Arithmetic Mean-Geometric Mean Inequality
The Arithmetic Mean-Geometric Mean Inequality (AM-GM) states that the arithmetic mean of a non-empty set of nonnegative real numbers is greater than or equal to the geometric mean of the same set. (Note that in this case the set of numbers is really a multiset, with repetitions of elements allowed.) For example, for the set , the Arithmetic Mean, 25, is greater than the Geometric Mean, 18; AM-GM guarantees this is always the case.
In general, AM-GM states that for a set of nonnegative real numbers , the following always holds: