1. The problem statement, all variables and given/known data Let n a positive number, and let An 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 An is countable. 2. Relevant equations Hint: For each positive number m, consider polynomials [itex]\sum[/itex] aixi from i=0 to n that satisfy [itex]\sum[/itex] lail ≤ m. 3. The attempt at a solution I want to prove this using induction, but I don't fully understand how to use the hint. How would I partition with algebraic numbers using it? Starting using A1, which are the roots of polynomials, I know that these algebraic numbers are countable because a1x1+a0=0 are the rational numbers, which are countable. What does the hint have to do with this?