bijection
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}.
(1999-08-29)