Exercise 9, § 6

Let E be a non-empty well-ordered set in which every element $x$ other than the least element of E has a predecessor (the greatest element of $]\leftarrow, x[$). Show that E is isomorphic to either $\mathbf{N}$ or an interval $[0, n]$ of $\mathbf{N}$ (remark that every segment $\neq E$ is finite by using Proposition 6 of no. 5; then use Theorem 3 of § 2, no. 5).