Use the principle of ordinary mathematical induction to

Chapter 5, Problem 32E

(choose chapter or problem)

Problem 32E

Use the principle of ordinary mathematical induction to prove the well-ordering principle for the integers.

Principle of Mathematical Induction

Let P(n) be a property that is defined for integers n, and let a be a fixed integer.

Suppose the following two statements are true:

1. P(a) is true.

2. For all integers k ≥ a, ifP(k) is true then P(k + 1) is true.

Then the statement

for all integers n ≥ a, P(n)

is true.