Are The Algebraic Numbers Countable?

Discrete Mathematics Level 1

A number \(\alpha \in \mathbb{R}\) is called algebraic if there exists a polynomial \(p(x)\) with rational coefficients such that \(p(\alpha) = 0\).

Let \(S \subset \mathbb{R}\) denote the set of algebraic numbers. Which of the following is true of \(S?\)