Definition 1. A surjective function or surjection is a function $f : X \to Y$ such that for all $y \in Y$,
\[\exists x \in X : f(x) = y.\]In other words,
\[\im f = Y.\]The set of all surjections from $X$ onto $Y$ is denoted by
\[\sur(X, Y).\]A surjective function is also known as an onto function.
References
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- Wikipedia contributors. Surjective function. Wikipedia, The Free Encyclopedia.