Are The Algebraic Numbers Countable?

Discrete Mathematics Level pending

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 $$S$$?

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