How Do I Calculate Electric Potential at the Location of a Point Charge?

[berra]

Homework Statement

What should I do when I calculate the potential of point charges at the point of one of the point charges?

Homework Equations

The definition of a potential from point charges are:
$$\phi(\textbf{r}) = (4\pi \epsilon_0)^{-1}\sum_{i}[q_i |\textbf{r}-\textbf{r}_{q_i}|^{-1}] + C$$

The Attempt at a Solution

Setting $q_i |\textbf{r}-\textbf{r}_{q_i}|^{-1}=0$ when $\textbf{r}-\textbf{r}_{q_i}=\textbf{0}$. Haven't seen this anywhere in the lecture material though, but I am guessing that is what one should do. If so, what is the "real" definition of the potential?

 

[vela]

The potential diverges as the location of the point charges. It's not defined there.