 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/iii/paper-47/4/b/solution

A metric dissimilarity must satisfy, for all

x, y, z

, the four properties

d (x, y) \geq 0, d (x, y) = 0 ⟺ x = y, d (x, y) = d (y, x), d (x, z) \leq d (x, y) + d (y, z) .

They are nonnegativity, identity of indiscernibles, symmetry and the triangle inequality. The following two transformations of the simple matching coefficient behave differently at the identity.

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