If f is a permutation of a finite set,
If n is a natural number, let n! = 1×2×3×...×n,
(n! is called "n factorial"),
4! = 1×2×3×4 = 24,
5! = 1×2×3×4×5 = 120.
If f is a permutation of a set of n elements,
The smallest such number t is called the order ord(f) of f.
Every permutation f of a finite set S has an order ord(f).
The proof is not difficult! Let us have a look at the proof.