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Given a triangle with sides of length a, b, and c, if a 2 + b 2 = c 2, then the angle between sides a and b is a right angle. For any three positive real numbers a, b, and c such that a 2 + b 2 = c 2, there exists a triangle with sides a, b and c as a consequence of the converse of the triangle inequality.
Economic inequality is an umbrella term for a) income inequality or distribution of income (how the total sum of money paid to people is distributed among them), b) wealth inequality or distribution of wealth (how the total sum of wealth owned by people is distributed among the owners), and c) consumption inequality (how the total sum of money spent by people is distributed among the spenders).
Income inequality has fluctuated considerably since measurements began around 1915, declining between peaks in the 1920s and 2007 (CBO data [2]) or 2012 (Piketty, Saez, Zucman data [15]). Inequality steadily increased from around 1979 to 2007, with a small reduction through 2016, [2] [16] [17] followed by an increase from 2016 to 2018. [18]
Unequal access to education in the United States results in unequal outcomes for students. Disparities in academic access among students in the United States are the result of multiple factors including government policies, school choice, family wealth, parenting style, implicit bias towards students' race or ethnicity, and the resources available to students and their schools.
Squared Euclidean distance does not form a metric space, as it does not satisfy the triangle inequality. [20] However it is a smooth, strictly convex function of the two points, unlike the distance, which is non-smooth (near pairs of equal points) and convex but not strictly convex.
gives the inequality. In the special case of n = 1, the Nash inequality can be extended to the L p case, in which case it is a generalization of the Gagliardo-Nirenberg-Sobolev inequality (Brezis 2011, Comments on Chapter 8). In fact, if I is a bounded interval, then for all 1 ≤ r < ∞ and all 1 ≤ q ≤ p < ∞ the following inequality holds
The most common metric for comparing social inequality in different nations is the Gini coefficient, which measures the concentration of wealth and income in a nation from 0 (evenly distributed wealth and income) to 1 (one person has all wealth and income).
In 2002, a "maximum-fee" system was introduced in Sweden that states that costs for childcare may be no greater than 3% of one's income for the first child, 2% for the second child, 1% for the third child, and free of charge for the fourth child in pre-school. 97.5% of children age 1–5 attend these public daycare centers.
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