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Is the principle of mathematical induction unable to prove cases of negative numbers?

  1. Jun 10, 2010 #1
    Is the principle of mathematical induction unable to prove theorem of negative numbers?
     
  2. jcsd
  3. Jun 10, 2010 #2

    CompuChip

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    Re: Is the principle of mathematical induction unable to prove cases of negative numb

    Why?
    If you can prove that if it holds for -n (with n a positive integer), it must hold for -(n + 1), then it is completely equivalent to induction over the positive numbers.
     
  4. Jun 10, 2010 #3

    Gib Z

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    Re: Is the principle of mathematical induction unable to prove cases of negative numb

    In fact, the Principle of Mathematical Induction allows us to prove results for Rational Numbers, or any countable set (sets with a bijection to the natural numbers). In practice this can be very hard to do though as it depends on you choosing a "nice" enough bijective function for the particular problem.
     
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