surjective function

Function such that every element of the codomain has a preimage

EntityQ229102

Also known as surjection · right-total function · onto function

Subclass of: function
, surjective relation

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a surjective function (also known as surjection, or onto function ) is a function f such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x) = y. In other words, for a function f : X → Y, the codomain Y is the image of the function's domain X. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y.

Overview

All data

17 statements · 18% with external sources · numbers in brackets are citations

Has characteristic: right-uniqueness
right-totality
Different from: injection
epimorphism
Has effect: data loss

On other databases

11 identifiers linking surjective function across the web's reference databases

Data quality

statements

18%

externally sourced

Source last edited September 18, 2026. AIDB refreshes this page daily.

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AIDB. (2026). surjective function (Q229102). Retrieved from https://aidb.si/e/surjective-function-Q229102