inequality of arithmetic and geometric means
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:alsoKnownAs |
gptkb:AM-GM_inequality
|
| gptkbp:appliesTo |
non-negative real numbers
|
| gptkbp:category |
gptkb:Mathematical_analysis
Inequalities |
| gptkbp:equalityHoldsWhen |
all numbers are equal
|
| gptkbp:firstPublished |
19th century
|
| gptkbp:form |
(a_1 + a_2 + ... + a_n)/n ≥ (a_1 * a_2 * ... * a_n)^{1/n}
|
| gptkbp:generalizes |
gptkb:Jensen's_inequality
|
| gptkbp:hasSpecialCase |
power mean inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
inequality of arithmetic and geometric means
|
| gptkbp:provenBy |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:relatedTo |
gptkb:Cauchy-Schwarz_inequality
gptkb:Holder's_inequality |
| gptkbp:state |
For any non-negative real numbers, the arithmetic mean is greater than or equal to the geometric mean.
|
| gptkbp:usedIn |
gptkb:mathematical_olympiads
gptkb:algebra analysis optimization |
| gptkbp:bfsParent |
gptkb:Jensen's_inequality
|
| gptkbp:bfsLayer |
6
|