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
▼ Rational addition operation
Definition D606
Real addition operation
Formulation 0
Let $\mathbb{R}$ be the D282: Set of real numbers.
Let $\pm$ be the D605: Rational addition operation.
The real addition operation is the D554: Binary operation \begin{equation} + : \mathbb{R} \times \mathbb{R} \to \mathbb{R}, \quad x + y = \{ a \pm b : a \in x \text{ and } b \in y \} \end{equation}
Children
▶ D607: Complex addition operation
Results
▶ R1904: Isotonicity of finite real summation