I am reading the following pages from my book on "foundations of potential theory" page 150/151:
I understand up to inequality $(4)$. I can't derive inequality $(5)$ from $(4)$. Please derive inequalities from $(5)$ to $(7)$.
EDIT: (Statement of continuity)
If for every $\epsilon > 0$, there exists a $\delta > \sqrt{(x-x_o)^2+(y-y_o)^2+(z-z_o)^2} > 0$ such that $\epsilon > \left| f(x,y,z) - f(x_0,y_0,z_0) \right| > 0 $, then $f(x,y,z)$ is continuous at $(x_0,y_0,z_0)$
How is this statement equivalent to equation $(5)$?