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Topic: Codomain

Related Topics

Injective

Surjection

Support (mathematics)

Indicator function

Lebesgue integration

Naive set theory

Limit (mathematics)

Countable

Indexed family

Riemann integral

Real number

Axiom of empty set

Set

Axiomatic set theory

Monotone convergence theorem

	Codomain - Wikipedia, the free encyclopedia
		A codomain in mathematics is the set of "output" values associated with (or mapped to) the domain of "input" arguments in a function.
		The codomain is not to be confused with the range, which is in general only a subset of B; in lower-level mathematics education, however, range is often taught as being equivalent to codomain.
		The codomain does not affect whether or not the function is an injection.
	en.wikipedia.org /wiki/Codomain (244 words)

	Range (mathematics) - Wikipedia, the free encyclopedia
		The range is a subset of the codomain, but is not necessarily equal to the codomain, since there may be elements of the codomain which are not elements of the range.
		Another way to think about this is to consider the codomain to be the set of all possible output values, while the range is the set of all actual outputs.
		The codomain of f is R, and f takes all nonnegative values but never takes negative values, and thus the range is in fact the set R
	en.wikipedia.org /wiki/Function_range (239 words)

	Function codomain : Codomain (Site not responding. Last check: 2007-11-07)
		Given a function f: A → B, the set B is called the codomain of f.
		The codomain isn't to be confused with the range f(A), which is in general only a subset of B.
		The codomain can affect whether or not the function is a surjection; in our example, g is a surjection while f isn't.
	www.termsdefined.net /co/codomain.html (298 words)

	PreCalculus
		The codomain is the type of output that the function was declared to produce.
		This would define the codomain to be the same as the range.
		This declaration states that the argument of the function, the domain, is a floating point number and that the returned value of the function, the codomain, is also a floating point number.
	home.att.net /~srschmitt/precalc/precalc-10-02-00.html (399 words)

	Encyclopedia: Codomain
		A codomain in mathematics is the set of "output" values associated with (or mapped to) the domain of "inputs" in a function.
		The codomain is not to be confused with the range f(A), which is in general only a subset of B; in lower-level mathematics education, however, range is often taught as being equivalent to codomain.
		Let the function f be a function on the real numbers: In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line.
	www.nationmaster.com /encyclopedia/Codomain (687 words)

	Codomain -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		The codomain is not to be confused with the (A series of hills or mountains) range f(A), which is in general only a (A set whose members are members of another set; a set contained within another set) subset of B.
		The codomain of f is R, but clearly f(x) never takes (A reply of denial) negative values, and thus the range is in fact the set R
		The codomain can affect whether or not the function is a (Click link for more info and facts about surjection) surjection; in our example, g is a surjection while f is not.
	www.absoluteastronomy.com /encyclopedia/c/co/codomain.htm (230 words)

	Glossary - Linear Algebra
		The codomain of a linear transformation is the vector space which contains the vectors resulting from the transformation's action.
		The column space of a matrix is the subspace of the codomain which is spanned by the columns of the matrix.
		The set of the images of all vectors in the domain is called the range of T, which in turn is contained in the codomain.
	www.math.umbc.edu /~campbell/Math221/Glossary (1250 words)

	Returns
		If the function uses the entire codomain, then the developer is limited to handling errors similar to the first two examples.
		Extending a function's codomain can be done easily when the codomain is an object reference: extend by allowing references to exceptions.
		By simply increasing the codomain of a function, we are able to model exceptions as return values.
	www.arcavia.com /kyle/Analysis/Return.html (624 words)

	Operations on Mappings (Site not responding. Last check: 2007-11-07)
		Given a mapping f with domain A and codomain B, return the image of A in B. Note that images and kernels are currently available only on certain intrinsic maps.
		Given the homomorphism f with domain A and codomain B, return the kernel of f.
		Given the homomorphism f with domain A and codomain B, return the cokernel of f.
	www.math.uiuc.edu /Software/magma/text160.html (153 words)

	Images and Preimages (Site not responding. Last check: 2007-11-07)
		Given a mapping f with domain A and codomain B, and a finite enumerated set, indexed set, or sequence S of elements belonging to A, return the image of S under f as an enumerated set, indexed set, or sequence of elements of B. C @ f : Structure, Map -> Structure
		Given a homomorphism f with domain A and codomain B, and a substructure C of A, return the image of C under f as a substructure of B. y @@ f : Elt, Map -> Elt
		Given a mapping f with domain A and codomain B, where f supports preimages, and an element y belonging to B, return the preimage of y under f as an element of A. If the mapping f is a homomorphism, then a single element is returned as the preimage of y.
	www.math.lsu.edu /magma/text228.htm (365 words)

	Homomorphisms (Site not responding. Last check: 2007-11-07)
		Given a homomorphism whose domain is an fp-group G and an element w of G, return the image of w under f as an element of the codomain of f.
		Given a homomorphism whose domain is an fp-group G and a subgroup H of G, return the image of H under f as a subgroup of the codomain of f.
		Given a homomorphism whose domain is an fp-group G and a subgroup H of the image of f, return the preimage of H under f as a subgroup of G. Some maps do not support inverse images.
	www.mat.niu.edu /help/math/magmahelp/text298.html (933 words)

	Homomorphisms
		Suppose M is a matrix module over the coefficient ring R whose elements are a by b matrices and have domain D and codomain C. Suppose also that N is a matrix module over the coefficient ring R whose elements are a by c matrices and have domain D and codomain C'.
		Note also that in this case the domain and codomains of H' are the generic R-spaces (tuple modules) corresponding to A (of dimension d) and B (of dimension e).
		The codomain N of the homomorphism a belonging to öm(M, N).
	www.math.niu.edu /help/math/magmahelp/text786.html (1723 words)

	Homomorphisms
		Given a homomorphism whose domain is a braid group B and an element e of B, return the image of e under f as element of the codomain of f.
		Given a homomorphism whose domain is a braid group B, return the image of B under f as a subgroup of the codomain of f.
		The symmetric group on n letters is an epimorphic image of the braid group on n strings, where for 0 < i < n the image of the Artin generator a_i is given by the transposition (i, i + 1).
	www.umich.edu /~gpcc/scs/magma/text453.htm (1073 words)

	[No title]
		The RANGE of a function is the set of values in the CODOMAIN for which there is a mapping from the DOMAIN.
		Note that the RANGE may be equal to the CODOMAIN, or may be a proper subset of the CODOMAIN.
		A common way to express a function in terms of an equation, is to choose a variable to represent a value in the RANGE, and set that equal to f(x), where f(x) maps x to variable y: Variable Variable representing representing a value in a value in the RANGE the DOMAIN
	www.unf.edu /public/cot3100/jgiles/lecture6 (1722 words)

	All Elementary Mathematics - Study Guide - Functions and graphs - Basic notions and properties of functions...
		A set X of all admissible real values of an argument x, at which a function y = f (x) is defined, is called a domain of a function.
		A set Y of all real values y, that a function adopts, is called a codomain of a function.
		Now we can formulate a definition of a function more exactly: such a rule (law) of a correspondence between a set X and a set Y, that for each element of a set X one and only one element of a set Y can be found, is called a function.
	www.bymath.com /studyguide/fun/sec/fun6.htm (742 words)

	Discrete mathematics:Functions and relations - Wikibooks
		This set is known as the codomain of a function.
		A surjective function, also called onto, is a function such that for every element y in the codomain, there is an element x in the domain which is mapped to y.
		That is, the range of a surjective function is equal to the entire codomain.
	en.wikibooks.org /wiki/Discrete_mathematics:Functions_and_relations (2883 words)

	Isomorphisms and Transformations
		An isomorphism can be created from the parent structures by coercing a tuple < [a, b, c, d], e, u > into the structure of isomorphisms between two hyperelliptic curves, or by creating it as a transformation of a given curve, i.e.
		Returns the hyperelliptic curve C' which is the codomain of the isomorphism specified by the data t, e and u, followed by the the isomorphism to the curve.
		Returns the inverse image of the isomorphism f at a point P in its codomain.
	www.math.niu.edu /help/math/magmahelp/text1027.html (1237 words)

	Operations on Mappings (Site not responding. Last check: 2007-11-07)
		Only for some intrinsic maps and for maps with certain domains and codomains, also the formation of image, kernel and cokernel is available.
		Given a mapping f with domain A and codomain B, return the image of A in B as a substructure of B. This function is currently supported only for some intrinsic maps and for maps with certain domains and codomains.
		Given the homomorphism f with domain A and codomain B, return the kernel of f as a substructure of A. This function is currently supported only for some intrinsic maps and for maps with certain domains and codomains.
	magma.maths.usyd.edu.au /magma/htmlhelp/text227.htm (243 words)

	Homomorphisms
		Suppose H is a matrix module whose elements have domain A and codomain B.
		The codomain N of the homomorphism a belonging to Hom(M, N).
		The image of the homomorphism a belonging to the module H =Hom(M, N), returned as a submodule of N. Note that if the domain and codomain of a are matrix modules themselves, the image will be with respect to the appropriate action (right or left).
	www.math.lsu.edu /magma/text794.htm (1720 words)

	quiz14ans (Site not responding. Last check: 2007-11-07)
		The CoDomain: The codomain is the list of all possible sums of these pairs of elements from the set of chosen integers.
		The Size of the CoDomain: The size of the codomain is
		The Function that Maps this domain to codomain: Each pair of integers maps to one and only one element in the codomain based on the value of the sum of the two elements in its pair - since the codomain was built specifically for this purpose, it is a total function.
	www.cs.umd.edu /class/fall2004/cmsc250/quiz/quiz14ans (432 words)

	PlanetMath: function (Site not responding. Last check: 2007-11-07)
		is a set (called the codomain of the function).
		Occasionally this can be confused with ordinary exponentiation (for example the function
		Some authors define the range of a function to be equal to the codomain, and others define the range of a function to be equal to the image.
	planetmath.org /encyclopedia/Codomain.html (139 words)

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