Definition:Bijection

Also see

 * Equivalence of Definitions of Bijection


 * Definition:Injection
 * Definition:Surjection
 * Definition:Permutation
 * Definition:Inverse Mapping


 * Definition:Set Equivalence

Basic Properties of a Bijection

 * In Bijection iff Left and Right Inverse, it is shown that a mapping $f$ is a bijection it has both a left inverse and a right inverse, and that these are the same, called the (two-sided) inverse.


 * In Bijection iff Inverse is Bijection, it is shown that the inverse mapping $f^{-1}$ of a bijection $f$ is also a bijection, and that it is the same mapping as the (two-sided) inverse.


 * In Composite of Bijection with Inverse is Identity Mapping, it is established that the inverse mapping $f^{-1}$ and the (two-sided) inverse are the same thing.


 * In Bijection iff Left and Right Cancellable, it is shown that a mapping $f$ is a bijection it is both left cancellable and right cancellable.