HOME  TheInfoList.com 
Number A NUMBER is a mathematical object used to count , measure , and label . The original examples are the natural numbers 1 , 2 , 3 , 4 and so forth. A notational symbol that represents a number is called a numeral . In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers ), for ordering (as with serial numbers ), and for codes (as with ISBNs ). In common usage, number may refer to a symbol, a word , or a mathematical abstraction . In mathematics , the notion of number has been extended over the centuries to include 0 , negative numbers , rational numbers such as 1/2 and −2/3, real numbers such as √2 and π , and complex numbers , which extend the real numbers by adding a square root of −1 . Calculations with numbers are done with arithmetical operations , the most familiar being addition , subtraction , multiplication , division , and exponentiation . Their study or usage is called arithmetic [...More...]  "Number" on: Wikipedia Yahoo 

Calculation A CALCULATION is a deliberate process that transforms one or more inputs into one or more results, with variable change. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm , to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people. For example, multiplying 7 by 6 is a simple algorithmic calculation. Estimating the fair price for financial instruments using the Black–Scholes Black–Scholes model is a complex algorithmic calculation. Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but produces ranges of possibilities rather than exact answers. To calculate means to ascertain by computing [...More...]  "Calculation" on: Wikipedia Yahoo 

Hypercomplex Number In mathematics , a HYPERCOMPLEX NUMBER is a traditional term for an element of a unital algebra over the field of real numbers . The study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory. CONTENTS * 1 History * 2 Definition * 3 Twodimensional real algebras * 4 Higherdimensional examples (more than one nonreal axis) * 4.1 Clifford algebras * 4.2 Cayley–Dickson construction * 4.3 Tensor products * 4.4 Further examples * 5 See also * 6 References * 7 Further reading * 8 External links HISTORYIn the nineteenth century number systems called quaternions , tessarines , coquaternions , biquaternions , and octonions became established concepts in mathematical literature, added to the real and complex numbers . The concept of a hypercomplex number covered them all, and called for a discipline to explain and classify them [...More...]  "Hypercomplex Number" on: Wikipedia Yahoo 

Mathematical Abstraction ABSTRACTION in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena . Two of the most highly abstract areas of modern mathematics are category theory and model theory . CONTENTS * 1 Description * 2 See also * 3 References * 4 Further reading DESCRIPTIONMany areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures . For example, geometry has its origins in the calculation of distances and areas in the real world; algebra started with methods of solving problems in arithmetic [...More...]  "Mathematical Abstraction" on: Wikipedia Yahoo 

One Half semi/demi (from Latin Latin ) Binary 0.1 or 0.011111111111... Ternary 0.11111111111... Decimal Decimal 0.5 or 0.499999999999... Duodecimal Duodecimal 0.6 or 0.5BBBBBBBBBBBB... Hexadecimal Hexadecimal 0.8 or 0.7FFFFFFFFFFF... Continued fraction or Singleprecision floating point 3F000000 (hex) = 00111111000000000000000000000000 (binary) ONE HALF is the irreducible fraction resulting from dividing one by two (1⁄2), or the fraction resulting from dividing any number by its double. Multiplication by one half is equivalent to division by two , or halving; conversely, division by one half is equivalent to multiplication by two, or "doubling". One half One half appears often in mathematical equations, recipes, measurements, etc. Half can also be said to be one part of something divided into two equal parts [...More...]  "One Half" on: Wikipedia Yahoo 

Mathematical Object A MATHEMATICAL OBJECT is an abstract object arising in mathematics . The concept is studied in philosophy of mathematics . In mathematical practice, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs . Commonly encountered mathematical objects include numbers , permutations , partitions , matrices , sets , functions , and relations . Geometry Geometry as a branch of mathematics has such objects as hexagons , points , lines , triangles , circles , spheres , polyhedra , topological spaces and manifolds . Another branch—algebra —has groups , rings , fields , grouptheoretic lattices , and ordertheoretic lattices . Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory , proofs and theorems are also mathematical objects [...More...]  "Mathematical Object" on: Wikipedia Yahoo 

Counting COUNTING is the action of finding the number of elements of a finite set of objects. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term enumeration refers to uniquely identifying the elements of a finite (combinatorial) set or infinite set by assigning a number to each element. Counting Counting using tally marks at Hanakapiai Beach Counting Counting sometimes involves numbers other than one; for example, when counting money, counting out change, "counting by twos" (2, 4, 6, 8, 10, 12, ...), or "counting by fives" (5, 10, 15, 20, 25, ...) [...More...]  "Counting" on: Wikipedia Yahoo 

Imaginary Unit The IMAGINARY UNIT or UNIT IMAGINARY NUMBER (I) is a solution to the quadratic equation x2 + 1 = 0. Since there is no real number with this property, it extends the real numbers, and under the assumption that the familiar properties of addition and multiplication (namely closure , associativity , commutativity and distributivity ) continue to hold for this extension, the complex numbers are generated by including it. Imaginary numbers are an important mathematical concept, which extends the real number system ℝ to the complex number system ℂ, which in turn provides at least one root for every nonconstant polynomial P(x). (See Algebraic closure and Fundamental theorem of algebra .) The term "imaginary " is used because there is no real number having a negative square . There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero , which has one double square root [...More...]  "Imaginary Unit" on: Wikipedia Yahoo 

Multiplication MULTIPLICATION (often denoted by the cross symbol " × ", by a point "⋅ ", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic ; with the others being addition , subtraction and division . The multiplication of whole numbers may be thought as a repeated addition ; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the value of the other one, the multiplier. Normally, the multiplier is written first and multiplicand second, though this can vary, especially in languages with different grammatical structures, such as Japanese , Japanese elementary schools teach writing the multiplicand first, and answers that reverse that order are marked as incorrect [...More...]  "Multiplication" on: Wikipedia Yahoo 

Subset In mathematics , especially in set theory , a set A is a SUBSET of a set B, or equivalently B is a SUPERSET of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called INCLUSION or sometimes CONTAINMENT. The subset relation defines a partial order on sets. The algebra of subsets forms a Boolean algebra in which the subset relation is called inclusion . CONTENTS * 1 Definitions * 2 Property * 3 ⊂ and ⊃ symbols * 4 Examples * 5 Other properties of inclusion * 6 See also * 7 References * 8 External links DEFINITIONSIf A and B are sets and every element of A is also an element of B, then: * A is a SUBSET of (or is included in) B, denoted by A B {displaystyle Asubseteq B} , or equivalently * B is a SUPERSET of (or includes) A, denoted by B A [...More...]  "Subset" on: Wikipedia Yahoo 

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 