A classic example of homeomorphism is between a sphere missing one point and a plane
To see this, place a sphere on the plane so that the sphere is tangent to the plane. Given any point in the plane, construct a line through that point from the "north" pole (assuming the point of tangency is the south pole); this necessarily intersects the sphere in a unique point other than the north pole. Similarly, given any point on the sphere other than the north pole, the line through the north pole and that point will intersect the plane at a unique point. Thus, the homeomorphism is established.
Since there is a homeomorphism between a sphere missing one point and a plane, does it make sense to say that a sphere has one more point than a plane, even though both sets are infinite and uncountable?