If you cut up the sphere's surface into pieces, the combined surface area will remain the same. If you then reassemble them in a different configuration into two spheres both the same size as the original, the surface area will be twice as much.
I don't see how that could be true. What am I missing here?
ETA: thanks for all the explanations. The most succinct answer seems to be because it assumes the surface is made of infinitely many points, and infinity breaks math. 2*inf = inf.
One more reason why it makes no sense to treat infinity as a number.
If you cut up the sphere's surface into pieces, the combined surface area will remain the same. If you then reassemble them in a different configuration into two spheres both the same size as the original, the surface area will be twice as much.
I don't see how that could be true. What am I missing here?
ETA: thanks for all the explanations. The most succinct answer seems to be because it assumes the surface is made of infinitely many points, and infinity breaks math. 2*inf = inf.
One more reason why it makes no sense to treat infinity as a number.