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:
“When children feel good about themselves, it’s like a snowball rolling downhill. They are continually able to recognize and integrate new proof of their value as they grow and mature.”
—Stephanie Martson (20th century)
“To cease to admire is a proof of deterioration.”
—Charles Horton Cooley (1864–1929)
“an age of unscrupulous and shameless book-making, it is a duty to give notice of the rubbish that cumbers the ground. There is no credit, no real power required for this task. It is the work of an intellectual scavenger, and far from being specially honourable.”
—Richard Holt Hutton (1826–1897)
“It was always accounted a virtue in a man to love his country. With us it is now something more than a virtue. It is a necessity. When an American says that he loves his country, he means not only that he loves the New England hills, the prairies glistening in the sun, the wide and rising plains, the great mountains, and the sea. He means that he loves an inner air, an inner light in which freedom lives and in which a man can draw the breath of self-respect.”
—Adlai Stevenson (1900–1965)
“A man willing to work, and unable to find work, is perhaps the saddest sight that fortune’s inequality exhibits under this sun.”
—Thomas Carlyle (1795–1881)