From the beginning, calculus has stubbornly insisted that everything — space and time, matter and energy, all objects that ever have been or will be — should be regarded as continuous. Accordingly, everything can and should be quantified by real numbers. In this idealized, imaginary world, we pretend that everything can be split finer and finer without end. The whole theory of calculus is built on that assumption. Without it, we couldn’t compute limits, and without limits, calculus would come to a clanking halt.
