What is the difference between Codomain and Range?

Codomain can be referred to as the whole set of a possible outcome that can possibly come out of a function, it is part of the definition of a function, and do restricts the function outputs too, while range refers to the outcome based on a defined function, that is, the set of values produced as a result of the functional relationship between the domain and codomain.

The Codomain contains the set of range, but the range is a part of the Codomain. The Codomain is meant to set a restriction for the outcome values, where the restriction, as defined by the function, is the range. For example, if a set is defined as A= {1, 2, 3, 4}, and B= {1, 2, 5, 8, 9}, and the functional relation f: A->B is defined as f(x) =2x. Therefore, the codomain is set B {1, 2, 5, 8, 9} while the range = {2, 8}.

To get the differences between Codomain and Range can be a bit difficult, because both in some senses have nearly the same meaning. Both codomain and Range are important calculations in mathematics that talk about the output of a function. However, there are some differences between codomain and Range. The codomain of a function is the target space into which a function maps elements of its domain. Range, on the other hand, can be regarded as the subset of codomain, because it is from the elements of codomain that range will be mapped out according to a specified function of the operation.

Let's consider this simple example to have a better view of the whole thing. Let A= (2 3 4 5 6 7) and B= ( 1 4 9 16 20 36 49). The function f : A -> B is defined by f (y) = y² . Here, the codomain is set B, and the Range is ( 4,9,16,36, 49). 5², which is 25 is not included in the Range because it is not in the codomain.