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| Conclusion |
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| Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if |
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| (i) it holds for n = 1 and |
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| (ii) it holds for n = k+1 whenever it holds for n = k. |
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| Remember: |
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| Proof by mathematical induction requires the fulfilment of both the conditions (i) and (ii) as stated above. |
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| Condition (i) creates the basis for carrying out induction and condition (ii) gives us the right to make a general assertion or of an automatic extension. |
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