Under the assumptions p ∈ (1, ∞) and ||f ||p = ||g||q, equality holds if and only if |f |p = |g|q almost everywhere. More generally, if ||f ||p and ||g||q are in (0, ∞), then Hölder's inequality becomes an equality if and only if there exist real numbers α, β > 0, namely ** Made in Germany Gender Inequality: Money Matters**. Women have less income and less capital than men almost everywhere. In Germany women earn on average 21 percent less per hour than men inequality translate: 不平等，不均等. Learn more in the Cambridge English-Chinese traditional Dictionary

The form above is perhaps the easiest in which to understand the inequality, since the square of the cosine can be at most 1, which occurs when the vectors are in the same or opposite directions. It can also be restated in terms of the vector coordinates v 1 , v 2 , u 1 {\displaystyle v_{1},v_{2},u_{1}} and u 2 {\displaystyle u_{2}} as ** Gender Inequality (Ch 10 pgs288-295) Cold-Hearted Surgeons and Their Women Victims Doctors recommended total hysterectomy for women when no cancer was present**. Hysterectomy is 90% avoidable Gender Inequality in Health Care What was to Blame? Reports show that women were twice a The difference between the IHDI and HDI is the human development cost of inequality, also termed - the overall loss to human development due to inequality. The IHDI allows a direct link to inequalities in dimensions, it can inform policies towards inequality reduction, and leads to better understanding of inequalities across population and. where the numbers p {\displaystyle p} and q {\displaystyle q} are Hölder conjugates.[1]

Many societies worldwide claim to be meritocracies—that is, that their societies exclusively distribute resources on the basis of merit. The term "meritocracy" was coined by Michael Young in his 1958 dystopian essay "The Rise of the Meritocracy" to demonstrate the social dysfunctions that he anticipated arising in societies where the elites believe that they are successful entirely on the basis of merit, so the adoption of this term into English without negative connotations is ironic;[3] Young was concerned that the Tripartite System of education being practiced in the United Kingdom at the time he wrote the essay considered merit to be "intelligence-plus-effort, its possessors ... identified at an early age and selected for appropriate intensive education" and that the "obsession with quantification, test-scoring, and qualifications" it supported would create an educated middle-class elite at the expense of the education of the working class, inevitably resulting in injustice and – eventually – revolution.[4] If ||f ||p = ∞ or ||g||q = ∞, then the right-hand side of Hölder's inequality is infinite. Therefore, we may assume that ||f ||p and ||g||q are in (0, ∞). inequality translate: desigualdad, desigualdad. Learn more in the Cambridge English-Spanish Dictionary Inequalities ppt revised 1. INEQUALITIES 2. Equal or Unequal?• We call a math statement an EQUATION when both sides of the statement are equal to each other. - Example: 10 = 5 + 3 + 2• We call a math statement an INEQUALITY when both sides of the statement are not equal to each other. - Example: 10 = 5 + 5 + 5 3 The coronavirus crisis spotlights the inequalities in American education By Christina Maxouris and Alice Yu, CNN. 4/17/2020. Stores stress over how to handle mask-less customers

Therefore, z {\displaystyle z} is a vector orthogonal to the vector v {\displaystyle v} (Indeed, z {\displaystyle z} is the projection of u {\displaystyle u} onto the plane orthogonal to v {\displaystyle v} .) We can thus apply the Pythagorean theorem to German Translation of inequality | The official Collins English-German Dictionary online. Over 100,000 German translations of English words and phrases After defining an inner product on the set of random variables using the expectation of their product, For the probability space ( Ω , F , P ) , {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} ),} let E {\displaystyle \mathbb {E} } denote the expectation operator. For real- or complex-valued random variables X {\displaystyle X} and Y {\displaystyle Y} on Ω , {\displaystyle \Omega ,} Hölder's inequality reads

- istration issued new guidelines on overtime pay, which will benefit an estimated 12.5 million workers
- There are many different proofs[6] of the Cauchy–Schwarz inequality other than the above two examples.[1][3] When consulting other sources, there are often two sources of confusion. First, some authors define ⟨⋅,⋅⟩ to be linear in the second argument rather than the first. Second, some proofs are only valid when the field is R {\displaystyle \mathbb {R} } and not C {\displaystyle \mathbb {C} } .[7]
- inequality - Wörterbuch Englisch-Deutsch. 90.000 Stichwörter und Wendungen sowie 120.000 Übersetzungen

Racial inequality can also result in diminished opportunities for members of marginalized groups, which in turn can lead to cycles of poverty and political marginalization. Racial and ethnic categories become a minority category in a society. Minority members in such a society are often subjected to discriminatory actions resulting from majority policies, including assimilation, exclusion, oppression, expulsion, and extermination.[50] For example, during the run-up to the 2012 federal elections in the United States, legislation in certain "battleground states" that claimed to target voter fraud had the effect of disenfranchising tens of thousands of primarily African American voters.[51] These types of institutional barriers to full and equal social participation have far-reaching effects within marginalized communities, including reduced economic opportunity and output, reduced educational outcomes and opportunities and reduced levels of overall health.[52] Let (Ω, F, ℙ) be a probability space, G ⊂ F a sub-σ-algebra, and p, q ∈ (1, ∞) Hölder conjugates, meaning that 1/p + 1/q = 1. Then, for all real- or complex-valued random variables X and Y on Ω, Inequality definition: Inequality is the difference in social status , wealth , or opportunity between people or... | Meaning, pronunciation, translations and example Let p1, ..., pn ∈ (0, ∞] and let θ1, ..., θn ∈ (0, 1) denote weights with θ1 + ... + θn = 1. Define p as the weighted harmonic mean, i.e.,

- Therefore, 0 ≤ ‖ u ‖ 2 − | ⟨ u , v ⟩ | 2 ‖ v ‖ 2 {\displaystyle 0\leq \|u\|^{2}-{\frac {|\langle u,v\rangle |^{2}}{\|v\|^{2}}}} , or | ⟨ u , v ⟩ | ≤ ‖ u ‖ ‖ v ‖ {\displaystyle |\langle u,v\rangle |\leq \|u\|\|v\|} .
- This assumes f , g {\displaystyle f,g} real and non negative, but the extension to complex functions is straightforward (use the modulus of f , g {\displaystyle f,g} ). It also assumes that ‖ f ‖ p , ‖ g ‖ q {\displaystyle \|f\|_{p},\|g\|_{q}} are neither null nor infinity, and that p , q > 1 {\displaystyle p,q>1} : all these assumptions can also be lifted as in the proof above.
- Given the sharp rise in inequality in recent decades, it is critical to more fully understand the connections between the realization of human rights and inequality—how we think about and measure inequality, the degree to which growing inequality threatens basic rights, and what the human rights framework says, and does not say, about inequality
- No existing measure of gender inequality fully captures the hardships that are disproportionately experienced by men in many countries and so they do not fully capture the extent to which any specific country is promoting the well-being of all its citizens, stated University of Essex Department of Psychology Professor Gijsbert Stoet
- French Translation of inequality | The official Collins English-French Dictionary online. Over 100,000 French translations of English words and phrases

- Researchers have many different yardsticks for measuring income — and all of them show a widening gap between the rich and everyone else.
- Deutsche Übersetzung von inequality | Der offizielle Collins Englisch-Deutsch Wörterbuch online. Über 100.000 Deutsche Übersetzungen von Englische Wörtern und Ausdrücke
- The economies of the world have developed unevenly, historically, such that entire geographical regions were left mired in poverty and disease while others began to reduce poverty and disease on a wholesale basis. This was represented by a type of North–South divide that existed after World War II between First world, more developed, industrialized, wealthy countries and Third world countries, primarily as measured by GDP. From around 1980, however, through at least 2011, the GDP gap, while still wide, appeared to be closing and, in some more rapidly developing countries, life expectancies began to rise.[73] However, there are numerous limitations of GDP as an economic indicator of social "well-being."[74]
- Entropic inequality measures like Theil's entropy actually are not entropies. They are redundancies [].The redundancy of a system at a given time is the difference between its maximum entropy (e.g. Theil: ln(A total /E total)) and its present entropy (e.g. Theil: Σ i=1..N (E i *ln(A i /E i))/E total []) at that time. In a system a certain amount of transformations is possible
- Then g is well-defined, measurable and |g(x)| ≤ 1/μ(B) for x ∈ B, hence ||g||1 ≤ 1. Furthermore,
- Evidence that inequality has only increased under the prevailing capitalist narrative leads him to declare that social democracy has failed. Such hyper-meritocratic, Western-centric justifications of inequality demonstrate the irrepressible human need to make sense of social inequality, at times in ways that stretch credulity
- Less inequality. One way to measure that is the Gini index. In theory, a Gini of zero means that everybody has exactly the same income, and a Gini of 100 that one person gets it all

Age discrimination is defined as the unfair treatment of people with regard to promotions, recruitment, resources, or privileges because of their age. It is also known as ageism: the stereotyping of and discrimination against individuals or groups based upon their age. It is a set of beliefs, attitudes, norms, and values used to justify age-based prejudice, discrimination, and subordination.[54] One form of ageism is adultism, which is the discrimination against children and people under the legal adult age.[55] An example of an act of adultism might be the policy of a certain establishment, restaurant, or place of business to not allow those under the legal adult age to enter their premises after a certain time or at all. While some people may benefit or enjoy these practices, some find them offensive and discriminatory. Discrimination against those under the age of 40 however is not illegal under the current U.S. Age Discrimination in Employment Act (ADEA).[56] Theorem (Kadison–Schwarz inequality,[19][20] named after Richard Kadison): If φ {\displaystyle \varphi } is a unital positive map, then for every normal element a {\displaystyle a} in its domain, we have φ ( a ∗ a ) ≥ φ ( a ∗ ) φ ( a ) {\displaystyle \varphi (a^{*}a)\geq \varphi (a^{*})\varphi (a)} and φ ( a ∗ a ) ≥ φ ( a ) φ ( a ∗ ) {\displaystyle \varphi (a^{*}a)\geq \varphi (a)\varphi (a^{*})} . inequality in China over the period of economic . reform. It presents the results of two main sources of evidence on income inequality and, assisted by various decompositions, explains the reasons income inequality has increased rapidly and the Gini coefficient is now almost 0.5. This paper evaluates the degree of incom

Based on countries for which an **Inequality**-adjusted Human Development Index value is calculated. c. Calculated by HDRO from the 2015-2020 period life tables from UNDESA (2017a). d. Data refer to 2017 or the most recent year available. e. Data refer to the most recent year available during the period specified Mailing Address CounterPunch PO Box 228 Petrolia, CA 95558 Telephone 1(707) 629-368 The triangle inequality for the standard norm is often shown as a consequence of the Cauchy–Schwarz inequality, as follows: given vectors x and y:

It can be easily proven by Hölder's inequality.[23] There are also non commutative versions for operators and tensor products of matrices.[24] dict.cc | Übersetzungen für 'inequality' im Englisch-Deutsch-Wörterbuch, mit echten Sprachaufnahmen, Illustrationen, Beugungsformen,. Social inequality occurs when resources in a given society are distributed unevenly, typically through norms of allocation, that engender specific patterns along lines of socially defined categories of persons. It is the differentiation preference of access of social goods in the society brought about by power, religion, kinship, prestige, race, ethnicity, gender, age, sexual orientation, and. Many familes love their children and have good intentions, yet lack the resources to nuture their child's health and development. CHILDHOOD POVERTY IS THE GREATEST THREAT TO CHILDREN'S PHYSICAL AND MENTAL HEALTH, AND A BARRIER TO THEIR DEVELOPMENT, ACHIEVEMENT AND FUTURE *In particular, if the sth absolute moment is finite, then the r th absolute moment is finite, too*. (This also follows from Jensen's inequality.)

The GII is an inequality index. It shows the loss in potential human development due to disparity between female and male achievements in three dimensions: reproductive health, empowerment and the labour market. Overall, the GII reflects how women are disadvantaged in these dimensions. The GII ranges between 0 and 1. Higher GII values indicate. Inequality definition is - the quality of being unequal or uneven: such as. How to use inequality in a sentence

- Inequality is the same with any equation but the only difference is that inequality does not use an equal sign instead it uses symbols. The inequality b>a represents that b is greater than a. Speed limits,mark, and others use inequality to express them. When solving an inequality a person need to have a true statement
- Since g is not almost everywhere equal to the zero function, we can have equality if and only if there exists a constant α ≥ 0 such that |fg| = α |g|−q/p almost everywhere. Solving for the absolute value of f gives the claim.
- Economic inequality compares the share of the _____ in society that is received by different groups; such as comparing the share of income received by the _____ to the share of income received by the _____ . answers a and c are correct. In the United States, the official definition of the poverty line traces back to a single person.
- The report revealed inequality by underfunding public services, such as healthcare and education, on the one hand, while under taxing corporations and the wealthy, and failing to clamp down on tax dodging, on the other. Number of billionaires doubled since financial crisis: Oxfam report
- The Cauchy–Schwarz inequality allows one to extend the notion of "angle between two vectors" to any real inner-product space by defining:[10][11]
- The Cauchy–Schwarz inequality proves that this definition is sensible, by showing that the right-hand side lies in the interval [−1, 1] and justifies the notion that (real) Hilbert spaces are simply generalizations of the Euclidean space. It can also be used to define an angle in complex inner-product spaces, by taking the absolute value or the real part of the right-hand side,[12][13] as is done when extracting a metric from quantum fidelity.
- Include nonlinear constraints by writing a function that computes both equality and inequality constraint values. A nonlinear constraint function has the syntax [c,ceq] = nonlinconstr(x) The function c(x) represents the constraint c(x) <= 0. The function ceq(x) represents the constraint ceq(x) = 0

Various generalizations of the Cauchy–Schwarz inequality exist. Hölder's inequality generalizes it to L p {\displaystyle L^{p}} norms. More generally, it can be interpreted as a special case of the definition of the norm of a linear operator on a Banach space (Namely, when the space is a Hilbert space). Further generalizations are in the context of operator theory, e.g. for operator-convex functions and operator algebras, where the domain and/or range are replaced by a C*-algebra or W*-algebra. We use Hölder's inequality and mathematical induction. For n = 1, the result is obvious. Let us now pass from n − 1 to n. Without loss of generality assume that p1 ≤ … ≤ pn. inequality translate: 不平等，不均等. Learn more in the Cambridge English-Chinese simplified Dictionary And black adults were three times as likely as white ones to have close family in jail or prison for over a year, per a study from Cornell University and Fwd.us. Sarah Ruiz-Grossman. Watch Critics Destroy Their Nike Gear Amid New Colin Kaepernick Campaign. Colin Kaepernick is the new face of Nike and conservatives are burning the brand's. GENEVA, Sep 23 2019 (IPS) - Increasing economic inequality is a defining challenge of our time. In recent years, it has triggered analysis and reflection by many scholars, politicians and others on its causes and consequences on economic growth and efficiency, politics and democracy, human rights, individual behaviors, access to health, social cohesion and environmental degradation

Class, race, and gender are forms of stratification that bring inequality and determines the difference in allocation of societal rewards. Occupation is the primary determinant of a person class since it affects their lifestyle, opportunities, culture, and kind of people one associates with. Class based families include the lower class who are the poor in the society. They have limited opportunities. Working class are those people in blue-collar jobs and usually, affects the economic level of a nation. The Middle classes are those who rely mostly on wives' employment and depends on credits from the bank and medical coverage. The upper middle class are professionals who are strong because of economic resources and supportive institutions.[25] Additionally, the upper class usually are the wealthy families who have economic power due to accumulative wealth from families but not and not hard earned income. Extreme inequality is one of the defining issues of our time, with the gap between rich and poor widening across the globe. But while economic inequality has become a prominent issue on the international development agenda, as well as in national political debates in many countries, the human rights community has barely begun to address its implications for the full range of human rights * The killing fields of inequality Increasing social distance between the poorest and the richest diminishes social*. cohesion, which in turn means more collective problems and fewer resources for In countries that have a universal health care system, health inequalities have been reduced. In Canada, for example, equity in the availability of health services has been improved dramatically through Medicare. People don't have to worry about how they will pay health care, or rely on emergency rooms for care, since health care is provided for the entire population. However, inequality issues still remain. For example, not everyone has the same level of access to services.[66][62][63] Inequalities in health are not, however, only related to access to health care. Even if everyone had the same level of access, inequalities may still remain. This is because health status is a product of more than just how much medical care people have available to them. While Medicare has equalized access to health care by removing the need for direct payments at the time of services, which improved the health of low status people, inequities in health are still prevalent in Canada.[67] This may be due to the state of the current social system, which bear other types of inequalities such as economic, racial and gender inequality. An 80-page note by Deutsche Bank sheds light on dramatically increasing income inequality in the U.S. and other Organization for Economic Cooperation and Development (OECD) economies

Using the measurability of U, V, 1G with respect to the sub-σ-algebra, the rules for conditional expectations, Hölder's inequality and 1/p + 1/q = 1, we see that A variety of global issues like HIV/AIDS, illiteracy, and poverty are often seen as "women's issues" since women are disproportionately affected.[37] In many countries, women and girls face problems such as lack of access to education, which limit their opportunities to succeed, and further limits their ability to contribute economically to their society.[38] Women are underrepresented in political activities and decision making processes throughout most of the world.[39] As of 2007, around 20 percent of women were below the $1.25/day international poverty line and 40 percent below the $2/day mark. More than one-quarter of females under the age of 25 were below the $1.25/day international poverty line and about half on less than $2/day.[40]

Inequality had persisted despite the official liberation of the peasants in 1807 and despite the fact that many had become independent freeholders by the 1850s (Eddie, 2008). Financial support by Deutsche Forschungsgemeinschaft through CRC TRR 190 (project number 280092119) is gratefully acknowledged One-step inequalities review. This is the currently selected item. Next lesson. Two-step inequalities. Sort by: Top Voted. One-step inequality word problem. Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization. Donate or volunteer today! Site Navigation. About. News Health inequalities can be defined as differences in health status or in the distribution of health determinants between different population groups.[59] Racial or ethnic inequality is the result of hierarchical social distinctions between racial and ethnic categories within a society and often established based on characteristics such as skin color and other physical characteristics or an individual's place of origin or culture. Racism is whereby some races are more privileged and are allowed to venture into the labor market and are better compensated than others. Ethnicity is the privilege one enjoys for belonging to a particular ethnic group. Even though race has no biological connection, it has become a socially constructed category capable of restricting or enabling social status.

If p = ∞ and q = 1, then |fg| ≤ ||f ||∞ |g| almost everywhere and Hölder's inequality follows from the monotonicity of the Lebesgue integral. Similarly for p = 1 and q = ∞. Therefore, we may also assume p, q ∈ (1, ∞). Inequality declines when carnage and disaster strike and increases when peace and stability return. The Great Leveler is the first book to chart the crucial role of violent shocks in reducing inequality over the full sweep of human history around the world

Dividing f and g by ||f ||p and ||g||q, respectively, we can assume that A lack of health equity is also evident in the developing world, where the importance of equitable access to healthcare has been cited as crucial to achieving many of the Millennium Development Goals. Health inequalities can vary greatly depending on the country one is looking at. Health equity is needed in order to live a healthier and more sufficient life within society. Inequalities in health lead to substantial effects that are burdensome on the entire society. Inequalities in health are often associated with socioeconomic status and access to health care. Health inequities can occur when the distribution of public health services is unequal. For example, in Indonesia in 1990, only 12% of government spending for health was for services consumed by the poorest 20% of households, while the wealthiest 20% consumed 29% of the government subsidy in the health sector.[68] Access to health care is heavily influenced by socioeconomic status as well, as wealthier population groups have a higher probability of obtaining care when they need it. A study by Makinen et al. (2000) found that in the majority of developing countries they looked at, there was an upward trend by quintile in health care use for those reporting illness. Wealthier groups are also more likely to be seen by doctors and to receive medicine.[69] Inequalities and Their Measurement This paper is a review of the recent advances in the measurement of inequality. Inequality can have several dimensions. Economists are mostly concerned with the income and consumption dimensions of inequality. Several inequality indices including the most widel

Inequality is growing. The rich consume much more than the poor and produce much more waste. Trash has become a symbol of our times. But what some people throw away, means money to others and a. The concept of economic growth is fundamental in capitalist economies. Productivity must grow as population grows and capital must grow to feed into increased productivity. Investment of capital leads to returns on investment (ROI) and increased capital accumulation. The hypothesis that economic inequality is a necessary precondition for economic growth has been a mainstay of liberal economic theory. Recent research, particularly over the first two decades of the 21st century, has called this basic assumption into question.[40] While growing inequality does have a positive correlation with economic growth under specific sets of conditions, inequality in general is not positively correlated with economic growth and, under some conditions, shows a negative correlation with economic growth.[20][40][78][80] Solving Linear Inequalities in One Variable Examples : Let a be a non zero real numbers and x be a variable. are known as linear inequalities in one variable. Same number may be added to (or subtracted from) both sides of an inequality without changing the sign of inequality. Both sides of an inequality can be multiplied (or divided) both by. Cultural ideals about women's work can also affect men whose outward gender expression is considered "feminine" within a given society. Transgender and gender-variant persons may express their gender through their appearance, the statements they make, or official documents they present. In this context, gender normativity, which is understood as the social expectations placed on us when we present particular bodies, produces widespread cultural/institutional devaluations of trans identities, homosexuality and femininity.[35] Trans persons, in particular, have been defined as socially unproductive and disruptive.[36] In the United States, Angela Davis argues that mass incarceration has been a modern tool of the state to impose inequality, repression, and discrimination upon African American and Hispanics.[53] The War on Drugs has been a campaign with disparate effects, ensuring the constant incarceration of poor, vulnerable, and marginalized populations in North America. Over a million African Americans are incarcerated in the US, many of whom have been convicted of a non-violent drug possession charge.[citation needed] With the States of Colorado and Washington having legalized the possession of marijuana, drug reformists and anti-war on drugs lobbyists are hopeful that drug issues will be interpreted and dealt with from a healthcare perspective instead of a matter of criminal law. In Canada, Aboriginal, First Nations, and Indigenous persons represent over a quarter of the federal prison population, even though they only represent 3% of the country's population.

Find gender inequality stock images in HD and millions of other royalty-free stock photos, illustrations and vectors in the Shutterstock collection. Thousands of new, high-quality pictures added every day So in some sense the source of higher inequality is Fed policies, which pushed stock prices and home prices higher, as Deutsche Bank's chief economist Torsten Sløk noted. The election and. 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). Two nations may have identical Gini coefficients but dramatically different economic (output) and/or quality of life, so the Gini coefficient must be contextualized for meaningful comparisons to be made.[6] On Inequality may unsettle those fuzzy-minded liberals who know they are committed to a more equal society but are not sure why. Given Frankfurt's convincing proof that bourgeois, academic ethics cannot sustain a critique of inequality, these liberals may find themselves turning to intellectual traditions that offer a more radical, systemic critique., Los Angeles Review of Book Research & Commentary Essential Sanitary Workers Strike for Hazard Pay and PPE in New Orleans May 18, 2020 / by Mike Ludwig

Germany is one of the world's richest countries, but inequality is on the rise. The wealthy are pulling ahead, while the poor are falling behind. For the middle classes, work is no longer a. This extends the fact φ ( a ∗ a ) ⋅ 1 ≥ φ ( a ) ∗ φ ( a ) = | φ ( a ) | 2 {\displaystyle \varphi (a^{*}a)\cdot 1\geq \varphi (a)^{*}\varphi (a)=|\varphi (a)|^{2}} , when φ {\displaystyle \varphi } is a linear functional. The case when a {\displaystyle a} is self-adjoint, i.e. a = a ∗ , {\displaystyle a=a^{*},} is sometimes known as Kadison's inequality. Gender discrimination, especially concerning the lower social status of women, has been a topic of serious discussion not only within academic and activist communities but also by governmental agencies and international bodies such as the United Nations. These discussions seek to identify and remedy widespread, institutionalized barriers to access for women in their societies. By making use of gender analysis, researchers try to understand the social expectations, responsibilities, resources and priorities of women and men within a specific context, examining the social, economic and environmental factors which influence their roles and decision-making capacity. By enforcing artificial separations between the social and economic roles of men and women, the lives of women and girls are negatively impacted and this can have the effect of limiting social and economic development.[34] Today, there is belief held by some that social inequality often creates political conflict and growing consensus that political structures determine the solution for such conflicts. Under this line of thinking, adequately designed social and political institutions are seen as ensuring the smooth functioning of economic markets such that there is political stability, which improves the long-term outlook, enhances labour and capital productivity and so stimulates economic growth. With higher economic growth, net gains are positive across all levels and political reforms are easier to sustain. This may explain why, over time, in more egalitarian societies fiscal performance is better, stimulating greater accumulation of capital and higher growth.[20] In mathematics, the Cauchy-Schwarz inequality, also known as the Cauchy-Bunyakovsky-Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas. It is considered to be one of the most important inequalities in all of mathematics. The inequality for sums was published by Augustin.

The inequality for sums was published by Augustin-Louis Cauchy (1821), while the corresponding inequality for integrals was first proved by Viktor Bunyakovsky (1859). Later the integral inequality was rediscovered by Hermann Amandus Schwarz (1888).[1] This finite-dimensional version generalizes to functions f and g taking values in a normed space which could be for example a sequence space or an inner product space. Let u {\displaystyle u} and v {\displaystyle v} be arbitrary vectors in a vector space over F {\displaystyle \mathbb {F} } with an inner product, where F {\displaystyle \mathbb {F} } is the field of real or complex numbers. We prove the inequality

- The incomes of the poorest are growing in 3 out of every 4 economies, according to a new report. Inequality by the Numbers. Explore the latest data on poverty, inequality, and shared prosperity around the world. Inequality and Shared Prosperity At-A-Glance. The latest data shows that in 70 of the 91 countries studied, the bottom 40 percent of.
- Socioeconomic status (SES) is a combined total measure of a person's work experience and of an individual's or family's economic and social position in relation to others, based on income, education, and occupation. It is often used as synonymous with social class, a set of hierarchical social categories that indicate an individual's or household's relative position in a stratified matrix of social relationships. Social class is delineated by a number of variables, some of which change across time and place. For Karl Marx, there exist two major social classes with significant inequality between the two. The two are delineated by their relationship to the means of production in a given society. Those two classes are defined as the owners of the means of production and those who sell their labour to the owners of the means of production. In capitalistic societies, the two classifications represent the opposing social interests of its members, capital gain for the capitalists and good wages for the labourers, creating social conflict.
- Latest Inequality news, comment and analysis from the Guardian, the world's leading liberal voic
- and the similar one for fg hold, and Hölder's inequality can be applied to the right-hand side. In particular, if f and g are in the Hilbert space L2(μ), then Hölder's inequality for p = q = 2 implies

Theorem (Modified Schwarz inequality for 2-positive maps):[21] For a 2-positive map φ {\displaystyle \varphi } between C*-algebras, for all a , b {\displaystyle a,b} in its domain, To prove the covariance inequality using the Cauchy–Schwarz inequality, let μ = E ( X ) {\displaystyle \mu =\operatorname {E} (X)} and ν = E ( Y ) {\displaystyle \nu =\operatorname {E} (Y)} , then Let S be a set and let F ( S , C ) {\displaystyle F(S,\mathbb {C} )} be the space of all complex-valued functions on S. Let N be an increasing seminorm on F ( S , C ) , {\displaystyle F(S,\mathbb {C} ),} meaning that, for all real-valued functions f , g ∈ F ( S , C ) {\displaystyle f,g\in F(S,\mathbb {C} )} we have the following implication (the seminorm is also allowed to attain the value ∞): Income inequality has increased dramatically in the United States over recent decades, surpassing its previous peak in the 1920s. In 2016, the average income among the bottom 24.9 million.

If u 1 , … , u n ∈ C {\displaystyle u_{1},\ldots ,u_{n}\in \mathbb {C} } and v 1 , … , v n ∈ C {\displaystyle v_{1},\ldots ,v_{n}\in \mathbb {C} } , and the inner product is the standard complex inner product, then the inequality may be restated more explicitly as follows (where the bar notation is used for complex conjugation): Yet social inequalities, already glaring, are reinforced by the management of the coronavirus and will explode with the economic and social crisis to come. In stark contrast, wealthy residents. While universal access to health care may not completely eliminate health inequalities,[62][63] it has been shown that it greatly reduces them.[64] In this context, privatization gives individuals the 'power' to purchase their own health care (through private health insurance companies), but this leads to social inequality by only allowing people who have economic resources to access health care. Citizens are seen as consumers who have a 'choice' to buy the best health care they can afford; in alignment with neoliberal ideology, this puts the burden on the individual rather than the government or the community.[65]

Inequality and Health How long and how well we live depends to a great degree, the evidence shows, on the level of economic inequality within our societies.(where we interpret any product with a factor of ∞ as ∞ if all factors are positive, but the product is 0 if any factor is 0).

If (S, Σ, μ) is a probability space, then p, q ∈ [1, ∞] just need to satisfy 1/p + 1/q ≤ 1, rather than being Hölder conjugates. A combination of Hölder's inequality and Jensen's inequality implies that Practice: Solutions of inequalities: graphical. This is the currently selected item. Testing solutions to systems of inequalities. Practice: Solutions of systems of inequalities. Next lesson. Graphing two-variable inequalities Our mission is to provide a free, world-class education to anyone, anywhere.. Since f is measurable, A ∈ Σ. By the definition of ||f ||∞ as the essential supremum of f and the assumption ||f ||∞ > 0, we have μ(A) > 0. Using the additional assumption on the σ-field Σ if necessary, there exists a subset B ∈ Σ of A with 0 < μ(B) < ∞. Define g on S by Though the above discussion is limited to specific Western ideologies, similar thinking can be found, historically, in differing societies throughout the world. While, in general, eastern societies tend toward collectivism, elements of individualism and free market organization can be found in certain regions and historical eras. Classic Chinese society in the Han and Tang dynasties, for example, while highly organized into tight hierarchies of horizontal inequality with a distinct power elite also had many elements of free trade among its various regions and subcultures.[18]

where S is the Cartesian product of S1 and S2, the σ-algebra Σ arises as product σ-algebra of Σ1 and Σ2, and μ denotes the product measure of μ1 and μ2. Then Tonelli's theorem allows us to rewrite Hölder's inequality using iterated integrals: If f and g are Σ-measurable real- or complex-valued functions on the Cartesian product S, then Status in society is of two types which are ascribed characteristics and achieved characteristics. Ascribed characteristics are those present at birth or assigned by others and over which an individual has little or no control. Examples include sex, skin colour, eye shape, place of birth, sexuality, gender identity, parentage and social status of parents. Achieved characteristics are those which we earn or choose; examples include level of education, marital status, leadership status and other measures of merit. In most societies, an individual's social status is a combination of ascribed and achieved factors. In some societies, however, only ascribed statuses are considered in determining one's social status and there exists little to no social mobility and, therefore, few paths to more social equality.[11] This type of social inequality is generally referred to as caste inequality. Although this does not exhaust the scope of age discrimination, in modern societies it is often discussed primarily with regards to the work environment. Indeed, non-participation in the labour force and the unequal access to rewarding jobs means that the elderly and the young are often subject to unfair disadvantages because of their age. On the one hand, the elderly are less likely to be involved in the workforce: At the same time, old age may or may not put one at a disadvantage in accessing positions of prestige. Old age may benefit one in such positions, but it may also disadvantage one because of negative ageist stereotyping of old people. On the other hand, young people are often disadvantaged from accessing prestigious or relatively rewarding jobs, because of their recent entry to the work force or because they are still completing their education. Typically, once they enter the labour force or take a part-time job while in school, they start at entry-level positions with low-level wages. Furthermore, because of their lack of prior work experience, they can also often be forced to take marginal jobs, where they can be taken advantage of by their employers. As a result, many older people have to face obstacles in their lives. If S is a measurable subset of Rn with the Lebesgue measure, and f and g are measurable real- or complex-valued functions on S, then Hölder inequality is Income inequality in Germany on the rise: study Researchers found a slight decline in income inequality in eastern Germany compared to the west, but the large gap between the two regions persists

where Var {\displaystyle \operatorname {Var} } denotes variance, and Cov {\displaystyle \operatorname {Cov} } denotes covariance. Inequalities containing quantities that can assume different numerical values may be true for some values of these quantities and false for others. Thus, the inequality x 2 —4x + 3 > 0 is true for x = 4 and false for x = 2. To solve such inequalities is to determine the limits within which the quantities entering into the inequalities must be. inequality, in mathematics, statement that a mathematical expression is less than or greater than some other expression; an inequality is not as specific as an equation equation, in mathematics, a statement, usually written in symbols, that states the equality of two quantities or algebraic expressions, e.g., x+3=5.The quantity x Click the link for more information., but it does contain. 108.5k Posts - See Instagram photos and videos from 'inequality' hashta

The variables considered most important in explaining inequality and the manner in which those variables combine to produce the inequities and their social consequences in a given society can change across time and place. In addition to interest in comparing and contrasting social inequality at local and national levels, in the wake of today's globalizing processes, the most interesting question becomes: what does inequality look like on a worldwide scale and what does such global inequality bode for the future? In effect, globalization reduces the distances of time and space, producing a global interaction of cultures and societies and social roles that can increase global inequities.[11] For example, x+4>12, where x is a real number. First, a person needs to find the x and he/she need to know if it is a solution. The answer will be x>8 and it is a true statement. This expression is about the location of x within the set of real numbers. A number line is one way to show the location relative to all other real numbers.[1](See figure Inequality 1)

Additionally, inequality has only worsened since the recession. According to a January note by Deutsche Bank on Income and Wealth Inequality in the United States, the top 10 percent owned roughly 75 percent of household wealth in 2013. As of 2015, the top 10 percent also took in more than 50 percent of the pre-tax income share, slightly. Titu's lemma (named after Titu Andreescu, also known as T2 lemma, Engel's form, or Sedrakyan's inequality) states that for positive reals, one has health inequality A generic term for any disparity in health status between the affluent and those who live in poverty. The UK government's Health Improvement and Modernisation Plan is designed to improve the health and life expectancy of the less well-off to reduce this gap Conversely, for 1 ≤ p ≤ ∞, observe first that the statement is obvious when ||f ||p = 0. Therefore, we assume ||f ||p > 0 in the following.

It's no secret that the US has an inequality problem. But actually looking at the disparity between the top and the bottom can still be staggering. Deutsche Bank's chief international economist. The Cauchy–Schwarz inequality is used to prove that the inner product is a continuous function with respect to the topology induced by the inner product itself.[8][9] Deutsche restarts job cuts after six-week pandemic hiatus; The shifting patterns of UK inequality. Income inequality, for example, can be increased through entrepreneurs making fortunes.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities: The notation a < b means that a is less than b Both Littlewood and Lyapunov imply that if f ∈ L p 0 ∩ L p 1 , {\displaystyle f\in L^{p_{0}}\cap L^{p_{1}},} then f ∈ L p {\displaystyle f\in L^{p}} for all p 0 < p < p 1 . {\displaystyle p_{0}<p<p_{1}.}

As above, let f and g denote measurable real- or complex-valued functions defined on S. If ||fg||1 is finite, then the pointwise products of f with g and its complex conjugate function are μ-integrable, the estimate Dictionary English-German. inequality noun Schwächen bei der kontinuierlichen Vermittlung von Deutsch als Zweitsprache, bei der Elterneinbeziehung, der Schulöffnung, der Erziehung zu Eigeninitiative, Unternehmensgeist, Teamfähigkeit und zu globalem Wirtschaften. this is likely to give rise to inequality of treatment between the. Gender as a social inequality is whereby women and men are treated differently due to masculinity and femininity by dividing labor, assigning roles, and responsibilities and allocating social rewards. Sex- and gender-based prejudice and discrimination, called sexism, are major contributing factors to social inequality. Most societies, even agricultural ones, have some sexual division of labour and gender-based division of labour tends to increase during industrialization.[32] The emphasis on gender inequality is born out of the deepening division in the roles assigned to men and women, particularly in the economic, political and educational spheres. Women are underrepresented in political activities and decision making processes in most states in both the Global North and Global South.[33]

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- In the special case v = 0 {\displaystyle v=0} the theorem is trivially true. Now assume that v ≠ 0 {\displaystyle v\neq 0} . Let λ ∈ C {\displaystyle \lambda \in \mathbb {C} } be given by λ = ⟨ u , v ⟩ / ‖ v ‖ 2 {\displaystyle \lambda =\langle u,v\rangle /\|v\|^{2}} , then
- Moreover, the two sides are equal if and only if u {\displaystyle \mathbf {u} } and v {\displaystyle \mathbf {v} } are linearly dependent (meaning they are parallel: one of the vector's magnitudes is zero, or one is a scalar multiple of the other).[4][5]
- Inequality Economic inequality, also known as income inequality and wealth inequality, is the difference found in various measures of economic well-being among individuals in a group, among groups in a population, or among countries. 9

where equality holds if and only if the vector ( u 1 , u 2 ) {\displaystyle (u_{1},u_{2})} is in the same or opposite direction as the vector ( v 1 , v 2 ) , {\displaystyle (v_{1},v_{2}),} or if one of them is the zero vector. Inequality synonyms and Inequality antonyms. Top synonym for inequality (another word for inequality) is disparity Practice: Inequality This is the currently selected item. Economics and finance · AP®︎ Microeconomics · Market failure and the role of government · Inequality