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recently I stumbled across the question whether for finite sets [itex]A,B[/itex] the function

[tex]d(A,B):=|A\cup B| - |A\cap B|[/itex]

is a http://en.wikipedia.org/wiki/Metric_distance" [Broken]? Trivially, [itex]d(A,A)=0[/itex] and of course [itex]d[/itex] is symmetric, but how about the triangle inequality? Does it hold?

Harald.

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# A metric on finite sets

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