Infinities are okay in math and physics, so long as you know how to handle them. When used right, they cancel each other out so that you get an answer that makes sense. But, sometimes, the math is just not able to escape those infinities, such as in the centre of a black hole. There’s obviously something happening there that physicists don’t understand, and a lot of research and theory goes into trying to figure out what that is. They’ll know it’s figured out when the infinity in the black hole’s singularity is elegantly cancelled out.
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