ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Binary endorelation
▼ Preordering relation
▼ Partial ordering relation
▼ Ordering relation
▼ Ordered set
▼ Dedekind cut
▼ Set of real numbers
Definition D370
Set of irrational numbers
Formulation 0
Let $\mathbb{R}$ be the D282: Set of real numbers.
Let $\mathbb{Q}$ be the D368: Set of rational numbers.
The set of irrational numbers is the D11: Set \begin{equation} \mathbb{I} : = \mathbb{R} \setminus \mathbb{Q} \end{equation}
Results
▶ R3379: Product of irrational numbers is not necessarily irrational
▶ R3381: Product of rational and irrational number is irrational
▶ R3380: Sum of rational and irrational number is irrational