Take a foot-long stick, cut it in half every day, you'd never come to the end.” -Chuang Tzu
Given the most powerful tools today, cutting a foot-long stick half every day would only take you roughly 50 days to reach the point where you only have a single nucleon to work with. Technically it is the end, since until now no one has been able to separate quarks from each other. A nucleon of course is made of up three quarks. In this sense, Chuang Tzu is wrong.
However, it can be argued that you can try to separate quarks, albeit very briefly, by colliding two nucleons after accelerating it close to the speed of light. By doing this you would just create more particles. In an effort to further “divide” a nucleon, you will end up having extra particles to worry about (Are they still part of the stick or not?, Do I have to continue “cutting” these in half too?, etc..). In this sense, you'd never come to an end. You will always have a particle which isn't elementary as we know it (quarks, leptons or guage bosons) to “cut”. If you take this line of argument, Chuang Tzu is correct.