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That is why the ancient Greek philosophers came up with the notion of the atom - they decided, totally arbitrarily, that there must be some point at which things could not be subdivided, and considered this to be an atom.Then some scientists came along and decided they had found the indivisible of all things, and called it an atom. Then some other scientists came along and proved that the atom could be subdivided, and so made nonsense of the word 'atom', since this thing was no longer atomic (in the Greek sense of the word).As to whether there is a point where things can no longer be divided - it begs a great number of questions by what do you mean when you regard something as divisible? For instance, scientists now believe that hadrons are composed of smaller particles called quarks, but they also believe that no single quark can ever be found on its own - so does that mean that a hadron is indivisible (in the sense that we cannot isolate the subdivision of it), or is it still divisible in that we can consider that it has those subdivisions even if they cannot be isolated?Is it always the case that the subdivision of a thing need be smaller than the thing it is a subdivision of (this begs the question as to what is size)? In quantum physics, we do not have sizes for particles, we only have sizes for the wave function of a particle, but the wave function for a sub-particle may actually be larger than the wave function for the whole particle.