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Fundamental Principle

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Mathematical induction is a method used to prove that a statement holds true for all natural numbers k.

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Let P(n) be a statement defined for each positive integer n.

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Then P(n) will be true for all positive integers n if the following two conditions are satisfied:

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(1) P(1) is true.

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(2) P(k) is true for some integer k + 1 implies that P(k + 1) is true.

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Because all the other values can use the result from the (1) and (2),

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Therefore, you can conclude that all the conditions with integers n are true.