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Math Help - recursive def

  1. #1
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    recursive def

    Give a recursive definition of the set of polynomials with integer coefficients.

    What I don't understand here is what is the set of polynomials with integer coefficients? Can someone give me an example?
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  2. #2
    Senior Member tukeywilliams's Avatar
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    I believe the following would be a recursive definition of the set of polynomials with integer coefficients:

     0 \in S (some arbitrary set)
    If  p(x) \in S , then  p(x) + cx^n \in S ,  c \in \mathbb{Z}, \ n \in \mathbb{Z}, \ n \geq 0 .

    The set of polynomials with integer coefficients is for example  \{x, x+1, x^2,2x^2+6x+7, x^3, \ldots \} .
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by TheRekz View Post
    Give a recursive definition of the set of polynomials with integer coefficients.

    What I don't understand here is what is the set of polynomials with integer coefficients? Can someone give me an example?
    It is the set of all polynomials with integer coefficients, like 7x^4+2x+3, and can be recursivly defined:

    1 \in P

     \forall p \in P, \forall a,b \in \mathbb{Z},\ axp+b \in P

    RonL
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  4. #4
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    which answer's right? captain black or tukeywilliams
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by TheRekz View Post
    which answer's right? captain black or tukeywilliams
    They could both be. So long as the both generate all polynomials with integer coefficients they are doing the same job. Now I think one is a betters answer than the other, but then I would wouldn't I.

    RonL
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