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Wikipedia About Absolute Value

for: value (ethics)

In mathematics, the absolute value (or modulus) of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3.

The absolute value of a number a is denoted by |a|.

Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.

Terminology and notation

Jean-Robert Argand introduced the term "module" 'unit of measure' in French in 1806 specifically for the complex absolute valueOxford English Dictionary, Draft Revision, June 2008 and it was borrowed into English in 1866 as the Latin equivalent "modulus".

The term "absolute value" has been used in this sense since at least 1806 in French and 1857 in English.

The notation | a | was introduced by Karl Weierstrass in 1841.

Other names for absolute value include "the numerical value" and "the magnitude", that is, ignoring the sign.

Real numbers

For any real number a the absolute value or modulus of a is denoted by | a | (a vertical bar on each side of the quantity) and is defined as

|a| = \begin{cases} a, & \mbox{if } a \ge 0 \\ -a, & \mbox{if } a < 0. \end{cases}

As can be seen from the above definition, the absolute value of a is always either positive or zero, but never negative. The same notation is used with sets to denote cardinality; the meaning depends on context.

From an analytic geometry point of view, the absolute value of a real number is that number's distance from zero along the real number line, and more generally the absolute value of the difference of two real numbers is the distance between them. Indeed the notion of an abstract distance function in mathematics can be seen to be a generalization of the absolute value of the difference (see "Distance" below).

Since the square-root function is normally defined as the positive square root, |a| = \sqrt{a^2}, which is sometimes even used as a definition of absolute value.

The absolute value has the following four fundamental properties:

Other important properties of the absolute value include:

b \ne 0) \,

|Preservation of division (equivalent to multiplicativeness) |- ||a-b| \ge ||a| - |b|| |(equivalent to subadditivity) |}

If b > 0, two other useful inequalities are:

|a| \le b \iff -b \le a \le b

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News about Absolute Value

Samena Capital Starts Japan-Focused Stock Hedge Fund After Rout

BloombergMay 12 (Bloomberg) -- Samena Capital , a London-based investment firm, will start a Japan-focused hedge fund seeking bargains in the nation’s stock market after the global credit crisis cut share prices.http://www.bloomberg.com/apps/news?pid=20601084&sid=a5MY.56s...

Credit Markets On the Mend, But Not Yet Healed

Fox NewsAnalysts say credit markets are healing but not yet fixed, which may help explain both the recent runup in stock prices and also the widespread fear that the runup is premature.http://feeds.foxbusiness.com/~r/foxbusiness/latest/~3/kjIrDL...

Phoenix Leads Munis; $900 Million in Build America Deals Set

BloombergMay 11 (Bloomberg) -- States and local governments led by Phoenix plan to borrow about $5.5 billion by selling long-term debt this week, including almost $900 million in taxable issues under the two-month-old Build America Bonds program.http://www.bloomberg.com/apps/news?pid=20601015&sid=ahqJ.OMl...

Phoenix Leads Munis; $750 Million in Build America Deals Set

BloombergMay 11 (Bloomberg) -- States and local governments led by Phoenix plan to borrow $5.5 billion with long-term debt this week, including about $750 million in taxable issues under the two-month-old Build America Bonds program.http://www.bloomberg.com/apps/news?pid=20601009&sid=a9erzuws...

How the Star 50 rankings were calculated

The Kansas City StarKansas City boasts its share of winners even amid difficult times, as this 19th edition of Star 50 reminds us.http://kansascity.com/business/story/1191433.html

News about Absolute Value

In the Great Global Macro Experiment, The Next Bubble to Burst is...

Safe HavenAren't hedge funds marketed as delivering superior " absolute " returns? Don't they preach diversification from the ... If the value is positive, then the portfolio is earning excess returns. In other words, a positive value for Jensen's ... http://www.safehaven.com/showarticle.cfm?id=11543&pv=1

Supplements Continue to Be a Priority for Consumers

Forbes ... on items that are not of absolute necessity when trying to balance higher costs in gasoline, groceries and other daily necessities," continued Ms. Blatman. "We were pleased to see that an overwhelming majority of supplement users recognize the value ... http://www.forbes.com/prnewswire/feeds/prnewswire/2008/10/06...

Unicredit's Profumo acknowledges errors

ForbesWe made some mistakes in evaluating the market scenario, that is absolute clear to us." Unicredit cut its earnings estimates ... It is among Europe's top five for assets, but the loss in share value puts it only among the top 10 for market ... http://www.forbes.com/feeds/ap/2008/10/06/ap5511762.html

BBC Blog Network

bbcOh my God, you're an absolute scumbag! I dont care if this doesnt get published, but please pass it on to Justin Or just edit ... Ridiculous, and completely wrong. It certainly wouldn't increase his market value like running a Flo-Jo like 9.5 would ... http://www.bbc.co.uk/blogs/profile?userid=4892983

Market turmoil: Are your investments safe?

Times of IndiaBut then over the next eight months and one week, markets have seen an absolute downside of 40% from its peak. That’s ... It is a very simple method whereby you invest a fixed sum of money every month and based on the value you end up buying a ... http://timesofindia.indiatimes.com/Business/Intl_Business/Ma...

Search results for Absolute Value

absolute value legal definition of absolute value. absolute value ...

The estimated or appraised worth of any object or property, calculated in money. The word value has many meanings and may be used in different senses.http://legal-dictionary.thefreedictionary.com/absolute+value

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Welcome to Sw Florida's Supreme Interior Home Cleaning, Lawn Care and Window Washing Company! When you hire someone to do a job, you want it done right.http://absolutevaluee.com

Absolute value - A complete course in algebra

Lesson 12 of a complete course in algebra ... 12. ABSOLUTE VALUE. The geometrical meaning. Absolute value equations. Absolute value inequalitieshttp://www.themathpage.com/alg/absolute-value.htm

absolute value definition of absolute value in the Free Online ...

absolute value, magnitude of a number or other mathematical expression disregarding its sign; thus, the absolute value is positive, whether the original expression is positive or ... http://encyclopedia2.thefreedictionary.com/absolute+value

Absolute Value Appraisal Network of New Jersey

Residential home appraisals for New Jersey ... REAL ESTATE PROPERTIES APPRAISED: Single family and multi-family (2-4) homeshttp://www.njappraise.com/

Wikipedia results for Absolute Value

Absolute value - Wikipedia, the free encyclopedia

In mathematics, the absolute value (or modulus) of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3.http://en.wikipedia.org/wiki/Absolute_value

Absolute value (algebra) - Wikipedia, the free encyclopedia

In mathematics, an absolute value is a function which measures the "size" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute ... http://en.wikipedia.org/wiki/Absolute_value_%28algebra%29

Absolute Value (album) - Wikipedia, the free encyclopedia

Absolute Value is the second full-length album by Boston rapper Akrobatik. It was released on February 19th, 2008 by Fat Beats Records. The album features guest appearances by hip ... http://en.wikipedia.org/wiki/Absolute_Value_(album)

Value (ethics) - Wikipedia, the free encyclopedia

In ethics, value is a property of objects, including physical objects as well as abstract objects (e.g. actions), representing their degree of importance.http://en.wikipedia.org/wiki/Absolute_value_(philosophy)

Absolute - Wikipedia, the free encyclopedia

Absolute may mean: Philosophy. Absolute (philosophy), a concept in philosophy; Moral absolutes, the belief that there are absolute standards against which moral questions can be ... http://en.wikipedia.org/wiki/Absolute
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Answers for Absolute Value

You have no idea.Absolute Value?You have no idea.Is your question "What values of x satisfy 'the absolute value of x equals 3' "? Yes, 3 and -3 are the answer.Maria SHow do I find if the Absolute value of a negative number is no solution or all numbers?Maria S|2y-9|>-5 => |2y-9|^2>(-5)^2 => 4y^2 -36y +81 > 25 => 4y^2 -36y +56 > 0 => y^2 -9y +14 > 0 solve => y^2 -9y +14 = 0 => y = 7 OR y = 2 since > 0 => y < 2 OR y > 7 QEDtuntuni11What does the absolute value mean and can it ever be a negative number?tuntuni11| -4 | = 4 | 0 | = 0 | 4 | = 4 Absolute value of a number x is the distance between x and 0 on the number line. Since distance is never negative, absolute value is never negative.mhmmWhat is the absolute value of the difference between the number of square meters in their areas?mhmmArea of square = 4x4 =16m2 Area of triangle = 1/2bcSinA = 1/2 x 16/3 x 16/3 sin60=64root3 all over 9 or 12.3168 m2 diff = 3.683 metres squaredmorgulis2003How do I determine the equation of an absolute value graph?morgulis2003Take only the x positive part of the graphic and find the equation as usual. y=mx+b m = (y2-y1)/(x2-x1) y1 = m*x1-b find b When this is found, you just have to ad absolute | y=mx+b | Hope ...
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