I thought this exemplified the difference between math and actuality rather well:
As the disk rotates and gets closer to flat, it hits the surface more and more frequently. This can be modeled with a math formula of 1 divided by some function of the angle between the surface and the disk.
As that angle approaches 0 (which it will be when it’s flat), this number goes to (mathematical) infinity.
So, what does it sound like, is it really a mathematically infinite sound? No of course not! Something else happens, the disk comes to a standstill and there’s no sound at all anymore.
In actuality, the physical phenomenon predicted by math formulas that go to a conceptual infinity, don’t happen. It’s pertinent to note that this is what a black hole is, it’s a mathematical singularity that was then posited to exist! But just like the disk above, this doesn’t mean a black hole is actual. It’s just a mathematical object.