I'm with you here, doing finite -> infinite -> finite transformations logically creates paradoxes. If those infinite points have no dimensions, how do their cumulative zeros add up to a positive number?

To the risk of sounding naive, I see this as a self-inflicted paradox, much like the immovable object and the irresistible force paradox. If it's a paradox like Schrödinger's cat thought experiment, then I'm cool with it, because it points the limits of theory by carrying it into absurdeness.