Definition:Bijection/Definition 4

Definition
A mapping $f \subseteq S \times T$ is a bijection :
 * for each $y \in T$ there exists one and only one $x \in S$ such that $\tuple {x, y} \in f$.

Also known as
Hence the terminology:
 * If a bijection exists between two sets $S$ and $T$, then $S$ and $T$ are in one-to-one correspondence.

This must not be confused with one-to-one mapping, a less technical term for an injection.

Because of this confusion, it is recommended that the terms bijection and injection be used universally.

Also see

 * Equivalence of Definitions of Bijection


 * Injection is Bijection iff Inverse is Injection