The principle of well-ordering says that every nonempty set of positive integers has a
Chapter 4, Problem 95(choose chapter or problem)
The principle of well-ordering says that every nonempty set of positive integers has a smallest member. Prove that the first principle of mathematical induction, that is, 1. P(1) is true 2. (4k)[P(k) true S P(k + 1) true] f S P(n) true for all positive integers n Section 4.1 Sets 251 implies the principle of well-ordering. (Hint: Assume that the first principle of mathematical induction is valid, and use proof by contradiction to show that the principle of well-ordering is valid. Let T be a nonempty subset of the positive integers that has no smallest member. Let P(n) be the property that every member of T is greater than n.)
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