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Definition: A nonnegative function g(x,y) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z), and is symmetric, so g(x,y)=g(y,x). A metric also satisfies g(x,x)=0, as well as the condition that g(x,y)=0 implies x=y.