MathLiveArithmetic mean–geometric mean inequality
States that the geometric mean of a list of non-negative real numbers is at most their arithmetic mean, with equality exactly when all the numbers are equal. It is used to bound averages and in optimization problems.
G \le AWhat the symbols mean
| geometric mean of the numbers x_1, ..., x_n | |
| arithmetic mean of the numbers x_1, ..., x_n |
About this formula
- FieldMathematics
- TopicInequalities
- LevelUniversity
- Also calledAM-GM inequality, inequality of arithmetic and geometric means, relation between AM GM, AM GM inequality, arithmetic geometric mean inequality
- SourceWikidata Q841170
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