Let be a Function defined on a Set and taking values in a set . Then is said to be onto (a.k.a. a Surjection) if, for any , there exists an for which .
Let the function be an Operator which Maps points in the Domain to every point in the Range and let be a Vector Space with . Then a Transformation defined on is onto if there is an such that for all .
See also Bijection, One-to-One