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The Elephant Curve, also known as the Lakner-Milanovic graph or the global growth incidence curve, is a graph that illustrates the unequal distribution of income growth for individuals belonging to different income groups. [1] The original graph was published in 2013 and illustrates the change in income growth that occurred from 1988 to 2008.
Proof [2]. Since + =, =. A graph = on the -plane is thus also a graph =. From sketching a visual representation of the integrals of the area between this curve and the axes, and the area in the rectangle bounded by the lines =, =, =, =, and the fact that is always increasing for increasing and vice versa, we can see that upper bounds the area of the rectangle below the curve (with equality ...
Thus we can find a graph with at least e − cr(G) edges and n vertices with no crossings, and is thus a planar graph. But from Euler's formula we must then have e − cr(G) ≤ 3n, and the claim follows. (In fact we have e − cr(G) ≤ 3n − 6 for n ≥ 3). To obtain the actual crossing number inequality, we now use a probabilistic argument.
Bernoulli's inequality can be proved for case 2, in which is a non-negative integer and , using mathematical induction in the following form: we prove the inequality for {,}, from validity for some r we deduce validity for +.
Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]
"Wealth Inequality in America," a six-minute video produced by a YouTube user named "Politizane," casts an interesting angle on the plummeting savings rate. Set to depressing piano music and ...
The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size.
Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general.