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For example, the sequence (1; 1.4; 1.41; 1.414; 1.4142; 1.41421; ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root of 2).
For example, the integers are made by adding 0 and negative numbers. The rational numbers add fractions, and the real numbers add infinite decimals. Complex numbers add the square root of −1. This chain of extensions canonically embeds the natural numbers in the other number systems. [6] [7]
For example, a condition can be expressed as x IS GREATER THAN y or more concisely as x GREATER y or x > y. More complex conditions can be abbreviated by removing repeated conditions and variables. For example, a > b AND a > c OR a = d can be shortened to a > b AND c OR = d. To support this syntax, COBOL has over 300 keywords.
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. [1] [2] Modern science is typically divided into two or three major branches: [3] the natural sciences (e.g., physics, chemistry, and biology), which study the physical world; and the social sciences (e.g., economics, psychology, and sociology), which ...
A National Front march from the 1970s, the movement from which the BNP emerged by 1982. The British National Party (BNP) [note 1] was founded by the extreme-right political activist John Tyndall.
This was known colloquially as the "Stockholm Solution". In 2007, the United States Federal Reserve noted, "In the early 1970s, Sweden had one of the highest income levels in Europe; today, its lead has all but disappeared...So, even well-managed financial crises don't really have a happy ending".
The name "Zimbabwe" stems from a Shona term for Great Zimbabwe, a medieval city in the country's south-east.Two different theories address the origin of the word. Many sources hold that "Zimbabwe" derives from dzimba-dza-mabwe, translated from the Karanga dialect of Shona as "houses of stones" (dzimba = plural of imba, "house"; mabwe = plural of ibwe, "stone").
The economy of Japan is a highly developed mixed economy, often referred to as an East Asian model. [24] It is the fourth-largest economy in the world by nominal GDP behind the United States, China, and Germany, and the fifth-largest by purchasing power parity (PPP), below India and Russia but ahead of Germany. [25]