Codomain, the Glossary
In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall.[1]
Table of Contents
20 relations: Class (set theory), Domain of a function, Function (mathematics), Function composition, Graph of a function, Image (mathematics), Injective function, Interval (mathematics), Linear map, Linear subspace, Mathematics, Matrix (mathematics), Range of a function, Rank (linear algebra), Set (mathematics), Set theory, Square root, Subset, Surjective function, Vector space.
Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.
See Codomain and Class (set theory)
Domain of a function
In mathematics, the domain of a function is the set of inputs accepted by the function. Codomain and domain of a function are Basic concepts in set theory and functions and mappings.
See Codomain and Domain of a function
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of. Codomain and function (mathematics) are Basic concepts in set theory and functions and mappings.
See Codomain and Function (mathematics)
Function composition
In mathematics, function composition is an operation that takes two functions and, and produces a function such that. Codomain and function composition are Basic concepts in set theory and functions and mappings.
See Codomain and Function composition
Graph of a function
In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x). Codomain and graph of a function are functions and mappings.
See Codomain and Graph of a function
Image (mathematics)
In mathematics, for a function f: X \to Y, the image of an input value x is the single output value produced by f when passed x. The preimage of an output value y is the set of input values that produce y. More generally, evaluating f at each element of a given subset A of its domain X produces a set, called the "image of A under (or through) f". Codomain and image (mathematics) are Basic concepts in set theory.
See Codomain and Image (mathematics)
Injective function
In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies. Codomain and injective function are Basic concepts in set theory and functions and mappings.
See Codomain and Injective function
Interval (mathematics)
In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".
See Codomain and Interval (mathematics)
Linear map
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. Codomain and linear map are functions and mappings.
Linear subspace
In mathematics, and more specifically in linear algebra, a linear subspace or vector subspaceThe term linear subspace is sometimes used for referring to flats and affine subspaces.
See Codomain and Linear subspace
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Matrix (mathematics)
In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
See Codomain and Matrix (mathematics)
Range of a function
In mathematics, the range of a function may refer to either of two closely related concepts. Codomain and range of a function are Basic concepts in set theory and functions and mappings.
See Codomain and Range of a function
Rank (linear algebra)
In linear algebra, the rank of a matrix is the dimension of the vector space generated (or spanned) by its columns.
See Codomain and Rank (linear algebra)
Set (mathematics)
In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
See Codomain and Set (mathematics)
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.
Square root
In mathematics, a square root of a number is a number such that y^2.
Subset
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). Codomain and subset are Basic concepts in set theory.
Surjective function
In mathematics, a surjective function (also known as surjection, or onto function) is a function such that, for every element of the function's codomain, there exists one element in the function's domain such that. Codomain and surjective function are Basic concepts in set theory and functions and mappings.
See Codomain and Surjective function
Vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.
References
[1] https://en.wikipedia.org/wiki/Codomain
Also known as Co-domain, Codomain (mathematics), Function codomain, Target of a function, Target set.