Derangement of a permutation
= Derangement of a permutation
{title2=$D_n$}
= Derangement
{synonym}
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