Codomain

The codomain of a function, sometimes called its set of destination, is the set into which every output of the function is constrained to fall; for a function written f from X to Y, Y is the codomain, and the term range is sometimes used ambiguously for either the codomain or the actual image of the function. A codomain is part of a function only when the function is defined as a triple consisting of a domain, a codomain and a graph; the image of the function, the set of all values the function actually takes, is a subset of its codomain but need not coincide with it, since a function that is not surjective leaves some elements of its codomain unreached. When a function is instead defined as nothing more than its graph, as is sometimes convenient in set theory when the domain is a proper class, the function formally has no codomain at all, though many authors still speak of one informally after first introducing the function in the form f from X to Y. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/