# surjective

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### Pronunciation

surjective (not comparable)

1. (mathematics) of, relating to, or being a surjection
• 1974, Thomas W. Hungerford, Algebra, Springer, page 5,
A function $\textstyle f$ is surjective (or onto) provided $\textstyle f(A)=B$ ; in other words,
for each $\textstyle b\in B,b=f(a)$ for some $\textstyle a\in A$ .
A function $\textstyle f$ is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective.
• 2010, Tullio Ceccherini-Silberstein, Michel Coornaert, Cellular Automata and Groups, Springer, page 133,
The Garden of Eden Theorem (Theorem 5.3.1) implies that every surjective cellular automaton with finite alphabet over an amenable group is necessarily pre-injective. In this section, we give an example of a surjective but not pre-injective cellular automaton with finite alphabet over the free group $\textstyle F_{2}$ .
• 2011, Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, Springer, 2nd Edition, page 156,
This function is surjective and injective, and hence bijective.
Synonym: onto