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Prove carefully that the well ordering principle implies the principal of mathematical induction. That is, suppose the P(n) is a predicate about natural numbers n. Suppose that P(1) is true, and suppose also that for all n ∈ N, P (n + 1) is true if P (n) is true. Using the well ordering principle prove that then P(n) is true for all n. (Hint: consider the set of natural numbers n for which P(n) is false.)