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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
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
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
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
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
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
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
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)
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
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
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
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)
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
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
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
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
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
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
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
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
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
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-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
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
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
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
Special functions of several complex variables
mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the
Theta_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
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
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)
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
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
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
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
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
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
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
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
Type of infinite number in set theory
{\displaystyle \Delta _{0}} -definable subsets of X {\displaystyle X} (see constructible universe). It is worth pointing out that the first claim can be weakened:
Inaccessible_cardinal
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
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
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
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
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
Study of mental functions and behaviors
mental functions in individual and social behavior. Others explore the physiological and neurobiological processes that underlie cognitive functions and
Psychology
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
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
Symbol representing a mathematical object
primarily for the argument of a function, in which case its value could be thought of as varying within the domain of the function. This is the motivation for
Variable_(mathematics)
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)
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
Topics referred to by the same term
L} , constructible universe, a particular class of sets which can be described entirely in terms of simpler sets L-function, meromorphic function on the
L_(disambiguation)
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
topology and integral geometry that integrates constructible functions and more recently definable functions by integrating with respect to the Euler characteristic
Euler_calculus
Proof in set theory
will be constructed from the set T of infinite binary strings to the set R of real numbers. Since T is uncountable, the image of this function, which is
Cantor's_diagonal_argument
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
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
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
Curve whose range contains the unit square
endpoints) is a continuous function whose domain is the unit interval [0, 1]. In the most general form, the range of such a function may lie in an arbitrary
Space-filling_curve
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
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
Token in a mathematical or logical formula
may be a variable (member from a universe of discourse), a constant, a function (mapping to another member of universe) or a predicate (mapping to T/F)
Symbol_(formal)
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
worst cases Busy beaver Circuit complexity Constructible function Cook-Levin theorem Exponential time Function problem Linear time Linear speedup theorem
List of computability and complexity topics
List_of_computability_and_complexity_topics
General-purpose programming language
run-time polymorphism may be achieved using function pointers. Control flow is provided through constructs such as if, for, do, while, and switch. The
C_(programming_language)
Extension of recursion theory to admissible ordinals beyond the natural numbers
{\displaystyle \Sigma _{1}(L_{\alpha })} functions, where L ξ {\displaystyle L_{\xi }} denotes a rank of Godel's constructible hierarchy. α {\displaystyle \alpha
Alpha_recursion_theory
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
Proof by Alan Turing
appears on the tape" (p. 146). This formula is TRUE, that is, it is "constructible", and he shows how to go about this. Then Turing proves two Lemmas,
Turing's_proof
Limitative results in mathematical logic
numbering, but which are not strong enough to have multiplication as a function, and so fail to prove the second incompleteness theorem; that is to say
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
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
Function in thermodynamics and statistical physics
terms of the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Axioms for the natural numbers
multiplication are often added as axioms. The respective functions and relations are constructed in set theory or second-order logic, and can be shown to
Peano_axioms
Concept in psychology and communication studies
concepts or the same term for different concepts, two essential attitude functions emerge from empirical research. For individuals, attitudes are cognitive
Attitude_(psychology)
Mixtures of organic and mineral material that are designed to approximate natural soils
chemical, and biological functions of natural soils. The target soil properties depend on the site location and final land use. Constructed soils are intended
Constructed_soil
Generic type features in C++
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++)
Mathematical approximation of a function
of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the
Taylor_series
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
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
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
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
Personality construct
Machiavellianism (sometimes abbreviated as MACH) is the name of a personality trait construct characterized by manipulativeness, indifference to morality, lack of empathy
Machiavellianism_(psychology)
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
Natural number
967,295 the largest known odd number of sides of a constructible polygon, but since constructibility is related to factorization, the list of odd numbers
4,294,967,295
Cubic equation unsolvable in real radicals
classically constructible since they are expressible in no higher than square roots, so in particular cos(θ/3) or sin(θ/3) is constructible and so is
Casus_irreducibilis
Statement that is taken to be true
{\displaystyle 0} is a constant symbol and S {\displaystyle S} is a unary function and the following axioms: ∀ x . ¬ ( S x = 0 ) {\displaystyle \forall x
Axiom
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
Experimental constructed language
developed naturally, seeing it as an exercise in exploring how languages could function. Nevertheless, it was featured in the Language Creation Conference's 6th
Ithkuil
Concept in theoretical computer science
Retrieved 7 July 2022. Green recursively constructs machines for any number of states and provides the recursive function that computes their score (computes
Busy_beaver
Mapping of mathematical formulas to a particular meaning
interpretation function I {\displaystyle I} of A {\displaystyle {\mathcal {A}}} assigns functions and relations to the symbols of the signature. To each function symbol
Structure (mathematical logic)
Structure_(mathematical_logic)
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
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
Mathematical set containing all objects
but this is not possible for Oberschelp's, since in it the singleton function is provably a set, which leads immediately to paradox in New Foundations
Universal_set
Sequence of program instructions invokable by other software
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-formed
Function (computer programming)
Function_(computer_programming)
Number of integers coprime to and less than n
conditions then the n-gon can be constructed. In 1837 Pierre Wantzel proved the converse, if the n-gon is constructible, then n must satisfy Gauss's conditions
Euler's_totient_function
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
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
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
, the son of the functionary Heknofre.
Biblical
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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.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, a great functionary.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Celtic
, great justiciary, or functionary.
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.
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.
Male
Egyptian
, an Egyptian functionary.
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.
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
Girl/Female
Tamil
Bird
Boy/Male
Hebrew American English
Who is like God? Gift from God. In the Bible, St. Michael was the conqueror of Satan and patron...
Girl/Female
Indian
Aim; Spiritual
Girl/Female
Hindu, Indian
Pride
Girl/Female
German, Greek
From Mount Olympus
Girl/Female
American, Christian, French, German, Indian, Swedish
White; Fair
Boy/Male
Indian
One who warns, Bright, Radiant, Blooming, Observer, Supervisor
Male
Irish
Irish name of unknown MIDIR means. In Celtic mythology, this is the name of a lord of the underworld, the husband of Fuamnach.
Surname or Lastname
English
English : patronymic from Bicker.
Boy/Male
Indian
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
CONSTRUCTIBLE FUNCTION
a.
Capable of contraction.
a.
Constructive.
adv.
In a constructive manner; by construction or inference.
a.
According to interpretation; constructive.
a.
Derived from, or depending on, construction or interpretation; not directly expressed, but inferred.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
n.
Capability of being contracted; quality of being contractible; as, the contractibility and dilatability of air.
a.
Pertaining to a master builder, or to architecture; evincing skill in designing or construction; constructive.
n.
One of a series of substances formed, in secreting cells, by constructive or anabolic processes, in the production of protoplasm; -- opposed to katastate.
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.
Destitute of function, or of an appropriate organ. Darwin.
a.
Having ability to construct or form; employed in construction; as, to exhibit constructive power.
a.
Building up; constructive; -- opposed to destructive.
a.
Capable of being extended, whether in length or breadth; susceptible of enlargement; extensible; extendible; -- the opposite of contractible or compressible.
a.
Capable of being instructed; teachable; docible.
adv.
In a functional manner; as regards normal or appropriate activity.
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.
pl.
of Functionary
a.
Pertaining to anabolism; an anabolic changes, or processes, more or less constructive in their nature.
n.
The constructive metabolism of the body, as distinguished from katabolism.