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Help proof by induction

  1. Jan 21, 2009 #1
    Let Pn be the statement : any postage of n >= 2 cents can be made of
    3-cent and 2-cent stamps. What is wrong with the following proof of
    Pn by induction? How can it be fixed without changing the induction
    step much?
    Base case : 2 = 2 and so P2 is true.
    Induction step : Fix some n >=2. Assume that Pk is true for k <= n, we
    will prove Pn+1.
    Since Pn-1 is true, we know that
    n - 1 = a * 2 + b * 3
    and hence
    n + 1 = (a+1)*2+b*3
     
  2. jcsd
  3. Jan 21, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    Let n be 2: the argument fails. If you want to talk about n - 1 then n has to be at least 3.
     
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