bijection

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)