3.
n.
A series of as many games as may be necessary to enable one side to win six. If at the end of the tenth game the score is a tie, the set is usually called a deuce set, and decided by an application of the rules for playing off deuce in a game. See Deuce.
a.
Established; prescribed; as, set forms of prayer.
a.
Fixed in position; immovable; rigid; as, a set line; a set countenance.
v. i.
To fit or suit one; to sit; as, the coat sets well.
v. t.
To determine; to appoint; to assign; to fix; as, to set a time for a meeting; to set a price on a horse.
a.
Regular; uniform; formal; as, a set discourse; a set battle.
imp. & p. p.
of Set
v. t.
To cause to sit; to make to assume a specified position or attitude; to give site or place to; to place; to put; to fix; as, to set a house on a stone foundation; to set a book on a shelf; to set a dish on a table; to set a chest or trunk on its bottom or on end.
a.
Firm; unchanging; obstinate; as, set opinions or prejudices.
v. i.
To be fixed for growth; to strike root; to begin to germinate or form; as, cuttings set well; the fruit has set well (i. e., not blasted in the blossom).
v. t.
To reduce from a dislocated or fractured state; to replace; as, to set a broken bone.
v. t.
To make to agree with some standard; as, to set a watch or a clock.
v. t.
To extend and bring into position; to spread; as, to set the sails of a ship.
v. t.
To put in order in a particular manner; to prepare; as, to set (that is, to hone) a razor; to set a saw.
v. t.
To compose; to arrange in words, lines, etc.; as, to set type; to set a page.
v. t.
To establish as a rule; to furnish; to prescribe; to assign; as, to set an example; to set lessons to be learned.
n.
A young plant for growth; as, a set of white thorn.