# Section 3.2: Problem 2 Solution

Working problems is a crucial part of learning mathematics. No one can learn... 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 in the structure
the following relations are definable:

(a) Ordering,
.

(b) Zero,
.

(c) Successor,
.

This exercise shows that the theory of
is, in fact, coincides with the theory of
.

(a)
.

(b)
.

(c)
.