A **codomain** in mathematics is the set of "output" values associated with (or mapped to) the domain of "inputs" in a function. For any given function , the set *B* is called the **codomain** of `f`. *X*, the set of input values, is called the domain of *f*, and *Y*, the set of **possible** output values, is called the **codomain**. The range of *f* is the set of all **actual** outputs {*f*(*x*) : *x* in the domain}. Beware that sometimes the codomain is incorrectly called the range because of a failure to distinguish between possible and actual values. 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. Mathematics is the study of quantity, structure, space and change. ...
In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ...
Information processing In information processing, output is the process of transmitting information (verb usage). ...
In mathematics and related technical fields, the term map or mapping is often a synonym for function. ...
Domain has several meanings: some kind of territory, such as (for example) a demesne or a realm In New Zealand a Town Domain is typically a public sport area administered by a Domain Board. ...
Information processing In information processing, input is the process of receiving information from an object. ...
In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ...
In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ...
In mathematics, the domain of a function is the set of all input values to the function. ...
In mathematics, the range of a function is the set of all values produced by a function. ...
In mathematics, the range of a function is the set of all values produced by a function. ...
A is a subset of B If X and Y are sets and every element of X is also an element of Y, then we say or write: X is a subset of (or is included in) Y; X âŠ† Y; Y is a superset of (or includes) X; Y âŠ‡ X...
Mathematics education is the study of practices and methods of both the teaching and learning of mathematics. ...
## Example
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. ...
defined by The codomain of *f* is **R**, but clearly *f*(*x*) never takes negative values, and thus the range is in fact the set **R**^{+}—non-negative reals, i.e. the interval [0,∞): A negative number is a number that is less than zero, such as −3. ...
In mathematics, interval is a concept relating to the sequence and set-membership of one or more numbers. ...
One could have defined the function *g* thus: While *f* and *g* have the same effect on a given number, they are not, in the modern view, the same function since they have different codomains. The codomain can affect whether or not the function is a surjection; in our example, *g* is a surjection while *f* is not. In mathematics, a surjective function (or onto function or surjection) is a function with the property that all possible output values of the function are generated when the input ranges over all the values in the domain. ...
## See also |