About: Bijection, injection and surjection

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In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to elements in its codomain. Given a function :

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rdfs:label	Bijection, injection and surjection (en)
rdfs:comment	In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to elements in its codomain. Given a function : (en)
sameAs	Bijection, injection and surjection
dbp:wikiPageUsesTemplate	dbt:Details dbt:I_sup dbt:Main dbt:Math dbt:Mvar dbt:Short_description dbt:Tmath
Subject	Basic concepts in set theory Functions and mappings Mathematical relations
Link from a Wikipage to an external page	http://jeff560.tripod.com/i.html
thumbnail	wiki-commons:Special:FilePath/Bijection.svg?width=300
foaf:depiction
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Bijection,_injection_and_surjection?oldid=1052846429&ns=0
Wikipage page ID	1830142 (xsd:integer)
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Wikipage revision ID	1052846429 (xsd:integer)
Link from a Wikipage to another Wikipage	Group (mathematics) Uniqueness quantification Axiom of choice Bijection Monomorphism Up to Cardinality Basic concepts in set theory Category (mathematics) Functions and mappings Mathematical relations Domain of a function Set (mathematics) Surjective function Horizontal line test Codomain Parameter Embedding Epimorphism Equivalence class Equivalence relation Function (mathematics) Composition operator If and only if Image (mathematics) Permutation Symmetric group Exponential function Expression (mathematics) Injective function Injective module Inverse function Map (mathematics) Transposition (logic) Isomorphism Mathematics Natural logarithm Nicolas Bourbaki
has abstract	In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to elements in its codomain. Given a function : * The function is injective, or one-to-one, if each element of the codomain is mapped to by at most one element of the domain, or equivalently, if distinct elements of the domain map to distinct elements in the codomain. An injective function is also called an injection. Notationally:or, equivalently (using logical transposition), * The function is surjective, or onto, if each element of the codomain is mapped to by at least one element of the domain. That is, the image and the codomain of the function are equal. A surjective function is a surjection. Notationally: * The function is bijective (one-to-one and onto, one-to-one correspondence, or invertible) if each element of the codomain is mapped to by exactly one element of the domain. That is, the function is both injective and surjective. A bijective function is also called a bijection. That is, combining the definitions of injective and surjective,where means "there exists exactly one x". * In any case (for any function), the following holds: An injective function need not be surjective (not all elements of the codomain may be associated with arguments), and a surjective function need not be injective (some images may be associated with more than one argument). The four possible combinations of injective and surjective features are illustrated in the adjacent diagrams. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Bijection,_injection_and_surjection
is Wikipage redirect of	Jectivity BiJection Bijection, injection, and surjection Bijection, surjection and injection
is Link from a Wikipage to another Wikipage of	Jectivity BiJection Bijection Bijection, injection, and surjection Domain of a function Bijection, surjection and injection Isotopy of an algebra Mathematical logic
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Bijection,_injection_and_surjection

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