surjective

Etymology

adj

1. (mathematics) of, relating to, or being a surjection
   1974, Thomas W. Hungerford, Algebra, Springer, page 5, A function f is surjective (or onto) provided f(A)=B; in other words, for each b∈B,b=f(a) for some a∈A. A function f is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective.
   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. 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