nLab
factorial

Contents

Contents

Definition

For kk \in \mathbb{N} a natural number, its factorial k!k! \in \mathbb{N} is the number obtained by multiplying all positive natural numbers less than or equal to kk:

k!1234(k1)k. k! \;\coloneqq\; 1 \cdot 2 \cdot 3 \cdot 4 \cdot \cdots \cdot (k-1) \cdot k \,.

In combinatorics, the definition usually extends to k=0k = 0 by setting 0!=10! = 1. This may be justified by defining k!k! to be the number of permutations of a set with kk elements.

References

See also

Last revised on September 11, 2018 at 10:22:50. See the history of this page for a list of all contributions to it.