Codomain
In mathematics, the
codomain or
target set of a function is the set Y into which all of the output of the function is constrained to fall. It is the set Y in the notation
f:
X →
Y. The codomain is also sometimes referred to as the range but that term is ambiguous as it may also refer to the image. The codomain is part of a function f if it is defined as described in 1954 by Nicolas Bourbaki, namely a triple, with F a functional subset of the Cartesian product
X ×
Y and
X is the set of first components of the pairs in F. The set F is called the
graph of the function. The set of all elements of the form
f, where x ranges over the elements of the domain X, is called the image of f. In general, the image of a function is a subset of its codomain. Thus, it may not coincide with its codomain. Namely, a function that is not surjective has elements y in its codomain for which the equation
f =
y does not have a solution. An alternative definition of
function by Bourbaki, namely as just a functional graph, does not include a codomain and is also widely used.