Strong induction
Description:
- Allows us to make a stronger assumption in the inductive step.
- Mathematical induction proves that we can climb as high as we like on a ladder, by proving that
- we can climb on the bottom rung (base case)
- we can climb all the previous rung then we can climb the next one
Strong induction principle:
- How to Prove
- 1. Inductive hypothesis: P(n): statement
- 2. Base case: Prove that some base values are true in order to prove for P(n+1)
- 3. Inductive step: Assume P(n = k) is true, prove that P(k+1) is also true
- when to use strong induction instead of normal induction
- solve the inductive step first, whether it is dependent on the previous cases
- recursion