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}