A definition may be a statement of the essential properties of a certain thing, or a statement of equivalence between one expression and another, usually more complex expression that gives the meaning of the first. These two senses are not mutually exclusive, nor are they equivalent. A thing being defined is called (from Latin) a definiendum; the expression which defines it is called a definiens. Definition - Kinds of definition. A number of different kinds and techniques of definition ...

Including:

• Definition - Kinds of definition
• Definition - Determining meaning: extension intension ambiguity and vagueness
• Definition - A definition of 'definition'
• Definition - A contribution to defining the term 'definition'
• Definition - Quotation

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• Definitions - Terms for Wiktionary

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Suppose we have decided to define a certain word or a concept associated with that word. Suppose also that we have identified which sense of the word we are interested in, and we have noted clear cases, some unclear cases, and some borderline cases of the application of the word. The question then is: how can this word be defined? What is desired here is a description of the intension of the word: that is, an account of the set of properties that characterizes all and only members of the extension. In that case, it seems the fo ...

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Definition, Definition - Kinds of definition, Definition - Determining meaning: extension intension ambiguity and vagueness, Definition - A definition of 'definition', Definition - A contribution to defining the term 'definition', Definition - Quotation

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A concrete category is formally defined as follows: a category C a faithful functor F : C → Set The faithful functor F is typically thought of as a forgetful functor, which assigns to every object of C its "underlying set", and to every morphism in C the corresponding function. Thus, a concrete category C consists not just of C itself, but of the category C and a corresponding forgetful functor F. In practice, the forgetful functor is usually clear, and we s ...

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Concrete category, Concrete category - Definition, Concrete category - Not all categories are concrete, Concrete category - Alternate definition

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The precise definition of a Baire space has undergone slight changes throughout history, mostly due to prevailing needs and viewpoints. First, we give the usual modern definition, and then we give a historical definition which is closer to the definition originally given by Baire. Baire space - Modern definition. A topological space is called a Baire space if the countable union of any collection of closed se ...

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Baire space, Baire space - Motivation, Baire space - Definition, Baire space - Modern definition, Baire space - Historical definition, Baire space - Examples, Baire space - Baire category theorem, Baire space - Properties

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Silver ratio - Definition as . The silver ratio (δS) is defined as the irrational number formed from the sum of 1 and the square root of 2. That is: It follows from this definition that: (δS − 1)2 = 2. Silver ratio - Definition as . The silver ratio can also be defined by the simple continued fract ...

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Silver ratio, Silver ratio - Definition, Silver ratio - Definition as, Silver ratio - Definition as, Silver ratio - Properties, Silver ratio - Silver means, Silver ratio - External link

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1 Hectogram is equal to 100 grams: {1Hg = 100g} A Hectogram is the tenth (1/10) of a kilogram: {1Hg = 0.1 Kg} ...

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Hectogram, Hectogram - Definition, Hectogram - Uses

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There are many equivalent properties that can be used to characterize a K3 surface. The definition given depends on the context: In differential geometry, a typical definition is of "a compact, complex, simply connected surface with trivial canonical line bundle". In algebraic geometry, the definition "a surface, X, with trivial canonical class such that H1(X,OX) = 0." is preferred since it generalizes to more arbitrary base fields (not just the complex numbers). Here, See also:

K3 surface, K3 surface - Definition, K3 surface - Important Properties, K3 surface - Examples

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Given a graph G = (V,E) with the degree matrix D for G is a square matrix defined as ...

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Degree matrix, Degree matrix - Definition, Degree matrix - Examples

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Uniform space - Entourage definition. A uniform space (X,Φ) is a set X equipped with a nonempty family of subsets of the Cartesian product X × X (Φ is called the uniform structure of X and its elements entourages (French:neighborhoods) or surroundings) with the following properties if U is in Φ, then U contains the diagonal { (x, x) : x in X }. if U is in Φ and V i ...

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Uniform space, Uniform space - History, Uniform space - Definition, Uniform space - Entourage definition, Uniform space - Uniform cover definition, Uniform space - Pseudometrics definition, Uniform space - Intuition, Uniform space - Examples, Uniform space - Uniformly continuous functions, Uniform space - Topology of uniform spaces, Uniform space - Completeness

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Radiance is defined by where the approximation holds for small A and Ω, L is the radiance (W·m-2·sr-1), Φ is the radiant flux or power (W), θ is the angle between the surface normal and the specified direction, A is the area of the source (m2), and Ω is the solid angle (sr). The spectral radiance (radiance per unit wavelength) is written Lλ and the radiance per unit freq ...

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Radiance, Radiance - Definition

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The nitride ion is N3- (a nitrogen atom plus three electrons). A nitride (compound) is a compound that has nitrogen with more electropositive elements. ...

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Nitride, Nitride - Definition, Nitride - Examples, Nitride - Discussion

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The nitrite ion is NO2-. A nitrite compound is one that contains this group, either an ionic compound, or an analogous covalent one. These may be considered salts or esters of nitrous acid. ...

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Nitrite, Nitrite - Definition, Nitrite - Examples, Nitrite - Discussion

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Luminance is defined by where L is the luminance (cd/m2), F is the luminous flux or luminous power (lm), θ is the angle between the surface normal and the specified direction, A is the area of the source (m2), and Ω is the solid angle (sr). ...

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Luminance, Luminance - Definition

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Given a homogeneous linear second-order ordinary differential equation Abel's identity can be written as where W(x) is the Wronskian of the two linearly independent solutions to the differential equation. ...

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Abel's identity, Abel's identity - Definition, Abel's identity - Derivation

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A graph homomorphism f from a graph G: = (V,E) to a graph G': = (V',E'), written is a mapping from the vertex set of G to the vertex set of G' such that whenever . The above definition is extended to directed graphs. Then, for a homomorphism , (f(u),f(v)) is an arc ...

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Graph homomorphism, Graph homomorphism - Definition, Graph homomorphism - Notes

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The chlorate ion ClO3-. A chlorate (compound) is a compound that contains this group, with chlorine in oxidation state +5. ...

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Chlorate, Chlorate - Definition, Chlorate - Examples, Chlorate - Preparation, Chlorate - Discussion

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Using Einstein's summation convention, the dyadic product may be defined by . Writing out the sums, this becomes . ...

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Dyadic product, Dyadic product - Example, Dyadic product - Definition

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For a given cardinal number κ and a stationary set S ⊆ κ, ◊S is the statement that there is a sequence such that every Aδ is a subset of δ for every B ⊆ κ, the set is stationary is usually written as just ◊. ...

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Diamondsuit, Diamondsuit - Definition, Diamondsuit - Properties and use

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A semicubical parabola is a curve defined parametrically as The parameter can be removed to yield the equation ...

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Semicubical parabola, Semicubical parabola - Definition, Semicubical parabola - Properties, Semicubical parabola - History

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