In Euclidean geometry, a point is a figure with only position but no size in space. Points are the basis of the whole Euclidean geometry. Euclid initially vaguely defined a point as "something without parts". In the two-dimensional Euclidean space, 1 points are expressed as 1 ordered number pairs. Similarly, in Cartesian coordinate system, any 1 point can be accurately located.
In modern mathematical language, the elements of any set are called "points", but they may have nothing to do with points in three-dimensional space.