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Definition. A metric space is a set X together with a function d (called a metric or distance function) which assigns a real number d (x, y) to every pair x, y X satisfying the properties (or axioms): 1  d (x, y) 0 and d (x, y) = 0 x = y, 2  d (x, y) = d (y, x), 3  d (x, y) + d (y, z) d (x, z).
Metric dimensions are easier to divide by three, or any number, because they only use one unit, or one scalable unit, of measure. Either kilometer, which is a multiple of the metric unit, the meter, or the meter, which is the unit, or the millimeter which is a divisor of the the meter. Example 5.7 km.