# surjection

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Related to surjection: bijection, Injective function

## surjection

[sər′jek·shən] (mathematics)

A mapping ƒ from a set

*A*to a set*B*such that for every element*b*of*B*there is an element*a*of*A*such that ƒ*(a)*=*b*. Also known as surjective mapping.## surjection

(mathematics)A function f : A -> B is surjective or onto or a
surjection if f A = B. I.e. f can return any value in B.
This means that its image is its codomain.

Only surjections have right inverses, f' : B -> A where f (f' x) = x since if f were not a surjection there would be elements of B for which f' was not defined.

See also bijection, injection.

Only surjections have right inverses, f' : B -> A where f (f' x) = x since if f were not a surjection there would be elements of B for which f' was not defined.

See also bijection, injection.

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