For one, wouldn’t that mean they have a volume of zero? how does that work?
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A statement in physics about singularities is at least as much about saying “we don’t know what is happening” than about saying “this is what it is”.
A singularity is where the existing mathematical models of reality break down – they no longer work. Prior to achieving a singularity, the density is very high but a word like “density” cannot strictly be applied to a singularity although perhaps it could be the average density of a small region surrounding a singularity. (which would be high but not infinity)
Descriptors like “infinitely dense” are for the consumption of the non-physicists or descriptors to say “it is very very large”. It is semantic and metaphorical rather than precise.
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