What is dimension of point?

A point is dimensionless. It doesn’t exist.

According to the limits presented to us by our physics, we can’t measure anything less than a plank’s length which is one over ten to the power 37 and a point isn’t even that.

Actually a point is only a property of a system of co-ordinates. It only distinguish one point in space with other but without existing (it’s imaginary). It’s as if a point in itself has no meaning in itself. If there were to exist one and only one point then there wouldn’t even be any sense to define it because all that there is is that point. It is the difference between these points that give meaning to a group/systems of points.

All we do is simply use these properties in math and physics.