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principal of mathematics induction........
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Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers (non-negative integers ). ... The simplest and most common form of mathematical induction proves that a statement involving a natural number n holds for all values of n .
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The principle of mathematical induction is then: If the integer 0 belongs to the class F and F is hereditary, every nonnegative integer belongs to F. Alternatively, if the integer 1 belongs to the class F and F is hereditary, then every positive integer belongs to F.
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