arithmetic mean–geometric mean inequality
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:abbreviation |
AM–GM inequality
|
| gptkbp:appliesTo |
non-negative real numbers
|
| gptkbp:describes |
relationship between arithmetic mean and geometric mean
|
| gptkbp:equality_holds_when |
all numbers are equal
|
| gptkbp:field |
gptkb:algebra
gptkb:mathematics analysis |
| gptkbp:first_proved_by |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:form |
(a_1 + a_2 + ... + a_n)/n ≥ (a_1 * a_2 * ... * a_n)^{1/n} for a_i ≥ 0
|
| gptkbp:generalizes |
power mean inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
arithmetic mean–geometric mean inequality
|
| gptkbp:relatedTo |
gptkb:Young's_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:used_in |
gptkb:probability_theory
number theory statistics optimization inequality proofs |
| gptkbp:bfsParent |
gptkb:Bunyakovsky_inequality
|
| gptkbp:bfsLayer |
7
|