(related to Corollary: Irrational Numbers are Uncountable)

- The set of real numbers $\mathbb R$ is uncountable, which was proven here.
- The set of rationals numbers $\mathbb Q$ is countable, which was proven here.
- Since the set of irrational numbers is defined as the set difference $\mathbb R\setminus\mathbb Q$, they are uncountable.∎

**Ebbinghaus, H.-D.**: "Einführung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition