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
Real addition operation