Countability of Trascendental Numbers

Remembering that the algebraic numbers are countable, and that the real numbers are uncountable, we can prove that the set of transcendental numbers is uncountable.

As the set of real numbers is the union of the set of algebraic numbers and the set of transcendental numbers, and the union of a countable set and an uncountable set is uncountable, we can conclude that the set of transcendental numbers is uncountable.