Be that as it may. I presented an argument (valid, I think.) I am not a mathematician, just a humble physical chemist. I understand that there are orders to infinities. Nevertheless, your assertion is not a refutation to the argument presented.
That's explains it. So, like my wife, (a chemical engineer), you guys think that electrons are important and actually "do" things.
We nuclear types, on the other hand, know that electrons are so light that they can be neglected in the bigger scheme of life. (Is ther life outside the nucleaus?) 8<)
OK, there are LOTS of reasons for this. Reason #1, the cardinality of the reals is the cardinality of the reals squared. Thus, since the surface of a sphere cannot be countable, it must be at least the cardinality of the reals.
Reason #2. Complex analysis. The complex numbers can be expressed as numbers on a plane (real and imaginary axes). The Riemann sphere is used in complex analysis by the projection that is in reason #3.
Reason #3. Put the south pole of a unit sphere on the origin of the plane. Consider a line segment between the north pole and the complex plane. That line segment intersects the sphere in one and only one place. In fact, rays eminating from the north pole that intersect the sphere, do so in only one point and also intersect the plane in only one point.
There are more reasons, but I would need LaTeX and this is, after all, a political forum.