Section Notes on Induction

Weak Induction

Step Label Description
1 Basis (or Base Case) Demonstrate that P(0) is true; i.e., show that property P is true for 0.
2 Induction Hypothesis Assume that P(k) is true for an unspecified integer k.
3 Inductive Step Under this assumption, show that P(k+1) is true.
4 Conclusion P(n) holds for all integers n ≥ 0.

Strong Induction

Step Label Description
1 Basis (or Base Case) Demonstrate that P(0) true; i.e., show that property P is true for 0.
2 Induction Hypothesis Assume that P(k) is true for for all k less than an unspecified integer n.
3 Inductive Step Under this assumption, show that P(n) is true.
4 Conclusion P(n) holds for all integers n ≥ 0.