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Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as 5 (an integer), 3/4 (a rational number that is not an integer), 8.6 (a rational number expressed in decimal representation), and π (3.1415926535..., an irrational number). As a subset of the real numbers, the integers, such as 5, express discrete rather than continuous quantities. Complex numbers include real numbers as a special case. Real numbers can be divided into rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two. A real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue indefinitely. The real numbers are sometimes thought of as points on an infinitely long line called the number line or real line. History

Vulgar fractions had been used by the Egyptians around 1000 BC; the Vedic "Sulba Sutras" ("The rules of chords") in, ca. 600 BC, include what may be the first 'use' of irrational numbers. The concept of irrationality was implicitly accepted by early Indian mathematicians since Manava (c. 750–690 BC), who were aware that the square roots of certain numbers such as 2 and 61 could not be exactly determined. Around 500 BC, the Greek mathematicians led by Pythagoras realized the need for irrational numbers, in particular the irrationality of the square root of 2. The Middle Ages saw the acceptance of zero, negative, integral and fractional numbers, first by Indian and Chinese mathematicians, and then by Arabic mathematicians, who were also the first to treat irrational numbers as algebraic objects, which was made possible by the development of algebra. Arabic mathematicians merged the concepts of "number" and "magnitude" into a more general idea of real numbers. The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c. 850–930) was the first to accept irrational numbers as solutions...

...Basic Algebraic Properties of RealNumbers
The numbers used to measure real-world quantities such as length, area, volume, speed, electrical charges, probability of rain, room temperature, gross national products, growth rates, and so forth, are called realnumbers. They include such number as , , , , , , , and .
The basic algebraic properties of the real...

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Real World Radical Formulas
Janeth Mendiola
MAT222: Intermediate Algebra
Instructor Lalla Thompson
March 21, 2014
Real World Radical Formulas
Radical formulas are used in the real world in the fields such as finance, medicine, engineering, and physics to name a few. In the finance department they use it to find the interest, depreciation and compound interest. In medicine it can be used to calculate the...

... 4. Repeat the previous three steps, except this time use the two terms that have just been written as the dividend.
5. Repeat step 4. This time, there is nothing to "pull down".
The polynomial above the bar is the quotient q(x), and the number left over (−123) is the remainder r(x).
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Applications
Factoring polynomials
Sometimes one or more roots of a polynomial are known, perhaps having been found using...

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This file MAT 222 Week 3 Assignment Real World Radical Formulas contains solutions to the following tasks: 1.103. Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 (www.sailing.com). For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function. a).Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet....

...integers in two different ways. 1729 = 93 + 103 = 13 + 123. (This was the subject of a very famous mathematical anecdote involving Srinivasa Ramanujan and G.H. Hardy, circa 1917. See A Mathematician's Apology by Hardy.
Rank, Prime number, Found by, Found date, Number of digits
1st, 257,885,161 − 1, GIMPS, 2013 January 25, 17,425,170 2nd, 243,112,609 − 1, GIMPS, 2008 August 23, 12,978,189
3rd, 242,643,801 − 1, GIMPS, 2009 April 12, 12,837,064...

...Polynomial
The graph of a polynomial function of degree 3
In mathematics, polynomials are the simplest class of mathematical expressions (apart from the numbers and expressions representing numbers). A polynomial is an expression constructed from variables (also called indeterminates) and constants (usually numbers, but not always), using only the operations of addition, subtraction, multiplication, and non-negative integer exponents (which are...

...In mathematics, a realnumber is a value that represents a quantity along a continuous line. The realnumbers 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...

...universal precautions. Suppose the spread of a direct contact disease in a stadium is modeled by the exponential equation P(t) = 10,000/(1 + e3-t) where P(t) is the total number of people infected after t hours. (Use the estimate for e (2.718) or the graphing calculator for e in your calculations.)
1. Estimate the initial number of people infected with the disease. Show how you found your answer.
Answer: A total of 474 people would be initially infected....