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
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Ringoid
▼ Semiring
▼ Ring
▼ Additive group
▼ Additive monoid
▼ Additive semigroup
▼ Additive groupoid
▼ Additive binary operation
▼ Natural number addition operation
▼ Integer addition operation
Definition D605
Rational addition operation
Formulation 0
Let $\mathbb{Q}$ be the D368: Set of rational numbers.
Let $\pm$ be the D604: Integer addition operation.
Let $\cdot$ be the D608: Integer multiplication operation.
The rational addition operation is the D554: Binary operation \begin{equation} + : \mathbb{Q} \times \mathbb{Q} \to \mathbb{Q}, \quad [(a, b)] + [(c, d)] = [(a d + b c, b d)] \end{equation}
Children
▶ D606: Real addition operation