Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
non-negative real numbers
|
| gptkbp:category |
inequalities
elementary mathematics |
| gptkbp:describes |
relationship between arithmetic mean and geometric mean
|
| gptkbp:equalityCondition |
all numbers are equal
|
| gptkbp:field |
gptkb:algebra
gptkb:mathematics analysis |
| gptkbp:firstPublished |
gptkb:Augustin-Louis_Cauchy
1821 |
| gptkbp:form |
(a1 + a2 + ... + an)/n ≥ (a1*a2*...*an)^(1/n)
|
| gptkbp:generalizes |
inequality of arithmetic and geometric means for two numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
AM-GM inequality
|
| gptkbp:relatedTo |
gptkb:Cauchy-Schwarz_inequality
gptkb:Holder's_inequality gptkb:Jensen's_inequality |
| gptkbp:state |
arithmetic mean of non-negative real numbers is greater than or equal to their geometric mean
|
| gptkbp:usedIn |
gptkb:mathematical_olympiads
optimization inequality proofs |
| gptkbp:bfsParent |
gptkb:arithmetic-geometric_mean_inequality
|
| gptkbp:bfsLayer |
5
|