Let $n$ a positive number, and let $A_n$ be the algebraic numbers obtained as roots of polynomials with integer coefficients that have degree $n$. Using the fact that every polynomial has a finite number of roots, show that $A_n$ is countable.
Hint: For each positive number $m$, consider polynomials
$\sum_{i=0}^n a_i x^i$ that satisfy
$\sum | a_i | \le m$.
I'm having difficulty grasping the concepts and method to write the proof. Can someone please explain in simple terms?
Thank you.