bijection

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.

(2001-05-10)