Derangement of a permutation ($D_n$)

A permutation with no fixed points. Applying the inclusion-exclusion principle to the events that each element is fixed gives $D_n=n!{\sum }_{k=0}^n(-1{)}^k/k!$. Therefore $D_n/n!\to e^{-1}$, and the alternating-series remainder is at most $1/(n+1)!$.

// Destination: foundations-of-mathematics.bigb