I'm reading [2] and got stuck in interpretting the following statement at the end of Page 146.
we 'cut' $\Sigma = \mathbb{C} \cup \{ \infty \}$ along the negative real line from $0$ to $\infty$ as in Fig.4.22 (See below), and the remaining region $E = \mathbb{C} - \{ z \in \mathbb{R} | z \leq 0 \}$...
Could someone explain why the cut line represents $z \leq 0$?
Any help would be appreciated!
Reference
[2] Jones, Gareth A., and David Singerman. Complex functions: an algebraic and geometric viewpoint. Cambridge university press, 1987.