# Math Help - polynomials

1. ## polynomials

how do I show that the set of polynomials with interger coefficients is countable?

2. See my response to your similar question about the algebraic numbers. If you're still stuck, say where you're stuck and I'll help you with the details.

3. Originally Posted by ricky
how do I show that the set of polynomials with interger coefficients is countable?
The set of all such polynomials of degree less than or equal to $n$, denoted by $\mathbb{Z}_n[x]$ is clearly countable via the obvious identification $\displaystyle f:\mathbb{Z}_n[x]\to\mathbb{Z}^{n+1}:\sum_{k=0}^{n}\alpha_k x^k\mapsto (\alpha_0,\cdots,\alpha_k)$. Note then that $\displaystyle \mathbb{Z}[x]=\bigcup_{n\in\mathbb{N}}\mathbb{Z}_n[x]$ and so..