I have some sets of numbers, and I'd like to have a way to talk about how close these sets are to each other. I'm not sure what properties it should have (e.g. does it need to be a metric?). But I hope there are examples of better defined problems like this out there with some good solutions.
Some considerations. {1} should be closer to {1.1} than it is to {2}. And {.9,1.1} should be closer to {1} than {0,2} is. But is {1,1.1} closer to {1} than {2}? I suspect any distance function will have at least one parameter to control the tradeoff between nearness of points and cardinality of the sets.