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Any tolerance on a part less than +/- 0.001 isn't real. If I can change the size of the part enough to blow it out of tolerance by putting my hand on it and putting some of my body temperature into it then it's just not real.
I used to work with those kinds of tolerances. Sensors for supersonic vehicles definitely need them and the tools to make them as well. Our tolerances were as tight as 0.01 arcseconds in rotations of motors smaller then my hand.