Codomain

English

Etymology

From Template:Prefix.

Pronunciation

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Noun

1. Template:Lb 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.
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   • 2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd Edition, Template:W, page 192,

     Once we have described $f$ as a function from $A$ to $B$, by convention we will call $B$ the codomain, even though other sets, of which $B$ is a subset, could have been used.Template:...If $y$ is an element of the codomain, then $y\in 𝐼𝑚𝑔(f,A)$ iff there is some $x$ in the domain such that $f$ maps $x$ to $y$.

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   1. Template:Lb The set B.

Usage notes

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 Template:M is often synonymous with codomain, but can also be used as a synonym for image.

Synonyms

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Antonyms

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Translations

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• Russian: область значений
• Swedish: Template:T+

Further reading

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• Codomain on Template:W

Anagrams

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