how would you define a mathematical point?

Hello

How would you define a mathematical point? Here is my 'crude' opinion. A point is simply a supposition from mathematician's point of view that a certain number is there where the point or dot is; although it (the number) is not there. But it serves the purpose. What do you say? Please let me hear. Thanks.

A point is zero-dimensional mathematical object,
which can be specified in n-dimensional space using n coordinates.

But if we tell that point (A) location is x,y,z it tells us nothing in real world.
This only specify the point in some unknown 3-D coordinate system.

We must tell directions for x,y and z. It needs minimum 4 points more,
ie. we must know coordinate system origo and one point in each axis.

But however our origo is still a relative point in space.

So we cant never tell where our point really is because we dont have any absolute
coordinate system in mathematical or real space.

So we must create new coordinate system and point wherein the observer is located.

et cetera , et cetera ............

Simple Conclusion: Absolute point is nothing in some unknown place in unknown system.
But we can create our own zero-dimensional things anywhere in ourself created systems in unknown places and systems. ????