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单词 function
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function


func·tion

F0361500 (fŭngk′shən)n.1. The action or purpose for which a person or thing is suited or employed, especially:a. A person's role or occupation: in my function as chief editor.b. Biology The physiological activity of an organ or body part: The heart's function is to pump blood.c. Computers A procedure within an application.2. An official ceremony or a formal social occasion: disliked attending receptions and other company functions.3. Something closely related to another thing and dependent on it for its existence, value, or significance: Growth is a function of nutrition.4. Abbr. f Mathematics a. A variable so related to another that for each value assumed by one there is a value determined for the other.b. A rule of correspondence between two sets such that there is exactly one element in the second set assigned to each element in the first set. Also called mapping.intr.v. func·tioned, func·tion·ing, func·tions 1. To have or perform a function; serve: functioned as ambassador.2. To deal with or overcome the challenges of everyday life: For weeks after his friend's funeral he simply could not function.
[Latin fūnctiō, fūnctiōn-, performance, execution, from fūnctus, past participle of fungī, to perform, execute.]
func′tion·less adj.Synonyms: function, duty, office, role
These nouns denote the actions and activities assigned to, required of, or expected of a person: the function of a teacher; a bank clerk's duty; performed the office of financial adviser; the role of a parent.

function

(ˈfʌŋkʃən) n1. the natural action or intended purpose of a person or thing in a specific role: the function of a hammer is to hit nails into wood. 2. an official or formal social gathering or ceremony3. a factor dependent upon another or other factors: the length of the flight is a function of the weather. 4. (Mathematics) maths logic Also called: map or mapping a relation between two sets that associates a unique element (the value) of the second (the range) with each element (the argument) of the first (the domain): a many-one relation. Symbol: f(x) The value of f(x) for x = 2 is f(2)vb (intr) 5. to operate or perform as specified; work properly6. (foll by as) to perform the action or role (of something or someone else): a coin may function as a screwdriver. [C16: from Latin functiō, from fungī to perform, discharge] ˈfunctionless adj

func•tion

(ˈfʌŋk ʃən)

n. 1. the kind of action or activity proper to a person, thing, or institution; the purpose for which something is designed or exists; role. 2. any ceremonious public or social gathering or occasion. 3. a factor related to or dependent upon other factors: Price is a function of supply and demand. 4. a. Also called correspondence , map, mapping, transformation. a relation between two sets in which one element of the second set is assigned to each element of the first set, as the expression y=x2; operator. b. a formula expressing a relation between the angles of a triangle and its sides, as sine or cosine. c. hyperbolic function. 5. the grammatical role a linguistic form has or the position it occupies in a particular construction. 6. the contribution made by a social activity or structure to the maintenance of a social system. v.i. 7. to work; operate. 8. to have or exercise a function; serve. [1525–35; < Latin functiō a performance, execution, derivative of fungī to perform, execute] func′tion•less, adj.

func·tion

(fŭngk′shən)1. A relationship between two sets that matches each member of the first set with a unique member of the second set. Functions are often expressed as an equation, such as y = x + 5, meaning that y is a function of x such that for any value of x, the value of y will be 5 greater than x.2. A quantity whose value depends on the value given to one or more related quantities. For example, the area of a square is a function of the length of its sides.

function


Past participle: functioned
Gerund: functioning
Imperative
function
function
Present
I function
you function
he/she/it functions
we function
you function
they function
Preterite
I functioned
you functioned
he/she/it functioned
we functioned
you functioned
they functioned
Present Continuous
I am functioning
you are functioning
he/she/it is functioning
we are functioning
you are functioning
they are functioning
Present Perfect
I have functioned
you have functioned
he/she/it has functioned
we have functioned
you have functioned
they have functioned
Past Continuous
I was functioning
you were functioning
he/she/it was functioning
we were functioning
you were functioning
they were functioning
Past Perfect
I had functioned
you had functioned
he/she/it had functioned
we had functioned
you had functioned
they had functioned
Future
I will function
you will function
he/she/it will function
we will function
you will function
they will function
Future Perfect
I will have functioned
you will have functioned
he/she/it will have functioned
we will have functioned
you will have functioned
they will have functioned
Future Continuous
I will be functioning
you will be functioning
he/she/it will be functioning
we will be functioning
you will be functioning
they will be functioning
Present Perfect Continuous
I have been functioning
you have been functioning
he/she/it has been functioning
we have been functioning
you have been functioning
they have been functioning
Future Perfect Continuous
I will have been functioning
you will have been functioning
he/she/it will have been functioning
we will have been functioning
you will have been functioning
they will have been functioning
Past Perfect Continuous
I had been functioning
you had been functioning
he/she/it had been functioning
we had been functioning
you had been functioning
they had been functioning
Conditional
I would function
you would function
he/she/it would function
we would function
you would function
they would function
Past Conditional
I would have functioned
you would have functioned
he/she/it would have functioned
we would have functioned
you would have functioned
they would have functioned
Thesaurus
Noun1.function - (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)function - (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)mapping, mathematical function, single-valued function, mapmultinomial, polynomial - a mathematical function that is the sum of a number of termsmath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementmathematical relation - a relation between mathematical expressions (such as equality or inequality)expansion - a function expressed as a sum or product of terms; "the expansion of (a+b)^2 is a^2 + 2ab + b^2"inverse function - a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=xKronecker delta - a function of two variables i and j that equals 1 when i=j and equals 0 otherwisemetric, metric function - a function of a topological space that gives, for any two points in the space, a value equal to the distance between themtransformation - (mathematics) a function that changes the position or direction of the axes of a coordinate systemisometry - a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points; "the isometries of the cube"operator - (mathematics) a symbol or function representing a mathematical operationcircular function, trigonometric function - function of an angle expressed as a ratio of the length of the sides of right-angled triangle containing the anglethreshold function - a function that takes the value 1 if a specified function of the arguments exceeds a given threshold and 0 otherwiseexponential, exponential function - a function in which an independent variable appears as an exponent
2.function - what something is used forfunction - what something is used for; "the function of an auger is to bore holes"; "ballet is beautiful but what use is it?"purpose, use, roleusefulness, utility - the quality of being of practical useraison d'etre - the purpose that justifies a thing's existence
3.function - the actions and activities assigned to or required or expected of a person or groupfunction - the actions and activities assigned to or required or expected of a person or group; "the function of a teacher"; "the government must do its part"; "play its role"role, office, partduty - work that you are obliged to perform for moral or legal reasons; "the duties of the job"capacity - a specified function; "he was employed in the capacity of director"; "he should be retained in his present capacity at a higher salary"hat - an informal term for a person's role; "he took off his politician's hat and talked frankly"portfolio - the role of the head of a government department; "he holds the portfolio for foreign affairs"lieu, stead, place, position - the post or function properly or customarily occupied or served by another; "can you go in my stead?"; "took his place"; "in lieu of"second fiddle - a secondary role or function; "he hated to play second fiddle to anyone"
4.function - a relation such that one thing is dependent on another; "height is a function of age"; "price is a function of supply and demand"relation - an abstraction belonging to or characteristic of two entities or parts together
5.function - a formal or official social gathering or ceremony; "it was a black-tie function"social affair, social gathering - a gathering for the purpose of promoting fellowship
6.function - a vaguely specified social eventfunction - a vaguely specified social event; "the party was quite an affair"; "an occasion arranged to honor the president"; "a seemingly endless round of social functions"social function, social occasion, occasion, affairsocial event - an event characteristic of persons forming groupsparty - an occasion on which people can assemble for social interaction and entertainment; "he planned a party to celebrate Bastille Day"celebration, jubilation - a joyful occasion for special festivities to mark some happy eventceremonial, ceremonial occasion, ceremony, observance - a formal event performed on a special occasion; "a ceremony commemorating Pearl Harbor"fundraiser - a social function that is held for the purpose of raising moneyphoto op, photo opportunity - an occasion that lends itself to (or is deliberately arranged for) taking photographs that provide favorable publicity for those who are photographedsleepover - an occasion of spending a night away from home or having a guest spend the night in your home (especially as a party for children)
7.function - a set sequence of steps, part of larger computer programfunction - a set sequence of steps, part of larger computer programsubprogram, subroutine, procedure, routinesoftware, software package, software program, software system, computer software, package - (computer science) written programs or procedures or rules and associated documentation pertaining to the operation of a computer system and that are stored in read/write memory; "the market for software is expected to expand"computer program, computer programme, programme, program - (computer science) a sequence of instructions that a computer can interpret and execute; "the program required several hundred lines of code"cataloged procedure - a set of control statements that have been placed in a library and can be retrieved by namecontingency procedure - an alternative to the normal procedure; triggered if an unusual but anticipated situation ariseslibrary routine - a debugged routine that is maintained in a program libraryrandom number generator - a routine designed to yield a random numberrecursive routine - a routine that can call itselfreusable routine - a routine that can be loaded once and executed repeatedlyexecutive routine, supervisory routine - a routine that coordinates the operation of subroutinestracing routine - a routine that provides a chronological record of the execution of a computer programservice routine, utility routine - a routine that can be used as needed
Verb1.function - perform as expected when applied; "The washing machine won't go unless it's plugged in"; "Does this old car still run well?"; "This old radio doesn't work anymore"operate, work, run, godouble - do double duty; serve two purposes or have two functions; "She doubles as his wife and secretary"roll - begin operating or running; "The cameras were rolling"; "The presses are already rolling"run - be operating, running or functioning; "The car is still running--turn it off!"cut - function as a cutting instrument; "This knife cuts well"work - operate in or through; "Work the phones"service, serve - be used by; as of a utility; "The sewage plant served the neighboring communities"; "The garage served to shelter his horses"malfunction, misfunction - fail to function or function improperly; "the coffee maker malfunctioned"
2.function - serve a purpose, role, or function; "The tree stump serves as a table"; "The female students served as a control group"; "This table would serve very well"; "His freedom served him well"; "The table functions as a desk"serveservice, serve - be used by; as of a utility; "The sewage plant served the neighboring communities"; "The garage served to shelter his horses"suffice, answer, do, serve - be sufficient; be adequate, either in quality or quantity; "A few words would answer"; "This car suits my purpose well"; "Will $100 do?"; "A 'B' grade doesn't suffice to get me into medical school"; "Nothing else will serve"prelude - serve as a prelude or opening toact as - function as or act like; "This heap of stones will act as a barrier"
3.function - perform duties attached to a particular office or place or function; "His wife officiated as his private secretary"officiateserve - do duty or hold offices; serve in a specific function; "He served as head of the department for three years"; "She served in Congress for two terms"

function

noun1. purpose, business, job, concern, use, part, office, charge, role, post, operation, situation, activity, exercise, responsibility, task, duty, mission, employment, capacity, province, occupation, raison d'être (French) The main function of merchant banks is to raise capital. result, effect, consequence, outcome, end result Your success will be a function of how well you can work.2. reception, party, affair, gathering, bash (informal), lig (Brit. slang), social occasion, soiree, do (informal) We were going down to a function in London.verb1. work, run, operate, perform, be in business, be in running order, be in operation or action, go The authorities say the prison is now functioning properly.2. act, serve, operate, perform, behave, officiate, act the part of, do duty, have the role of, be in commission, be in operation or action, serve your turn On weekdays, one third of the room functions as a workspace.

function

noun1. The proper activity of a person or thing:job, purpose, role, task.2. A large or important social gathering:affair, celebration, festivity, fete, gala, occasion, party, soiree.Informal: do.Slang: bash.verb1. To react in a specified way:act, behave, operate, perform, work.2. To perform a function effectively:go, operate, run, take, work.3. To perform the duties of another:act, officiate, serve.
Translations
功能运行

function

(ˈfaŋkʃən) noun a special job, use or duty (of a machine, part of the body, person etc). The function of the brake is to stop the car. 功能 功能 verb (of a machine etc) to work; to operate. This typewriter isn't functioning very well. 運行 运行ˈfunctional adjective1. designed to be useful rather than to look beautiful. functional clothes; a functional building. 實用的 实用的2. able to operate. It's an old car, but it's still functional. 能工作的 能工作的

function


bodily functions

euphemism The normal workings of the body, especially those usually done in private, such as urinating or defecating. When you have three sons, bodily functions are a common topic of discussion around the house.See also: function

function as (something)

To have a particular purpose or fill a certain role. Mrs. Smith will function as your homeroom teacher for the rest of the year now that Mrs. Jones is on maternity leave.See also: function

bodily functions

Euph. anything the body does automatically or as a normal occurrence, especially urinating and defecating. The dog needed to go outside and perform her bodily functions. It is not polite to discuss bodily functions at the dinner table.See also: function

function as

v. To serve a purpose or play a role similar to that of something else: The beaks of some wading birds function as spears for catching fish.See also: function

function


function,

in mathematics, a relation f that assigns to each member x of some set X a corresponding member y of some set Y; y is said to be a function of x, usually denoted f(x) (read "f of x "). In the equation y=f(x), x is called the independent variable and y the dependent variable. In practice, X and Y will most often be sets of numbers, vectors, points of some geometric object, or the like. For example, X might be a solid body and f(x) the temperature at the point x in X; in this case, Y will be a set of numbers. The formula A=πr 2 expresses the area of a circle as a function of its radius. A function f is often described in terms of its graph, which consists of all points (x,y) in the plane such that y=f(x). Although a function f assigns a unique y to each x, several x 's may yield the same y ; e.g., if y=f(x)=x 2 (x is a number), then f(2)=f(−2). If this never occurs, then f is called a one-to-one, or injective, function.

function

the consequence for a social system of a social occurrence, where this occurrence is regarded as making an essential contribution to the working and maintenance of this system. See FUNCTIONALISM, STRUCTURAL-FUNCTIONALISM, PARSONS, MERTON, FUNCTIONAL(IST) EXPLANATION, FUNCTIONAL PREREQUISITES, POSTULATE OF FUNCTIONAL INDISPENSABILITY.

A distinction is also made between consequences of social action that are intended and recognized by the actors involved, and consequences that are unintended and unrecognized by the actors involved. See MANIFEST AND LATENT FUNCTIONS, MERTON, INTENDED AND UNINTENDED CONSEQUENCES OF SOCIAL ACTION.

Function

 

in linguistics, the ability of a given linguistic form to fulfill a certain function; the term is used to denote the meaning or purpose of a linguistic form. Function refers to the dependence or relationship among the units of a language as these units are revealed at all levels of the language’s system.

In order to determine the function of a linguistic unit it is necessary to determine the unit’s role in a given language or linguistic system. For example, it is possible to isolate from a sentence its communicative function, which is to supply information about something, and its nominative function, which is to name the subject about which the information is supplied. Each linguistic unit exists solely because it serves a specific aim that is distinct from the aim of another linguistic unit; that is, each linguistic unit fulfills a specific function. The many different functions of linguistic units include functions of identification and of delimitation and differentiation. In the functions of delimitation and differentiation, the linguistic units themselves are distinguished. For exam-pie, a phoneme serves to differentiate among different words and morphemes or to indicate the boundaries between them.

Functions are analyzed when the units of a language are described and also when the language itself is described as a system. Among the main functions of a language are the communicative, cognitive, reflective, and performatory functions. The phatic function is the use of speech to establish personal contact rather than to communicate information. The nominative function is the use of language to name objects and concrete phenomena. Other functions of a language are the expressive and appellative functions.

The functions of a language also include functions relating to levels of language, that is, phonological, morphological, and grammatical functions. From the functional point of view, a linguistic system is a complex structure that may be differentiated according to its means of expression (written or spoken language), its social role (literary language, socially differentiated dialects, or slang), or its aesthetic orientation (poetic language). A linguistic system may also be differentiated in terms of concrete objectives of communication, and to that end makes use of specialized systems of terminology.

E. S. KUBRIAKOVA

Function

 

a fundamental concept of mathematics expressing the dependence of one variable on another.

If the variables x and y are connected so that to every value of x there corresponds a definite value of y, then y is said to be a (single-valued) function of x. Frequently x is referred to as the independent variable, and y as the dependent variable. Common ways of denoting this type of connection between x and y are y = f(x)andy = F(x). If the relation between x and y is such that to some values of x there correspond many (possibly even infinitely many) values of y, then y is said to be a multivalued function of x.

A function y = f(x) is said to be defined if we are given a set A of values taken on by x (the domain of the function), a set B of values taken on by y (the range of the function), and a rule that associates to values of x in A values of y in B. The simplest domains of functions are the real line, a closed interval a ≤ x ≤ b, and an open interval a < × < b.

The most frequent way of assigning to values of x the corresponding values of y is to give a formula that indicates what operations must be applied to x to obtain y. Examples of such formulas are y = x2 and y = 1/(1 + x2). In addition to the four arithmetic operations, the list of computing (or analytic) operations usually includes the operation of passing to the limit (that is, the operation that associates to a sequence of numbers a1, a2, a3. . . . its limit lim an whenever the limit exists), although there are no general methods for carrying out the operation. In 1905, H. Lebesgue defined an analytically representable function as a function whose values are obtained from the values of x by means of the four arithmetic operations and the operation of passing to the limit. All the functions known as elementary functions, such as sin x, cos x, ax, Function, log x, and arc tan x, are analytically representable. For example,

In 1885, K. Weierstrass proved the analytic representability of an arbitrary continuous function. Specifically, he proved that every function continuous on a closed interval is the uniform limit of a sequence of polynomials of the form

c0 + c1x + c2x2 + . . . cnxn

In addition to the analytic method there are other methods of defining functions. For example, in trigonometry cos x is defined as the projection of a unit vector on an axis that forms with the vector an angle of x radians, and in algebra Function is defined as the number whose square is ψx. The possibility of representing these functions by means of analytic formulas can be established only through deep study of the functions. In this connection the Dirichlet function ɸ(x) may be mentioned. It equals 1 if x is rational and 0 if x is irrational. The Dirichlet function was first introduced in this “formula-free” manner but was subsequently shown to be given analytically by the formula

It is important to note that there exist functions that cannot be represented, in the sense given above, by any analytic formula. Examples of such functions are functions that are not Lebesgue measurable.

A concept close to that of a function defined by a single formula is that of a function defined by different formulas in different parts of its domain of definition. One relevant example is the function f(x) = x for x ≤ 1 and f(x) = x2 for x > 1. Another is the Dirichlet function ψ(x) as defined above in a “formula-free” manner.

Figure 1

Sometimes a function y = f(x) is given by its graph, that is, the set of points (x, y) in the plane such that x is in the domain of definition of the function and y = f(x). In applications it often suffices for the graph of a function to be drawn in the plane (see Figure 1), the functional values being obtained directly from the drawing. For example, the upper layers of the atmosphere can be studied by means of balloons equipped with recording instruments that yield directly curves of variation of temperature and pressure.

For a mathematically correct definition of a function it is not enough to draw the function’s graph, since such a procedure is intrinsically inaccurate. A graphic definition of a function thus requires giving an exact geometric construction of the graph. In most cases the construction is given by means of an equation— that is, we are brought back to the analytic definition of a function. There do exist, however, purely geometric ways of constructing certain graphs; for example, a straight line is determined by giving the coordinates of two of its points.

In engineering and in the sciences it often happens that the variables x and y are known to be functionally related but the relation itself is unknown. A more or less extensive table of pairs of numbers “belonging” to the function can be obtained by carrying out a number of experiments in each of which a value of x and the corresponding value of y are measured. On many occasions the finding of an analytic formula for a function by means of such a table has constituted an important scientific discovery. An example is the discovery, by R. Boyle and E. Mariotte, of the formula pv = C connecting the pressure and volume of a gas sample. From a purely mathematical point of view, the defining of a function by means of a table of number pairs is entirely correct provided we take as the domain of definition of the function the set of first entries of the pairs in the table and assume that in each case the second entry is strictly accurate.

Functions of more than one variable also play an important role in mathematics and its applications. Suppose, for example, that to every set of values of the three variables x, y, and z there corresponds a definite value of a fourth variable u. We then say that u is a (single-valued) function of the variables x, y, and z, and we write u = f(x, y, z). The formulas u = x + 2y and u = (x + y2) sin z provide examples of the analytic definition of functions of two and three variables, respectively. There are analogous definitions of multivalued functions of more than one variable. A function z = f(x, y) of two variables may also be defined by means of its graph, that is, the set of triples (x, y, z) in three-dimensional space with (x, y) in the domain of definition of the function and z = f(x, y). In simple cases such a graph is some surface.

The development of mathematics in the 19th and 20th centuries led to further generalizations of the function concept. First, complex, rather than real, numbers were admitted as values of the variables; later, variable mathematical objects of an arbitrary nature were considered. For example, if to every circle x in the plane we associate its area y, then y is a function of x, where x is a geometric figure and not a number. Similarly, if to every sphere x in three-dimensional space we associate its center y, then neither x nor y is a number.

A general definition of a single-valued function follows. Let A = {x} and B = {y} be two nonempty sets of arbitrary objects and let M be the set of ordered pairs (x, y), x ∈ A, y ∈ B, such that every x ∈ A belongs to exactly one pair in M. Then M defines a function y = f(x) on A whose value at x0 ∈ A is the second element y0 ∈ B of the pair in M with first element x0.

This generalized definition of function eliminates the distinction between functions of one and many variables. For example, a function of three numerical variables x, y, and z may be regarded as a function of a single variable, namely, the point (x, y, z) in three-dimensional space. The definition also accommodates such generalizations of the function concept as functional and operator.

Like all mathematical concepts, the concept of a function was the result of a long evolutionary process. P. Fermât, for example, wrote in his Introduction to Plane and Solid Loci: “Whenever in a final equation two unknown quantities are found, we have a locus.” In essence, Fermât is speaking here of a functional dependence and its graphical representation, since for him “locus” means curve. The study of curves through their equations in R. Descartes’s Geometry (1637) also points to a clear notion of the mutual dependence of two variable quantities. In his Lectures on Geometry (1670), I. Barrow established by a geometric argument that differentiation and integration (of course, Barrow did not use these terms) are mutually inverse operations. This achievement indicates a very precise understanding of the concept of function. A geometric and mechanical form of the concept of function is also found in the work of I. Newton. The term “function” was first used in 1692 by G. von Leibniz. His usage of the term, however, was somewhat different from the modern usage. By a function Leibniz meant various intervals associated with a curve—for example, the abscissas of the curve’s points. In G. de L’Hôpital’s Infinitesimal Analysis (1696), which was the first published textbook on differential calculus, we do not encounter the term “function.”

In 1718, Johann Bernoulli became the first to define the function concept in a manner similar to that of today: “A function is a quantity formed of a variable and a constant.” This imprecise formulation suggests the idea of a function defined by an analytic formula. The same idea is found in L. Euler’s definition in his Introduction to the Analysis of Infinitesimals (1748): “A function of a variable quantity is an analytic expression formed, in any manner whatever, of the variable quantity and of numbers or constant quantities.” Euler also entertained the modern view of a function, which does not involve analytic expressions. Thus, in his Differential Calculus (1755), Euler states that “if certain quantities depend on others in such a way that the former vary with the latter, then the former are said to be functions of the latter.”

Nevertheless, a sufficiently sharp distinction was not made in the 18th century between a function and its analytic representation. This fact is reflected in Euler’s critique of D. Bernoulli’s solution (1753) of the problem of the vibrating string. Bernoulli’s solution was based on the assumption that every function was representable by a trigonometric series. Euler pointed out that this assertion implied the existence of an analytic expression for every function. He argued that it was possible for a function not to have an analytic representation; an example would be a function given by a graph “drawn freehand.” This critique carries weight even today. (Bernoulli, of course, considered only continuous functions, and such functions always admit of analytic representations; nevertheless, continuous functions need not admit of representations by trigonometric series.) Some of Euler’s other arguments, however, were false. For example, he thought that if a function is representable by a trigonometric series then the series is the function’s only analytic representation; in actuality, the function may be a “mixed” function represented by different formulas on different intervals. We now know that no contradiction is involved here, but in Euler’s time it was unthinkable that two analytic expressions could agree on part of an interval but not on all of it.

Such incorrect views hampered the development of the theory of trigonometric series. The essentially correct ideas of D. Bernoulli did not undergo further development until the work of J. Fourier (1822) and P. Dirichlet (1829).

In the 19th century the function concept came to be more frequently defined without any reference to analytic representability. Thus, in his treatise on the calculus (1810) the French mathematician S. Lacroix wrote: “Every quantity whose value depends on one or several others is called a function of the latter.” Fourier’s Analytical Theory of Heat (1822) contains the following sentence: “A function fx is an entirely arbitrary function, that is, it is a succession of given values that may or may not be subject to a general law and that correspond to all values x contained between 0 and some quantity X.” N. I. Lobachevskii’s definition in “On the Convergence of Trigonometric Series” (1834) is close to the modern one: “The general concept demands that we call a function of A: a number determined for every x and varying together with x. The value of a function may be given by an analytic expression, or condition, that permits the testing of all numbers and the selection of one of them. Finally, a dependence may exist that remains unknown.” Later in the same work he wrote: “A broad view of the theory admits the existence of a dependence only in the sense that we regard linked numbers as being given simultaneously.” Thus, the modern definition of function—that is, a definition free of any reference to analytic representability—appeared a number of times before being stated by Dirichlet, its presumed discoverer, in 1837.

In conclusion, an important discovery due to D. E. Men’shov should be mentioned: every finite Lebesgue measurable function defined on a closed interval can be expanded in a trigonometric series that converges almost everywhere. Since the functions usually encountered are measurable, it is essentially correct to say that, except on a set of measure zero, every function admits of an analytic representation.

REFERENCES

Il’in, V. A., and E. G. Pozniak. Osnovy matematicheskogo analiza, 3rd ed., parts 1–2. Moscow, 1971–73.
Kudriavtsev, L. D. Matematkheskii analiz, 2nd ed., vols. 1–2. Moscow, 1973.
Nikol’skii, S. M. Kurs matematicheskogo analiza, 2nd ed., vols. 1–2. Moscow, 1975.

I. P. NATANSON

Function

 

in philosophy, a relationship between two objects (or within a group of objects) such that a change in one results in a change in the other. Functions may be considered in terms of (1) the consequences—favorable, unfavorable (or dysfunctional), or neutral (that is, afunctional)—of change in one parameter affecting other parameters of an object, in which case we speak of functionality, or (2) the interrelated functioning of the individual parts within a given whole.

The scientific concept of function was introduced by G. von Leibniz. Subsequently regarded as one of the fundamental categories in philosophy, functions attracted increasing interest with the adoption of functional methods of research in various scientific disciplines. The functional approach was most fully developed by E. Cassirer in his theory of concepts, or “functions.” This attempt to construct a theory of knowledge on the basis of the functional approach had a definite influence on the philosophical concept of function. Current research deals with the validity, admissibility, and demonstrability of functional statements and explanations that are commonly used in the biological and social sciences, especially in connection with the study of goaldirected systems.

REFERENCES

Iudin, B. G. “Sistemnye predstavleniia v funktsional’nom podkhode.” In the collection Sistemnye issledovaniia: Ezhegodnik 1973. Moscow, 1973. Pages 108–26.
Frege, G. Funktion und Begriff. Jena, 1891.
Wright, L. “Functions.” Philosophical Review, vol. 82, April 1973, pp. 139–68.
Cummins, R. “Functional Analysis.” The Journal of Philosophy, 1975, vol. 72, no. 20.
In Russian translation:
Cassirer, E. Poznanie i deistvitel’nost’: Poniatie o substantsii i poniatie ofunktsii. St. Petersburg, 1912.
See also references under SYSTEM and SYSTEMS APPROACH.B. G. IUDINIn sociology. (1) The role of a given social institution or social process with respect to the needs of a social system at a higher level of organization or with respect to the interests of the classes, social groups, and individuals constituting that system—for example, the function of the state, of the family, or of art with respect to society. A distinction is drawn between overt functions, which coincide with the openly proclaimed goals and tasks of institutions and social groups, and covert, or latent, functions, which are only revealed with the passage of time and differ from the announced intentions of the participants.
(2) The dependent relationship found to exist between the various components of a single social process wherein changes in one part of the system result from changes in another part—for example, changes in the relative size of urban and rural populations as a function of industrial development.
The Marxist approach to the study of functions is based on the class analysis of the institutions themselves as well as of the corresponding needs and interests.

REFERENCES

See references under SYSTEM and STRUCTURAL-FUNCTIONAL ANALYSIS.

A. G. ZDRAVOMYSLOV

Function

 

an action performed by human beings, animals, and plants to maintain life processes and to make possible adaptation to environmental conditions. Physiologists study functions at the molecular, cellular, tissular, organic, and systemic levels, as well as those at the level of the integral organism. The systemic functions of animals include respiration, cardiovascular activity, digestion, vision, hearing, and equilibrium. Since all functions are based on the continuous process of metabolism, they are studied in order to elucidate the physical, chemical, and structural changes that take place in the body (in the system of organs or in individual organs and tissues). Of considerable importance in this respect is research in developmental biology, a field concerned with the processes and propelling forces of individual development (ontogeny).

The comparative historical method introduced into physiology by I. M. Sechenov, I. P. Pavlov, and N. E. Vvedenskii played a major part in the comprehensive study of functions. L. A. Orbeli and his school pioneered the study of the physiological, biochemical, and structural bases of the evolution of functions (evolutionary physiology). Their work influenced the study of functional changes induced by various factors of natural or artifical origin, for example, changes in climatic conditions, motor activity, composition and properties of food, insufficiency or excess of atmospheric oxygen, and weightlessness, as well as the study of adaptation to environmental conditions.

The study of the evolution of functions and, especially, the adaptability of functions to the environment is closely associated with the investigation of the mechanisms that regulate functions (seeHUMORAL REGULATION, HORMONAL REGULATION, and NEURO-HUMORAL REGULATION). The views of K. M. Bykov and his school on the relationship between the cerebral cortex and the internal organs marked an important stage in the study of functions (seeCORTICOVISCERAL RELATIONS). Development of the concept of corticovisceral relations led to an explanation of the regulation of the visceral systems of the body based on the idea that their activity is a distinctive form of behavior. Inasmuch as the functions of the visceral systems, like the behavior of the organism as a whole, are always adaptive, they develop in the fairly strict sequence of the individual reactions that constitute them and, moreover, possess the capacity to “learn,” that is, become perfected. The objective of research in this field is to elucidate the mechanisms and patterns of regulation of functions in order to make possible intervention to normalize the body’s vital activities in the event of abnormal or extreme conditions.

V. N. CHERNIGOVSKII and K. A. LANGE

function

[′fəŋk·shən] (computer science) In FORTRAN, a subroutine of a particular kind which returns a computational value whenever it is called. (mathematics) A mathematical rule between two sets which assigns to each member of the first, exactly one member of the second.

function

Maths logic a relation between two sets that associates a unique element (the value) of the second (the range) with each element (the argument) of the first (the domain): a many-one relation. Symbol: f(x) The value of f(x) for x = 2 is f(2) FORMULA

function

(mathematics)(Or "map", "mapping") If D and C are sets(the domain and codomain) then a function f from D to C,normally written "f : D -> C" is a subset of D x C such that:

function

(2)For each d in D there exists some c in C such that (d,c) isan element of f. I.e. the function is defined for everyelement of D.

function

(3)For each d in D, c1 and c2 in C, if both (d,c1) and (d,c2)are elements of f then c1 = c2. I.e. the function is uniquelydefined for every element of D.

See also image, inverse, partial function.

function

(programming)Computing usage derives from the mathematicalterm but is much less strict. In programming (except infunctional programming), a function may return differentvalues each time it is called with the same argument valuesand may have side effects.

A procedure is a function which returns no value but hasonly side-effects. The C language, for example, has noprocedures, only functions. ANSI C even defines a type,void, for the result of a function that has no result.

function

In programming, a self-contained software routine that performs a task. Functions can do a large amount of processing or as little as adding two numbers and deriving a result. Values are passed to the function, and values may be returned. Or, the function may just perform the operation and not return a resulting value. The concept of a function within a program is that, once written, it can be used over and over again without the programmer having to duplicate the same lines of code in the program each time that same processing is desired.

Standard and Programmer-Defined
Programming languages provide a set of standard functions as well as allow programmers to define their own functions. For example, the C and C++ programming languages are built entirely of functions and always contain a "main" function.

The Application Programming Interface (API)
Functions in one program can also be called for by other programs and shared. For example, operating systems can contain more than a thousand functions to display data, print, read and write disks and perform myriad tasks. Programmers write their applications to interact with the OS using these functions. This list of functions is called the "application programming interface" (API).

Function Calls
Functions are activated by placing a "function call" statement in the program. The function call often includes values (parameters) that are passed to the function. When called, the function performs the operation and returns control to the instruction following the call. The function may return a value or not. Writing a program in a language such as C/C++ involves calling language functions, one's own functions and operating system functions (APIs). There is a whole lot of function calling. See function prototype, API and interface.

A Function Call Example: Open and Read
The example below shows two very simplified API functions to open and read a file.

The OPEN function is called to read the file "budget.txt," and the function returns a value in the variable HANDLE. If the file was opened successfully, HANDLE might contain a positive number, but if not, a negative one. The value in HANDLE is then passed to the READ function to read so many bytes (LENGTH) of the file into a memory area called INPUTBUFFER. The OPEN function returns the number of bytes read in the SIZE variable.

 handle = open("budget.txt"); size = read(handle, InputBuffer, length);
LegalSeeReturnFinancialSeeProbability density functionSee FN
See FCTN

function


  • all
  • noun
  • verb

Synonyms for function

noun purpose

Synonyms

  • purpose
  • business
  • job
  • concern
  • use
  • part
  • office
  • charge
  • role
  • post
  • operation
  • situation
  • activity
  • exercise
  • responsibility
  • task
  • duty
  • mission
  • employment
  • capacity
  • province
  • occupation
  • raison d'être
  • result
  • effect
  • consequence
  • outcome
  • end result

noun reception

Synonyms

  • reception
  • party
  • affair
  • gathering
  • bash
  • lig
  • social occasion
  • soiree
  • do

verb work

Synonyms

  • work
  • run
  • operate
  • perform
  • be in business
  • be in running order
  • be in operation or action
  • go

verb act

Synonyms

  • act
  • serve
  • operate
  • perform
  • behave
  • officiate
  • act the part of
  • do duty
  • have the role of
  • be in commission
  • be in operation or action
  • serve your turn

Synonyms for function

noun the proper activity of a person or thing

Synonyms

  • job
  • purpose
  • role
  • task

noun a large or important social gathering

Synonyms

  • affair
  • celebration
  • festivity
  • fete
  • gala
  • occasion
  • party
  • soiree
  • do
  • bash

verb to react in a specified way

Synonyms

  • act
  • behave
  • operate
  • perform
  • work

verb to perform a function effectively

Synonyms

  • go
  • operate
  • run
  • take
  • work

verb to perform the duties of another

Synonyms

  • act
  • officiate
  • serve

Synonyms for function

noun (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)

Synonyms

  • mapping
  • mathematical function
  • single-valued function
  • map

Related Words

  • multinomial
  • polynomial
  • math
  • mathematics
  • maths
  • mathematical relation
  • expansion
  • inverse function
  • Kronecker delta
  • metric
  • metric function
  • transformation
  • isometry
  • operator
  • circular function
  • trigonometric function
  • threshold function
  • exponential
  • exponential function

noun what something is used for

Synonyms

  • purpose
  • use
  • role

Related Words

  • usefulness
  • utility
  • raison d'etre

noun the actions and activities assigned to or required or expected of a person or group

Synonyms

  • role
  • office
  • part

Related Words

  • duty
  • capacity
  • hat
  • portfolio
  • lieu
  • stead
  • place
  • position
  • second fiddle

noun a relation such that one thing is dependent on another

Related Words

  • relation

noun a formal or official social gathering or ceremony

Related Words

  • social affair
  • social gathering

noun a vaguely specified social event

Synonyms

  • social function
  • social occasion
  • occasion
  • affair

Related Words

  • social event
  • party
  • celebration
  • jubilation
  • ceremonial
  • ceremonial occasion
  • ceremony
  • observance
  • fundraiser
  • photo op
  • photo opportunity
  • sleepover

noun a set sequence of steps, part of larger computer program

Synonyms

  • subprogram
  • subroutine
  • procedure
  • routine

Related Words

  • software
  • software package
  • software program
  • software system
  • computer software
  • package
  • computer program
  • computer programme
  • programme
  • program
  • cataloged procedure
  • contingency procedure
  • library routine
  • random number generator
  • recursive routine
  • reusable routine
  • executive routine
  • supervisory routine
  • tracing routine
  • service routine
  • utility routine

verb perform as expected when applied

Synonyms

  • operate
  • work
  • run
  • go

Related Words

  • double
  • roll
  • run
  • cut
  • work
  • service
  • serve

Antonyms

  • malfunction
  • misfunction

verb serve a purpose, role, or function

Synonyms

  • serve

Related Words

  • service
  • serve
  • suffice
  • answer
  • do
  • prelude
  • act as

verb perform duties attached to a particular office or place or function

Synonyms

  • officiate

Related Words

  • serve
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更新时间：2024/12/22 22:59:24