Surjective function
In mathematics, a surjective function (also known as surjection, or onto function) is a function f that every element y can be mapped from element x so that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y.
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- enIn mathematics, a surjective function (also known as surjection, or onto function) is a function f that every element y can be mapped from element x so that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y.
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- enIn mathematics, a surjective function (also known as surjection, or onto function) is a function f that every element y can be mapped from element x so that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y. The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French word sur means over or above, and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain. Any function induces a surjection by restricting its codomain to the image of its domain. Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection. The composition of surjective functions is always surjective. Any function can be decomposed into a surjection and an injection.
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- Axiom of choice
- Bijection, injection and surjection
- Bijective function
- Cardinality
- Cardinal number
- Cartesian product
- Category:Basic concepts in set theory
- Category:Functions and mappings
- Category:Mathematical relations
- Category:Types of functions
- Category (mathematics)
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- Codomain
- Cover (algebra)
- Covering map
- Disjoint sets
- Domain of a function
- Elements of Mathematics
- Enumeration
- Epimorphism
- Equivalence class
- Equivalence relation
- Even number
- Exponential function
- Fiber bundle
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- France
- Function (mathematics)
- Function composition
- Function graph
- General linear group
- Graph of a function
- Group (mathematics)
- Identity function
- Image (mathematics)
- Index set
- Injective
- Injective function
- Integer
- Inverse function
- Invertible matrix
- Left-total relation
- Map (mathematics)
- Mathematician
- Mathematics
- Matrix (mathematics)
- Matrix exponential
- Modular arithmetic
- Morphism
- Natural logarithm
- Nicolas Bourbaki
- Odd number
- Partition of a set
- Preimage
- Projection (set theory)
- Projection map
- Quotient set
- Real number
- Restriction of a function
- Right-cancellative
- Right-total relation
- Right-unique relation
- Schröder–Bernstein theorem
- Section (category theory)
- Split epimorphism
- Stirling numbers of the second kind
- Subset
- Twelvefold way
- Unique (mathematics)
- Wikt:sur
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- Fonzion suriettiva
- Função sobrejectiva
- Funció exhaustiva
- Función sobreyectiva
- Funcție surjectivă
- Functio superiectiva
- Fungsi surjektif
- Funkcja „na”
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- Funzione suriettiva
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- Surjectie
- Surjection
- Surjection
- Surjective function
- Surjective function
- Surjeksjon
- Surjektio
- Surjektio
- Surjektiv
- Surjektive Funktion
- Surjektiv funksjon
- Surjektiv funktion
- Surjektivna funkcija
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