It is a real, true, result, in a space that is based on different rules than our physical reality. A ball in R^3 is composed of a countably infinite number of zero-dimensional points. It's an abstract concept that doesn't really have much to do with a physical ball that consists of a finite number of atoms.

Fundamentally, math is something that describes a large collection of possible worlds. Our universe is just a small subset of all the things that could be, and when using math to understand reality we have to remember that.