Characterization (mathematics)
In mathematics, a characterization of an object is a set of conditions that, while different from the definition of the object, is logically equivalent to it. To say that "Property P characterizes object X" is to say that not only does X have property P, but that X is the only thing that has property P (i.e., P is a defining property of X). Similarly, a set of properties P is said to characterize X, when these properties distinguish X from all other objects. Even though a characterization identifies an object in a unique way, several characterizations can exist for a single object. Common mathematical expressions for a characterization of X in terms of P include "P is necessary and sufficient for X", and "X holds if and only if P".
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Affine spaceAndrew M. GleasonApproximation theoryBasu's theoremBohr–Mollerup theoremCategorizationCharacterCharacter (mathematics)Characterisation (mathematics)Characterisation theoremCharacterisation theoremsCharacterization (disambiguation)Characterization of probability distributionsCharacterization theoremCharacterization theoremsCharacterizations of the category of topological spacesCharacterizations of the exponential functionConjectureCurtis–Hedlund–Lyndon theoremDarmois–Skitovich theoremDiagonal morphismDistance geometryEntropy (information theory)Exponential functionExtension (semantics)Finite-state transducerFlorian PopForbidden graph characterizationHeyde theoremJohannes MollerupKac–Bernstein theoremLoximuthal projectionMathematicsMaxwell's theoremMemorylessnessMenger's theoremMorera's theoremNowhere commutative semigroupOutline of discrete mathematicsPoincaré conjecture
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Characterization (mathematics)
In mathematics, a characterization of an object is a set of conditions that, while different from the definition of the object, is logically equivalent to it. To say that "Property P characterizes object X" is to say that not only does X have property P, but that X is the only thing that has property P (i.e., P is a defining property of X). Similarly, a set of properties P is said to characterize X, when these properties distinguish X from all other objects. Even though a characterization identifies an object in a unique way, several characterizations can exist for a single object. Common mathematical expressions for a characterization of X in terms of P include "P is necessary and sufficient for X", and "X holds if and only if P".
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En langage mathématique, la ca ...... ts » pourrait être spécifiée).
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In mathematics, a characteriza ...... leads to their categorization.
@en
Stwierdzenie, że „własność P c ...... ującego się za słowami co do).
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数学において、「性質 P が対象 X を特徴づける (cha ...... 型の違いを除いて特徴づける」というような主張も一般的である。
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En langage mathématique, la ca ...... ts » pourrait être spécifiée).
@fr
In mathematics, a characteriza ...... nd "X holds if and only if P".
@en
Stwierdzenie, że „własność P c ...... ującego się za słowami co do).
@pl
数学において、「性質 P が対象 X を特徴づける (cha ...... 型の違いを除いて特徴づける」というような主張も一般的である。
@ja
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Caractérisation (mathématiques)
@fr
Characterization (mathematics)
@en
Charakteryzacja (matematyka)
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特徴づけ (数学)
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