Section 10: Problem 2 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
(a) Show that in a well-ordered set, every element except the largest (if one exists) has an immediate successor.
(b) Find a set in which every element has an immediate successor that is not well-ordered.
(a) If an element
of the set is not the largest, then
is not empty and has the least element
, which is the successor of
as
and there is no
such that
.
(b)
.