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Mathematical function
In mathematics, a negligible function is a function μ : N → R {\displaystyle \mu :\mathbb {N} \to \mathbb {R} } such that for every positive integer c
Negligible_function
Mathematical set regarded as insignificant
null sets can be ignored when studying the integral of a measurable function. Negligible sets define several useful concepts that can be applied in various
Negligible_set
Computational concept
{1}{2}}+\gamma }} . Definition (negligible function): In the proof of this theorem, we need a definition of a negligible function. A function ϵ ( n ) {\displaystyle
Randomness_extractor
Indicator function of rational numbers
is negligible (for the Lebesgue measure). Thomae's function, a variation that is discontinuous only at the rational numbers. "Dirichlet-function", Encyclopedia
Dirichlet_function
Function in thermodynamics and statistical physics
sub-systems with negligible interaction energy, that is, we can assume the particles are essentially non-interacting. If the partition functions of the sub-systems
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Proving validity without revealing other data
statistically close, meaning that their statistical difference is a negligible function. We speak of computational zero-knowledge if no efficient algorithm
Zero-knowledge_proof
Type of functions designed for being unsolvable by root-finding algorithms
\{{\texttt {0}},{\texttt {1}}\}^{p(k)}}[A(r)=1]\right|<\mu (k)} for some negligible function μ {\displaystyle \mu } . (The notation x ← X {\displaystyle x\gets
Cryptographically secure pseudorandom number generator
Cryptographically_secure_pseudorandom_number_generator
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
In mathematics, with negligible exceptions
In mathematics, the term "almost all" means "all but a negligible quantity". More precisely, if X {\displaystyle X} is a set, "almost all elements of X
Almost_all
Solution of a confluent hypergeometric equation
In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric
Confluent hypergeometric function
Confluent_hypergeometric_function
Property of cryptographic hash functions
denotes some negligible function, and n is the security parameter. There are two different types of collision resistance. A hash function has weak collision
Collision_resistance
Notion in measure theory
equivalence class [ f ] {\displaystyle [f]} of bounded measurable functions modulo negligible functions a representative— which is henceforth written T ( [ f ]
Lifting_theory
Property whereby no efficient algorithm can distinguish two distributions
probabilistic polynomial time algorithm A, the following quantity is a negligible function in n: δ ( n ) = | Pr x ← D n [ A ( x ) = 1 ] − Pr x ← E n [ A ( x
Computational indistinguishability
Computational_indistinguishability
Polynomial function of degree 5
In mathematics, a quintic function is a function of the form g ( x ) = a x 5 + b x 4 + c x 3 + d x 2 + e x + f , {\displaystyle g(x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+ex+f
Quintic_function
Cryptographic scheme
{\text{Commit}}_{k}(x,open)={\text{Commit}}_{k}(x',open')} is a negligible function in k. This is a form of asymptotic analysis. It is also possible
Commitment_scheme
Function used in computer cryptography
values x, y such that f(x) = f(y)—with non-negligible probability. A hard-core predicate of a one-way function f is a predicate (i.e. single bit) b such
One-way_function
Property of some cryptosystems
\epsilon (k)} is a negligible function in the security parameter k {\displaystyle k} , i.e., for every (nonzero) polynomial function poly() there exists
Ciphertext indistinguishability
Ciphertext_indistinguishability
Objects extending the notion of functions
{\displaystyle G=M/N} of "moderate" modulo "negligible" nets of functions, where "moderateness" and "negligibility" refers to growth with respect to the index
Generalized_function
cryptography a universal one-way hash function (UOWHF, often pronounced "woof") is a type of universal hash function of particular importance to cryptography
Universal one-way hash function
Universal_one-way_hash_function
Abstract machine that models computation
possible to amplify soundness until the soundness error becomes a negligible function of the running time of the verifier. This is achieved by repeating
Interactive_proof_system
with negligible probability in the statistical security parameter since it only engages in the protocol once. Security level Key size Negligible function
Security_parameter
Collection of efficiently-computable functions which emulate a random oracle
which kind of oracle is given to her is negligible in n {\displaystyle n} . In an oblivious pseudorandom function, abbreviated OPRF, information is concealed
Pseudorandom_function_family
Response that characterizes how an ear receives a sound from a point in space
A head-related transfer function (HRTF) is a response that characterizes how an ear receives a sound from a point in space. As sound strikes the listener
Head-related transfer function
Head-related_transfer_function
Product of numbers from 1 to n
_{1}^{n}\ln x\,dx=n\ln n-n+1.} Exponentiating the result (and ignoring the negligible + 1 {\displaystyle +1} term) approximates n ! {\displaystyle n!} as (
Factorial
128-bit number used to identify information in computer systems
UUID will be duplicated is not zero, it is close enough to zero to be negligible. Thus, anyone can create large numbers of UUIDs and use them as identifiers
Universally_unique_identifier
Generalized version of classical Green's function
Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations
Multiscale_Green's_function
Fact that observing a situation changes it
it to reflect that light. While the effects of observation are often negligible, the object still experiences a change. This effect can be found in many
Observer_effect_(physics)
One-way cryptographic tool
given fk(x), find a pre-image x' such that fk(x' ) = fk(x)) is negligible. If each function in the collection above is a one-way permutation, then the collection
Trapdoor_function
running-time of Π ( n , x ) {\displaystyle \Pi (n,x)} , and there exists a negligible function μ {\displaystyle \mu } such that the following properties hold: Correctness:
Oblivious_RAM
Statistical description for the behavior of fermions
etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of
Fermi–Dirac_statistics
Measure for evaluating probabilistic forecasts
In decision theory, both a scoring rule as well as a scoring function provide an ex post summary measure for the evaluation of the quality of a prediction
Scoring_rule
Type of cryptographic software obfuscation
polynomial-time adversary A, there is a negligible function ε ( k ) {\displaystyle \varepsilon (k)} (i.e., a function that eventually grows slower than 1
Indistinguishability obfuscation
Indistinguishability_obfuscation
Distance between two statistical objects
close if Δ ( X k , Y k ) {\displaystyle \Delta (X_{k},Y_{k})} is a negligible function in k {\displaystyle k} . Total variation distance (sometimes just
Statistical_distance
State in which the rate of mortality from senescence is stable or decreasing
Aging, because the increase in rate of mortality as a function of chronological age may be negligible at extremely old ages, an idea referred to as the late-life
Biological_immortality
functions is negligible outside of regions of high recombination, such as recombination hotspots or ends of chromosomes. While many mapping functions
Genetic_map_function
Energy held by an object because of its position relative to other objects
source of the gravitational field, this variation in field strength is negligible and we can assume that the force of gravity on a particular object is
Potential_energy
Technique for selecting hash functions
{\displaystyle O(m/p)} , which becomes negligible when p ≫ m {\displaystyle p\gg m} . The family of simpler hash functions h a ( x ) = ( a x mod p ) mod
Universal_hashing
Shape containing unit line segments in all directions
the needle between any two locations that are parallel while sweeping negligible area. The needle will follow the shape of an "N". It moves from the first
Kakeya_set
Type of root vegetable
(3+1⁄2 oz), and are 93% water, 4% carbohydrates, and 1% protein, with negligible fat. The boiled greens are a rich source (more than 20% of the Daily Value
Turnip
Measure of a system's order
correlation functions, the equal-time correlation function is non-zero for all lattice points below the critical temperature, and is non-negligible for only
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Visible difference in brightness or color
luminance}}}.} The rationale behind this is that a small difference is negligible if the average luminance is high, while the same small difference matters
Contrast_(vision)
Probability distribution
size much larger than 2, the difference between these two priors becomes negligible. (See section Bayesian inference for further details.) ν = α + β is referred
Beta_distribution
Notion in calculus
calculus, the differential represents the principal part of the change in a function y = f ( x ) {\displaystyle y=f(x)} with respect to changes in the independent
Differential_of_a_function
Use of functions that call themselves
three or more functions are possible; for example, function 1 calls function 2, function 2 calls function 3, and function 3 calls function 1 again. Indirect
Recursion_(computer_science)
Lens with a thickness that is negligible
of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called
Thin_lens
Order of arachnids
and speed of solifuges, and their potential danger to humans, which is negligible. The order's name is derived from the Latin sol meaning "sun" and fugere
Solifugae
Resistance of a fluid to shear deformation
of deformation. However, the dependence on some of these properties is negligible in certain cases. For example, the viscosity of a Newtonian fluid does
Viscosity
Average uncertainty in variable's states
become big. But the key insight was showing a reduction in entropy by non negligible amounts as one expands H leading inturn to unbounded growth of a mathematical
Entropy_(information_theory)
variations in input prices were negligible: In economics, production technology is typically represented by the production function f {\displaystyle f} , which
Generalized Ozaki cost function
Generalized_Ozaki_cost_function
{A}}^{f_{a}(x)}(p,g)\to 1]-{\text{Pr }}[{\mathcal {A}}^{R}(p,g)\to 1]} is negligible. The first probability is taken over the choice of the seed s = (p, g
Naor–Reingold pseudorandom function
Naor–Reingold_pseudorandom_function
Cryptographic primitives that involve lattices
algorithm that can efficiently break the cryptographic scheme with non-negligible probability, then there exists an efficient algorithm that solves a certain
Lattice-based_cryptography
The existence of pseudorandom generators is related to the existence of one-way functions
circuit C and any non-negligible ε = 1/poly(n), Probx~U [C(ƒ(x)) = B(x)] ≤ 1/2+ε In other words, it is hard to predict B(x) from function ƒ(x). Here an outline
Pseudorandom generator theorem
Pseudorandom_generator_theorem
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid.
Aharonov–Bohm_effect
Deterioration of function with age
can extend lifespans by 50% in rats, the existence of species having negligible senescence, and the existence of potentially immortal organisms such as
Senescence
Equation relating the rate of an electrochemical reaction to the overpotential
electrode the Tafel equation assumes that the reverse half reaction rate is negligible compared to the forward reaction rate. The exchange current is the current
Tafel_equation
Type of computing function
more likely to abuse a resource if the cost of abusing the resource is negligible: the underlying reason spam has become so rampant is that sending an e-mail
Memory-bound_function
Generalization of mass, length, area and volume
subset of a null set is called a negligible set. A negligible set need not be measurable, but every measurable negligible set is automatically a null set
Measure_(mathematics)
Sociological theory of society
provocation of actions, and that the importance of social rigidity is negligible. Although the actions of humans without doubt do not always engender positive
Structural_functionalism
Term in set theory
or nearly is used to refer to all but a negligible amount of elements in the set. The notion of "negligible" depends on the context, and may mean "of
Almost
Set of techniques to measure and visualize aspects of the nervous system
of quantitative (computational) techniques to study the structure and function of the central nervous system, developed as an objective way of scientifically
Neuroimaging
Concept in contact mechanics
on the situation, and three cases are distinguished: the clearance is negligible: a) the parts are rigid bodies, b) the parts are elastic bodies; c) the
Bearing_pressure
Interpretation of quantum mechanics
interpretation of quantum mechanics that postulates that, in addition to the wave function, a particle possesses a definite position at all times, even when unobserved
De_Broglie–Bohm_theory
Bounds of a sequence
behaved") are discontinuities which make up a negligible subset. The limit superior of a real-valued function defined on an interval containing a point x
Limit inferior and limit superior
Limit_inferior_and_limit_superior
Medical discipline focused on the practical reversal of the aging process
gerontologist Aubrey de Grey has initiated a project, strategies for engineered negligible senescence (SENS), to study how to reverse the damage caused by aging
Rejuvenation
Block cipher
tweakable block cipher designed as part of the Skein hash function, an entry in the NIST hash function competition. Threefish uses no S-boxes or other table
Threefish
Measure of the electric polarizability of a dielectric material
}}\gg 1} is associated with a good conductor; such materials with non-negligible conductivity yield a large amount of loss that inhibit the propagation
Permittivity
Cryptanalytic method for unauthorized users to access data
designed cryptosystem the chance of successfully guessing the key is negligible. When cracking passwords, this method is very fast when used to check
Brute-force_attack
Cryptography primitive
and with negligible memory requirements. At FSE 2007, Joan Daemen and Gilles Van Assche presented a practical attack on the Panama hash function that generates
Panama_(cryptography)
Subspecies of bacterium
various species of mosquitoes, fungus gnats, and blackflies but which have negligible effects on other organisms. The major advantage of B. thuringiensis products
Bacillus thuringiensis israelensis
Bacillus_thuringiensis_israelensis
Challenge • Navajo I • Neal Koblitz • Needham–Schroeder protocol • Negligible function • NEMA (machine) • NESSIE • Network Security Services • Neural cryptography
Index of cryptography articles
Index_of_cryptography_articles
Enzyme involved in amino acid metabolism
difference is that ALT is found predominantly in the liver, with clinically negligible quantities found in the kidneys, heart, and skeletal muscle, while AST
Aspartate_transaminase
N ∞ ( R n ) {\displaystyle C_{N}^{\infty }(\mathbb {R} ^{n})} of negligible functions is defined in the same way but with the partial derivatives instead
Colombeau_algebra
Digital identifier derived from the data by an algorithm
probability of a collision — two files yielding the same fingerprint — must be negligible, compared to the probability of other unavoidable causes of fatal errors
Fingerprint_(computing)
Technique aimed to increase the size of a human penis
also medical studies that indicate that the lengthening effects can be negligible. Some doctors say that most men seeking penis enlargement have normal-sized
Penis_enlargement
Loss of political control in antiquity
effectively consolidated. By 476, the position of Western Roman Emperor wielded negligible military, political, or financial power, and had no effective control
Fall of the Western Roman Empire
Fall_of_the_Western_Roman_Empire
2009 password-based key derivation function
users only need to perform the function once per operation (e.g., authentication), and so the time required is negligible. However, a brute-force attack
Scrypt
Burrowing eusocial rodent
ISSN 2050-084X. PMC 5783610. PMID 29364116. Buffenstein R (May 2008). "Negligible senescence in the longest living rodent, the naked mole-rat: insights
Naked_mole-rat
Group of similar cells performing a specific function
is negligible. These cells have hard and extremely thick secondary walls due to uniform distribution and high secretion of lignin and have a function of
Tissue_(biology)
Extremely small quantity in calculus; thing so small that there is no way to measure it
ordering is used, which is equivalent to considering higher powers of x as negligible compared to lower powers. David O. Tall refers to this system as the super-reals
Infinitesimal
Political institution in ancient Rome
republic, in practice the actual authority of the imperial senate was negligible, and the emperor held the true power in the state. As such, membership
Roman_Senate
Christian church based in Rome
number of men and women who have deep-seated homosexual tendencies is not negligible. This inclination, which is objectively disordered, constitutes for most
Catholic_Church
Two-dimensional laminar boundary layer that forms on a semi-infinite plate
argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge
Blasius_boundary_layer
Highest velocity attainable by a falling object
force is usually dismissed and not taken into account, as its effects are negligible. As the speed of an object increases, so does the drag force acting on
Terminal_velocity
Criterion for model selection
term. To the extent that R ( x , θ ) {\displaystyle R(x,\theta )} is negligible and π ( θ ∣ M ) {\displaystyle \pi (\theta \mid M)} is relatively linear
Bayesian information criterion
Bayesian_information_criterion
Chemical compound
although the roles of estrone and estriol as estrogens are said not to be negligible. Estradiol, like other steroid hormones, is derived from cholesterol.
Estradiol
Process to determine the highest profits for a firm
flight. The marginal costs of flying one more passenger on the flight are negligible until all the seats are filled. The airline would maximize profit by filling
Profit_maximization
hard-core bit b(x) and a uniformly random bit with negligible advantage over the length of x. A hard-core function can be defined similarly. That is, if x is
Hard-core_predicate
Approximation method in statistics
zero or strictly controlled so as to be negligible. When errors in the independent variable are non-negligible, models of measurement error can be used;
Least_squares
Coenzyme, notable for its synthesis and oxidation role
month at 37 °C. The lithium and sodium salts of CoA are more stable, with negligible degradation noted over several months at various temperatures. Aqueous
Coenzyme_A
Prehistoric monument in England
continental Europe, indicating that local WHG in Britain contributed negligibly to later populations." Olalde (2018): "Another striking observation is
Stonehenge
Discrete probability distribution
subinterval for which the probability of an event occurring twice is "negligible". With this assumption one can derive the Poisson distribution from the
Poisson_distribution
Americans of Korean ancestry
North Korea (Democratic People's Republic of Korea) accounting for a negligible number. An estimated 20,000 second generation Korean Americans are "dual
Korean_Americans
Psychological or sexual drive or energy
"sex differences in self-reported sexual behavior (masturbation) were negligible in a bogus pipeline condition in which participants believed lying could
Libido
Optical device for recording images
can cause inaccurate representations of the subject's position. While negligible with distant subjects, this error becomes prominent with closer ones.
Camera
Conservation law for two-phase flow in porous media
incompressible Immiscible phases Negligible capillary pressure effects (this implies that the pressures of the two phases are equal) Negligible gravitational forces
Buckley–Leverett_equation
Study of the physiology of the kidney
ultrafiltrate that resembles plasma (except that the ultrafiltrate has negligible plasma proteins) to enter Bowman's space. Filtration is driven by Starling
Renal_physiology
End of an organism's life
biological functioning eventually die from biological aging, known in life sciences as "senescence." Some organisms experience negligible senescence,
Death
Software that manages computer hardware resources
a way similarly to embedded and real-time OSes. This overhead is not negligible: to the direct cost of mode switching it's necessary to add the indirect
Operating_system
Relationship between an object and a representation of that object
critical thinking about the discrepancies: whether or not they are either negligible or significant in each context, how to reduce them (thus iterating a map
Map–territory_relation
Class of functions in cryptography
In cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected
Pseudorandom_permutation
NEGLIGIBLE FUNCTION
NEGLIGIBLE FUNCTION
Girl/Female
Irish
From the Irish name Damhnait, meaning fit or eligible. Famous bearer: The martyr St Dympna,...
Boy/Male
Tamil
Tamil name means eligible, Good Man
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, Functionary of the Interior.
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.
Boy/Male
Hindu
Tamil name means eligible, Good Man
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
, an Egyptian functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a high Egyptian functionary.
Boy/Male
Indian
Eligible; Correct One
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.
Biblical
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Male
Egyptian
, a great functionary.
Male
Celtic
, great justiciary, or 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.
NEGLIGIBLE FUNCTION
NEGLIGIBLE FUNCTION
Boy/Male
Hindu, Indian
Lovely
Boy/Male
Hindu
Auspicious
Boy/Male
Australian, Finnish
God is Gracious
Boy/Male
Hindu
Preceptor of the universe
Boy/Male
Indian
God of the sun.
Male
English
English unisex name derived from the name of the Native American people, from Dakota Sioux Å ahÃyena, CHEYENNE means "little Å ahÃya" or "little red-talker."
Surname or Lastname
English
English : perhaps from Middle English nonnerie ‘nunnery’, applied as a topographic name for someone who lived by a nunnery or a metonymic occupational name for someone who worked at one.
Boy/Male
American, British, English, French
Prayer; St Clair
Boy/Male
British, English
Combination of Lee and Ann Name
Boy/Male
Indian, Punjabi, Sikh
One who Loves Peace of Mind
NEGLIGIBLE FUNCTION
NEGLIGIBLE FUNCTION
NEGLIGIBLE FUNCTION
NEGLIGIBLE FUNCTION
NEGLIGIBLE FUNCTION
a.
Worthy to be chosen or selected; suitable; desirable; as, an eligible situation for a house.
a.
Pertaining to, or connected with, a function or duty; official.
n.
One of a class eligible to the office of senator, but not yet chosen, who could sit and speak in the senate, but could not vote; -- so called because he might indicate his opinion by walking over to the side of the party he favored when a vote was taken.
n.
The state or quality of being ineligible.
adv.
In an ineligible manner.
a.
Destitute of function, or of an appropriate organ. Darwin.
a.
That may neglicted, disregarded, or left out of consideration.
pl.
of Functionary
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
a.
Pertaining to the function of an organ or part, or to the functions in general.
v. t.
To assign to some function or office.
n.
The quality of being eligible; eligibleness; as, the eligibility of a candidate; the eligibility of an offer of marriage.
a.
Ineligible.
a.
Not eligible; not qualified to be chosen for an office; not worthy to be chosen or prefered; not expedient or desirable.
n.
In the English naval service, the second rank attained by a combatant officer after a term of service as naval cadet. Having served three and a half years in this rank, and passed an examination, he is eligible to promotion to the rank of lieutenant.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
a.
Eligible again; capable of reelection; as, reeligible to the same office.
adv.
In an eligible manner.
adv.
In a functional manner; as regards normal or appropriate activity.
a.
That may be selected; proper or qualified to be chosen; legally qualified to be elected and to hold office.