codomain

Etymology

co- + domain

noun

1. (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.
   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
   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∈ mathit Img(f,A) iff there is some x in the domain such that f maps x to y.
   For example, the codomain of g(X)=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