Section 10: Problem 1 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Show that every well-ordered set has the least upper bound property.
If for a nonempty subset of a well-ordered set the set of its upper bounds is nonempty, then it has the smallest element, which must be the least upper bound of the subset.