Things such as infinity, singularities, or discontinuities, are mathematical concepts. Mathematics allows two dimensional worlds, or 8 dimensional worlds, and many other things that are not possible in a physical world. Physicists often use mathematics to describe the physical world, but the match is not always exact. So what? That doesn’t mean either is wrong, they just are not exactly right.
Mathematicians and scientists get jobs, awards, and honors when they come up with theories that are closer approximations to what we hope is "exactly right".