Given an well-ordered class $(A,\leq)$ we want to proof that every element $a \in A$ can be reached by applying the successor relation on a the smallest element of $A$ or on an limes element of $A$ finitely often.
I tryed to construct an infinite decreasing sequence $a_{n+1} \leq a_n$ with $a_i \in A$ and no $m$ such that $a_m = a_{m+1}$. But my problem is that I cannot define a limes element $b \in A$ with $b < a$ and no limes element $c$ with $b < c < a$. Any hints?