Dictionary

codomain en · NOUN

Pronunciation

• (US) audio
• /ˌkoʊ.doʊˈmeɪn/ (US)

Etymology

Etymology tree Proto-Indo-European *ḱe? Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Latin co-lbor. English co- Proto-Indo-European *dem- Proto-Indo-European *-s Proto-Indo-European *dṓmder. Proto-Italic *domanos Latin dominus Proto-Indo-European *-(i)yós Proto-Italic *-ijos Proto-Italic *-ios Old Latin -ios Latin -iusnom. Latin -ium Latin dominiumder. Old French demainebor. Middle English demayne English domain English codomain From co- + domain.

Meanings

1. 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.
   • For example, the codomain of g(X)#61;X³ 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. 2017, Alan Garfinkel, Jane Shevtsov, Yina Guo, Modeling Life: The Mathematics of Biological Systems, Springer, page 12:
   • 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.[…]If y is an element of the codomain, then y#92;in#92;mathit#123;Img#125;(f,A) iff there is some x in the domain such that f maps x to y. 2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd edition, Jones & Bartlett Learning, page 192:
   • 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. 1994, Richard A. Holmgren, A First Course in Discrete Dynamical Systems, Springer, page 11:
2. (broadly, of a binary relation R between A and B) 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. ▸ The set B.

Forms

Antonyms

domain (antonym(s) of “target set of a function”)

Synonyms

range (target set of a function)

Translations (11)

de Zielmenge (target set of a function) · ru область значений (target set of a function) · pt contradomínio (target set of a function) · pl przeciwdziedzina (target set of a function) · sv målmängd (target set of a function) · is aðmengi (target set of a function) · is bakmengi (target set of a function) · cs obor hodnot (target set of a function) · is ítak (target set of a function) · da dispositionsmængde (target set of a function) · ja 終域 (target set of a function)