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function |
6 definitions found From Webster's Revised Unabridged Dictionary (1913) [web1913]: Function \Func"tion\, n. 1. (Eccl.) A religious ceremony, esp. one particularly impressive and elaborate. Every solemn `function' performed with the requirements of the liturgy. --Card. Wiseman. 2. A public or social ceremony or gathering; a festivity or entertainment, esp. one somewhat formal. This function, which is our chief social event. --W. D. Howells. From Webster's Revised Unabridged Dictionary (1913) [web1913]: Fluent \Flu"ent\, n. 1. A current of water; a stream. [Obs.] 2. [Cf. F. fluente.] (Math.) A variable quantity, considered as increasing or diminishing; -- called in the modern calculus, the {function} or {integral}. From Webster's Revised Unabridged Dictionary (1913) [web1913]: Function \Func"tion\, n. [L. functio, fr fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf F. fonction. Cf {Defunct}.] 1. The act of executing or performing any duty, office, or calling; per formance. ``In the function of his public calling.'' --Swift. 2. (Physiol.) The appropriate action of any special organ or part of an animal or vegetable organism; as the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body. 3. The natural or assigned action of any power or faculty, as of the soul, or of the intellect; the exertion of an energy of some determinate kind As the mind opens, and its functions spread. --Pope. 4. The course of action which peculiarly pertains to any public officer in church or state; the activity appropriate to any business or profession. Tradesmen . . . going about their functions. --Shak. The malady which made him incapable of performing his regal functions. --Macaulay. 5. (Math.) A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other Thus the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x^{2}, 3^{x}, Log x, and Sin. x, are all functions of x. {Algebraic function}, a quantity whose connection with the variable is expressed by an equation that involves only the algebraic operations of addition, subtraction, multiplication, division, raising to a given power, and extracting a given root; -- opposed to transcendental function. {Arbitrary function}. See under {Arbitrary}. {Calculus of functions}. See under {Calculus}. {Carnot's function} (Thermo-dynamics), a relation between the amount of heat given off by a source of heat, and the work which can be done by it It is approximately equal to the mechanical equivalent of the thermal unit divided by the number expressing the temperature in degrees of the air thermometer, reckoned from its zero of expansion. {Circular functions}. See {Inverse trigonometrical functions} (below). -- Continuous function, a quantity that has no interruption in the continuity of its real values, as the variable changes between any specified limits. {Discontinuous function}. See under {Discontinuous}. {Elliptic functions}, a large and important class of functions, so called because one of the forms expresses the relation of the arc of an ellipse to the straight lines connected therewith. {Explicit function}, a quantity directly expressed in terms of the independently varying quantity; thus in the equations y = 6x^{2}, y = 10 -x^{3}, the quantity y is an explicit function of x. {Implicit function}, a quantity whose relation to the variable is expressed indirectly by an equation; thus y in the equation x^{2} + y^{2} = 100 is an implicit function of x. {Inverse trigonometrical functions}, or {Circular function}, the lengths of arcs relative to the sines, tangents, etc Thus AB is the arc whose sine is BD and (if the length of BD is x) is written sin ^{-1}x, and so of the other lines. See {Trigonometrical function} (below). Other transcendental functions are the exponential functions, the elliptic functions, the gamma functions, the theta functions, etc {One-valued function}, a quantity that has one and only one value for each value of the variable. -- {Transcendental functions}, a quantity whose connection with the variable cannot be expressed by algebraic operations; thus y in the equation y = 10^{x} is a transcendental function of x. See {Algebraic function} (above). -- {Trigonometrical function}, a quantity whose relation to the variable is the same as that of a certain straight line drawn in a circle whose radius is unity, to the length of a corresponding are of the circle. Let AB be an arc in a circle, whose radius OA is unity let AC be a quadrant, and let OC DB and AF be drawnpependicular to OA and EB and CG parallel to OA and let OB be produced to G and F. E Then BD is the sine of the arc AB OD or EB is the cosine, AF is the tangent, CG is the cotangent, OF is the secant OG is the cosecant, AD is the versed sine, and CE is the coversed sine of the are AB If the length of AB be represented by x (OA being unity) then the lengths of Functions. these lines (OA being unity) are the trigonometrical functions of x, and are written sin x, cos x, tan x (or tang x), cot x, sec x, cosec x, versin x, coversin x. These quantities are also considered as functions of the angle BOA. From Webster's Revised Unabridged Dictionary (1913) [web1913]: Function \Func"tion\, Functionate \Func"tion*ate\, v. i. To execute or perform a function; to transact one's regular or appointed business. From WordNet r 1.6 [wn]: function n 1: a mathematical relation such that each element of one set is associated with at least one element of another set [syn: {mathematical function}] 2: what something is used for "the function of an auger is to bore holes"; "ballet is beautiful but what use is it?" [syn: {purpose}, {role}, {use}] 3: 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" or "play its role" or "do its duty" [syn: {office}, {part}, {role}] 4: a relation such that one thing is dependent on another; "height is a function of age"; "price is a function of supply and demand" 5: a formal or official social gathering or ceremony; "it was a black-tie function" 6: a set sequence of steps, part of larger computer program [syn: {routine}, {subroutine}, {subprogram}, {procedure}] v 1: function properly; "The washing machine won't go unless it's plugged in" [syn: {work}, {operate}, {go}, {run}] [ant: {malfunction}] 2: 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" [syn: {serve}] 3: act as an official in a specific function [syn: {officiate}] From The Free On-line Dictionary of Computing (13 Mar 01) [foldoc]: function 1.(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: 1. For each d in D there exists some c in C such that (d,c) is an element of f. I.e. the function is defined for every element of D. 2. 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 uniquely defined for every element of D. See also {image}, {inverse}, {partial function}. 2. Computing usage derives from the mathematical term but is much less strict. In programming (except in {functional programming}), a function may return different values each time it is called with the same argument values and may have {side effects}. A {procedure} is a function which returns no value but has only {side-effects}. The {C} language, for example, has no procedures, only functions. {ANSI C} even defines a {type}, {void}, for the result of a function that has no result. (1996-09-01)
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