We are trying to prove that a proposition P(n) is true for all n > 0 using mathematical induction. Suppose we are trying to prove the k + 1 case, P(k+ 1), using strong mathematical induction. What are we allowed to do which we wouldn't do if we had been using weak mathematical induction? We are able to prove P(k+1) as an inequality instead of just an equality. We do not need to make an assumption about the lower bound for k (for example, we do not need to assume that k > 0). We can prove that P(k+1) → P(k+2) instead of P(k) → P(k + 1). We can use the fact that P(k-1) is true, for as long as (k − 1) > 0.

We are trying to prove that a proposition P(n) is true for all n > 0 using mathematical induction. Suppose we are trying to prove the k + 1 case, P(k+ 1), using strong mathematical induction. What are we allowed to do which we wouldn't do if we had been using weak mathematical induction? We are able to prove P(k+1) as an inequality instead of just an equality. We do not need to make an assumption about the lower bound for k (for example, we do not need to assume that k > 0). We can prove that P(k+1) → P(k+2) instead of P(k) → P(k + 1). We can use the fact that P(k-1) is true, for as long as (k − 1) > 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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