Injective function
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct elements; that is, f(x1) = f(x2) implies x1 = x2. (Equivalently, x1 ≠ x2 implies f(x1) ≠ f(x2) in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain.
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- enIn mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct elements; that is, f(x1) = f(x2) implies x1 = x2. (Equivalently, x1 ≠ x2 implies f(x1) ≠ f(x2) in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain.
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- enIn mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct elements; that is, f(x1) = f(x2) implies x1 = x2. (Equivalently, x1 ≠ x2 implies f(x1) ≠ f(x2) in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain. A homomorphism between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular for vector spaces, an injective homomorphism is also called a monomorphism. However, in the more general context of category theory, the definition of a monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see Homomorphism § Monomorphism for more details. A function that is not injective is sometimes called many-to-one.
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- enInjective function
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- Algebraic structure
- Axiom of choice
- Bijective function
- Cantor–Bernstein–Schroeder theorem
- Cardinal number
- Cartesian plane
- Category:Basic concepts in set theory
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- Category of sets
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- Constructive mathematics
- Contraposition
- Distinct (mathematics)
- Domain of a function
- Element (mathematics)
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- Empty function
- Empty set
- Exponential function
- File:Injection.svg
- File:Injective composition2.svg
- Finite set
- Function (mathematics)
- Homomorphism
- Horizontal line test
- Identity function
- Image (function)
- Image (mathematics)
- Inclusion function
- Inclusion map
- Indecomposability (constructive mathematics)
- Inverse function
- John Wiley & Sons
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- Mathematical intuition
- Mathematics
- Monomorphism
- Naive Set Theory (book)
- Natural logarithm
- Partial bijection
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- Up to isomorphism
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- Birebir fonksiyon
- Disĵeto
- Eintæk vörpun
- Fonzion iniettiva
- Função injectiva
- Funció injectiva
- Función inyectiva
- Funciono injektiva
- Funcție injectivă
- Functio iniectiva
- Fungsi injektif
- Funkcja różnowartościowa
- Funtzio injektibo
- Funzione iniettiva
- Injeccion (matematicas)
- Injectie (wiskunde)
- Injection (mathematica)
- Injection (mathématiques)
- Injective function
- Injective function
- Injekcija (matematika)
- Injeksjon i matematikk
- Injektiivne funktsioon
- Injektio
- Injektiv
- Injektive Funktion
- Injektiv funksjon
- Injektiv funktion
- Injektív leképezés
- Injektivna funkcija
- Injektivna funkcija
- Injektivna preslikava
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- Инекция
- Инъективті функция
- Инъекция (математика)
- Инјективна функција
- Инјективно пресликавање
- פונקציה חד-חד-ערכית
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