Section 6'4: The Strong Principle of Mathematical Induction

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Section 6.4 The Strong Principle of Mathematical
Induction

• Mathematical Proofs A Transition to Advanced
  Mathematics, 2nd ed by Chartrand,Polimeni, and
  Zhang

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The Principle of Mathematical Induction

• For each positive integer n, let P(n) be a
  statement. If
• P(1) is true and
• The implication
• If P(k), then P(k1)
• is true for every positive integer k,
• then P(n) is true for every positive integer n.

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The Strong Principle of Mathematical
Induction(or Complete Induction)

• For each positive integer n, let P(n) be a
  statement. If
• P(1) is true and
• The implication
• If P(i) for every integer i with 1 i k,
• then P(k1)
• is true for every integer k,
• then P(n) is true for every positive integer.

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Differences

• Show P(1) is true for both kinds of induction.
• If P(k), then P(k1)
• If P(i) for every integer i with 1 i k, then
  P(k1)