<mathematics> 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.
For a general bijection f from the set A to the set B:
f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B.
A and B could be disjoint sets.
See also injection, surjection, isomorphism, permutation.
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