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Definition: Let f: A -> B. f is injective (one-to-one) if it does not map different arguments to the same result:
f is surjective (onto) if every element of B is hit by some argument:
f: A ->injective B : <=> f: A -> B /\ (forall x0 in A, x1 in A: f(x0) = f(x1) => x0 = x1).
f is bijective if it is injective and surjective:
f: A ->surjective B : <=> f: A -> B /\ (forall y in B: exists x in A: f(x) = y).
f: A ->bijective B : <=> f: A ->injective B /\ f: A ->surjective B.