Note on the metric axioms

In the geometric approach, dissimilarities are treated as distances in space, and they must follow the rules that govern metric distance between objects.  Specifically, the dissimilarity  function d assigns to every pair of objects A and B a nonnegative number according to the following three axioms:

•  Minimality:   d(A,B) >= d(A,A) =0;  The dissimilarity  between two objects is greater than or equal to the dissimilarity between an object and itself, which is zero.
   
• Symmetry:   d(A,B) = d(B,A);  Dissimilarity is not directional; the dissimilarity of A to B is the same as the dissimilarity of B to A.
  
• The triangle inequality:   d(A,B)  +  d(B,C) >= d(A,C); A and C cannot be farther apart in similarity space than the sum of their distances to any other object B.