Surjective

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 #92;textstyleF#95;2.

This function is surjective and injective, and hence bijective.