title: Lloyd's of London

text: The "recruit to dilute" fraud allegations were heard in an eight-month trial in 2000 in the case "Sir William Jaffray & Ors v. The Society of Lloyd's" and were rejected by the judge; an appeal was heard in 2002 and unanimously rejected. On each occasion the allegation that there had been a policy to recruit to dilute was dismissed and Names were urged to settle; however, at first instance the judge described the Names as "the innocent victims [...] of staggering incompetence" and the appeal court found that representations that Lloyd's had a rigorous auditing system were false and strongly hinted that one of Lloyd's main witnesses, former chairman Murray Lawrence, had lied in his testimony.


title: Lloyd's of London

text: Lloyd's then instituted some major structural changes: corporate members with limited liability were permitted to join and underwrite insurance; no new unlimited-liability Names were allowed to join (although a few hundred existing ones remained); financial requirements for underwriting were changed, to prevent excess underwriting that was not backed by liquid assets; and market oversight significantly increased. Lloyd's rebounded and started to thrive again after the catastrophic losses arising out of the World Trade Center attack, but it faced increased competition from newly-created companies in Bermuda and other markets.


title: Lloyd's of London

text: In 2006 the Berkshire Hathaway subsidiary National Indemnity Company (NICO) agreed to assume all of Equitas' assets and liabilities, providing $7bn of new reinsurance cover for future claims payments in addition to the $8.7bn of existing reserves within Equitas. The transfer (in two phases between 2007 and 2009) represented "finality" under English law for all affected Names, who now faced "no further liability whatsoever" to the pre-1993 losses.


title: Lloyd's of London

text: Lloyd's is not an insurance company; it is a market of members. As the oldest continuously active insurance marketplace in the world, Lloyd's has retained some unusual structures and practices that differ from all other insurance providers today. Originally created as a non-incorporated association of subscribing members, it was incorporated by the Lloyd's Act 1871 and is currently governed under the Lloyd's Acts of 1871 through to 1982.


title: Lloyd's of London

text: Lloyd's itself does not underwrite insurance business, leaving that to its members. Instead, the Society operates effectively as a market regulator, setting rules under which members operate and offering centralised administrative services to those members.


title: Lloyd's of London

text: The Lloyd's Act 1982 defines the management structure and rules under which the market operates. Under the Act, the Council of Lloyd's is responsible for the management and supervision of the market. It is regulated by the Prudential Regulation Authority and the Financial Conduct Authority.


title: Lloyd's of London

text: The Council normally has six working, six external and six nominated members. The appointment of nominated members, including that of the chief executive officer, is confirmed by the Governor of the Bank of England. The working and external members are elected by Lloyd's members. The chairman and deputy chairmen are elected annually by the Council from among the working members of the Council. All members are approved by the regulating bodies.


title: Lloyd's of London

text: The Council can discharge some of its functions directly by making decisions and issuing resolutions, requirements, rules and bylaws. The Council delegates most of its daily oversight roles, particularly relating to ensuring the market operates successfully, to the Franchise Board.


title: Lloyd's of London

text: The Franchise Board lays down guidelines for all syndicates and operates a business planning and monitoring process to safeguard high standards of underwriting and risk management, thereby improving sustainable profitability and enhancing the financial strength of the market. The Board is chaired by the chairman of Lloyd's and has three executive members, three non-executives connected to the market and five independent non-executives.


title: Lloyd's of London

text: There are two classes of people and firms active at Lloyd's. The first are members, or providers of capital. The second are agents, brokers, and other professionals who support the members, underwrite the risks and represent outside customers (for example, individuals and companies seeking insurance, or insurance companies seeking reinsurance).


title: Lloyd's of London

text: For most of Lloyd's history, rich individuals known as Names backed policies written at Lloyd's with all of their personal wealth and took on unlimited liability. Since 1994, Lloyd's has allowed corporate members into the market, with limited liability. The asbestosis losses in the early 1990s devastated the finances of many Names: upwards of 1,500 out of 34,000 Names (4.4 per cent) were declared bankrupt. This scared away other potential Names. In 2011 individual Names provide only 11 per cent of capacity at Lloyd's, with UK-listed and other corporate members providing 30 per cent and the remainder via the international insurance industry. No new Names with unlimited liability are admitted, and the importance of individual Names will continue to decline as they slowly withdraw, convert (generally into limited liability partnerships), or die. In 2014, Names with unlimited liability provided just 2 per cent of the overall capacity in Lloyd's.


title: Lloyd's of London

text: Managing agents sponsor and manage syndicates. They canvas members for commitments of capacity, create the syndicate, hire underwriters, and oversee all of the syndicate's activities. Managing agents may run more than one syndicate, as borne out in the fact that in 2021 the 75 syndicates writing business at Lloyd's were operated by just 50 managing agents.


title: Lloyd's of London

text: Members' agents co-ordinate the members' underwriting and act as a buffer between Lloyd's, the managing agents and the members. They were introduced in the mid-1970s and grew in number until many went bust; many of the businesses merged, and there are now only four left (Argenta, Hampden, Alpha and LMAS, which has no active Names). It is mandatory that unlimited Names write through a members' agent, and many limited liability members also choose to do so.


title: Lloyd's of London

text: Coverholders are a major source of business for Lloyd's. Their numbers have grown steadily in recent years and in 2021 there were 4,054, producing an increasingly meaningful share of the market's overall premium income. The balance of Lloyd's business is distributed around the world through a network of brokers.


title: Lloyd's of London

text: Coverholders allow Lloyd's syndicates to operate in a region or country as if they were a local insurer. This is achieved by Lloyd's syndicates delegating their underwriting authority to coverholders. A coverholder can have restricted or full authority to underwrite specified business on behalf of a Lloyd's syndicate. It will usually issue the insurance documentation and will often also handle claims. The document setting out the terms of the coverholder's delegated authority is known as a binding authority.


title: Lloyd's of London

text: Outsiders, whether individuals or other insurance companies, cannot transact business directly with Lloyd's syndicates. They must hire an approved Lloyd's broker, who are the only customer-facing organisations at Lloyd's. They are therefore often referred to as intermediaries. Lloyd's brokers shop customers' risks around the syndicates, trying to obtain the best coverage and most competitive terms.


title: Lloyd's of London

text: When corporations became admitted as Lloyd's members, they often disliked the traditional structure. Insurance companies did not want to rely on the underwriting skills of syndicates they did not control, so they started their own. An integrated Lloyd's vehicle (ILV) is a group of companies that combines a corporate member, a managing agent, and a syndicate under common ownership. Some ILVs allow minority contributions from other members, but most now try to operate on an exclusive basis.


title: Lloyd's of London

text: Lloyd's capital structure, often referred to as the "chain of security", provides financial security to policyholders and capital efficiency to members. The Corporation is responsible for setting both member and central capital levels to achieve a level of capitalisation that is robust and allows members the potential to earn superior returns.


title: Lloyd's of London

text: There are three "links" in the chain: the funds in the first and second links are held in trust, primarily for the benefit of insureds whose policies are underwritten by the relevant member. Members underwrite for their own account and are not liable for other members' losses (i.e. liabilities are several, not joint).


title: Lloyd's of London

text: The third link consists largely of the Lloyd's Central Fund, which contains mutual assets held by the Corporation which are available, subject to Council approval as required, to meet any member's liabilities. As well as the Central Fund, the third link contains Corporation assets, subordinated debt, and a "callable layer" which can be invoked should the final link require topping up.


title: Lloyd's of London

text: Each Lloyd's syndicate is responsible for determining how much money to hold in reserve for its known liabilities and its estimated unknown liabilities, and each may choose to release some of its reserves for prior-year claims if it (and its independent auditors) deems it appropriate. Conversely, reserves may need to be strengthened if prior-year loss estimates deteriorate. Overall reserve releases can improve the syndicate's "accident year" combined ratio (the sum of the loss ratio and the expense ratio), whereas overall reserve increases can worsen the accident year combined ratio. The combined ratio after these reserve movements is known as the "calendar year" result.


title: Lloyd's of London

text: Lloyd's worst results in its long history were in the 1989 through 1991 years, each producing overall losses of over £2bn; the late 1990s were also punctuated by repeated and significant underwriting losses. In 2001 the calendar year result was a 140 per cent combined ratio, driven largely by claims arising out of the World Trade Center attack, reserve increases for prior-year liabilities and deteriorating pricing levels. However, the market subsequently enjoyed profitability in most years except those marked by unusual levels of large natural catastrophes. For example, the 2005 Atlantic hurricane season (which included Hurricane Katrina) drove the Lloyd's overall combined ratio to 112 per cent, while the 2017 Atlantic hurricanes coupled with destructive wildfires in California caused the Lloyd's market to report a 114 per cent combined ratio result in that year.


title: Lloyd's of London

text: In its most recent annual report, for 2021, Lloyd's reported an underwriting profit of £1.74bn, plus a £948m gain on investments to produce an overall pre-tax profit of £2.28bn, compared to a pre-tax loss of £887m in 2020. The 2021 calendar-year combined ratio was 93.5 per cent, which was Lloyd's first profitable result since 2016. Gross premiums written totalled £39.2bn, which was an increase from £35.5bn in 2020, without taking exchange-rate fluctuations into account. Notable losses in the year included Hurricane Ida, the North American winter storm known as 'Storm Uri' and the European floods affecting several countries such as Germany and Belgium.


title: Lloyd's of London

text: The following table details some key financial metrics for the Lloyd's market for the past 10 years, as reported in each year's annual report:


title: Lloyd's of London

text: Lloyd's syndicates write a diverse range of policies, both direct insurance and reinsurance, covering property, casualty, marine, energy, motor, aviation and many other types of risk. Lloyd's also has a unique niche in unusual, specialist business such as kidnap and ransom, fine art, specie, aviation war, satellites, personal accident, bloodstock and other insurances.


title: Lloyd's of London

text: Lloyd's is famous for writing policies to cover famous, unusual, or bizarre events. For example, Lloyd's has insured:


title: Lloyd's of London

text: The present Lloyd's building, at 1 Lime Street, was designed by architect Richard Rogers and was completed in 1986. It stands on the site of the old Roman Forum. The 1925 building's facade survives, appearing strangely stranded with the modern building visible through the gates on the northern side on Leadenhall Street. In 2011 it became a listed building.


title: Lloyd's of London

text: In the main Underwriting Room of Lloyd's stands the "Lutine" bell, salvaged in 1858, which was rung when the fate of a ship "overdue" at its destination port became known. If the ship was safe, the bell would be rung twice; if it had sunk, the bell would be rung once. (This had the practical purpose of immediately stopping the sale or purchase of "overdue" reinsurance on that vessel.) Nowadays it is only rung for ceremonial purposes, such as the visit of a distinguished guest, or for the annual Remembrance Day service and anniversaries of major world events.


title: Lloyd's of London

text: Brokers and underwriters are still normally held to, and apparently prefer, a more formal style of attire than many nearby City of London banks and financial institutions.


title: Economic development

text: In the economics study of the public sector, economic and social development is the process by which the economic well-being and quality of life of a nation, region, local community, or an individual are improved according to targeted goals and objectives.


title: Economic development

text: The term has been used frequently in the 20th and 21st centuries, but the concept has existed in the West for far longer. "Modernization", "Westernization", and especially "industrialization" are other terms often used while discussing economic development. Historically, economic development policies focused on industrialization and infrastructure; since the 1960s, it has increasingly focused on poverty reduction.


title: Economic development

text: Whereas economic development is a policy intervention aiming to improve the well-being of people, economic growth is a phenomenon of market productivity and increases in GDP; economist Amartya Sen describes economic growth as but "one aspect of the process of economic development". Economists primarily focus on the growth aspect and the economy at large, whereas researchers of community economic development concern themselves with socioeconomic development as well.


title: Economic development

text: The precise definition of economic development has been contested: while economists in the 20th century viewed development primarily in terms of economic growth, sociologists instead emphasized broader processes of change and modernization. Development and urban studies scholar Karl Seidman summarizes economic development as "a process of creating and utilizing physical, human, financial, and social assets to generate improved and broadly shared economic well-being and quality of life for a community or region". Daphne Greenwood and Richard Holt distinguish economic development from economic growth on the basis that economic development is a "broadly based and sustainable increase in the overall "standard of living" for individuals within a community", and measures of growth such as per capita income do not necessarily correlate with improvements in quality of life.


title: Economic development

text: Economic development implies economic growth plus progressive changes in certain important variables which determine the well-being of the people, e.g: health, education.


title: Economic development

text: Though the concept's origin is uncertain, some scholars argue that development is closely bound up with the evolution of capitalism and the demise of feudalism. Others link it to the postcolonial state.


title: Economic development

text: Mansell and Wehn also state that economic development has been understood by non-practitioners since the World War II to involve economic growth, namely the increases in per capita income, and (if currently absent) the attainment of a standard of living equivalent to that of industrialized countries. Economic development can also be considered as a static theory that documents the state of an economy at a certain time. According to Schumpeter and Backhaus (2003), the changes in this equilibrium state documented in economic theory can only be caused by intervening factors coming from the outside.


title: Economic development

text: Economic development originated in the post-war period of reconstruction initiated by the United States. In 1949, during his inaugural speech, President Harry Truman identified the development of undeveloped areas as a priority for the west:


title: Economic development

text: There have been several major phases of development theory since 1945. Alexander Gerschenkron argued that the less developed the country is at the outset of economic development (relative to others), the more likely certain conditions are to occur. Hence, all countries do not progress similarly. From the 1940s to the 1960s the state played a large role in promoting industrialization in developing countries, following the idea of modernization theory. This period was followed by a brief period of basic needs development focusing on human capital development and redistribution in the 1970s. Neoliberalism emerged in the 1980s pushing an agenda of free trade and removal of import substitution industrialization policies.


title: Economic development

text: In economics, the study of economic development was borne out of an extension to traditional economics that focused entirely on national product, or the aggregate output of goods and services. Economic development was concerned with the expansion of people's entitlements and their corresponding capabilities, morbidity, nourishment, literacy, education, and other socio-economic indicators. Borne out of the backdrop of Keynesian economics (advocating government intervention), and neoclassical economics (stressing reduced intervention), with the rise of high-growth countries (Singapore, South Korea, Hong Kong) and planned governments (Argentina, Chile, Sudan, Uganda), economic development and more generally development economics emerged amidst these mid-20th century theoretical interpretations of how economies prosper. Also, economist Albert O. Hirschman, a major contributor to development economics, asserted that economic development grew to concentrate on the poor regions of the world, primarily in Africa, Asia and Latin America yet on the outpouring of fundamental ideas and models.


title: Economic development

text: It has also been argued, notably by Asian and European proponents of infrastructure-based development, that systematic, long-term government investments in transportation, housing, education, and healthcare are necessary to ensure sustainable economic growth in emerging countries.


title: Economic development

text: During Robert McNamara's 13 years at the World Bank, he introduced key changes, most notably, shifting the Bank's economic development policies toward targeted poverty reduction. Prior to his tenure at the World Bank, poverty did not receive substantial attention as part of international and national economic development; the focus of development had been on industrialization and infrastructure. Poverty also came to be redefined as a condition faced by people rather than countries. According to Martha Finnemore, the World Bank under McNamara's tenure "sold" states poverty reduction "through a mixture of persuasion and coercion."


title: Economic development

text: The development of a country has been associated with different concepts but generally encompasses economic growth through higher productivity, political systems that represent as accurately as possible the preferences of its citizens, the extension of rights to all social groups and the opportunities to get them and the proper functionality of institutions and organizations that are able to attend more technically and logistically complex tasks (i.e. raise taxes and deliver public services). These processes describe the State's capabilities to manage its economy, polity, society and public administration. Generally, economic development policies attempt to solve issues in these topics.


title: Economic development

text: With this in mind, economic development is typically associated with improvements in a variety of areas or indicators (such as literacy rates, life expectancy, and poverty rates), that may be causes of economic development rather than consequences of specific economic development programs. For example, health and education improvements have been closely related to economic growth, but the causality with economic development may not be obvious. In any case, it is important to not expect that particular economic development programs be able to fix many problems at once as that would be establishing unsurmountable goals for them that are highly unlikely they can achieve. Any development policy should set limited goals and a gradual approach to avoid falling victim to something Prittchet, Woolcock and Andrews call ‘premature load bearing’.


title: Economic development

text: Many times the economic development goals of specific countries cannot be reached because they lack the State's capabilities to do so. For example, if a nation has little capacity to carry out basic functions like security and policing or core service delivery it is unlikely that a program that wants to foster a free-trade zone (special economic zones) or distribute vaccinations to vulnerable populations can accomplish their goals. This has been something overlooked by multiple international organizations, aid programs and even participating governments who attempt to carry out ‘best practices’ from other places in a carbon-copy manner with little success. This isomorphic mimicry –adopting organizational forms that have been successful elsewhere but that only hide institutional dysfunction without solving it on the home country –can contribute to getting countries stuck in ‘capability traps’ where the country does not advance in its development goals. An example of this can be seen through some of the criticisms of foreign aid and its success rate at helping countries develop.


title: Economic development

text: Beyond the incentive compatibility problems that can happen to foreign aid donations –that foreign aid granting countries continue to give it to countries with little results of economic growth but with corrupt leaders that are aligned with the granting countries’ geopolitical interests and agenda –there are problems of fiscal fragility associated to receiving an important amount of government revenues through foreign aid. Governments that can raise a significant amount of revenue from this source are less accountable to their citizens (they are more autonomous) as they have less pressure to legitimately use those resources. Just as it has been documented for countries with an abundant supply of natural resources such as oil, countries whose government budget consists largely of foreign aid donations and not regular taxes are less likely to have incentives to develop effective public institutions. This in turn can undermine the country's efforts to develop.


title: Economic development

text: Contractionary monetary policy is a tool used by central banks to slow down a country’s economic growth. An example would be raising interest rates to decrease lending. In the United States, the use of contractionary monetary policy has increased women’s unemployment. Seguino and Heintz uses a panel dataset for each 50 states with unemployment, labor force participation by race, and annual labor market statistics. In addition, for contractionary monetary policy, they utilize the federal funds rate, the short-term interest rates charged to banks. Seguino and Heintz Seguino concludes that the impact of a one percentage point increase in the federal funds rate relative to white and black women’s unemployment is 0.015 and 0.043, respectively


title: Economic development

text: One growing understanding in economic development is the promotion of regional clusters and a thriving metropolitan economy. In today's global landscape, location is vitally important and becomes a key in competitive advantage.


title: Economic development

text: International trade and exchange rates are key issues in economic development. Currencies are often either under-valued or over-valued, resulting in trade surpluses or deficits. Furthermore, the growth of globalization has linked economic development with trends on international trade and participation in global value chains (GVCs) and international financial markets. The last financial crisis had a huge effect on economies in developing countries. Economist Jayati Ghosh states that it is necessary to make financial markets in developing countries more resilient by providing a variety of financial institutions. This could also add to financial security for small-scale producers.


title: Economic development

text: Economic development has evolved into a professional industry of highly specialized practitioners. The practitioners have two key roles: one is to provide leadership in policy-making, and the other is to administer policy, programs, and projects. Economic development practitioners generally work in public offices on the state, regional, or municipal level, or in public-private partnerships organizations that may be partially funded by local, regional, state, or federal tax money. These economic development organizations function as individual entities and in some cases as departments of local governments. Their role is to seek out new economic opportunities and retain their existing business wealth.


title: Economic development

text: There are numerous other organizations whose primary function is not economic development that work in partnership with economic developers. They include the news media, foundations, utilities, schools, health care providers, faith-based organizations, and colleges, universities, and other education or research institutions.


title: Economic development

text: There are various types of macroeconomic and sociocultural indicators or "metrics" used by economists and geographers to assess the relative economic advancement of a given region or nation. The World Bank's "World Development Indicators" are compiled annually from officially recognized international sources and include national, regional and global estimates.


title: Economic development

text: GDP per capita is gross domestic product divided by mid-year population. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidizes not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources.


title: Economic development

text: European development economists have argued that the existence of modern transportation networks- such as high-speed rail infrastructure constitutes a significant indicator of a country's economic advancement: this perspective is illustrated notably through the Basic Rail Transportation Infrastructure Index (known as BRTI Index) and related models such as the (Modified) Rail Transportation Infrastructure Index (RTI).


title: Economic development

text: In an effort to create an indicator that would help measure gender equality, the UN has created two measures: the Gender-Related Development Index (GDI) and the Gender Empowerment Measure (GEM). These indicators were first introduced in the 1995 UNDP Human Development Report.


title: Economic development

text: The Gender Empowerment Measure (GEM) focuses on aggregating various indicators that focus on capturing the economic, political, and professional gains made by women. The GEM is composed of just three variables: income earning power, share in professional and managerial jobs, and share of parliamentary seats.


title: Economic development

text: The Gender Development (GDI) measures the gender gap in human development achievements. It takes disparity between men and women into account in through three variables, health, knowledge, and living standards.


The 1892 United States presidential election was the 27th quadrennial presidential election, held on Tuesday, November 8, 1892. In a rematch of the closely contested 1888 presidential election, former Democratic President Grover Cleveland defeated incumbent Republican President Benjamin Harrison. Cleveland's victory made him the first and, to date, the only person in American history to be elected to a non-consecutive second presidential term. It was also the first time incumbents were defeated in consecutive elections—the second being Jimmy Carter's defeat of Gerald Ford in 1976, followed by Carter's subsequent loss to Ronald Reagan in 1980. Additionally, Harrison's loss marked the second time an elected president lost the popular vote twice, the first being John Quincy Adams in the 1820s. This feat was not repeated until Donald Trump lost the popular vote in 2016 and 2020.


title: 1892 United States presidential election

text: Though some Republicans opposed Harrison's re-nomination, Harrison defeated James G. Blaine and William McKinley on the first presidential ballot of the 1892 Republican National Convention. Cleveland defeated challenges by David B. Hill and Horace Boies on the first presidential ballot of the 1892 Democratic National Convention, becoming both the first presidential candidate and the first Democrat to win his party's presidential nomination in three elections. Groups from The Grange and the Knights of Labor joined together to form a new party called the Populist Party. It had a ticket led by former Congressman James B. Weaver of Iowa.


text: The campaign centered mainly on economic issues, especially the protectionist 1890 McKinley Tariff. Cleveland ran on a platform of lowering the tariff and opposed the Republicans' 1890 voting rights proposal. Cleveland was also a proponent of the gold standard, while the Republicans and Populists both supported bimetalism.


text: Cleveland swept the Solid South and won several important swing states, taking a majority of the electoral vote and a plurality of the popular vote. Weaver won 8.5% of the popular vote and carried several Western states, while John Bidwell of the Prohibition Party won 2.2% of the popular vote. The Democrats did not win another presidential election until 1912.


text: By the beginning of 1892, many Americans were ready to return to Cleveland's political policies. Although he was the clear frontrunner for the Democratic presidential nomination, he was far from the universal choice of the party's supporters; many, such as the journalists Henry Watterson and Charles Anderson Dana, thought that if he were to attain the nomination, their party would lose in November, but few could challenge him effectively. Though he had remained relatively quiet on the issue of silver versus gold, often deferring to bimetalism, Senate Democrats in January 1891 voted for free coinage of silver. Furious, he sent a letter to Ellery Anderson, who headed the New York Reform Club, to condemn the party's apparent drift towards inflation and agrarian control, the "dangerous and reckless experiment of free, unlimited coinage of silver at our mints." Advisors warned that such statements might alienate potential supporters in the South and West and risk his chances for the nomination, but Cleveland felt that being right on the issue was more important than the nomination. After making his position clear, he worked to focus his campaign on tariff reform, hoping that the silver issue would dissipate.


text: A challenger emerged in the form of David B. Hill, former governor of and incumbent senator from New York. In favor of bimetalism and tariff reform, Hill hoped to make inroads with Cleveland's supporters while appealing to those in the South and Midwest who were not keen on nominating Cleveland for a third consecutive time. Hill had begun to run for the position of president unofficially as early as 1890, and even offered former Postmaster General Donald M. Dickinson his support for the vice-presidential nomination. But he was not able to escape his past association with Tammany Hall, and lack of confidence in his ability to defeat Cleveland for the nomination kept Hill from attaining the support he needed. By the time of the convention, Cleveland could count on the support of a majority of the state Democratic parties, though his native New York remained pledged to Hill.


text: In a narrow first-ballot victory, Cleveland received 617.33 votes, barely 10 more than needed, to 114 for Hill, 103 for Governor Horace Boies of Iowa, a populist and former Republican, and the rest scattered. Although the Cleveland forces preferred Isaac P. Gray from Indiana for vice president, Cleveland directed his own support to the convention favorite, Adlai E. Stevenson I from Illinois. As a supporter of using paper greenbacks and free silver to inflate the currency and alleviate economic distress in rural districts, Stevenson balanced the ticket headed by Cleveland, who supported hard-money and the gold standard. At the same time, it was hoped that his nomination represented a promise not to ignore regulars, and so potentially get Hill and Tammany Hall to support the Democratic ticket to their fullest in the coming election.


text: Benjamin Harrison's administration was widely viewed as unsuccessful, and as a result, Thomas C. Platt (a political boss in New York) and other disaffected party leaders mounted a dump-Harrison movement coalescing around veteran candidate James G. Blaine from Maine, a favorite of Republican party regulars. Blaine had been the Republican nominee in 1884 when he lost to Cleveland.


text: Privately, Harrison did not want to be renominated for the presidency, but he remained opposed to the nomination going to Blaine, who he was convinced intended to run, and thought himself the only candidate capable of preventing that. Blaine, however, did not want another fight for the nomination and a rematch against Cleveland in the general election. His health had begun to fail, and three of his children had recently died (Walker and Alice in 1890, and Emmons in 1892). Blaine refused to run actively, but the cryptic nature of his responses to a draft effort fueled speculation that he was not averse to such a movement. For his part, Harrison curtly demanded that he either renounce his supporters or resign his position as Secretary of State, with Blaine choosing the latter a scant three days before the National Convention. A boom began to build around the "draft Blaine" effort, with supporters hoping to cause a break towards their candidate.


text: Senator John Sherman of Ohio, who had been the leading candidate for the nomination at the 1888 Republican Convention before Harrison won it, was also brought up as a possible challenger. Like Blaine, however, he was averse to another bitter battle for the nomination and, "like the rebels down South, want to be let alone." This inevitably turned attention to Ohio Governor William McKinley, who was indecisive as to his intentions in spite of his ill feelings toward Harrison and his popularity among the Republican base. Although not averse to receiving the nomination, he did not expect to win it either. However, should Blaine and Harrison fail to attain the nomination after a number of ballots, he felt he could be brought forth as a harmony candidate. Despite the urging of Republican power broker Mark Hanna, McKinley did not put himself forward as a potential candidate, afraid of offending Harrison and Blaine's supporters, while also feeling that the coming election would not favor the Republicans.


text: In any case, the president's forces had the nomination locked up by the time delegates met in Minneapolis, Minnesota, on June 7–10, 1892. Richard Thomas of Indiana delivered Harrison's nominating speech. Harrison was nominated on the first ballot with 535.17 votes to 182 for McKinley, 181.83 for Blaine, and the rest scattered. McKinley protested when the Ohio delegation threw its entire vote in his name, despite not being formally nominated, but Joseph B. Foraker, who headed the delegation, managed to silence him on a point of order. With the ballots counted, many observers were surprised at the strength of the McKinley vote, which almost overtook Blaine. Whitelaw Reid of New York, editor of the "New York Tribune" and recent United States Ambassador to France, was nominated for vice president. The incumbent vice president, Levi P. Morton, was supported by many at the convention, including Reid himself, but did not wish to serve another term. Harrison also did not want Morton on the ticket.


text: In 1891, the American farmers' alliances met with delegates from labor and reform groups in Cincinnati, Ohio, to discuss the formation of a new political party. They formed the People's Party, commonly known as the "Populists", a year later in St. Louis, Missouri.


text: Leonidas L. Polk was the initial frontrunner for the presidential nomination. He had been instrumental in the party's formation and held great appeal with its agrarian base, but he unexpectedly died while in Washington, D.C., on June 11. Another candidate mentioned frequently for the nomination was Walter Q. Gresham, an appellate judge who had made a number of rulings against the railroads that made him a favorite of some farmer and labor groups, and it was felt that his rather dignified image would make the Populists appear as more than minor contenders. Both Democrats and Republicans feared his nomination for this reason, and while Gresham toyed with the idea, he ultimately was not ready to make a complete break with the two parties, declining petitions for his nomination right up to and during the Populist Convention. Later he would endorse Grover Cleveland for the presidency.


text: At the first Populist national convention in Omaha, Nebraska, in July 1892, James B. Weaver from Iowa was nominated for president on the first ballot, now lacking any serious opposition. While his nomination brought with it significant campaigning experience from over several decades, he also had a longer tract of history for which Republicans and Democrats could criticize him, and he also alienated many potential supporters in the South, having participated in Sherman's March to the Sea. James G. Field from Virginia was nominated for vice-president to try and rectify this problem while also attaining the regional balance often seen in Republican and Democratic tickets.


text: The Populist platform called for nationalization of the telegraph, telephone, and railroads, free coinage of silver, a graduated income tax, and creation of postal savings banks.


text: The sixth Prohibition Party National Convention assembled in Music Hall in Cincinnati, Ohio. There were 972 delegates present from all states except Louisiana and South Carolina.


text: Two major stories about the convention loomed before it assembled. In the first place, some members of the national committee sought to merge the Prohibition and Populist Parties. While there appeared a likelihood that the merger would materialize, it was clear that it was not going to happen by the time that the convention convened. Secondly, the southern states sent a number of black delegates. Cincinnati hotels refused to serve meals to blacks and whites at the same time, and several hotels refused service to the black delegates altogether.


text: The convention nominated John Bidwell from California for president on the first ballot. Prior to the convention, the race was thought to be close between Bidwell and William Jennings Demorest, but the New York delegation became irritated with Demorest and voted for Bidwell 73–7. James B. Cranfill from Texas was nominated for vice-president on the first ballot with 417 votes to 351 for Joshua Levering from Maryland and 45 for others.


text: The first Socialist Labor Party National Convention assembled in New York City and, despite running on a platform that called for the abolition of the positions of president and vice-president, decided to nominate candidates for those positions: Simon Wing from Massachusetts for president and Charles Matchett from New York for vice-president. They were on the ballot in five states: Connecticut, Massachusetts, New Jersey, New York, and Pennsylvania.


text: The tariff issue dominated this rather lackluster campaign. Harrison defended the protectionist McKinley Tariff passed during his term. For his part, Cleveland assured voters that he opposed absolute free trade and would continue his campaign for a reduction in the tariff. Cleveland also denounced the Lodge Bill, a voting rights bill that sought to protect the rights of African American voters in the South. William McKinley campaigned extensively for Harrison, setting the stage for his own run four years later.


text: The campaign took a somber turn when, in October, First Lady Caroline Harrison died. Despite the ill health that had plagued Mrs. Harrison since her youth and had worsened in the last decade, she often accompanied Mr. Harrison on official travels. On one such trip, to California in the spring of 1891, she caught a cold. It quickly deepened into her chest, and she was eventually diagnosed with tuberculosis. A summer in the Adirondack Mountains failed to restore her to health. An invalid the last six months of her life, she died in the White House on October 25, 1892, just two weeks before the national election. As a result, all of the candidates ceased campaigning.


text: The margin in the popular vote for Cleveland was 400,000, the largest since Grant's re-election in 1872. The Democrats won the presidency and both houses of Congress for the first time since 1856. President Harrison's re-election bid was a decisive loss in both the popular and electoral count, unlike President Cleveland's re-election bid four years earlier, in which he won the popular vote, but lost the electoral vote.


text: Cleveland was the third of only five presidents to win re-election with a smaller percentage of the popular vote than in previous elections, although in the two prior such incidents — James Madison in 1812 and Andrew Jackson in 1832 — not all states held popular elections and a similar vote decrease would happen again for Franklin D. Roosevelt in 1940 and 1944 and Barack Obama in 2012. Ironically, Cleveland saw his popular support decrease not only from his electoral win in 1884 but also from his electoral loss in 1888.


text: At the county level, Cleveland fared much better than Harrison. The Republicans' vote was not nearly as widespread as the Democrats'. In 1892, it was still a sectionally based party mainly situated in the East, Midwest, and West and was barely visible south of the Mason–Dixon line. In the South, the party was holding on in only a few counties. In East Tennessee and tidewater Virginia, the vote at the county level showed some strength, but it barely existed in Alabama, Mississippi, and Texas.


text: In a continuation of its collapse there during the 1890 Congressional elections, the Republican Party even struggled in its Midwestern strongholds, where general electoral troubles from economic woes were acutely exacerbated by the promotion of temperance laws and, in Wisconsin and Illinois, the aggressive support of state politicians for English-only compulsory education laws. Such policies, which particularly in the case of the latter were associated with an upwelling of nativist and anti-Catholic attitudes amongst their supporters, resulted in the defection of large sections of immigrant communities, especially Germans, to the Democratic Party. Cleveland carried Wisconsin and Illinois with their 36 combined electoral votes, a Democratic victory not seen in those states since 1852 and 1856 respectively, and which would not be repeated until Woodrow Wilson's election in 1912. While not as dramatic a loss as in 1890, it would take until the next election cycle for more moderate Republican leaders to pick up the pieces left by the reformist crusaders and bring alienated immigrants back to the fold.


text: Of the 2,683 counties making returns, Cleveland won in 1,389 (51.77%), Harrison carried 1,017 (37.91%), while Weaver placed first in 276 (10.29%). One county (0.04%) split evenly between Cleveland and Harrison.


text: Populist James B. Weaver, calling for free coinage of silver and an inflationary monetary policy, received such strong support in the West that he became the only third-party nominee between 1860 and 1912 to carry a single state. The Democratic Party did not have a presidential ticket on the ballot in the states of Colorado, Idaho, Kansas, North Dakota, or Wyoming, and Weaver won the first four of these states. Weaver also performed well in the South as he won counties in Alabama, Georgia, Mississippi, North Carolina, and Texas. Populists did best in Alabama, where electoral chicanery probably carried the day for the Democrats.


text: The Prohibition ticket received 270,879 votes, or 2.2% nationwide. It was the largest total vote and highest percentage of the vote received by any Prohibition Party national ticket.


text: Wyoming, having attained statehood two years earlier, became the first state to allow women to vote in a presidential election since 1804. (Women in New Jersey had the right to vote under the state's original constitution, but this right was rescinded in 1807.)


text: Wyoming was also one of six states (along with North Dakota, South Dakota, Montana, Washington, and Idaho) participating in their first presidential election. This was the most new states voting since the first election.


text: The election witnessed many states splitting their electoral votes. Electors from the state of Michigan were selected using the congressional district method (the winner in each congressional district wins one electoral vote, the winner of the state wins two electoral votes). This resulted in a split between the Republican and Democratic electors: nine for Harrison and five for Cleveland. In Oregon, the direct election of presidential electors combined with the fact that one Weaver elector was endorsed by the Democratic Party and elected as a Fusionist, resulted in a split between the Republican and Populist electors: three for Harrison and one for Weaver. In California, the direct election of presidential electors combined with the close race resulted in a split between the Republican and Democratic electors: eight for Cleveland and one for Harrison. In Ohio, the direct election of presidential electors combined with the close race resulted in a split between the Republican and Democratic electors: 22 for Harrison and one for Cleveland. In North Dakota, two electors from the Democratic-Populist Fusion ticket won and one Republican Elector won. This created a split delegation of electors: one for Weaver, one for Harrison, and one for Cleveland.


text: Source: Data from Walter Dean Burnham, "Presidential ballots, 1836–1892" (Johns Hopkins University Press, 1955) pp 247–57.


title: Limit (mathematics)

text: In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.


title: Limit (mathematics)

text: The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory.


title: Limit (mathematics)

text: and is read as "the limit of of as approaches equals ". The fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (→ or formula_2), as in


title: Limit (mathematics)

text: Grégoire de Saint-Vincent gave the first definition of limit (terminus) of a geometric series in his work "Opus Geometricum" (1647): "The "terminus" of a progression is the end of the series, which none progression can reach, even not if she is continued in infinity, but which she can approach nearer than a given segment."


title: Limit (mathematics)

text: The modern definition of a limit goes back to Bernard Bolzano who, in 1817, introduced the basics of the epsilon-delta technique to define continuous functions. However, his work was not known during his lifetime.


title: Limit (mathematics)

text: Augustin-Louis Cauchy in 1821, followed by Karl Weierstrass, formalized the definition of the limit of a function which became known as the (ε, δ)-definition of limit.


title: Limit (mathematics)

text: The modern notation of placing the arrow below the limit symbol is due to G. H. Hardy, who introduced it in his book "A Course of Pure Mathematics" in 1908.


title: Limit (mathematics)

text: The expression 0.999... should be interpreted as the limit of the sequence 0.9, 0.99, 0.999, ... and so on. This sequence can be rigorously shown to have the limit 1, and therefore this expression is meaningfully interpreted as having the value 1.


title: Limit (mathematics)

text: Formally, suppose is a sequence of real numbers. When the limit of the sequence exists, the real number is the "limit" of this sequence if and only if for every real number , there exists a natural number such that for all , we have .


title: Limit (mathematics)

text: The formal definition intuitively means that eventually, all elements of the sequence get arbitrarily close to the limit, since the absolute value is the distance between and .


title: Limit (mathematics)

text: Not every sequence has a limit. If it does, then it is called "convergent", and if it does not, then it is "divergent". One can show that a convergent sequence has only one limit.


title: Limit (mathematics)

text: The limit of a sequence and the limit of a function are closely related. On one hand, the limit as approaches infinity of a sequence is simply the limit at infinity of a function —defined on the natural numbers . On the other hand, if is the domain of a function and if the limit as approaches infinity of is for "every" arbitrary sequence of points in which converges to , then the limit of the function as approaches is . One such sequence would be .


title: Limit (mathematics)

text: There is also a notion of having a limit "at infinity", as opposed to at some finite formula_6. A sequence formula_11 is said to "tend to infinity" if, for each real number formula_12, known as the bound, there exists an integer formula_13 such that for each formula_14,


title: Limit (mathematics)

text: That is, for every possible bound, the magnitude of the sequence eventually exceeds the bound. This is often written formula_16 or simply formula_17. Such sequences are also called unbounded.


title: Limit (mathematics)

text: It is possible for a sequence to be divergent, but not tend to infinity. Such sequences are called oscillatory. An example of an oscillatory sequence is formula_18.


title: Limit (mathematics)

text: For the real numbers, there are corresponding notions of tending to positive infinity and negative infinity, by removing the modulus sign from the above definition:


title: Limit (mathematics)

text: Sequences which do not tend to infinity are called bounded. Sequences which do not tend to positive infinity are called bounded above, while those which do not tend to negative infinity are bounded below.


title: Limit (mathematics)

text: The discussion of sequences above is for sequences of real numbers. The notion of limits can be defined for sequences valued in more abstract spaces. One example of a more abstract space is metric spaces. If formula_21 is a metric space with distance function formula_22, and formula_23 is a sequence in formula_21, then the limit (when it exists) of the sequence is an element formula_25 such that, given formula_26, there exists an formula_13 such that for each formula_14, the equation


title: Limit (mathematics)

text: An important example is the space of formula_32-dimensional real vectors, with elements formula_33 where each of the formula_34 are real, an example of a suitable distance function is the Euclidean distance, defined by


title: Limit (mathematics)

text: In some sense the "most" abstract space in which limits can be defined are topological spaces. If formula_39 is a topological space with topology formula_40, and formula_23 is a sequence in formula_39, then the limit (when it exists) of the sequence is a point formula_43 such that, given a (open) neighborhood formula_44 of formula_45, there exists an formula_13 such that for every formula_14,


title: Limit (mathematics)

text: This section deals with the idea of limits of sequences of functions, not to be confused with the idea of limits of functions, discussed below.


title: Limit (mathematics)

text: The field of functional analysis partly seeks to identify useful notions of convergence on function spaces. For example, consider the space of functions from a generic set formula_49 to formula_50. Given a sequence of functions formula_51 such that each is a function formula_52, suppose that there exists a function such that for each formula_53,


title: Limit (mathematics)

text: Then the sequence formula_55 is said to converge pointwise to formula_4. However, such sequences can exhibit unexpected behavior. For example, it is possible to construct a sequence of continuous functions which has a discontinuous pointwise limit.


title: Limit (mathematics)

text: Another notion of convergence is uniform convergence. The uniform distance between two functions formula_57 is the maximum difference between the two functions as the argument formula_53 is varied. That is,


title: Limit (mathematics)

text: Then the sequence formula_55 is said to uniformly converge or have a uniform limit of formula_4 if formula_62 with respect to this distance. The uniform limit has "nicer" properties than the pointwise limit. For example, the uniform limit of a sequence of continuous functions is continuous.


title: Limit (mathematics)

text: Many different notions of convergence can be defined on function spaces. This is sometimes dependent on the regularity of the space. Prominent examples of function spaces with some notion of convergence are Lp spaces and Sobolev space.


title: Limit (mathematics)

text: means that can be made to be as close to as desired, by making sufficiently close to . In that case, the above equation can be read as "the limit of of , as approaches , is ".


title: Limit (mathematics)

text: Formally, the definition of the "limit of formula_64 as formula_5 approaches formula_8" is given as follows. The limit is a real number formula_6 so that, given an arbitrary real number formula_26 (thought of as the "error"), there is a formula_69 such that, for any formula_5 satisfying formula_71, it holds that formula_72. This is known as the (ε, δ)-definition of limit.


title: Limit (mathematics)

text: The inequality formula_73 is used to exclude formula_8 from the set of points under consideration, but some authors do not include this in their definition of limits, replacing formula_71 with simply formula_76. This replacement is equivalent to additionally requiring that formula_4 be continuous at formula_8.


title: Limit (mathematics)

text: It can be proven that there is an equivalent definition which makes manifest the connection between limits of sequences and limits of functions. The equivalent definition is given as follows. First observe that for every sequence formula_79 in the domain of formula_4, there is an associated sequence formula_81, the image of the sequence under formula_4. The limit is a real number formula_6 so that, for "all" sequences formula_84, the associated sequence formula_85.


title: Limit (mathematics)

text: It is possible to define the notion of having a limit "from above" or "left limit", and a notion of a limit "from below" or "right limit". These need not agree. An example is given by the positive indicator function, formula_86, defined such that formula_87 if formula_88, and formula_89 if formula_90. At formula_91, the function has a "left limit" of 0, a "right limit" of 1, and its limit does not exist.


title: Limit (mathematics)

text: In this expression, the infinity is considered to be signed: either formula_94 or formula_95. The "limit of f as x tends to positive infinity" is defined as follows. It is a real number formula_6 such that, given any real formula_26, there exists an formula_12 so that if formula_99, formula_100. Equivalently, for any sequence formula_101, we have formula_85.


title: Limit (mathematics)

text: The definition is given as follows. Given any real number formula_105, there is a formula_69 so that for formula_71, the absolute value of the function formula_108. Equivalently, for any sequence formula_84, the sequence formula_110.


title: Limit (mathematics)

text: In non-standard analysis (which involves a hyperreal enlargement of the number system), the limit of a sequence formula_111 can be expressed as the standard part of the value formula_112 of the natural extension of the sequence at an infinite hypernatural index "n=H". Thus,


title: Limit (mathematics)

text: Here, the standard part function "st" rounds off each finite hyperreal number to the nearest real number (the difference between them is infinitesimal). This formalizes the natural intuition that for "very large" values of the index, the terms in the sequence are "very close" to the limit value of the sequence. Conversely, the standard part of a hyperreal formula_114 represented in the ultrapower construction by a Cauchy sequence formula_111, is simply the limit of that sequence:


title: Limit (mathematics)

text: Let formula_117 be a sequence in a topological space formula_39. For concreteness, formula_39 can be thought of as formula_50, but the definitions hold more generally. The limit set is the set of points such that if there is a convergent subsequence formula_121 with formula_122, then formula_45 belongs to the limit set. In this context, such an formula_45 is sometimes called a limit point.


title: Limit (mathematics)

text: A use of this notion is to characterize the "long-term behavior" of oscillatory sequences. For example, consider the sequence formula_18. Starting from n=1, the first few terms of this sequence are formula_126. It can be checked that it is oscillatory, so has no limit, but has limit points formula_127.


title: Limit (mathematics)

text: This notion is used in dynamical systems, to study limits of trajectories. Defining a trajectory to be a function formula_128, the point formula_129 is thought of as the "position" of the trajectory at "time" formula_130. The limit set of a trajectory is defined as follows. To any sequence of increasing times formula_131, there is an associated sequence of positions formula_132. If formula_5 is the limit set of the sequence formula_79 for any sequence of increasing times, then formula_5 is a limit set of the trajectory.


title: Limit (mathematics)

text: Technically, this is the formula_136-limit set. The corresponding limit set for sequences of decreasing time is called the formula_137-limit set.


title: Limit (mathematics)

text: An illustrative example is the circle trajectory: formula_138. This has no unique limit, but for each formula_139, the point formula_140 is a limit point, given by the sequence of times formula_141. But the limit points need not be attained on the trajectory. The trajectory formula_142 also has the unit circle as its limit set.


title: Limit (mathematics)

text: A particular expression of interest which is formalized as the limit of a sequence is sums of infinite series. These are "infinite sums" of real numbers, generally written as


title: Limit (mathematics)

text: This is defined through limits as follows: given a sequence of real numbers formula_11, the sequence of partial sums is defined by


title: Limit (mathematics)

text: If the limit of the sequence formula_146 exists, the value of the expression formula_147 is defined to be the limit. Otherwise, the series is said to be divergent.


title: Limit (mathematics)

text: However, while for sequences there is essentially a unique notion of convergence, for series there are different notions of convergence. This is due to the fact that the expression formula_147 does not discriminate between different orderings of the sequence formula_11, while the convergence properties of the sequence of partial sums "can" depend on the ordering of the sequence.


title: Limit (mathematics)

text: A series which converges for all orderings is called unconditionally convergent. It can be proven to be equivalent to absolute convergence. This is defined as follows. A series is absolutely convergent if formula_152 is well defined. Furthermore, all possible orderings give the same value.


title: Limit (mathematics)

text: Otherwise, the series is conditionally convergent. A surprising result for conditionally convergent series is the Riemann series theorem: depending on the ordering, the partial sums can be made to converge to any real number, as well as formula_153.


title: Limit (mathematics)

text: A useful application of the theory of sums of series is for power series. These are sums of series of the form


title: Limit (mathematics)

text: Often formula_155 is thought of as a complex number, and a suitable notion of convergence of complex sequences is needed. The set of values of formula_156 for which the series sum converges is a circle, with its radius known as the radius of convergence.


title: Limit (mathematics)

text: The above definition of a limit is true even if formula_157. Indeed, the function need not even be defined at . However, if formula_158 is defined and is equal to formula_6, then the function is said to be continuous at the point formula_8.


title: Limit (mathematics)

text: Equivalently, the function is continuous at formula_8 if formula_162 as formula_163, or in terms of sequences, whenever formula_84, then formula_165.


title: Limit (mathematics)

text: then is not defined (see Indeterminate form), yet as moves arbitrarily close to 1, correspondingly approaches 2:


title: Limit (mathematics)

text: In addition to limits at finite values, functions can also have limits at infinity. For example, consider the function


title: Limit (mathematics)

text: As becomes extremely large, the value of approaches , and the value of can be made as close to as one could wish—by making sufficiently large. So in this case, the limit of as approaches infinity is , or in mathematical notation,formula_173


title: Limit (mathematics)

text: An important class of functions when considering limits are continuous functions. These are precisely those functions which "preserve limits", in the sense that if formula_4 is a continuous function, then whenever formula_30 in the domain of formula_4, then the limit formula_177 exists and furthermore is formula_178.


title: Limit (mathematics)

text: Let formula_179 be a continuous function between topological spaces formula_39 and formula_181. By definition, for each open set formula_182 in formula_181, the preimage formula_184 is open in formula_39.


title: Limit (mathematics)

text: Now suppose formula_30 is a sequence with limit formula_45 in formula_39. Then formula_177 is a sequence in formula_181, and formula_178 is some point.


title: Limit (mathematics)

text: Choose a neighborhood formula_182 of formula_178. Then formula_184 is an open set (by continuity of formula_4) which in particular contains formula_45, and therefore formula_184 is a neighborhood of formula_45. By the convergence of formula_199 to formula_45, there exists an formula_13 such that for formula_14, we have formula_203.


title: Limit (mathematics)

text: Then applying formula_4 to both sides gives that, for the same formula_13, for each formula_14 we have formula_207. Originally formula_182 was an arbitrary neighborhood of formula_178, so formula_210. This concludes the proof.


title: Limit (mathematics)

text: In real analysis, for the more concrete case of real-valued functions defined on a subset formula_211, that is, formula_212, a continuous function may also be defined as a function which is continuous at every point of its domain.


title: Limit (mathematics)

text: In topology, limits are used to define limit points of a subset of a topological space, which in turn give a useful characterization of closed sets.


title: Limit (mathematics)

text: In a topological space formula_39, consider a subset formula_214. A point formula_45 is called a limit point if there is a sequence formula_11 in formula_217 such that formula_30.


title: Limit (mathematics)

text: The reason why formula_11 is defined to be in formula_217 rather than just formula_214 is illustrated by the following example. Take formula_222 and formula_223. Then formula_224, and therefore is the limit of the constant sequence formula_225. But formula_226 is not a limit point of formula_214.


title: Limit (mathematics)

text: A closed set, which is defined to be the complement of an open set, is equivalently any set formula_228 which contains all its limit points.


title: Limit (mathematics)

text: The derivative is defined formally as a limit. In the scope of real analysis, the derivative is first defined for real functions formula_4 defined on a subset formula_211. The derivative at formula_53 is defined as follows. If the limit


title: Limit (mathematics)

text: For sequences of real numbers, a number of properties can be proven. Suppose formula_11 and formula_239 are two sequences converging to formula_45 and formula_241 respectively.


title: Limit (mathematics)

text: A property of convergent sequences of real numbers is that they are Cauchy sequences. The definition of a Cauchy sequence formula_11 is that for every real number formula_26, there is an formula_13 such that whenever formula_251,


title: Limit (mathematics)

text: Informally, for any arbitrarily small error formula_253, it is possible to find an interval of diameter formula_253 such that eventually the sequence is contained within the interval.


title: Limit (mathematics)

text: Cauchy sequences are closely related to convergent sequences. In fact, for sequences of real numbers they are equivalent: any Cauchy sequence is convergent.


title: Limit (mathematics)

text: In general metric spaces, it continues to hold that convergent sequences are also Cauchy. But the converse is not true: not every Cauchy sequence is convergent in a general metric space. A classic counterexample is the rational numbers, formula_255, with the usual distance. The sequence of decimal approximations to formula_256, truncated at the formula_32th decimal place is a Cauchy sequence, but "does not converge in" formula_255.


title: Limit (mathematics)

text: A metric space in which every Cauchy sequence is also convergent, that is, Cauchy sequences are equivalent to convergent sequences, is known as a complete metric space.


title: Limit (mathematics)

text: One reason Cauchy sequences can be "easier to work with" than convergent sequences is that they are a property of the sequence formula_11 alone, while convergent sequences require not just the sequence formula_11 but also the limit of the sequence formula_45.


title: Limit (mathematics)

text: Beyond whether or not a sequence formula_11 converges to a limit formula_45, it is possible to describe how fast a sequence converges to a limit. One way to quantify this is using the order of convergence of a sequence.


title: Limit (mathematics)

text: A formal definition of order of convergence can be stated as follows. Suppose formula_117 is a sequence of real numbers which is convergent with limit formula_45. Furthermore, formula_266 for all formula_32. If positive constants formula_268 and formula_269 exist such that


title: Limit (mathematics)

text: then formula_271 is said to converge to formula_272 with order of convergence formula_269. The constant formula_268 is known as the asymptotic error constant.


title: Limit (mathematics)

text: Limits can be difficult to compute. There exist limit expressions whose modulus of convergence is undecidable. In recursion theory, the limit lemma proves that it is possible to encode undecidable problems using limits.


title: Limit (mathematics)

text: There are several theorems or tests that indicate whether the limit exists. These are known as convergence tests. Examples include the ratio test and the squeeze theorem. However they may not tell how to compute the limit.


title: Jannah

text: In Islam, Jannah (, pl. "jannāt",lit. "paradise, garden", is the final abode of the righteous. According to one count, the word appears 147 times in the Quran. Belief in the afterlife is one of the six articles of faith in Sunni and Twelver Shi'ism, a place where "believers" ("Mumin") will enjoy pleasure, while the unbelievers ("Kafir") will suffer in "Jahannam". Both "Jannah" and "Jahannam" are believed to have several levels, in both cases, the higher the level, the more desirable -- in "Jannah" the higher the prestige and pleasure, in "Jahannam" the less the suffering. The afterlife experiences are described as physical, psychic and spiritual. Jannah is described with physical pleasures such as gardens, houris, wine that has no aftereffects, and "divine pleasure". Their reward of pleasure will vary according to the righteousness of the person. The characteristics of "Jannah" often have direct parallels with those of "Jahannam". The pleasure and delights of "Jannah" described in the Quran, are matched by the excruciating pain and horror of "Jahannam".


title: Jannah

text: Jannah is also referred to as the abode of Adam and Eve, before they have been expelled. Most Muslims hold that Jannah (as well as "Jahannam") coexist with the temporal world, rather than being created after Judgement Day. Although humans may not pass the boundaries to the otherworld, the otherworld may interact with the temporal world of humans.


title: Jannah

text: "Jannah" is found frequently in the Qur'an (2:30, 78:12) and often translated as "Heaven" in the sense of an abode where believers are rewarded in afterlife. Another word, "samāʾ" (usually pl. "samāwāt") is also found frequently in the Quran and translated as "heaven", but in the sense of the sky above or celestial sphere. (It is often used in the phrase "as-samawat wal-ard" "the heavens and the earth", an example being Q.38:10.) The Quran describes both "samāʾ" and "jannah" as being above us.


title: Jannah

text: "Jannah" is also frequently translated as "paradise". But another term with a more direct connection to that term is also found. ' (Arabic: ), the literal term meaning paradise was borrowed from the Persian word ' (), being also the source of the English word "paradise", is used in verses Q.18:107 and Q.23:11. "Firdaus" also designates the highest level of heaven.


title: Jannah

text: In contrast to "jannah", the words "", ', ', "", and other terms are used to refer to the concept of hell. There are many words in the Arabic language for both Heaven and Hell and those words also appear in the Quran and hadith. Most of them have become part of the Islamic belief.


title: Jannah

text: Scholars do not all agree on who will end up in Jannah, and the criteria for whether or not they will. Issues include whether all Muslims, even those who've committed major sins, will end up in Jannah; whether any non-Muslims will go there or all go to Jahannam.


title: Jannah

text: The Quran specifies the qualities for those allowed to inhabit Jannah (according to Smith and Haddad) as: "those who refrain from doing evil, keep their duty, have faith in God's revelations, do good works, are truthful, penitent, heedful, and contrite of heart, those who feed the needy and orphans and who are prisoners for God's sake."


title: Jannah

text: Another source (Sebastian Günther and Todd Lawson) gives as the basic criterion for salvation in the afterlife more detail on articles of faith: the belief in the oneness of God (), angels, revealed books, messengers, as well as repentance to God, and doing good deeds ("amal salih"). All these qualities are qualified by the doctrine that ultimately salvation can only be attained through God's judgment.


title: Jannah

text: The idea that jinn as well as humans could find salvation was widely accepted, based on the Quran (Q.55:74) where the saved are promised maidens "untouched before by either men or jinn" -- suggesting to classical scholars al-Suyūṭī and al-Majlisī that jinn also are provided their own kind of houri maidens in paradise. Like humans, their destiny in the hereafter depends on whether they accept God's guidance. Angels, on the other hand, because they are not subject to desire and so are not subject to temptation, work in paradise serving the "blessed" (humans and jinn) guiding them, officiating marriages, conveying messages, praising them, etc.


title: Jannah

text: Muslim scholars disagree about exact criteria for salvation of Muslim and non-Muslim. Although most agree that Muslims will be finally saved -- "shahids" (martyrs) who die in battle, are expected to enter paradise immediately after death -- non-Muslims are another matter.


title: Jannah

text: Those arguing against non-Muslim salvation regard this verse to have applied only until the arrival of Muhammad, after which it was abrogated by another verse:


title: Jannah

text: Historically the Ash'ari school of theology was known for having an optimistic perspective on salvation for Muslims, but a very pessimistic view of those who heard about Muhammad and his character, yet rejected him. The Maturidi school also generally agreed that even sinners among Muslims would eventually enter paradise, but its unclear whether they thought only Muslim would go to Jannah, or if non-Muslims who understood and obeyed "God's universal law" would be saved also. The Muʿtazila school held that free will and individual accountability was necessary for Divine justice, thus rejecting the idea of intercession ("Shafa'a") by Muhammad on behalf of sinners. Unlike other schools it believed Jannah and Jahannam would be created only after Judgement Day. Like most Sunni, Shia Islam hold that all Muslims will eventually go to Jannah,


title: Jannah

text: and like the Ash'ari school, believe heedless and stubborn unbelievers will go to hell, while those ignorant of the truth of Islam but "truthful to their own religion", will not. Modernist scholars Muhammad Abduh and Rashid Rida rejected the notion that the People of the Book are excluded from Jannah, referring to another verse.


title: Jannah

text: Sources on Jannah include the Quran, Islamic traditions, creeds, Quranic commentaries ("tafsir") and "other theological writing".


title: Jannah

text: "Third Islamic century traditionalists amplified the eschatological material enormously particularly in areas on where "the Quran is relatively silent" about the nature of Jannah. Some of the more popular Sunni manuals of eschatology are "Kitāb al-rūḥ" of Ibn Qayyim al-Jawzīyaand "al-Durra al-fākhira ft kashf 'ulūm al-ākhira" of Abǖ Ḥāmid al-Ghazālī.


title: Jannah

text: Inside Jannah, the Quran says the saved "will have whatever they wish for, forever"; (Q.25:16). Other verses give more specific descriptions of the delights of paradise:


title: Jannah

text: ... Those ˹believers˺ will recline on furnishings lined with rich brocade. And the fruit of both Gardens will hang within reach.<br>


title: Jannah

text: ... In both ˹Gardens˺ will be maidens of modest gaze, who no human or jinn has ever touched before.<br>


title: Jannah

text: Choirs of angels will sing in Arabic (the only language used in paradise), the streets will be as familiar as those of the dwellers' own countries, inhabitants will eat and drink 100 times more than earthly bodies could hold and will enjoy it 100 times more, their rooms will have thick carpets and brocade sofas, on Fridays they will go to a market to receive new clothing to enhance their beauty, they will not suffer bodily ailments or be subject to functions such as sleeping, spitting, or excreting; they will be forever young.


title: Jannah

text: As the gates of Jannah are opened for the arrival of the saved into Jannah they will be greeted (Q.39:73) by angels announcing, "Peace be upon you, because ye have endured with patience; how excellent a reward is paradise!" ().


title: Jannah

text: Inside there will be neither too much heat nor bitter cold; there will be fountains (), abundant shade from spreading tree branches green with foliage (Q.53:14-16, also ). They will be passed a cup () full of wine "wherefrom they will get [no] aching of the head” (hangovers) [Q.56:19], and "which leads to no idle talk or sinfulness" (),


title: Jannah

text: and every meat () and trees from which an unceasing supply of fruits grow (), "that looks similar ˹but tastes different˺";() adornment with golden and pearl bracelets () and green garments of fine silk and brocade (); attended upon by [ghulman] (), servant-boys (eternal youths (56:17, 74:19)) like spotless pearls ().


title: Jannah

text: While the Quran never mentions God being in the Garden, the faithful are promised the opportunity to gaze upon His face, something the inhabitants of the Fire will be deprived of.


title: Jannah

text: Inhabitants will rejoice in the company of any parents, spouses, and children who were admitted to paradise () —conversing and recalling the past.


title: Jannah

text: While the Quran is full of "graphic" descriptions of the "physical pleasures" for the inhabitants of the Garden, it also states that the "acceptance


title: Jannah

text: ["riḍwān"] from God" felt by the inhabitants "is greater" than the pleasure of the Gardens (Q.9:72), the true beauty of paradise, the greatest of all rewards, surpassing all other joys. On the day on which God brings the elect near to his throne (""), "some faces shall be shining in contemplating their Lord".


title: Jannah

text: The visit is described as Muhammad leading the men and Fatimah leading the women to approach the Throne, "which is described as a huge esplanade of musk". As "the veil of light before the Throne lifts, God appears with the radiance of the full moon, and His voice can be heard saying, 'Peace be upon you.'"


title: Jannah

text: Hadith include stories of the saved being served an enormous feast where "God Himself is present to offer to His faithful ones delicacies kneaded into a kind of pancake". In another series of narratives, God personally invites the inhabitants of Jannah "to visit with Him every Friday".


title: Jannah

text: "Perhaps no aspect of Islamic eschatology has so captured the imagination" of both "Muslims and non-Muslims" as houri ("ḥūr"). Men will get untouched Houri in paradise (), virgin companions of equal age () and have large, beautiful eyes (). Houri have occasioned "spectacular elaborations" by later Islamic eschatological writers, but also "some derision by insensitive Western observers and critics of Islam".


title: Jannah

text: The Quran also states the saved "will have pure spouses," (without indicating gender) (, ), accompanied by any children that did not go to Jahannam (), and attended to by servant-boys with the spotless appearance similar to a protected pearls ().


title: Jannah

text: Despite the Quranic description above, Houris have been described as women who will accompany faithful Muslims in Paradise. Muslim scholars differ as to whether they refer to the believing women of this world or a separate creation, with the majority opting for the latter.


title: Jannah

text: The Qur'an describes paradise as a "great kingdom" (Q.76:20) stretching out over and above the entire world, and "lofty" (Q.69:22).


title: Jannah

text: Paradise is "as vast as the heavens and the earth" (Q.3:133). There are four rivers: one each of water, milk, honey, and wine (). (They were later identified as "Kawthar", "Kafur", "Tasnim", and "Salsabil".)


title: Jannah

text: Despite the details given in the Quran about Jannah/Garden, "nowhere" is there found "an ordered picture of the structure" of the abode. "For the most part Islamic theology has not concerned itself with questions about the location and structure of the Garden and the Fire on the understanding that only God knows these particulars."


title: Jannah

text: Many sources agree that paradise has "various degrees and levels". One conservative Salafi source, quotes as evidence a sahih hadith where Muhammad reassures the mother of a martyr, “O Umm Haarithah, there are gardens in Paradise ... and your son has attained the highest "Firdaws"”, indicating a hierarchy of levels, but does not how many there are.


title: Jannah

text: On the basis of "several scriptural suggestions", scholars have created "a very detailed structure" of paradise, but there is more than one, and not all of the traditions on location of paradise and hell "are easily pictured or indeed mutually reconcilable".


title: Jannah

text: For example, Q.23:17 states: "We created above you seven paths [Ṭarā'iq]", from which is drawn a heaven of seven tiers (which is also "a structure familiar to Middle Eastern cosmogony since the early Babylonian days"). Another school of thought insists Jannah actually has "eight layers or realms" as the Quran gives "eight different names ... for the abode of the blessed".


title: Jannah

text: Some descriptions of Jannah/the Garden indicate that the most spacious and highest part of the Garden, is Firdaws which is directly under the Throne, and the place from which the four rivers of Paradise flow. Others say the uppermost portion is either the Garden of Eden or 'Iliyi, and that is the second level from the top.


title: Jannah

text: Another possibility is that there are four separate realms of the blessed, of which either Firdaws or Eden is the uppermost. This is based on Surah 55,


title: Jannah

text: which talks about two Gardens: ("As for him who fears standing before his Lord there are two Gardens [Jannatan]") [S 55:46). All descriptions following


title: Jannah

text: this verse are of things in pairs, (i.e. in the Arabic dual form) -- two fountains flowing, fruit of every kind


title: Jannah

text: Still others have proposed that the seven levels suggested by the Qur'an are the seven heavens, above which is the Garden or final abode of felicity, while many see paradise as only one entity with many names. (According to one source -- a member of the fatwa team at Islamweb.net -- only God knows the exact number of the levels of Paradise, but reliable hadith say the number of levels of Jannah may be the same as the number of verses in the Quran, i.e. over 6000 verses.)


title: Jannah

text: the highest level of heaven ("al-firdaws") as being said to be so close that its inhabitants could hear the sound of God's throne above. This exclusive location is where the messengers, prophets, Imams, and martyrs ("shahids") dwell. Al-Suyuti and "Kitāb aḥwāl al-qiyāma" each gives names to the levels that don't always coincide (see table to right).


title: Jannah

text: Two verses of the Quran (Q.7:40, 39:73) mention "gates" or "doors" (using the plural form) as the entrance of paradise, but say nothing about their number, names or any other characteristics.


title: Jannah

text: As in the case of the levels of Jannah, later sources elaborate, giving names and functions but don't agree on all details (see table to right).


title: Jannah

text: In traditions, each level of the eight principal gates of Paradise is described as generally being divided into a hundred degrees guarded by angels (in some traditions Ridwan). The highest level is known as "" (sometimes called Eden) or Illiyin. Entrants will be greeted by angels with salutations of peace or As-Salamu Alaykum.


title: Jannah

text: Jannah is accessible vertically through its gates (Q.7:40), by ladders ("ma'arij") (Q.70:3), or sky-ropes ("asbab"). However, only select beings such as angels and prophets can enter. Iblis (Satan) and devils are kept at bay by angels who throw stars at them, whenever they try to climb back to heaven (Q.37:6-10). Notably and contrary to many Christian ideas on heaven, God (Allah) does not reside in paradise.


title: Jannah

text: A few hadith name four rivers in paradise, or coming from paradise, as: Saihan (Syr Darya), Jaihan (Amu Darya), Furat (Euphrates) and Nil (Nile). Salsabil is the name of a spring that is the source of the rivers of Rahma (mercy) and Al-Kawthar (abundance). Sidrat al-Muntaha is a Lote tree that marks the end of the seventh heaven, the boundary where no angel or human can pass. Muhammad is supposed to have taken a pomegranate from jannah, and shared it with Ali, as recorded by Nasir al-Din al-Tusi. However, some scholars, like Ghazali, reject that Muhammad took the fruit, argued he had only a vision instead.


title: Jannah

text: According to scholars Jane I. Smith, Yvonne Y. Haddad, while there are Muslims of a "philosophical or mystical"


title: Jannah

text: bent who interpret descriptions of heaven and hell "metaphorically", "the vast majority of believers", understand verses of the Quran on Jannah (and hellfire) "to be real and specific, anticipating them" with joy or terror, although this view "has generally not insisted that the realities of the next world will be identical with those of this world".


title: Jannah

text: Besides the material notion of the paradise, descriptions of it are also interpreted as allegories, whose meaning is the state of joy believers will experience in the afterlife. For some theologians, seeing God is not a question of sight, but of awareness of God's presence. Although early Sufis, such as Hallaj, took the descriptions of Paradise literal, later Sufi traditions usually stressed out the allegorical meaning.


title: Jannah

text: While some Quranic verses suggest hellfire is eternal and some that its punishment "will not necessarily be forever", verses on Jannah are less ambiguous. Eternality assured in verses about paradise such as Q.3:198, 4:57, and 57:12, (which say that the righteous will be "khālidūn fīhā" [eternally in it]), and Q.35:35, which describes the reward of "dār al-maqāma" [the abode of everlastingness]. Consequently, neither "theologians nor the traditionalists" have had any doubts about the eternal nature of paradise or the residence of the righteous in it.


title: Jannah

text: One of the characteristics of Jannah (like hellfire) is that events are not "frozen in one eternal moment", but form cycles of "endless repetition" and "unceasing self renewing clockwork", as described by classical scholars on the afterlife al-Suyūṭī and al-Majlisī. For example, when a fruit is plucked from a tree, a new fruit immediately appears to takes its place; when a hungry inhabitant sees a bird whose meat they would like to eat it falls already roasted into their hands, and after they are done eating the bird "regains its form shape and flies away"; not only do houri regain their virginity after being deflowered by one of the saved, they grow like fruit on trees or plants on the land and "whenever one of them is taken" by one of the saved in paradise one for his pleasure, "a new one springs forth in her place". (So too, in hellfire are the skin of the damned replaced each time they are burned off by the fire to be burned again, and drowning sinners driven back into the sea by giant snakes and scorpions every time they reach the safety of shore.)


title: Jannah

text: Muslim scholars differ on whether the Garden of Eden (), in which Adam and Eve (Adam and "Hawwa") dwelled before being expelled by God, is the same as the afterlife abode of the righteous believers, i.e. paradise. Most scholars in the early centuries of Islamic theology and the centuries onwards thought it was and that this indicated that paradise was located on earth. It was argued that when God commanded Adam to "go down" ("ihbit") from the garden, this did not indicate a vertical movement (such as "falling" from a heaven above to earth), but instead was used in the same sense as Moses telling Israelites to "go down to Egypt". However, over the centuries as paradise came to be thought of more and more as "a transcendent, otherworldy realm", the idea of it being located somewhere on earth fell out of favor. The Garden of Eden, on the other hand lacked many transcendent, otherworldy characteristics. Al-Balluti (887 – 966) reasoned that the Garden of Eden lacked the perfection and eternal character of a final paradise: Adam and Eve lost the primordial paradise, while the paradisiacal afterlife lasts forever; if Adam and Eve were in the otherworldly paradise, the devil ("Shaiṭān") could not have entered and deceive them, since there is no evil or idle talk in paradise; Adam slept in his garden, but there is no sleep in paradise.


title: Jannah

text: Many adherences of the Muʿtazila, also refused to identify Adam's abode with paradise, because they argued that paradise and hell would not be created until after Day of Judgement, an idea proposed by Dirar b. Amr. Most Muslim scholars, however, assert that paradise and hell have been created already and coexists with the contemporary world, taking evidence from the Quran, Muhammad's heavenly journey, and the life in the graves.


title: Jannah

text: Islamic exegesis does not regard Adam and Eve's expulsion from paradise as punishment for disobedience or a result from abused free will on their part, but as part of God's God's wisdom ("ḥikma") and plan for humanity to experience the full range of his attributes, his love, forgiveness, and power to his creation. By experiencing hardship, they better appreciate paradise and its delights. Khwaja Abdullah Ansari (1006–1088) describes Adam and Eve's expulsion as ultimately caused by God, since man has no choice but to comply to God's will. But this does not mean that complying is not a "sin" and that humans should not blame themselves for it. This is exemplified by Adam and Eve in the Quran (Q.7:23 “Our Lord! We have wronged ourselves. If You do not forgive us and have mercy on us, we will certainly be losers.”)


title: Jannah

text: Jannah shares the name "Garden of the Righteous" with the Jewish concept of paradise. In addition, paradise in Judaism is described as a garden, much like the Garden of Eden, where people live and walk and dance with God and his angels, wear garments of light, and eat the fruit of the tree of life. Like the feast of Jannah, Jewish eschatology describes the messiah holding a Seudat nissuin, called the Seudat Chiyat HaMatim, with the righteous of every nation at the end time.


title: Jannah

text: Jesus in the Gospels uses various images for heaven that are similarly found in Jannah: feast, mansion, throne, and paradise. In Jannah, humans stay as humans. However, the Book of Revelation describes that in heaven Christ “will transform our lowly bodies so that they will be like his glorious body” (Philippians 3:21). God (Allah) does not reside in paradise or heaven. However, in Christianity, the new heavens and earth will be a place where God dwells with humans.


title: Carl Perkins

text: Carl Lee Perkins (April 9, 1932 – January 19, 1998) was an American guitarist, singer and songwriter. A rockabilly great and pioneer of rock and roll, he began his recording career at the Sun Studio, in Memphis, beginning in 1954. Among his best-known songs are "Blue Suede Shoes", "Honey Don't", "Matchbox" and "Everybody's Trying to Be My Baby".


title: Carl Perkins

text: According to fellow musician Charlie Daniels, "Carl Perkins' songs personified the rockabilly era, and Carl Perkins' sound personifies the rockabilly sound more so than anybody involved in it, because he never changed." Perkins's songs were recorded by artists (and friends) as influential as Elvis Presley, the Beatles, Jimi Hendrix, Johnny Cash and Eric Clapton, which further established his prominent place in the history of popular music. Paul McCartney said "if there were no Carl Perkins, there would be no Beatles."


title: Carl Perkins

text: Nicknamed the "King of Rockabilly", Perkins was inducted into the Rock and Roll Hall of Fame, the Rockabilly Hall of Fame, the Memphis Music Hall of Fame, and the Nashville Songwriters Hall of Fame. He also received a Grammy Hall of Fame Award.


title: Carl Perkins

text: Carl Lee Perkins was born on April 9, 1932 in Tiptonville, Tennessee, the son of poor sharecroppers Louise and Buck Perkins (misspelled on his birth certificate as "Perkings"). Beginning at the age of six, he worked long hours in the cotton fields with his family, whether school was in session or not. Siblings included brothers Jay and Clayton. The boys grew up hearing southern gospel music sung by white friends in church and by black field workers and sharecroppers in the cotton fields. On Saturday nights Perkins would listen to the "Grand Ole Opry", broadcast from Nashville on his father's radio.


title: Carl Perkins

text: Roy Acuff's broadcasts from the Opry inspired Perkins to ask his parents for a guitar. Since they could not afford to buy one, his father made one from a cigar box and a broomstick. Eventually, a neighbor sold his father a worn-out Gene Autry guitar. Perkins could not afford new strings, and when they broke, he had to retie them. The knots cut his fingers when he would slide to another note, so he began bending the notes, stumbling onto a type of blue note.


title: Carl Perkins

text: Perkins taught himself parts of Acuff's "Great Speckled Bird" and "The Wabash Cannonball", having heard them played on the "Opry". He also has cited Bill Monroe's fast playing and vocals as an early influence. Perkins also learned from John Westbrook, an African-American field worker in his sixties who played blues and gospel music on an old acoustic guitar. Westbrook advised Perkins to "Get down close to it. You can feel it travel down the strangs, come through your head and down to your soul where you live. You can feel it. Let it vib-a-rate."


title: Carl Perkins

text: In January 1947, the Perkins family moved from Lake County, Tennessee, to Madison County, 70 miles from Memphis, the largest city in West Tennessee and a center of a great variety of music played by both black and white artists. At age fourteen Perkins wrote a country song called "Let Me Take You to the Movie, Magg". Sam Phillips was persuaded by the quality of that song to sign Perkins to his Sun Records label.


title: Carl Perkins

text: Perkins and his brother Jay had their first paying job (in tips) as entertainers during late 1946 at the Cotton Boll tavern on Highway 45, twelve miles south of Jackson, Tennessee, starting on Wednesday nights. Perkins was 14 years old. One of the songs they played was an up-tempo country blues shuffle version of Bill Monroe's "Blue Moon of Kentucky". Free drinks were one of the perks of playing in a tavern, and Perkins drank four beers that first night. Within a month Carl and Jay began playing Friday and Saturday nights at the Sand Ditch tavern, near the western boundary of Jackson. Both places were the scene of occasional fights, and both of the Perkins brothers gained a reputation as fighters.


title: Carl Perkins

text: During the next couple of years, as they became better known, the Perkins brothers began playing other taverns around Bemis and Jackson, including El Rancho, the Roadside Inn, and the Hilltop. Carl persuaded his brother Clayton to join them and play the upright bass, to complete the sound of the band.


title: Carl Perkins

text: Perkins began performing regularly on WTJS in Jackson during the late 1940s as a sometime member of the Tennessee Ramblers. He appeared on the radio program"Hayloft Frolic", on which he performed two songs. Sometimes one was "Talking Blues", as done by Robert Lunn on the "Grand Ole Opry". Perkins and his brothers began appearing on "The Early Morning Farm and Home Hour". Positive listener response resulted in a 15-minute segment sponsored by Mother's Best Flour. By the end of the 1940s, the Perkins Brothers were the best-known band in the Jackson area. Perkins had day jobs during most of these early years, including picking cotton, working at various factories and plants, and as a pan greaser for the Colonial Baking Company. His brothers had similar pick-up jobs.


title: Carl Perkins

text: In January 1953, Perkins married Valda Crider, whom he had known for a number of years. When his job at the bakery was reduced to part-time, Valda, who had her own job, encouraged Perkins to begin working the taverns full-time. He began playing six nights a week. Later the same year he added W.S. "Fluke" Holland to the band as a drummer. Holland had no previous experience as a musician but had a good sense of rhythm.


title: Carl Perkins

text: Malcolm Yelvington, who remembered the Perkins Brothers when they played in Covington, Tennessee, in 1953, noted that Carl had an unusual blues-like style all his own. By 1955 Perkins had made tapes of his material with a borrowed tape recorder, and he sent them to companies such as Columbia and RCA. But he used addresses such as "Columbia Records, New York City" and seemed dismayed at the lack of response. "I had sent tapes to RCA and Columbia and had never heard a thing from 'em."


title: Carl Perkins

text: In July 1954, Perkins and his wife heard a new release of "Blue Moon of Kentucky" by Elvis Presley, Scotty Moore and Bill Black on the radio. As the song faded out, Perkins said, "There's a man in Memphis who understands what we're doing. I need to go see him." According to another telling of the story, it was Valda who said that he should go to Memphis. Later, Presley told Perkins he had traveled to Jackson and had seen Perkins and his group playing at El Rancho.


title: Carl Perkins

text: Years later, the musician Gene Vincent told an interviewer that, rather than Elvis's version of "Blue Moon of Kentucky" being a "new sound", "a lot of people were doing it before that, especially Carl Perkins."