Exercise 3, § 2

Let E be an ordered set. Show that there exist two subsets A, B of E such that $A \cup B = E$ and $A \cap B = \emptyset$, and such that A is well-ordered and B has no least element (for example, take B to be the union of those subsets of E which have no least element). \* Give an example in which there are several partitions of E into two subsets having these properties. \*