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komponisto comments on Rationality Quotes January 2010 - Less Wrong
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Not when the question is whether any examples exist!
OK, but it takes two minutes to prove that an anti-metric space with more than one point can't exist. If x != y, then d(x, y) + d(y, x) > d(x, x).
Unless you allow negative distances, in which case an anti-metric space is just a mirror image of a metric space.