Given the D1275: Set of basic numbers $[-\infty, \infty]$, we define the following arithmetic rules:

(1)	\begin{equation} \forall \, x \in (- \infty, \infty] : \infty + x = x + \infty = \infty \end{equation}
(2)	\begin{equation} \forall \, x \in [- \infty, \infty) : - \infty + x = x + (- \infty) = - \infty \end{equation}
(3)	\begin{equation} \forall \, x \in (- \infty, \infty] : \infty \cdot 0 = 0 \cdot \infty = 0 \end{equation}
(4)	\begin{equation} \forall \, x \in [- \infty, \infty) : - \infty \cdot 0 = 0 \cdot (- \infty) = 0 \end{equation}
(5)	\begin{equation} \forall \, x \in (-\infty, \infty) : (x < \infty) \text{ and } (- \infty < x) \end{equation}
(6)	\begin{equation} \infty \cdot \infty = (- \infty) \cdot (- \infty) = \infty \end{equation}
(7)	\begin{equation} \infty \cdot (- \infty) = - \infty \cdot \infty = - \infty \end{equation}
(8)	\begin{equation} - (\infty) = - \infty \end{equation}
(9)	\begin{equation} - (- \infty) = \infty \end{equation}

In particular, expressions such as $\infty - \infty$ and $- \infty + \infty$ are left undefined (are not accepted as well-founded formulas).