Proof of Power Means Inequality
We will prove weighted power means inequality, for the purpose of the proof we will assume without loss of generality that:
and
Proof for unweighted power means is easily obtained by substituting .
Read more about this topic: Generalized Mean
Famous quotes containing the words proof of, proof, power, means and/or inequality:
“The insatiable thirst for everything which lies beyond, and which life reveals, is the most living proof of our immortality.”
—Charles Baudelaire (18211867)
“The chief contribution of Protestantism to human thought is its massive proof that God is a bore.”
—H.L. (Henry Lewis)
“Sometimes, because of its immediacy, television produces a kind of electronic parable. Berlin, for instance, on the day the Wall was opened. Rostropovich was playing his cello by the Wall that no longer cast a shadow, and a million East Berliners were thronging to the West to shop with an allowance given them by West German banks! At that moment the whole world saw how materialism had lost its awesome historic power and become a shopping list.”
—John Berger (b. 1926)
“Mutual repect implies discretion and reserve even in love itself; it means preserving as much liberty as possible to those whose life we share. We must distrust our instinct of intervention, for the desire to make ones own will prevail is often disguised under the mask of solicitude.”
—Henri-Frédéric Amiel (18211881)
“Love is a great thing. It is not by chance that in all times and practically among all cultured peoples love in the general sense and the love of a man for his wife are both called love. If love is often cruel or destructive, the reasons lie not in love itself, but in the inequality between people.”
—Anton Pavlovich Chekhov (18601904)