In mathematics, a partial function from X to Y is a function ƒ: X' → Y, where X' is a subset of X. It generalizes the concept of a function by not forcing f to map every element of X to an element of Y (only some subset X' of X). If X' = X, then ƒ is called a total function and is equivalent to a function. Partial functions are often used when the exact domain, X', is not known (e.g. many functions in computability theory).
Specifically, we will say that for any x ∈ X, either:
- ƒ(x) = y ∈ Y (it is defined as a single element in Y) or
- ƒ(x) is undefined.
For example we can consider the square root function restricted to the integers
Thus g(n) is only defined for n that are perfect squares (i.e. 0, 1, 4, 9, 16, ...). So, g(25) = 5, but g(26) is undefined.
Read more about Partial Function: Domain of A Partial Function, Total Function, Discussion and Examples
Famous quotes containing the words partial and/or function:
“America is hard to see.
Less partial witnesses than he
In book on book have testified
They could not see it from outside....”
—Robert Frost (1874–1963)
“If the children and youth of a nation are afforded opportunity to develop their capacities to the fullest, if they are given the knowledge to understand the world and the wisdom to change it, then the prospects for the future are bright. In contrast, a society which neglects its children, however well it may function in other respects, risks eventual disorganization and demise.”
—Urie Bronfenbrenner (b. 1917)