The set of all algebraic numbers is countable.

The statement "the set of all algebraic numbers is countable" is true. A number is said to be algebraic if it is a root of a polynomial equation with integer coefficients. For each polynomial equation, there are a finite number of possible roots, as the highest degree of the polynomial determines the number of roots. Since there are countably many polynomial equations with integer coefficients, and each equation has a finite number of roots, the set of algebraic numbers can be formed by taking the union of countably many finite sets. Therefore, the set of algebraic numbers is countable.