<mathematics, logic> A function is bijective or a bijection or a one-to-one correspondence if it is both injective (no two values map to the same value) and surjective (for every element of the codomain there is some element of the domain which maps to it). I.e. there is exactly one element of the domain which maps to each element of the codomain. Only bijective functions have inverses f' where f(f'(x)) = f'(f(x)) = x.
See also injection, surjection, isomorphism.
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