Definition. Set bijection [dm-000A]

Liam O'Connor

A bijection between sets $A$ and $B$ is a one to one correspondence between their elements. That is, $R \subseteq A \times B$ is a bijection between $A$ and $B$ if, for each $x \in A$ , there is exactly one $y \in B$ such that $x\ R\ y$ , and vice versa.