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Division (mathematics) DIVISION is one of the four basic operations of arithmetic , the others being addition , subtraction , and multiplication . The division of two natural numbers is the process of calculating the number of times one number is contained within one another. :7 For example, in the picture on the right, the 20 apples are divided into groups of five apples, and there exist four groups, meaning that five can be contained within 20 four times, or 20 ÷ 5 = 4. Division can also be thought of as the process of evaluating a fraction , and fractional notation (a/b and a⁄b) is commonly used to represent division. Division can be viewed either as quotition or as partition . In quotition, 20 ÷ 5 means the number of 5s that must be added to get 20. In partition, 20 ÷ 5 means the size of each of 5 parts into which a set of size 20 is divided. Division is the inverse of multiplication; if a × b = c, then a = c ÷ b, as long as b is not zero [...More...]  "Division (mathematics)" on: Wikipedia Yahoo 

MATLAB MATLAB MATLAB (MATrix LABoratory) is a multiparadigm numerical computing environment and fourthgeneration programming language . A proprietary programming language developed by MathWorks , MATLAB MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms , creation of user interfaces , and interfacing with programs written in other languages, including C , C++ C++ , C# , Java , Fortran and Python . Although MATLAB MATLAB is intended primarily for numerical computing, an optional toolbox uses the MuPAD symbolic engine , allowing access to symbolic computing abilities. An additional package, Simulink , adds graphical multidomain simulation and modelbased design for dynamic and embedded systems . As of 2017, MATLAB MATLAB has over 2 million users across industry and academia [...More...]  "MATLAB" on: Wikipedia Yahoo 

GNU Octave GNU GNU OCTAVE is software featuring a highlevel programming language , primarily intended for numerical computations . Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab Matlab . It may also be used as a batchoriented language. Since it is part of the GNU Project GNU Project , it is free software under the terms of the GNU General Public License GNU General Public License . Octave is one of the major free alternatives to Matlab, others being FreeMat FreeMat and Scilab . Scilab, however, puts less emphasis on (bidirectional) syntactic compatibility with Matlab Matlab than Octave does [...More...]  "GNU Octave" on: Wikipedia Yahoo 

Complex Numbers A COMPLEX NUMBER is a number that can be expressed in the form a + bi, where a and b are real numbers , and i is the imaginary unit (which satisfies the equation i2 = −1). In this expression, a is called the real part of the complex number, and b is called the imaginary part. If z = a + b i {displaystyle z=a+bi} , then we write Re ( z ) = a , {displaystyle operatorname {Re} (z)=a,} and Im ( z ) = b . {displaystyle operatorname {Im} (z)=b.} Complex numbers extend the concept of the onedimensional number line to the twodimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (a, b) in the complex plane. A complex number whose real part is zero is said to be purely imaginary , whereas a complex number whose imaginary part is zero is a real number [...More...]  "Complex Numbers" on: Wikipedia Yahoo 

Polynomial In mathematics , a POLYNOMIAL is an expression consisting of variables (or indeterminates ) and coefficients , that involves only the operations of addition , subtraction , multiplication , and nonnegative integer exponents of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example in three variables is x3 + 2xyz2 − yz + 1. Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations , which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define POLYNOMIAL FUNCTIONS, which appear in settings ranging from basic chemistry and physics to economics and social science ; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties , central concepts in algebra and algebraic geometry [...More...]  "Polynomial" on: Wikipedia Yahoo 

Number Theory NUMBER THEORY or, in older usage, ARITHMETIC is a branch of pure mathematics devoted primarily to the study of the integers . It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers ) or defined as generalizations of the integers (e.g., algebraic integers ). Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry ). Questions in number theory are often best understood through the study of analytical objects (e.g., the Riemann zeta function Riemann zeta function ) that encode properties of the integers, primes or other numbertheoretic objects in some fashion (analytic number theory ) [...More...]  "Number Theory" on: Wikipedia Yahoo 

Mathematical Software MATHEMATICAL SOFTWARE is software used to model , analyze or calculate numeric, symbolic or geometric data. It is a type of application software which is used for solving mathematical problems or mathematical study. There are various views to what is the mathematics , so there is various views of the category of mathematical software which used for them, over from narrow to wide sense. A type of mathematical software (math library ) also used by built in the part of an another scientific software . A most primary them (for example, to calculate elementary function by floating point arithmetic ) may be in the category of mathematical software. They are often usually built in the general purpose systems as middleware . So to speak, mathematical software is not only an application software but also basis of the another scientific software [...More...]  "Mathematical Software" on: Wikipedia Yahoo 

Rational Number In mathematics , a RATIONAL NUMBER is any number that can be expressed as the quotient or fraction p/q of two integers , a numerator p and a nonzero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "THE RATIONALS", the FIELD OF RATIONALS or the FIELD OF RATIONAL NUMBERS is usually denoted by a boldface Q (or blackboard bold Q {displaystyle mathbb {Q} } , Unicode ℚ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient ". The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10 , but also for any other integer base (e.g. binary , hexadecimal ). A real number that is not rational is called irrational [...More...]  "Rational Number" on: Wikipedia Yahoo 

Programming Language A PROGRAMMING LANGUAGE is a formal language that specifies a set of instructions that can be used to produce various kinds of output . Programming languages generally consist of instructions for a computer . Programming languages can be used to create programs that implement specific algorithms . The earliest known programmable machine preceded the invention of the digital computer and is the automatic flute player described in the 9th century by the brothers Musa in Baghdad , "during the Islamic Golden Age ". From the early 1800s, "programs" were used to direct the behavior of machines such as Jacquard looms and player pianos . Thousands of different programming languages have been created, mainly in the computer field, and many more still are being created every year [...More...]  "Programming Language" on: Wikipedia Yahoo 

ASCII ASCII ASCII (/ˈæski/ ( listen ) ASSkee ), :6 abbreviated from AMERICAN STANDARD CODE FOR INFORMATION INTERCHANGE, is a character encoding standard (the Internet Assigned Numbers Authority (IANA) prefers the name US ASCII ASCII ). ASCII ASCII codes represent text in computers, telecommunications equipment , and other devices. Most modern characterencoding schemes are based on ASCII, although they support many additional characters. ASCII ASCII chart from a 1972 printer manual (b1 is the least significant bit) [...More...]  "ASCII" on: Wikipedia Yahoo 

Closure (mathematics) A set has CLOSURE under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is CLOSED under the operation. For example, the positive integers are closed under addition, but not under subtraction: 1 2 {displaystyle 12} is not a positive integer even though both 1 and 2 are positive integers. Another example is the set containing only zero, which is closed under addition, subtraction and multiplication (because 0 + 0 = 0 {displaystyle 0+0=0} , 0 0 = 0 {displaystyle 00=0} , and 0 0 = 0 {displaystyle 0times {0}=0} ). Similarly, a set is said to be CLOSED UNDER A COLLECTION OF OPERATIONS if it is closed under each of the operations individually [...More...]  "Closure (mathematics)" on: Wikipedia Yahoo 

Fractional Part The FRACTIONAL PART of a non‐negative real number x {displaystyle x} is the excess beyond that number's integer part . If the latter is defined as the largest integer not greater than x, called floor of x or x {displaystyle lfloor xrfloor } , its fractional part can be written as: frac ( x ) = x x , x > 0 {displaystyle operatorname {frac} (x)=xlfloor xrfloor ,;x>0} . For a positive number written in a conventional positional numeral system (such as binary or decimal ), its fractional part hence equals the digits appearing after the radix point . CONTENTS * 1 For negative numbers * 2 Unique decomposition into integer and fractional parts * 3 Relation to continued fractions * 4 See also * 5 References FOR NEGATIVE NUMBERSHowever, in case of negative numbers, there are various conflicting ways to extend the fractional part function to them: It is either defined in the same way as for positive numbers, i.e [...More...]  "Fractional Part" on: Wikipedia Yahoo 

Limit (mathematics) 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 in general) and are used to define continuity , derivatives , and integrals . 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 . In formulas, a limit is usually written as lim n c f ( n ) = L {displaystyle lim _{nto c}f(n)=L} and is read as "the limit of f of n as n approaches c equals L". Here "lim" indicates limit, and the fact that function f(n) approaches the limit L as n approaches c is represented by the right arrow (→), as in f ( n ) L [...More...]  "Limit (mathematics)" on: Wikipedia Yahoo 

Gottfried Wilhelm Leibniz GOTTFRIED WILHELM (VON) LEIBNIZ (/ˈlaɪbnɪts/ ; German: or ; French : Godefroi Guillaume Leibnitz; 1 July 1646 – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy , having developed differential and integral calculus independently of Isaac Newton Isaac Newton . Leibniz\'s notation has been widely used ever since it was published. It was only in the 20th century that his Law Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation (by means of nonstandard analysis ) [...More...]  "Gottfried Wilhelm Leibniz" on: Wikipedia Yahoo 

Colon (punctuation) ؋ ₳ ฿ ₿ ₵ ¢ ₡ ₢ $ ₫ ₯ ֏ ₠ € ƒ ₣ ₲ ₴ ₭ ₺ ₾ ₼ ℳ ₥ ₦ ₧ ₱ ₰ £ 元 圆 圓 ﷼ ៛ ₽ ₹ ₨ ₪ ৳ ₸ ₮ ₩ ¥ 円 UNCOMMON TYPOGRAPHY asterism ⁂ hedera ❧ index, fist ☞ interrobang ‽ irony punctuation ⸮ lozenge ◊ tie ⁀ RELATED* * Diacritics * Logic symbols * Whitespace characters IN OTHER SCRIPTS * Chinese * Hebrew * Japanese * Korean * Category Category * Portal Portal * Book Book * v * t * e The COLON ( : ) is a punctuation mark consisting of two equally sized dots centered on the same vertical line. A colon precedes an explanation or an enumeration , or list [...More...]  "Colon (punctuation)" on: Wikipedia Yahoo 

Nth Root In mathematics , an NTH ROOT of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x r n = x , {displaystyle r^{n}=x,} where n is the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root . Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. For example: * 3 is a square root of 9, since 32 = 9. * −3 is also a square root of 9, since (−3)2 = 9.A real number or complex number has n complex roots of degree n. While the roots of 0 are not distinct (all equaling 0), the n nth roots of any other real or complex number are all distinct. If n is even and x is real and positive, one of its nth roots is positive, one is negative, and the rest are either nonexistent (in the case when n = 2) or complex but not real; if n is even and x is real and negative, none of the nth roots is real [...More...]  "Nth Root" on: Wikipedia Yahoo 