It follows from the definition of permutations that the number of different ordered arrangements the elements of a finite set \(V\) with \(|V|=n\), \(n\ge 1, n\in\mathbb N\) is given by the factorial \(n!\), which is defined as the product. \[n!:=n\cdot (n-1)\cdot (n-2)\cdot\ldots\cdot 2\cdot 1.\]
For \(V=\emptyset\) we have \(|V|=0\) and set
\[0!:=1.\]
Proofs: 1
Explanations: 1
Proofs: 2 3 4 5 6 7 8 9 10 11 12 13 14
Propositions: 15 16 17 18 19 20
Solutions: 21
Theorems: 22 23 24