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}

▾ 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

▾ 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

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}

Let $\pm$ be the D605: Rational addition operation.

The

Child definitions

Results