> and thats totally fine because the real world does not contain infinities

Anyone who positively claims that infinities do or do not exist in nature don’t know what they’re talking about.

Physics is full of infinities. They show up all the time in relativity (gravitational singularities) and quantum physics (renormalization, rigged Hilbert spaces with integration over infinite distributions).

For some of these infinities (like the ones we have to deal with in quantum mechanics), it’s unclear (to me, at least) whether or not they have any sort of “real” equivalent. For things like gravitational singularities, our current theories predict the physical existence of infinite quantities (density, gravitational field, etc.).