A real number is said to be algebraic if it is a root of a polynomial equationwith integer...

A real number is said to be algebraic if it is a root of a polynomial equation

with integer coefficients. Note that the algebraic numbers include the rationals and all roots of rationals (such as ). If a number is not algebraic, it is called transcendental.

(a) Show that the set of polynomials with integer coefficients is countable.

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(b) Show that the set of algebraic numbers is countable.

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(c) Are there more algebraic numbers or transcendental numbers?