In
mathematics, a
partial function from
X to
Y (written as ) is a
function , for some
subset X' 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 , then
f 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).