[bahy-jek-shuh
n] 
| a map or function that is one-to-one and onto. |
| bi·jec·tion (bī-jěk'shən) n. Mathematics A function that is both one-to-one and onto. [bi-1 + (in)jection or (pro)jection.] |
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)