Tom,
Euclid was correct: A point is something that doesn't have parts. In other words, it is indivisible. Something (1) every part of which (2) has parts is endlessly divisible because after a division any resulting part (2) may be identified with (1). It behaves like Cantor's dust.
Tom: "And if you want to say that physics lives in a different, superior, world than mathematics -- an atom has parts. Is it endlessly divisible?"
My sentence was incomplete. Something every part of which has parts is a continuum.
While the idea of atoms meant a tomos = not divisible, the example shows that mathematical models do not necessarily correspond to physical reality.
E.: ""A point has a different quality. It has measure zero.""
Tom: "A measure is a quantity, not a quality.
In contrast to G. Cantor, I see the measure exactly zero and the measure infinitum absolutum qualities rather than quantities. That's why they are to be treated with care.
There are many more mathematical objects than a point, of measure zero."
There are no truly physical objects of measure zero.
Best,
Eckard