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In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case.
These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the real numbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently standard axiomatic definition is that real numbers form the unique complete totally ordered field (R,+,·,<), up to isomorphism, Whereas popular constructive definitions of real numbers include declaring them as equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, or certain infinite "decimal representations", together with precise interpretations for the arithmetic operations and the order relation. These definitions are equivalent in the realm of classical mathematics.
This page contains text from Wikipedia, the Free Encyclopedia -
http://en.wikipedia.org/wiki/Real_number
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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photo: AP / Ahn Young-joon
22 Dec 2014
SEOUL, South Korea — President Barack Obama is “recklessly” spreading rumors of a Pyongyang-orchestrated cyberattack of Sony Pictures, North Korea says, as it warns of strikes against the White House, Pentagon and “the whole U.S. mainland, that cesspool of terrorism.”. Such rhetoric is routine from North Korea’s massive propaganda machine during times of high tension with Washington ... The U.S ... ....
photo: AP / Jake Simkin
22 Dec 2014
December 22, 2014 -- Updated 0528 GMT (1328 HKT). (CNN) -- Juergen Todenhoefer's journey was a tough one. dangerous, but also eye-opening. The author traveled deep into ISIS territory -- the area they now call their "caliphate" -- visiting Raqqa and Deir Ezzor in Syria, as well as Mosul in Iraq. Mosul, Iraq's second largest city, was taken by ISIS in a Blitzkrieg-like sweep in June ... A new name for ISIS?. Senior ISIS leaders killed in U.S ... ....
photo: AP / Manu Fernandez
22 Dec 2014
In issuing the indictment, Judge Jose Castro went against a prosecutor's Dec ... He set bail for her at 2.7 million euros ($3.3 million) and 15 million euros for her husband ... Suspected abuse of company funds to cover the couple's expenses at their Barcelona home, salsa dancing classes and stays at luxury hotels is among evidence Castro has compiled about Aizoon, a real estate and consulting firm Cristina co-owned with her husband ... ....
photo: US Navy / Keith DeVinney
22 Dec 2014
A French former airline director has claimed that the US military may have shot down Malaysia Airlines flight MH370 and covered it up. Marc Dugain, who headed Proteus Airlines and is an established author, speculated that the Americans may have targeted the aircraft because they feared a September 11-style attack on a military base in the Indian Ocean ... “It’s an extremely powerful military base ... 13 theories on what happened to MH370 ... ....
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Yahoo Daily News
22 Dec 2014
Later, we learned the real number was closer to 100 million. And the criminal in that case, Albert Gonzalez, now serving a 20-year prison sentence, is said to have stolen 170 million account numbers in all ... Moreover, if 100 million consumers' credit card numbers were really stolen and used effectively by criminals, either you or your significant other would almost certainly be victims of fraud this year....
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The Times of India
20 Dec 2014
CHENNAI. Keeping the city streets free of garbage is not the only challenge the corporation faces ... While corporation officials say they receive more than a 100 complaints a month in this regard, residents claim the real number is higher ... It is a never ending problem.". Others said the real issue was the garbage strewn all round bins, spreading stench and posing health hazards ... ....
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Deutsche Welle
20 Dec 2014
Should establishment politicians talk to representatives of the PEGIDA movement? Yes, say conservative politicians in the eastern German state of Saxony ... Lutz Bachmann is PEGIDA's previously apolitical organizer ... Hashtags against PEGIDA ... "The real number is probably between 50,000 and 100,000." ... It is indeed a fact that municipalities currently face serious problems accommodating the increasing numbers of asylum seekers ... ....
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The Boston Globe
19 Dec 2014
Heather Boonstra joins HuffPost Live to discuss the current teen pregnancy statistics in the United States. ....
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Al Jazeera
19 Dec 2014
Reached for comment by Al Jazeera, Alessandro Langella, the head of the operational team of Naples' - a police force that deals with financial crimes - explained that "the real number of circulating fakes is probably larger than the official one, as it is impossible to determine the exact quantity in the economy". ....
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South China Morning Post
18 Dec 2014
Professor Li Liping, director of the Injury Prevention Research Centre at Shantou University's medical school, said the real number of road fatalities could be even higher because a death was only included in the road toll if it occurred within one week of the traffic accident ... Li attributed the high numbers to low standards of driving and the ......
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The Independent
18 Dec 2014
1 ... 2 ... I have written before about claims that the 2012 US presidential election was “the first Twitter election” ... Today, my campaign to force the Scottish Labour Party to publish the numbers voting in the party members and trade unionists sections of the leadership election college enters its next phase ... The party claims 12,000 members, which is a mere 200 per constituency, but it is widely assumed that the real numbers are lower ... ....
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Newsday
18 Dec 2014
Add comment Reprints + -. Head coach Jeff Fisher of the St. Louis Rams looks on against the Arizona Cardinals during their game at Edward Jones Dome on Dec. 11, 2014 in St Louis. Photo Credit. Getty Images / Dilip Vishwanat. advertisement . advertise on newsday. Tom Coughlin and Jeff Fisher have a lot in common ... One win separates them. But the real number that shows the vast difference between the two is 28 ... Coughlin? He's never called one ... ... ....
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Huffington Post
18 Dec 2014
Think about it. No matter how good your product is, you still need a stellar team to design it, build it, improve it, sell it and service it ... CEOs care about and are measured against these very real numbers, so it's no wonder they're taking aim and launching initiatives to boost employee engagement. In fact, CEOs say "increasing employee engagement" is their number one strategic priority, according to a 2013 Conference Board survey ... > ....
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The Business Review
17 Dec 2014
When Snapchat CEO Evan Spiegel famously spurned Facebook's offer to buy the company, reports put the number at $3 billion ... “if you knew the real number you would book us all a suite at Bellvue [sic]" ... I think while he liked the team and idea of Facebook, he's been disappointed with the number he's getting from Zuck, so he's now characterizing his ......
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The Independent
17 Dec 2014
The Sony hack keeps on giving. this time Snapchat, the app which allows users to share photographs that are automatically deleted, has emerged as the unsuspected victom of the group known as the Guardians of Peace ... Turns out Facebook offered more ... "If you knew the real number you would book us all a suite at Bellvue [all sic]." ... Another email from Lasky read ... .)" ... World News in Pictures. ....
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The Guardian
17 Dec 2014
The social news site has acceded to a DMCA takedown request from Sony and removed a hub for sharing the company’s hacked files ... Photograph. -/AFP/Getty Images ... On Monday, the film company sent a legal letter to a number of news sites around the world, including the New York Times and Re/Code, demanding that they “destroy the stolen information” ... “If you knew the real number you would book us all a suite at Bellvue,” was Lynton’s reply ... ....
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The State
17 Dec 2014
Oconee County is hoping to land its first Michelin jobs, but the deal for a distribution center isn’t done yet, county officials said ... Greenville, Spartanburg, Anderson, Laurens and Lexington ... County officials said those figures are conservative and the real numbers could wind up being $250 million for capital expenditure and 180 for jobs, with most of the positions coming from a third-party staffing service....
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