Permutation/Examples

Examples of Permutations

Arbitrary Permutation on Sets

Let $A = \set {a_1, a_2, a_3, a_4}$.

Let $f \subseteq {A \times B}$ be the mapping defined as:

$f = \set {\tuple {a_1, a_3}, \tuple {a_2, a_4}, \tuple {a_3, a_1}, \tuple {a_4, a_2} }$

Then $f$ is a permutation on $A$.

Addition of Constant on $\Z$

Let $\Z$ denote the set of integers.

Let $a \in \Z$.

Let $f: \Z \to \Z$ denote the mapping defined as:

$\forall x \in \Z: \map f x = x + a$

Then $f$ is a permutation on $\Z$.