contradomínio

Contradomínio is a term used in mathematics, specifically in the study of functions. When defining a function f from a set A to a set B, the set B is referred to as the contradomínio of f. It represents the set of all possible values that the function f can potentially output. This is distinct from the image of the function, which is the subset of the contradomínio that contains only the values actually produced by the function for some input in its domain. In simpler terms, the contradomínio is the "target set" for the function's outputs, while the image is the set of "actual outputs." For example, if a function f maps integers to integers, the contradomínio is the set of all integers. However, if f(x) = x^2, the image would be the set of non-negative integers, which is a subset of the contradomínio. Understanding the contradomínio is crucial for grasping concepts like surjectivity, where a function is surjective if its image is equal to its contradomínio.