is the set of all polynomials of degree n with integer coefficients.

Prove that is countable.

By induction:

Since a is an integer, we can put the integers in a 1-1 correspondence with the naturals numbers. Namely, define

Assume P(k) is true for a fixed but arbitrary , where P(k) is defined as

Prove P(k+1) is true

I need help in order to proceed.