Definition of "codomain"

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 {\displaystyle f} as a function from A {\displaystyle A} to B {\displaystyle B} , by convention we will call B {\displaystyle B} the codomain, even though other sets, of which B {\displaystyle B} is a subset, could have been used. […] If y {\displaystyle y} is an element of the codomain, then y ∈ I m g ( f , A ) {\displaystyle y\in {\mathit {Img}}(f,A)} iff there is some x {\displaystyle x} in the domain such that f {\displaystyle f} maps x {\displaystyle x} to y {\displaystyle y} .

2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd Edition, Jones & Bartlett Learning, page 192

For example, the codomain of g ( X ) = X 3 {\displaystyle 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.

2017, Alan Garfinkel, Jane Shevtsov, Yina Guo, Modeling Life: The Mathematics of Biological Systems, Springer, page 12