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Concept in complexity theory
theory, a time-constructible function is a function f from natural numbers to natural numbers with the property that f(n) can be constructed from n by a
Constructible_function
Number constructible via compass and straightedge
coordinate system, a point is constructible if and only if its Cartesian coordinates are both constructible numbers. Constructible numbers and points have also
Constructible_number
Regular polygon that can be constructed with compass and straightedge
is constructible if any root of the nth cyclotomic polynomial is constructible. Restating the Gauss–Wantzel theorem: A regular n-gon is constructible with
Constructible_polygon
Possible axiom for set theory in mathematics
{\displaystyle L} represents the constructible sets. In Zermelo–Fraenkel set theory (ZF), the property of being constructible is expressible as a single formula
Axiom_of_constructibility
Particular class of sets which can be described entirely in terms of simpler sets
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L , {\displaystyle L,} is a particular class
Constructible_universe
Given more time, a Turing machine can solve more problems
notion of a time-constructible function. A function f : N → N {\displaystyle f:\mathbb {N} \rightarrow \mathbb {N} } is time-constructible if there exists
Time_hierarchy_theorem
Topics referred to by the same term
B over A Constructible universe, Kurt Gödel's model L of set theory, constructed by transfinite recursion Constructible function, a function whose values
Constructibility
Both deterministic and nondeterministic machines can solve more problems given more space
common functions that we work with are space-constructible, including polynomials, exponents, and logarithms. For every space-constructible function f :
Space_hierarchy_theorem
Memory space for a deterministic Turing machine
assumed. □ The above theorem implies the necessity of the space-constructible function assumption in the space hierarchy theorem. L = DSPACE(O(log n))
DSPACE
Extension of the factorial function
gamma function (represented by Γ {\displaystyle \Gamma } , capital Greek letter gamma) is the most common extension of the factorial function to complex
Gamma_function
Function in algebraic geometry
In algebraic geometry, the Behrend function of a scheme X, introduced by Kai Behrend, is a constructible function ν X : X → Z {\displaystyle \nu _{X}:X\to
Behrend_function
Natural number
Fermat primes is equal to the number of sides of the largest regular constructible polygon with a straightedge and compass that has an odd number of sides
32_(number)
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
Axiom of set theory
of choice is not a theorem of ZF by constructing an inner model (the constructible universe) that satisfies ZFC, thus showing that ZFC is consistent if
Axiom_of_choice
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
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 and the
Function_(mathematics)
The function assigning to α {\displaystyle \alpha } the α {\displaystyle \alpha } th level L α {\displaystyle L_{\alpha }} of Godel's constructible hierarchy
Primitive recursive set function
Primitive_recursive_set_function
Theorem in algebraic geometry
cohomology lie not in a field but instead in a constructible sheaf. They prove that for a constructible sheaf F {\displaystyle {\mathcal {F}}} on an affine
Lefschetz_hyperplane_theorem
Standard system of axiomatic set theory
particular inner models, such as in the constructible universe. However, some statements that are true about constructible sets are not consistent with hypothesized
Zermelo–Fraenkel_set_theory
Probability that random variable X is less than or equal to x
cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,
Cumulative distribution function
Cumulative_distribution_function
Mathematical-logic system based on functions
as λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped
Lambda_calculus
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Paradox in set theory
the function F(fx) could be its own argument: in that case there would be a proposition F(F(fx)), in which the outer function F and the inner function F
Russell's_paradox
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
formula 7.2) extended the formula to constructible sheaves over a curve (Raynaud 1965). Suppose that F is a constructible sheaf over a genus g smooth projective
Grothendieck–Ogg–Shafarevich formula
Grothendieck–Ogg–Shafarevich_formula
Infinite cardinal number
all prime numbers, the set of all rational numbers, the set of all constructible numbers (in the geometric sense), the set of all algebraic numbers,
Aleph_number
pairing function, and π 1 , π 2 {\displaystyle \pi _{1},\pi _{2}} be its projection functions for inversion. Theorem: Any function constructible via the
Gödel's_β_function
Mathematical function, inverse of an exponential function
to base b, written logb x = y, so log10 1000 = 3. As a single-variable function, the logarithm to base b is the inverse of exponentiation with base b.
Logarithm
Psychological concept
In psychology, a construct, also called a hypothetical construct or psychological construct, is a sophisticated cognitive framework that individuals and
Construct_(psychology)
complexity functions, then f + g, fg, and 2f are also proper complexity functions. Similar notions include honest functions, space-constructible functions, and
Proper_complexity_function
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
Complexity class
NTIME is also related to DSPACE in the following way. For any time constructible function t(n), we have N T I M E ( t ( n ) ) ⊆ D S P A C E ( t ( n ) ) {\displaystyle
NTIME
Mathematical set containing no elements
exists precisely one function f {\displaystyle f} from ∅ {\displaystyle \varnothing } to A , {\displaystyle A,} the empty function. As a result, the empty
Empty_set
Coding guidelines by Gerald J. Holzmann
about 60 lines of code per function. The code's assertions density should average to minimally two assertions per function. Assertions must be used to
The Power of 10: Rules for Developing Safety-Critical Code
The_Power_of_10:_Rules_for_Developing_Safety-Critical_Code
Probability distribution
real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 exp ( − ( x − μ ) 2 2 σ 2 ) . {\displaystyle f(x)={\frac
Normal_distribution
Subfield of mathematics
set theory (with or without the axiom of choice), by developing the constructible universe of set theory in which the continuum hypothesis must hold.
Mathematical_logic
Concept in mathematics
modification of Gödel's constructible hierarchy, L, that circumvents certain technical difficulties that exist in the constructible hierarchy. The J-Hierarchy
Jensen_hierarchy
Concept in the analysis of dynamical systems
Lyapunov functions for linear systems, and conservation laws can often be used to construct Lyapunov functions for physical systems. A Lyapunov function for
Lyapunov_function
Mathematical set formed from two given sets
as simply ×Xi. If f is a function from X to A and g is a function from Y to B, then their Cartesian product f × g is a function from X × Y to A × B with
Cartesian_product
Size of a possibly infinite set
cardinality or Hume's principle. It will be shown later that such a function can be constructed without the need to define it axiomatically. An alternative approach
Cardinal_number
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
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Function definition that is not bound to an identifier
higher-order functions or used for constructing the result of a higher-order function that needs to return a function. If the function is only used once
Anonymous_function
Theorem in computability theory
can be applied to construct fixed points of certain operations on computable functions, to generate quines, and to construct functions defined via recursive
Kleene's_recursion_theorem
topology and integral geometry that integrates constructible functions and more recently definable functions by integrating with respect to the Euler characteristic
Euler_calculus
Fundamental trigonometric functions
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle:
Sine_and_cosine
General-purpose programming language
pointers Supports procedure-like construct as a function returning void Supports dynamic memory via standard library functions Includes the C preprocessor
C_(programming_language)
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both
List of trigonometric identities
List_of_trigonometric_identities
Mathematical concept
Recursion Theorem (version 2). Given a set g1, and class functions G2, G3, there exists a unique function F: Ord → V such that F(0) = g1, F(α + 1) = G2(F(α))
Transfinite_induction
Iterative optimization method
is an iterative optimization method which exploits the convexity of a function in order to find its maxima or minima. The MM stands for “Majorize-Minimization”
MM_algorithm
Sheaf cohomology on the étale site
constant sheaves are constructible, and constructible sheaves are torsion. Every torsion sheaf is a filtered inductive limit of constructible sheaves. In applications
Étale_cohomology
Study of mathematical algorithms for optimization problems
solutions. The function f is variously called an objective function, criterion function, loss function, cost function (minimization), utility function or fitness
Mathematical_optimization
Trigonometric values in terms of square roots and fractions
those that can be constructed with a compass and straight edge, and the values are called constructible numbers. The trigonometric functions of angles that
Exact_trigonometric_values
Function computable with bounded loops
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all
Primitive_recursive_function
Scale to rate how well one is meeting various problems in living
The Global Assessment of Functioning (GAF) is a numeric scale used by mental health clinicians and physicians to rate subjectively the social, occupational
Global Assessment of Functioning
Global_Assessment_of_Functioning
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
Quickly growing function
Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not
Ackermann_function
Proposition in mathematical logic
i.e. from ZFC. Gödel's proof shows that both CH and AC hold in the constructible universe L {\displaystyle L} , an inner model of ZF set theory, assuming
Continuum_hypothesis
Algebraic structure with addition, multiplication, and division
using the field of constructible numbers. Real constructible numbers are, by definition, lengths of line segments that can be constructed from the points
Field_(mathematics)
Real number uniquely specified by description
rational number, is constructible. The positive square root of 2 is constructible. However, the cube root of 2 is not constructible; this is related to
Definable_real_number
System of mathematical set theory
to build the constructible universe. He constructed a function on the class of all ordinals that, for each ordinal, builds a constructible set by applying
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Feature in the C++ programming language
the double version with max<double>(). This function template can be instantiated with any copy-constructible type for which the expression y < x is valid
Template_(C++)
Smooth and compactly supported function
kernels used to construct mollifiers. Some authors use the term more broadly for any compactly supported smooth function. Such functions are important examples
Bump_function
Type of logical system
discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain
First-order_logic
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
Function-Spacer-Lipid (FSL) Kode constructs (Kode Technology) are amphiphatic, water dispersible biosurface engineering constructs that can be used to
Function-spacer-lipid Kode construct
Function-spacer-lipid_Kode_construct
Mathematical logic concept
cardinals that cannot exist in the constructible universe (L) of any model of set theory. Nevertheless, the constructible universe contains all the ordinal
Absoluteness_(logic)
Input to a mathematical function
of a function is a value provided to obtain the function's result. It is also called an independent variable. For example, the binary function f ( x
Argument_of_a_function
Pair of mathematical objects
the ordered pair. Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs, cf. picture. Let ( a 1 , b 1 )
Ordered_pair
Set theory concept
earlier sources such as Whitehead and Russell. Universe (mathematics) Constructible universe Grothendieck universe Inaccessible cardinal S (set theory)
Von_Neumann_universe
Programming language
ActionScript. Hack's type system allows types to be specified for function arguments, function return values, and class properties; however, types of local
Hack_(programming_language)
Software programming optimization technique
memoized function object in a decorator pattern. In pseudocode, this can be expressed as follows: function construct-memoized-functor (F is a function object
Memoization
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability
Likelihood_function
Undecidability of equality of real numbers
{R} } functions. Suppose that E includes these expressions: x (representing the identity function) ex (representing the exponential functions) sin x
Richardson's_theorem
System of mathematical set theory
Devlin, Keith J. (1984). Constructibility. Berlin: Springer-Verlag. ISBN 0-387-13258-9. Gostanian, Richard (1980). "Constructible Models of Subsystems of
Kripke–Platek_set_theory
Syntactically valid part of a program formed from lexical tokens
language constructs, not functions. So while (true) is a language construct, while add(10) is a function call. In PHP print is a language construct. <?php
Language_construct
Swiss mathematician (1707–1783)
mathematical terminology and notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy
Leonhard_Euler
Circle with radius of one
Triangles constructed on the unit circle can also be used to illustrate the periodicity of the trigonometric functions. First, construct a radius OP
Unit_circle
Set-theoretic tree with uncountable branches
Solovay showed in unpublished work that there are Kurepa trees in Gödel's constructible universe (Jech 1971). More precisely, the existence of Kurepa trees
Kurepa_tree
Impossible task in computing
that the intuitive notion of "effectively calculable" is captured by the functions computable by a Turing machine (or equivalently, by those expressible
Entscheidungsproblem
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
Function returning one of only two values
switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the
Boolean_function
Programming construct
computer programming, a function object is a construct allowing an object to be invoked or called as if it were an ordinary function, usually with the same
Function_object
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
Used to count, measure, and label
straightedge and compass, the constructible numbers are those complex numbers whose real and imaginary parts can be constructed using straightedge and compass
Number
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
Function that is continuous everywhere but differentiable nowhere
mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass_function
Technique for creating lexically scoped first class functions
lexical closure or function closure, is a technique for implementing lexically scoped name binding in a language with first-class functions. Operationally
Closure (computer programming)
Closure_(computer_programming)
Enclaved Holy See's independent city-state
Holy See, the pope is ex officio the head of state, a function dependent on his primordial function as bishop of the diocese of Rome and head of the Catholic
Vatican_City
Size of a set in mathematics
disproved from the axioms of ZFC by showing that both CH and AC hold in his constructible universe: an inner model of ZFC. The existence of a model of ZFC in
Cardinality
Control flow construct for executing code repeatedly
In computer programming, a loop is a control flow construct that allows code to be executed repeatedly, usually with minor alterations between repetitions
Loop_(statement)
Computer memory needed by an algorithm
{NSPACE}}(n^{c})} The space hierarchy theorem states that, for all space-constructible functions f ( n ) , {\displaystyle f(n),} there exists a problem that can
Space_complexity
Group of ancient Mesopotamian deities
(the god of the heavens) and Ki (the goddess of earth), and their primary function was to decree the fates of humanity. In Sumerian, the name of this group
Anunnaki
In logic, a statement which is always true
be deduced from the truth or falsity of each variable. A valuation is a function that assigns each propositional variable to either T (for truth) or F (for
Tautology_(logic)
Fractal curve
appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" by the Swedish mathematician Helge von Koch
Koch_snowflake
Class of mathematical set whose elements are all subsets
construction of the von Neumann universe V {\displaystyle V} and Gödel's constructible universe L {\displaystyle L} are transitive sets. The universes V {\displaystyle
Transitive_set
General-purpose programming language
manipulation. Functions are created in Python by using the def keyword. A function is defined similarly to how it is called, by first providing the function name
Python_(programming_language)
Name for a resident of a particular geographical area
coast. Many demonyms function both endonymically and exonymically (used by the referents themselves or by outsiders); others function only in one of those
Demonym
Thesis on the nature of computability
Church–Turing thesis is a thesis about the nature of computable functions. It states that a function on the natural numbers can be calculated by an effective
Church–Turing_thesis
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
Male
Egyptian
, an Egyptian functionary.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, a great functionary.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Biblical
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Male
Egyptian
, the son of the functionary Heknofre.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, an Egyptian functionary.
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
Girl/Female
Indian
Lover; Voice of Sweet Bird
Male
Hebrew
(×ֶלְיְהï‹×¢Öµ×™× Ö·×™) Hebrew name ELYEHOWEYNAY means "unto God are my eyes." In the bible, this is the name of many characters, including a priest and a Korahite temple doorkeeper.
Boy/Male
Hindu, Indian, Traditional
Lord Vishnu
Boy/Male
Hindu, Indian
Name of Goddess Durga
Surname or Lastname
English
English : from the Middle English personal name Lovin, Old English Lēofhūn, composed of the elements lēof ‘dear’, ‘beloved’ + hūn ‘bear cub’.English : habitational name from the city of Louvain in Belgium (Dutch Leuven).
Boy/Male
Hindu, Indian
Playful in Bloom
Girl/Female
Indian
Progressed
Boy/Male
American, British, English
Divine Warrior
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sikh, Telugu
Lord of God; Heart of God; Heart of the Guru
Boy/Male
Hindu
Manifestation of the Trinity - Brahma, Vishnu and Shiva
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
a.
Building up; constructive; -- opposed to destructive.
n.
The constructive metabolism of the body, as distinguished from katabolism.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
adv.
In a constructive manner; by construction or inference.
a.
Derived from, or depending on, construction or interpretation; not directly expressed, but inferred.
a.
Capable of being instructed; teachable; docible.
a.
Pertaining to anabolism; an anabolic changes, or processes, more or less constructive in their nature.
a.
Constructive.
a.
According to interpretation; constructive.
n.
The act or process, by which living tissues or cells take up and convert into their own proper substance the nutritive material brought to them by the blood, or by which they transform their cell protoplasm into simpler substances, which are fitted either for excretion or for some special purpose, as in the manufacture of the digestive ferments. Hence, metabolism may be either constructive (anabolism), or destructive (katabolism).
a.
Having ability to construct or form; employed in construction; as, to exhibit constructive power.
pl.
of Functionary
n.
One of a series of substances formed, in secreting cells, by constructive or anabolic processes, in the production of protoplasm; -- opposed to katastate.
adv.
In a functional manner; as regards normal or appropriate activity.
a.
Capable of being extended, whether in length or breadth; susceptible of enlargement; extensible; extendible; -- the opposite of contractible or compressible.
a.
Capable of expansion; that may be dilated; -- opposed to contractible; as, the lungs are dilatable by the force of air; air is dilatable by heat.
a.
Pertaining to a master builder, or to architecture; evincing skill in designing or construction; constructive.
n.
Capability of being contracted; quality of being contractible; as, the contractibility and dilatability of air.
a.
Capable of contraction.
a.
Destitute of function, or of an appropriate organ. Darwin.