Definition of "surjective"

A function f {\displaystyle \textstyle f} is surjective (or onto) provided f ( A ) = B {\displaystyle \textstyle f(A)=B} ; in other words, for each b ∈ B , b = f ( a ) {\displaystyle \textstyle b\in B,b=f(a)} for some a ∈ A {\displaystyle \textstyle a\in A} . / A function f {\displaystyle \textstyle f} is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective.

1974, Thomas W. Hungerford, Algebra, Springer, page 5

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 F 2 {\displaystyle \textstyle F_{2}} .

2010, Tullio Ceccherini-Silberstein, Michel Coornaert, Cellular Automata and Groups, Springer, page 133

This function is surjective and injective, and hence bijective.

2011, Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, 2nd edition, Springer, page 156