1. Assigning to every element of a set [ie] a mathematical or conceptual model) of an element of the same set or another set. The process of making a one-to-one or one-to-many correspondence< 2. Given two sets E and F, a mapping (from E to F) is any correspondence, rule, method, diagram, indication, construction, process, algorithm, computation, machine, device, force, drive, reflex, instinct, command, or any other cause whose effect is that, given any element in E, one and only one element in F results. E is known as the mapping's domain; F is its range, in which the mapping takes its values. F is not necessarily different from E.
3. Mapping may also be a heuristic process, when the intention is to model reality, since some information may not be known (as in early maps of the world which depicted the territories of fabulous monsters and beings on the edges of the flat earth).