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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- Jul 30th 2007, 10:29 PMTheRekzrecursive 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? - Jul 30th 2007, 10:47 PMtukeywilliams
I believe the following would be a recursive definition of the set of polynomials with integer coefficients:

$\displaystyle 0 \in S $(some arbitrary set)

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

The set of polynomials with integer coefficients is for example $\displaystyle \{x, x+1, x^2,2x^2+6x+7, x^3, \ldots \} $. - Jul 31st 2007, 01:50 AMCaptainBlack
- Jul 31st 2007, 07:32 AMTheRekz
which answer's right? captain black or tukeywilliams

- Jul 31st 2007, 08:01 AMCaptainBlack