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  2. Environmental issues - Wikipedia

    en.wikipedia.org/wiki/Environmental_issues

    Environment destruction caused by humans is a global, ongoing problem. [4] Water pollution also cause problems to marine life. [ 5 ] Some scholars believe that the projected peak global population of roughly 9-10 billion people could live sustainably within the earth's ecosystems if humans worked to live sustainably within planetary boundaries .

  3. Inequality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inequality_(mathematics)

    For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < ⁠ 1 / 2 ⁠ and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < ⁠ 1 / 2 ⁠.

  4. Social inequality - Wikipedia

    en.wikipedia.org/wiki/Social_inequality

    There are five systems or types of social inequality: wealth inequality, treatment and responsibility inequality, political inequality, life inequality, and membership inequality. Political inequality is the difference brought about by the ability to access governmental resources which therefore have no civic equality.

  5. Educational inequality in the United States - Wikipedia

    en.wikipedia.org/wiki/Educational_inequality_in...

    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.

  6. QM-AM-GM-HM inequalities - Wikipedia

    en.wikipedia.org/wiki/QM-AM-GM-HM_Inequalities

    There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.

  7. Triangle inequality - Wikipedia

    en.wikipedia.org/wiki/Triangle_inequality

    The first of these quadratic inequalities requires r to range in the region beyond the value of the positive root of the quadratic equation r 2 + r − 1 = 0, i.e. r > φ − 1 where φ is the golden ratio. The second quadratic inequality requires r to range between 0 and the positive root of the quadratic equation r 2 − r − 1 = 0, i.e. 0 ...

  8. Economic inequality - Wikipedia

    en.wikipedia.org/wiki/Economic_inequality

    Global share of wealth by wealth group, Credit Suisse, 2021 Share of income of the top 1% for selected developed countries, 1975 to 2015. 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 ...

  9. AM–GM inequality - Wikipedia

    en.wikipedia.org/wiki/AM–GM_inequality

    Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square. The full inequality is an extension of this idea to n dimensions.