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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. The Metric System of measurement is the standard used by most scientific disciplines. The system is based upon measures of distance (in meters), volume (in liters), and mass (in grams).ote that web browsers do not support use of superscripts and subscripts very well, so the notation 10^ 2 means 10 to the power of 2, or 10 squared. Similarly, the notation 10- 2 should be read as 10 to the power of -2.