CSCB36H3 Lecture : Day 1 Sep 12
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= { 0, 1, 2, } P(0), p(0) => p(1), p(1) => p(2), . Suppose p(0) holds, for all n 0, [p(n) => p(n+1)] Suppose also for any n 0, if p(n) holds, then p(n+1) holds. Suppose for any n > 0, if p(j) holds whenever 0 j < n, then p(n) P(0), p(0) => p(1), p(0) and p(1) => p(2), p(0) + (p(1) + p(2) => p(3), . Suppose a and a . A has a minimum element i. e a # m s. t m m" for all m" a. P(n): n cents of postage can be made using only 4c & 7c stamps. n = k * 4 + l * 7 for some k, l . Prove p(n) holds for all n 18. Then k *4 + l * 7 = 1 * 4 + 2 * 7 = 18. Induction step: let n 0. (arbitrary number greater than 0)
