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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.[1] A notational symbol that represents a number is called a numeral.[2] 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,[3] negative numbers,[4] rational numbers such as 1/2 and −2/3, real numbers[5] such as √2 and π, and complex numbers,[6] which extend the real numbers by adding a square root of −1.[4] 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
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Calculation
A calculation is a deliberate process that transforms one or more inputs into one or more results, with variable change
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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.[1][2][3] Two of the most highly abstract areas of modern mathematics are category theory and model theory.Contents1 Description 2 See also 3 References 4 Further readingDescription[edit] Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures
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One Half
semi-/demi- (from Latin)Binary 0.1 or 0.011111111111...Ternary 0.11111111111...Decimal 0.5 or 0.499999999999...Duodecimal 0.6 or 0.5BBBBBBBBBBBB...Hexadecimal 0.8 or 0.7FFFFFFFFFFF...Continued fraction [0; 1, 1] or [0; 2]Single-precision floating point3F000000 (hex) = 00111111000000000000000000000000 (binary) One half
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
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Counting
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
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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, group-theoretic lattices, and order-theoretic lattices. Categories are simultaneously homes to mathematical objects and mathematical objects in their own right
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Multiplication
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
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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
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1,000,000
1,000,000
1,000,000
(one million), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001
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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 another one.[1]:7 For example, in the picture on the right, the 20 apples are divided into four groups of five apples, meaning that twenty divided by five gives four, or four is the result of division of twenty by five. This is denoted as 20 / 5 = 4, 20 ÷ 5 = 4, or 20/5 = 4.[2] 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
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Subtraction
Subtraction
Subtraction
is an arithmetic operation that represents the operation of removing objects from a collection. It is signified by the minus sign (−). For example, in the adjacent picture, there are 5 − 2 apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, 5 − 2 = 3. Subtraction
Subtraction
represents removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices. Subtraction
Subtraction
follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It is not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Subtraction
Subtraction
of 0 does not change a number
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