Derangement exponential series #

This file proves that the probability of a permutation on n elements being a derangement is 1/e. The specific lemma is num_derangements_tendsto_inv_e.

source

theorem num_derangements_tendsto_inv_e :

filter.tendsto (λ (n : ℕ), ↑(num_derangements n) / ↑(n.factorial)) filter.at_top (nhds (rexp (-1)))