If there were an infinite amount of matter in a finite volume, we would be infinitely dense (well, some are anyway, but that's a different definition altogether

If there were an infinite amount of matter in a finite volume, we would be infinitely dense (well, some are anyway, but that's a different definition altogether), which would make Earth something that it is altogether not. Are you infinitely dense? (I am not; I can't prove it, but I suspect you are less than infinitely dense.)