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}

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}

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

The

Children

▶ | D607: Complex addition operation |

Results

▶ | R1904: Isotonicity of finite real summation |