relative change is the difference of the absolute value of two numbers.
the difference of the absolute value of two numbers?
relative change
bullet::::- min(, ),









































bullet::::- min ("x", "y"),









































bullet::::- ("x" + "y")/2, and









































bullet::::- ( + )/2.









































section::::formulae.









































measures of relative difference are unitless numbers expressed as a fraction. corresponding values of percent difference would be obtained by multiplying these values by 100 (and appending the % sign to indicate that the value is a percentage).









































one way to define the relative difference of two numbers is to take their absolute difference divided by the maximum absolute value of the two numbers.
relative change and difference
the field of the rational numbers can be assigned one of a number of absolute value functions, including the trivial function formula_12 when formula_13, the more usual formula_14, and the "p"-adic absolute value functions. by ostrowski's theorem, every non-trivial absolute value on the rational numbers is equivalent to either the usual absolute value or some -adic absolute value. the rational field is not complete with respect to non-trivial absolute values; with respect to the trivial absolute value, the rational field is a discrete topological space, so complete. the completion with respect to the usual absolute value (from the order) is the field of real numbers. by this construction the field of real numbers is archimedean both as an ordered field and as a normed field. on the other hand, the completions with respect to the other non-trivial absolute values give the fields of -adic numbers, where is a prime integer number (see below); since the -adic absolute values satisfy the ultrametric property, then the -adic number fields are non-archimedean as normed fields (they cannot be made into ordered fields).
archimedean property