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Key points about mathematical induction 본문
Key points about mathematical induction:
- Mathematical induction is used to prove that some statements A(i) hold for all values of .
- An induction proof consists of two parts: the base case and the induction step.
- The base case assures that A(i) holds for some (not necessarily small) values of .
- The base case and the induction step must be consistent: if the induction step uses A(n) and , then the base case should cover at least 2 consecutive values of n.
- The induction step for proving A(n+1) can use A(n) or even all A(i) for i≤n. The latter is called strong induction.
- Sometimes proving a stronger statement by induction may be easier.
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