The Free On-line Dictionary of Computing (30 December 2018):
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,