codomain

Noun

codomain (plural codomains)

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.
   • 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
   • 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...2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd edition, Jones & Bartlett Learning, page 192
   1. (broadly) The set B.