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List Of Types Of Numbers Numbers can be classified according to how they are represented or according to the properties that they have. CONTENTS * 1 Main types * 2 Number Number representations * 3 Signed numbers * 4 Types of integer * 5 Algebraic numbers * 6 Nonstandard numbers * 7 Computability and definability * 8 References MAIN TYPESNatural numbers ( N {displaystyle mathbb {N} } ): The counting numbers {1, 2, 3, …} are commonly called natural numbers; however, other definitions include 0, so that the nonnegative integers {0, 1, 2, 3, …} are also called natural numbers. Whole numbers ( W {displaystyle mathbb {W} } ): The numbers {0, 1, 2, 3, …}. Integers ( Z {displaystyle mathbb {Z} } ): Positive and negative counting numbers, as well as zero: {…, 3, 2, 1, 0, 1, 2, 3…}. Rational numbers ( Q {displaystyle mathbb {Q} } ): Numbers that can be expressed as a ratio of an integer to a nonzero integer [...More...]  "List Of Types Of Numbers" on: Wikipedia Yahoo 

Significant Figures The SIGNIFICANT FIGURES of a number are digits that carry meaning contributing to its measurement resolution . This includes all digits except: * All leading zeros ; * Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures ); and * Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports. Significance arithmetic are approximate rules for roughly maintaining significance throughout a computation. The more sophisticated scientific rules are known as propagation of uncertainty [...More...]  "Significant Figures" on: Wikipedia Yahoo 

Accuracy And Precision PRECISION is a description of random errors , a measure of statistical variability . ACCURACY has two definitions: * More commonly, it is a description of systematic errors , a measure of statistical bias ; as these cause a difference between a result and a "true" value, ISO calls this trueness. * Alternatively, ISO defines accuracy as describing a combination of both types of observational error above (random and systematic), so high accuracy requires both high precision and high trueness.In simplest terms, given a set of data points from a series of measurements, the set can be said to be precise if the values are close to the average value of the quantity being measured, while the set can be said to be accurate if the values are close to the true value of the quantity being measured. The two concepts are independent of each other, so a particular set of data can be said to be either accurate, or precise, or both, or neither [...More...]  "Accuracy And Precision" on: Wikipedia Yahoo 

Knuth's Uparrow Notation In mathematics , KNUTH\'S UPARROW NOTATION is a method of notation for very large integers , introduced by Donald Knuth Donald Knuth in 1976. It is closely related to the Ackermann function and especially to the hyperoperation sequence. The idea is based on the fact that multiplication can be viewed as iterated addition and exponentiation as iterated multiplication . Continuing in this manner leads to tetration (iterated exponentiation) and to the remainder of the hyperoperation sequence, which is commonly denoted using Knuth arrow notation [...More...]  "Knuth's Uparrow Notation" on: Wikipedia Yahoo 

Conway Chained Arrow Notation CONWAY CHAINED ARROW NOTATION, created by mathematician John Horton Conway , is a means of expressing certain extremely large numbers . It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2 → 3 → 4 → 5 → 6. As with most combinatorial notations, the definition is recursive . In this case the notation eventually resolves to being the leftmost number raised to some (usually enormous) integer power [...More...]  "Conway Chained Arrow Notation" on: Wikipedia Yahoo 

Graham's Number GRAHAM\'S NUMBER is an enormous number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory . It is named after mathematician Ronald Graham , who used the number as a simplified explanation of the upper bounds of the problem he was working on in conversations with popular science writer Martin Gardner . Gardner later described the number in Scientific American Scientific American in 1977, introducing it to the general public. At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof. The number was published in the 1980 Guinness Book of World Records Guinness Book of World Records , adding to its popular interest [...More...]  "Graham's Number" on: Wikipedia Yahoo 

Powers Of 10 In mathematics , a POWER OF 10 is any of the integer powers of the number ten ; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few nonnegative powers of ten are: 1 , 10 , 100 , 1000 , 10000 , 100000 , 1000000 , 10000000 . ... (sequence A011557 in the OEIS ) CONTENTS * 1 Positive powers * 2 Negative powers * 3 Googol * 4 Scientific notation * 5 See also * 6 Further reading * 7 References POSITIVE POWERSIn decimal notation the nth power of ten is written as '1' followed by n zeroes. It can also be written as 10n or as 1En in E notation . See order of magnitude and orders of magnitude (numbers) for named powers of ten. There are two conventions for naming positive powers of ten, called the long and short scales [...More...]  "Powers Of 10" on: Wikipedia Yahoo 

Scientific Notation SCIENTIFIC NOTATION (also referred to as SCIENTIFIC FORM, STANDARD FORM or STANDARD INDEX FORM) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form . It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations . On scientific calculators it is known as "SCI" display mode. DECIMAL NOTATION SCIENTIFIC NOTATION 2 7000200000000000000♠2×100 300 7002300000000000000♠3×102 4,321.768 7003432176800000000♠4.321768×103 −53,000 2995470000000000000♠−5.3×104 6,720,000,000 7009672000000000000♠6.72×109 0.2 6999200000000000000♠2×10−1 0.000 000 007 51 6991751000000000000♠7.51×10−9In scientific notation all numbers are written in the form m × 10n (m times ten raised to the power of n), where the exponent n is an integer , and the coefficient m is any real number , called the significand or mantissa [...More...]  "Scientific Notation" on: Wikipedia Yahoo 

Ancient Rome In historiography , ANCIENT ROME refers to the Roman civilization from the founding of the city of Rome Rome in the 8th century BC to the collapse of the Western Roman Empire Roman Empire in the 5th century AD, encompassing the Roman Kingdom , Roman Republic and Roman Empire Roman Empire until the fall of the western empire. The term is sometimes used to just refer to the kingdom and republic periods, excluding the subsequent empire . The civilization began as an Italic settlement in the Italian peninsula , dating from the 8th century BC, that grew into the city of Rome Rome and which subsequently gave its name to the empire over which it ruled and to the widespread civilisation the empire developed [...More...]  "Ancient Rome" on: Wikipedia Yahoo 

Ratio In mathematics, a RATIO is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as quantities of persons, objects, lengths, weights, etc. A ratio may be either a whole number or a fraction . A ratio may be written as "a to b" or a:b, or it may be expressed as a quotient of "a and b". When the two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number . A quotient of two quantities that are measured with different units is called a rate [...More...]  "Ratio" on: Wikipedia Yahoo 

Improper Fraction A FRACTION (from Latin Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, onehalf, eightfifths, threequarters. A common, vulgar, or simple fraction (examples: 1 2 displaystyle tfrac 1 2 and 17/3) consists of an integer numerator displayed above a line (or before a slash), and a nonzero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals. The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole [...More...]  "Improper Fraction" on: Wikipedia Yahoo 

Mixed Number A FRACTION (from Latin Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, onehalf, eightfifths, threequarters. A common, vulgar, or simple fraction (examples: 1 2 {displaystyle {tfrac {1}{2}}} and 17/3) consists of an integer numerator displayed above a line (or before a slash), and a nonzero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals. The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole [...More...]  "Mixed Number" on: Wikipedia Yahoo 

Positive Real Numbers In mathematics , the set of POSITIVE REAL NUMBERS, R > 0 = { x R x > 0 } {displaystyle mathbb {R} _{>0}=left{xin mathbb {R} mid x>0right}} , is the subset of those real numbers that are greater than zero. In a complex plane , R > 0 {displaystyle mathbb {R} _{>0}} is identified with the POSITIVE REAL AXIS and is usually drawn as a horizontal ray . This ray is used as reference in the polar form of a complex number . The real positive axis corresponds to complex numbers z = z e i {displaystyle z=zmathrm {e} ^{mathrm {i} varphi }} with argument = 0 {displaystyle varphi =0} . CONTENTS * 1 Notation * 2 Properties * 3 Logarithmic measure * 4 See also * 5 References NOTATIONAlternative to R > 0 {displaystyle mathbb {R} _{>0}} , the nonstandard symbols R + {displaystyle mathbb {R} _{+}} and R + {displaystyle mathbb {R} ^{+}} are often used [...More...]  "Positive Real Numbers" on: Wikipedia Yahoo 

Inequality (mathematics) In mathematics , an INEQUALITY is a relation that holds between two values when they are different (see also: equality ). * The notation a ≠ b means that a is NOT EQUAL TO b. It does not say that one is greater than the other, or even that they can be compared in size. If the values in question are elements of an ordered set , such as the integers or the real numbers , they can be compared in size. * The notation a < b means that a is LESS THAN b. * The notation a > b means that a is GREATER THAN b. In either case, a is not equal to b. These relations are known as STRICT INEQUALITIES. The notation a < b may also be read as "a is strictly less than b" [...More...]  "Inequality (mathematics)" on: Wikipedia Yahoo 

Regular Polygon Regular polygons Edges and vertices n Schläfli symbol {n} Coxeter–Dynkin diagram Symmetry group Symmetry group Dn , order 2n [...More...]  "Regular Polygon" on: Wikipedia Yahoo 

Polygonal Number In mathematics , a POLYGONAL NUMBER is a number represented as dots or pebbles arranged in the shape of a regular polygon . The dots are thought of as alphas (units). These are one type of 2dimensional figurate numbers . CONTENTS* 1 Definition and examples * 1.1 Triangular numbers * 1.2 Square numbers * 1.3 Pentagonal numbers * 1.4 Hexagonal numbers * 2 Formula * 2.1 Every hexagonal number is also a triangular number * 3 Table of values * 4 Combinations * 5 See also * 6 Notes * 7 References * 8 External links DEFINITION AND EXAMPLESThe number 10 for example, can be arranged as a triangle (see triangular number ): But 10 cannot be arranged as a square . The number 9, on the other hand, can be (see square number ): Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number ): By convention, 1 is the first polygonal number for any number of sides [...More...]  "Polygonal Number" on: Wikipedia Yahoo 