codomain
English edit
Etymology edit
Pronunciation edit
Noun edit
codomain (plural codomains)
 (mathematics, mathematical 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.
 2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd Edition, Jones & Bartlett Learning, page 192,
 Once we have described as a function from to , by convention we will call the codomain, even though other sets, of which is a subset, could have been used. […] If is an element of the codomain, then iff there is some in the domain such that maps to .
 2017, Alan Garfinkel, Jane Shevtsov, Yina Guo, Modeling Life: The Mathematics of Biological Systems, Springer, page 12:
 For example, the codomain of 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.
 (more generally, of a binary relation R between A and B) The set B.
Usage notes edit
The codomain always contains the image of the function (the actual set of points to which points of the domain are mapped), but is larger (i.e. strictly contains the image) if the function is not surjective.
The term range is often synonymous with codomain, but can also be used as a synonym for image.
Synonyms edit
 (target set of a function): range
Antonyms edit
 (antonym(s) of “target set of a function”): domain
Translations edit
target set of a function

Further reading edit
 Domain of a function on Wikipedia.Wikipedia
 Image (mathematics) on Wikipedia.Wikipedia
 Range (mathematics) on Wikipedia.Wikipedia
 Injective function on Wikipedia.Wikipedia
 Surjective function on Wikipedia.Wikipedia
 Bijection on Wikipedia.Wikipedia
 Codomain on Wolfram MathWorld