A second problem is that there are serious questions about how coherent is the description of space and its occupants that results when we conflate physical space with geometry, and geometry in turn with a system of numbers. Neither points (since they lack any extension at all), nor lines (since they lack width and depth), nor planes (since they lack depth), can be said to occupy space. (Edward Feser, Aristotle's Revenge, p. 278)
No, they do not occupy space. They constitute space.
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