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Give a recursive definition of:

  1. Mar 8, 2009 #1
    Give a recursive definition of

    a) the set of odd positive integers
    b) the set of positive integer powers of 3
    c) the set of polynomials with integer coefficients


    I have the first two:
    a) f(0)=1, f(n)=f(n-1)+2 for n>=1
    b) f(0)=1, f(n)=3f(n-1) for n>=1

    For c, I am not even quite sure exactly what it is asking or where to begin?
     
  2. jcsd
  3. Mar 9, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi caseyd1981! Welcome to PF! :smile:

    Hint: the first step is find a way of putting them in order. :wink:
     
  4. Mar 10, 2009 #3
    Oh boy, I'm not sure that I follow...??
     
  5. Mar 10, 2009 #4

    tiny-tim

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    If it's recursive, you must put them in order, so that you know which is the next one at each stage …

    and you can't put them, for example, in the order x+1, x+2, x+3, … , going "up to infinity", and then start on 2x+1, 2x+2, 2x+3, …, because 2x+1 won't be the next one to anything.

    So you need a way of putting them in order, without ever "going off to infinity" and leaving some behind for later.

    How can you do that? :smile:
     
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