Tabula called... she wants her rasa back for all definitions!To me, a point is a geometrical object, and I don't need geometry to describe information. But if you feel it's useful, we can work on a definition. I will insist, however, that we do not confuse geometry, a mathematical space, with physical space. Though we can sometimes find useful analogies between mathematical and physical spaces, the two are not the same, just as a map is not the terrain. How do I know that they are not the same? I can do things to geometry with my mind that I cannot do to physical space.
With that, let's define a point.
A mathematical SPACE is the alegbraic structure that results when a number field is combined with one or more operations defined on the field.
We may consider the elements of a mathematical SPACE to be vectors. A map between vectors in the SPACE is called a function. Some SPACEs allow for a special function called an inner product that satisfies certain conditions. Such SPACEs induce a geometry by defining, among other things, the notions of length and angle within the SPACE.
A POINT is a vector in a geometrical SPACE.
We may describe a POINT by an n-tuple of numbers \( (x_1, x_2, ..., x_n) \). This representation is not unique. The minimum n necessary to describe a POINT is the DIMENSION of the SPACE.