Define the following order on the set Z × Z: (a, b) < (c, d)
if either a < c or a = c and b < d. This is referred to as
the dictionary order on Z × Z.
(a) Show that there are infinitely many elements (x, y) in Z × Z
satisfying the inequalities (0, 0) < (x, y) < (1, 1).
(b) Show that Axioms O1–O3 ( Trichotomy, Transitivity, Addition
for inequalities) are satisfied for this...