Briefly explain the differences between ‘mathematical induction’ and ‘strong induction’.
Briefly explain the differences between ‘mathematical induction’ and ‘strong induction’.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Briefly explain the differences between ‘mathematical induction’ and ‘strong induction’.
Expert Solution
Step 1
Remark:
Mathematical Induction: Let P(n) be a statement defined for all integer n. Then suppose the property holds
(a) P(1) is true and (b) if P(k) is true then P(k+1) is also true, for some Integer k.
Then we will say that P(n) is true for all integer n.
strong induction: Let P(n) be a statement defined for all integer n. Then suppose the property holds
(a) P(1) is true and (b) if P(1), P(2), P(3),..., P(k) all are true then P(k+1) is also true, for some Integer k.
Then we will say that P(n) is true for all integer n.
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