Bijective function

A function is bijective if and only if it has a two-sided inverse function. Two sets have the same cardinality precisely when a bijection exists between them.

• The function $f:\mathbb Z\to\mathbb Z$, $f(n)=n+1$, is bijective.
• The map $\{1,2,3\}\to\{a,b,c\}$ defined by $1\mapsto a$, $2\mapsto b$, and $3\mapsto c$ is bijective.