codomain
Pronunciation
  • (America) IPA: /ˌkoʊ.doʊˈmeɪn/
Noun

codomain (plural codomains)

  1. (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 : XY.
    • 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 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\in\mathit{Img}(f,A) iff there is some x in the domain such that f maps x to y.
    • 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.
Synonyms
  • (target set of a function) range
Antonyms
  • (target set of a function) domain



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