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

q.e.d

| | | | created: 2020-03-15 08:05:00 | modified: 2020-03-15 08:06:42 | by: *bookofproofs* | references: [983]

[983] **Ebbinghaus, H.-D.**: “Einführung in die Mengenlehre”, BI Wisschenschaftsverlag, 1994, 3