codomain

Pronunciation

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Pronunciation

- (
*America*) IPA: /ˌkoʊ.doʊˈmeɪn/

**codomain** (*plural* codomains)

- (
*mathematics, analysis*) The target set into which a function is formally defined to map elements of its domain; the set denoted*Y*in the notation*f*:*X*→*Y*.**1994**, Richard A. Holmgren,*A First Course in Discrete Dynamical Systems*, Springer, page 11 ↗,- Definition 2.5.
*A function is onto if each element of the***codomain**has at least one element of the domain assigned to it. In other words, a function is onto if the range equals the**codomain**.

- Definition 2.5.
**2006**, Robert L. Causey,*Logic, Sets, and Recursion*, 2nd Edition, Jones & Bartlett Learning, page 192 ↗,- Once we have described f as a function from A to B, by convention we will call B the
, even though other sets, of which B is a subset, could have been used. […] If y is an element of the*codomain***codomain**, then y\in\mathit{Img}(f,A) iff there is some x in the domain such that f maps x to y.

- Once we have described f as a function from A to B, by convention we will call B the
**2017**, Alan Garfinkel, Jane Shevtsov, Yina Guo,*Modeling Life: The Mathematics of Biological Systems*, Springer, page 12 ↗,- For example, the
**codomain**of g(X) = X^3 consists of all real numbers. A function links each element in its domain to some element in its**codomain**. Each domain element is linked to exactly one**codomain**element.

- For example, the

- (
*target set of a function*) range

- (
*target set of a function*) domain

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