No, those are fine. Well, almost. They're not uniquely broken, at least.

Mathematics would have me believe "the sum of all positive integers" is a negative number. They can provide glorious proofs of that fact. When you insert the result into the physics equations, the equations work.

But the idea is, on its face, stupid. Any child would tell you as much. The equations only "work" on that premise because they're almost right.

But that's not a problem with infinity, it's a problem with something we're assuming when we go to write the proof in the first place. And whatever that problem is... it's almost certainly the thing stopping us from solving the Riemann hypothesis.