In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.
Read more about Inequality Of Arithmetic And Geometric Means: Background, The Inequality, Geometric Interpretation, Example Application, Proofs of The AM–GM Inequality
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“Nature is unfair? So much the better, inequality is the only bearable thing, the monotony of equality can only lead us to boredom.”
—Francis Picabia (1878–1953)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
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“In mathematics he was greater
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—François, Duc De La Rochefoucauld (1613–1680)