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In classical Euclidean geometry, a point is a primitive notion that models an exact location in space, and has no length, width, or thickness. In modern mathematics, a point is considered as an element of some set, a point set. A space is a point set with some additional structure. An isolated point has no other neighboring points in a given subset.
Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy; for example, "there is exactly one line that passes through two different points".
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