Consecutive_Subsets_of_N

Let $\N_k$ denote the initial segment of the natural numbers determined by $k$ $\N_k = \left\{{0, 1, 2, 3, \ldots, k - 1}\right\}$ Then $\N_k = \N_{k + 1} \setminus \left\{{k}\right\}$ In particular $\N_{k - 1} = \N_k \setminus \left\{{k - 1}\right\}$