Partial function
From open-encyclopedia.com - the free encyclopedia.
In mathematics and computer science, a partial function from the domain X to the codomain Y is a binary relation over X and Y which is functional, that is, associates with every element in set X with at most one element in set Y. If a partial function associates with every element in its domain precisely one element of its codomain, then it is a "total function". Note that with this terminology, not every partial function is a "true" function.
This above diagram does not represent a "well-defined" function because the element 1 in X is not associated with anything.
The natural logarithm function from the real numbers to the reals is only partial, as the logarithm of non-positive reals is not a real number.
See also injective function, surjective function and bijection.
