They don’t go all the way to zero distance from the electron when they calculate the electron’s true mass and charge; they stop short of zero at an arbitrary distance. Once a scientist chooses a suitably close distance, all the calculations using the “true” mass and charge agree with one another. This is a process called renormalization. “It is what I would call a dippy process,” wrote physicist Richard Feynman, even though Feynman won his Nobel Prize for perfecting the art of renormalization.
