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Proposition: Factorial

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

$$0!:=1.$$

Table of Contents

Proofs: 1

Mentioned in:

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

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References

Bibliography

1. Aigner, Martin: "Diskrete Mathematik", vieweg studium, 1993