One-to-one correspondence

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Given a function ${\displaystyle f:A\to B}$, the image of an element${\displaystyle a\in A}$ is the element ${\displaystyle f(a)\in B}$ in the codomain. The pre-image of an element ${\displaystyle b\in B}$ is any element ${\displaystyle a\in A}$ in the domain such that ${\displaystyle f(a)=b}$. Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set.