[AmishDude]

North Pole. No kidding! There's a 1-1 correspondence between all points on the infinite plane and all points on the surface of a sphere -- minus the North Pole. It's infinity.

[Faraday]

There's a 1-1 correspondence between all points on the infinite plane and all points on the surface of a sphere -- minus the North Pole. It's infinity.

Imagine a sphere entirely above an infinite flat plane. From any point on the plane, draw an infinite straight line through the center point of the sphere. The line will intersect the sphere at two points. These points are unique for each point on the flat plane surface. In cartesian geometry, the plane passing through the center of the sphere parallel to the exterior plane will intersect a circle on the sphere which no point on the plane can touch by the above method. Therefore the surface of a sphere has more than twice as many points as an infinite surface.

[lewislynn]

There's a 1-1 correspondence between all points on the infinite plane and all points on the surface of a sphere

Then at what point can the sphere or plane no longer be dissected?

[stands2reason]

Fractals are pretty.:-)