Definition:Extended Real Number Line

The extended real numbers is the set of real numbers together with two values, $$\mathbb{R} \cup \left\{{+\infty,-\infty}\right\}$$ where $$+\infty,-\infty \ $$ have the properties


 * 1) $$\forall x \in \mathbb{R}, x < +\infty \ $$
 * 2) $$\forall x \in \mathbb{R}, x > -\infty \ $$