The irrational numbers are the set difference $\mathbb R\setminus\mathbb Q$ between the set of real numbers $\mathbb R$ and the set of rational numbers $\mathbb Q$.
Obviously, the set is not empty, since $\sqrt 2\in\mathbb R\setminus\mathbb Q$ due to discovery of Ancient Greeks.
Chapters: 1
Corollaries: 2
Definitions: 3
Motivations: 4
Proofs: 5
Propositions: 6
