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.

On"to (?), prep. [On + to. Cf. Into.]

On the top of; upon; on. See On to, under On, prep.

 

© Webster 1913.

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