1. The problem statement, all variables and given/known data Prove that the set of algebraic numbers is countably infinite. 2. Relevant equations If there exists a bijective map between N and a set A, N and A have the same cardinality 3. The attempt at a solution Rather than coming up with a bijective map between S =the set of algebraic numers and N =natural numbers, I proved S is countable but i also have to prove that S is infinite. So, I wanted to design an injective function f:N to S. Can anyone come up with sucn an injective function?