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.
    Synonyms: onto
  • French: surjectif
  • Russian: сюръективный
  • Spanish: sobreyectivo

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