Arithmetic Mean-Geometric Mean Inequality
The Arithmetic Mean-Geometric Mean Inequality (AM-GM or AMGM) is an elementary inequality, generally one of the first ones taught in number theory courses.
The AM-GM states that for any multiset of positive real numbers, the arithmetic mean of the set is greater than or equal to the geometric mean of the set. Or:
For a set of nonnegative real numbers , the following always holds:
For example, for the set , the Arithmetic Mean, 25, is greater than the Geometric Mean, 18; AM-GM guarantees this is always the case.
- Basic Inequalities by Adeel Khan
- Inequalities: An Application of RMS-AM-GM-HM by Adeel Khan
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