onto (thing)

A function f:A→X is said to be onto if it maps some element of the domain A onto every element of the range X. That is, its image is equal to its range. In symbols, "f[A]=X", or

∀ x in X ∃ a in A s.t. f(a)=x.

For example, the function f(x,y) = x² - y² is onto R, but f(x,y)=x²+y² is not (it takes on only non-negative values).

A function which is onto is also said to be surjective.