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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)
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
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
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
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
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
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
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
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
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)
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
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
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 of measure zero containing a
Kakeya_set
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
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
Collection of mathematical objects
points in space, lines, other geometric shapes, variables, functions, or even other sets. Sets cannot be mathematically defined, since they form a primitive
Set_(mathematics)
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 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
Mathematical concept
inverse of f is the function f−1:ℝ→ℝ defined by f−1(y)=y+75. Let f be a function whose domain is the set X, and whose range is the set Y. Then f is invertible
Inverse_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
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
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
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
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 (nowhere-differentiable function)
Weierstrass_function_(nowhere-differentiable_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
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
Ratio of polynomial functions
and Q are polynomial functions of x and Q is not the zero function. The domain of f is the set of all values of x for which the denominator Q(x) is not
Rational_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
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 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
function. Given any set A, the identity function iA is the set {(x,x)∣x∈A}, and this is a set in both ZFC and NFU for different reasons. A function f
Implementation of mathematics in set theory
Implementation_of_mathematics_in_set_theory
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)
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
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
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
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
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
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
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
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
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
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
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
Subset of a function's codomain
codomain and the 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
Range_of_a_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
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)
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
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
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
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
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
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
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
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
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
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
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
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)
Set of elements common to all of some sets
In set theory, the intersection of two sets A and B, denoted by A∩B, is the set containing all elements of A that also belong to B or equivalently, all
Intersection_(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 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
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
Negative of a convex function
convex cap, or upper convex. A real-valued function f on an interval (or, more generally, a convex set in vector space) is said to be concave if, for
Concave_function
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 description of quantum state
operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions
Wave_function
Axiom of set theory
Axiom—For any set X of nonempty sets, there exists a choice function f that is defined on X and maps each set of X to an element of that set. Formally, this
Axiom_of_choice
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
Degree of differentiability of a function or map
therefore first made for functions defined on open subsets of Euclidean space. For functions on closed intervals, closures of open sets, or more general subsets
Smoothness
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
Finite collection of distinct objects
function from a larger finite set to a smaller finite set. The natural numbers are defined abstractly by the Peano axioms, and can be constructed set-theoretically
Finite_set
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
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
particularly in the subfields of set theory and topology, a set C is said to be saturated with respect to a function f:X→Y if C is a subset of f's domain
Saturated_set
Collection of sets in mathematics that can be defined based on a property of its members
also be generalised to classes. A class function is not a function in the usual sense, since it is not a set; it is rather a formula Φ ( x , y ) {\displaystyle
Class_(set_theory)
Mathematical set containing no elements
the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories
Empty_set
Mathematical set formed from two given sets
in ZFC follows from the axioms of pairing, union, power set, and specification. Since functions are usually defined as a special case of relations, and
Cartesian_product
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
Generalized notion of measure in mathematics
generalization of the concept of (positive) measure by allowing the set function to take negative values, i.e., to acquire sign. There are two slightly
Signed_measure
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
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
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
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
Egyptian god of the desert, storms, violence, and foreigners
possession of Horus's eye, when it appears on Set's head. Because Thoth is a moon deity in addition to his other functions, it would make sense, according to te Velde
Set_(deity)
Quickly growing function
Ackermann function as a sequence of unary functions, one can set Am(n)=A(m,n). The function then becomes a sequence A0,A1,A2,... of unary functions, defined
Ackermann_function
Region with boundary of finite measure
(locally) finite perimeter. Basically, a set is a Caccioppoli set if its characteristic function is a function of bounded variation, and its perimeter
Caccioppoli_set
Tasks in machine learning
algorithms that can learn from and make predictions on data. Such algorithms function by making data-driven predictions or decisions, through building a mathematical
Training, validation, and test data sets
Training,_validation,_and_test_data_sets
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
Paradox in set theory
the problem in terms of both logic and set theory, and in particular in terms of Frege's definition of function: There is just one point where I have encountered
Russell's_paradox
A set function is called fractionally subadditive, or XOS (not to be confused with OXS), if it is the maximum of several non-negative additive set functions
Fractionally subadditive valuation
Fractionally_subadditive_valuation
Mathematical function
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as
Jacobi_elliptic_functions
Extension of the factorial function
gamma function, denoted by Γ {\displaystyle \Gamma } (capital Greek letter gamma), is the most common extension of the factorial function to complex
Gamma_function
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
Function that is discontinuous at rationals and continuous at irrationals
Thomae's function is Riemann integrable on any interval. The function's integral is equal to 0 {\displaystyle 0} over any set because the function is equal
Thomae's_function
Monotone maps have countable discontinuities
describes the set of discontinuities of a monotone real-valued function of a real variable; all discontinuities of such a (monotone) function are necessarily
Discontinuities of monotone functions
Discontinuities_of_monotone_functions
in particular in measure theory, an inner measure is a function on the power set of a given set, with values in the extended real numbers, satisfying some
Inner_measure
travel, tourism, insurance
SET FUNCTION
SET FUNCTION
Female
Egyptian
, a wife and daughter of Antef.
Female
Egyptian
, an uncertain goddess.
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Surname or Lastname
English
English : variant spelling of See.
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’.
Female
Egyptian
, second wife of Antef.
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Surname or Lastname
English
English : perhaps a variant of Sait, from the Old English personal name Sǣgēat (‘sea Geat’).
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Female
Hungarian
Hungarian form of Greek Elisabet, ERZSÉBET means "God is my oath."
Male
English
Short form of English Stephen, STE means "crown."
Female
Egyptian
, a sister of Sekherta.
Female
Egyptian
, the wife of Osirtesen.
Female
Egyptian
, the wife of the usurper Sipthah.
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.
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Female
Egyptian
, a sister of Sekherta.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Female
Egyptian
, the mother of Fai-hor-ou-oer.
SET FUNCTION
SET FUNCTION
SET FUNCTION
SET FUNCTION
SET FUNCTION
SET FUNCTION
SET FUNCTION
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