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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).
The metric system is a modern system, with all measurements based on the decimal system (everything based on 10 or multiples of). The METRIC system is based on increments of the number 10 in both volume and linear measurements. The units of linear measure are: Kilometer - 1,000; hectometer - 100; decimeter - 10; base - 1; decimeter - .1; centimeter - .01; millimeter - .001.