"of smaller units or small numbers of larger units for a measurement. These units were generally defined as a convenient multiple of a smaller unit or a convenient division of a larger unit. Thus, in pre-revolutionary France, the inch was divided into 12 lines and each line was subdivided into 12 points. Similarly, astronomers introduced the light-year to describe large distances. The metric system on the other hand uses prefixes to denote multipliers of the one basic unit. For example, the prefix ""kilo"" is used to denote a multiplier of 1000; thus one kilometre is 1000 metres, one kilogram is"
"true. The decimal SI prefixes ""kilo"", ""mega"", ""giga"", ""tera"", etc., are powers of 10 = 1000. The binary prefixes ""kibi"", ""mebi"", ""gibi"", ""tebi"", etc. respectively refer to the corresponding power of 2 = 1024. In casual usage, when 1024 is a close enough approximation of 1000, the two corresponding prefixes are equivalent. Note: this page mixes between two kinds of entropies: These two definitions are not entirely equivalent, see Entropy in thermodynamics and information theory. For comparison, the Avogadro constant is entities per mole, based upon the number of atoms in 12 grams of carbon-12 isotope. In 2012, some hard"
"Metric signature The signature of a metric tensor ""g"" (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, zero, and negative eigenvalues of the real symmetric matrix of the metric tensor with respect to a basis. In physics, the ""v"" represents for the time or virtual dimension, and the ""p"" for the space and physical dimension. Alternatively, it can be defined as the dimensions of a maximal positive and null subspace. By Sylvester's law of inertia these numbers do not depend on"
"representations; , etc. Zero has 768 possible representations (1536 if you include both signed zeros). Decimal64 floating point is a relatively new decimal floating-point format, formally introduced in the 2008 version of IEEE 754 as well as with . IEEE 754 allows two alternative representation methods for decimal64 values. The standard does not specify how to signify which representation is used, for instance in a situation where decimal64 values are communicated between systems: Both alternatives provide exactly the same range of representable numbers: 16 digits of significand and 3×2 = 768 possible decimal exponent values. (All the possible decimal exponent"
"Zetta- Zetta is a decimal unit prefix in the metric system denoting a factor of 10 or . The prefix was added as an SI prefix to the International System of Units (SI) in 1991 and has the symbol Z. Zetta is evocative of the Latin numeral , meaning ""seven"". Therefore it was used to denote the seventh power of 1000. A prefix of the same value, ""hepta"", was informally introduced a few years before the promulgation of zetta. It was formed from the Greek (), also meaning ""seven"". ""Hepta"" never received official sanction and is obsolete. Zeta (), although"
"Zero has 192 possible representations (384 when both signed zeros are included). Decimal32 floating point is a relatively new decimal floating-point format, formally introduced in the 2008 version of IEEE 754 as well as with . IEEE 754 allows two alternative representation methods for decimal32 values. The standard does not specify how to signify which representation is used, for instance in a situation where decimal32 values are communicated between systems. In one representation method, based on binary integer decimal (BID), the significand is represented as binary coded positive integer. The other, alternative, representation method is based on densely packed decimal"
"source of errors in programs, if software developers do not take into account that while the two zero representations behave as equal under numeric comparisons, they yield different results in some operations. The widely used two's complement encoding does not allow a negative zero. In a 1+7-bit sign-and-magnitude representation for integers, negative zero is represented by the bit string . In an 8-bit one's complement representation, negative zero is represented by the bit string . In all three encodings, positive zero is represented by . In IEEE 754 binary floating point numbers, zero values are represented by the biased exponent"
"measurement are spelled out, for example, codice_1 formats as ""3 THz"". Some of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI. The decimal prefix ""myria-"" (sometimes also written as ""myrio-"") (ten thousand) as well as the binary prefixes ""double-"" and ""demi-"", denoting a factor of 2 and (one half), respectively, were parts of the original metric system adopted by France in 1795. These were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960. Other metric prefixes used historically include hebdo- (10) and"
"on Units, considers the chances of official adoption to be remote. The prefix ""geop"" and term ""geopbyte"" has been used in the tech industry to refer to 10 bytes following ""brontobyte"". The ascending prefixes ""tera"" (), ""peta"" (), ""exa"" (), ""zetta"" (), and ""yotta"" () are based on the Greek-derived numeric prefixes ""tetra"" (4), ""penta"" (5), ""hexa"" (6), ""hepta"" (7), and ""octa"" or ""octo"" (8). In addition, the final letters of the alphabet, ""z"" and ""y"", appear in the largest SI prefixes, ""zetta"" and ""yotta"". Similarly, the descending prefixes ""zepto"" () and ""yocto"" () are derived from either Greek ""hepta"""
"Mega- Mega is a unit prefix in metric systems of units denoting a factor of one million (10 or ). It has the unit symbol M. It was confirmed for use in the International System of Units (SI) in 1960. ""Mega"" comes from . When units occur in exponentiation, such as in square and cubic forms, any multiples-prefix is considered part of the unit, and thus included in the exponentiation. In some fields of computing, ""mega"" may sometimes denote 1,048,576 (2) of information units, for example, a megabyte, a megaword, but denotes (10) units of other quantities, for example, transfer"
"Myria- Myria- (symbol my) is a now obsolete decimal metric prefix denoting a factor of 10 (ten thousand). It originates from the Greek μύριοι (""mýrioi"") (myriad). The prefix was part of the original metric system adopted by France in 1795, but was not adopted when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960. In 1685 John Wallis proposed the usage of myrio. Also, in 19th century English it was sometimes spelled myrio, in line with a puristic opinion by Thomas Young. The ""myriametre"" (10 km) is occasionally encountered in 19th-century train tariffs, or in some"
"Theta Theta (, ; uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; ""thē̂ta"" ; Modern: ""thī́ta"" ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals it has the value 9. In Ancient Greek, θ represented the aspirated voiceless dental plosive , but in Modern Greek it represents the voiceless dental fricative . In its archaic form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or point in circle"
"micri- (10). Double prefixes have been used in the past, such as ""micromillimetres"" or ""millimicrons"" (now nanometres), ""micromicrofarads"" (now picofarads), ""kilomegatons"" (now gigatons), ""hectokilometres"" (now 100 kilometres) and the derived adjective ""hectokilometric"" (typically used for qualifying the fuel consumption measures). These were disallowed with the introduction of the SI. Other obsolete double prefixes included ""decimilli-"" (10), which was contracted to ""dimi-"" and standardized in France up to 1961. In 2010, UC Davis student Austin Sendek started a petition to designate ""hella"" as the SI prefix for one octillion (Short scale; Long scale: Quadrilliard; 10). The petition gathered over 60,000 supporters"
"three multiples would be viable for use within a metric time system; they are: However, the next multiples are: Such lengths of time are relatively impractical for measuring human activities. For decimal multiples of the metric time unit to be practical, standard units and prefixes would need to be developed or revived for the 4th and 5th exponents so that it becomes viable for measuring human life. Historically, the metric system included a ""myria-"" prefix to represent 10 (and a counterpart ""dimi-"" prefix for 10), but SI (introduced in 1960) omitted the prefixes and prohibited using multiple prefixes such as"
"in France in 1795, but they were not retained when the SI prefixes were agreed internationally by the 11th CGPM conference in 1960. The prefix """"myrio-"""" was an alternative spelling variant for """"myria-"""", as proposed by Thomas Young. A binary prefix indicates multiplication by a power of two. The tenth power of 2 (2) has the value , which is close to . This has prompted the use of the metric prefixes ""kilo"", ""mega"", and ""giga"" to also denote the powers of 1024 which is common in information technology with the unit of digital information, the byte. Units of information"
"for tensors, it is common to use the letter ""R"" to represent three different things: These three are then distinguished from each other by their number of indices: the Riemann tensor has four indices, the Ricci tensor has two indices, and the Ricci scalar has zero indices. Those not using an index notation usually reserve ""R"" for the full Riemann curvature tensor. Alternatively, in a coordinate-free notation one may use ""Riem"" for the Riemann tensor, ""Ric"" for the Ricci tensor and ""R"" for the curvature scalar. The Yamabe problem was solved by Trudinger, Aubin, and Schoen. Namely, every Riemannian metric"
"rates: = . The prefix ""mebi-"" has been suggested as a prefix for 2 to avoid ambiguity. Mega- Mega is a unit prefix in metric systems of units denoting a factor of one million (10 or ). It has the unit symbol M. It was confirmed for use in the International System of Units (SI) in 1960. ""Mega"" comes from . When units occur in exponentiation, such as in square and cubic forms, any multiples-prefix is considered part of the unit, and thus included in the exponentiation. In some fields of computing, ""mega"" may sometimes denote 1,048,576 (2) of information"
"(兆, 京, 垓, 秭, 穰) and smaller Chinese numerals (微, 纖, 沙, 塵, 渺) were defined as translations for the SI prefixes as ""mega"", ""giga"", ""tera"", ""peta"", ""exa"", ""micro"", ""nano"", ""pico"", ""femto"", ""atto"", resulting in the creation of yet more values for each numeral. The Republic of China (Taiwan) defined 百萬 as the translation for ""mega"". This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent ""megahertz"". Today, the governments of both China and Taiwan use phonetic transliterations for the SI prefixes. However, the governments have each"
"in at most 6 iterations, except for a small set of initial numbers which converge instead to 0. The set of numbers that converge to zero depends on whether leading zeros are discarded (the usual formulation) or are retained (as in Kaprekar's original formulation). In the usual formulation, there are 60 three-digit numbers that converge to zero, for example 211. However, in Kaprekar's original formulation the leading zeros are retained, and only repdigits such as 111 or 222 map to zero. Below is a flowchart. Leading zeros are retained, however the only difference when leading zeros are discarded is that"
"Trailing zero In mathematics, trailing zeros are a sequence of 0 in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. Trailing zeros to the right of a decimal point, as in 12.3400, do not affect the value of a number and may be omitted if all that is of interest is its numerical value. This is true even if the zeros recur infinitely. For example, in pharmacy, trailing zeros are omitted from dose values to prevent misreading. However, trailing zeros may be useful for indicating the number of significant"
"over any ring. The zero matrix represents the linear transformation sending all vectors to the zero vector. In mathematics, the zero tensor is a tensor, of any order, all of whose components are zero. The zero tensor of order 1 is sometimes known as the zero vector. Taking a tensor product of any tensor with any zero tensor results in another zero tensor. Adding the zero tensor is equivalent to the identity operation. Zero element In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures. These alternate meanings may or may not"
"indicate text style. Theta Theta (, ; uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; ""thē̂ta"" ; Modern: ""thī́ta"" ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals it has the value 9. In Ancient Greek, θ represented the aspirated voiceless dental plosive , but in Modern Greek it represents the voiceless dental fricative . In its archaic form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or"
"acceptable. Myria- Myria- (symbol my) is a now obsolete decimal metric prefix denoting a factor of 10 (ten thousand). It originates from the Greek μύριοι (""mýrioi"") (myriad). The prefix was part of the original metric system adopted by France in 1795, but was not adopted when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960. In 1685 John Wallis proposed the usage of myrio. Also, in 19th century English it was sometimes spelled myrio, in line with a puristic opinion by Thomas Young. The ""myriametre"" (10 km) is occasionally encountered in 19th-century train tariffs, or in"
"a tetrad (set of four vectors) is introduced. The first two vectors, formula_6 and formula_7 are just a pair of standard (real) null vectors such that formula_8. For example, we can think in terms of spherical coordinates, and take formula_9 to be the outgoing null vector, and formula_10 to be the ingoing null vector. A complex null vector is then constructed by combining a pair of real, orthogonal unit space-like vectors. In the case of spherical coordinates, the standard choice is The complex conjugate of this vector then forms the fourth element of the tetrad. Two sets of signature and"
"metric tensor given by a single number ""s"" defined as , where ""v"" and ""p"" are as above, which is equivalent to the above definition when the dimension ""n"" = ""v"" + ""p"" is given or implicit. For example, ""s"" = 1 − 3 = −2 for and its mirroring ""s' "" = −""s"" = +2 for . The signature of a metric tensor is defined as the signature of the corresponding quadratic form. It is the number of positive and zero eigenvalues of any matrix (i.e. in any basis for the underlying vector space) representing the form, counted with"
"there can be formula_1 different fragments of four consecutive nucleotides; these fragments are called tetramers. TETRA works by tabulating the frequencies of each tetramer for a given sequence. From these frequencies z-scores are then calculated, which indicate how over- or under-represented the tetramer is in contraposition with what would be expected by looking to individual nucleotide compositions. The z-scores for each tetramer are assembled in a vector, and the vectors corresponding to different sequences are compared pair-wise, to yield a measure of how similar different sequences from the sample are. It is expected that the most similar sequences belong to"
"zero matrix) is 1. Then the above formula has ""s"" = 0 and formula_7 = 1, giving ""M"" and –""M"" as two square roots of ""M"". In general, the formula above will provide four distinct square roots ""R"", one for each choice of signs for ""s"" and ""t"". If the determinant ""δ"" is zero but the trace ""τ"" is nonzero, the formula will give only two distinct solutions. It also gives only two distinct solutions if ""δ"" is nonzero and ""τ"" = 4""δ"" (the case of duplicate eigenvalues), in which case one of the choices for ""s"" will make the"
"the 6th letter of the modern and classical Greek alphabet, denotes a value of seven (7) when used as a numeral. Examples: Zetta- Zetta is a decimal unit prefix in the metric system denoting a factor of 10 or . The prefix was added as an SI prefix to the International System of Units (SI) in 1991 and has the symbol Z. Zetta is evocative of the Latin numeral , meaning ""seven"". Therefore it was used to denote the seventh power of 1000. A prefix of the same value, ""hepta"", was informally introduced a few years before the promulgation of"
"real number formula_14. That formula_7 is non-degenerate means there are no non-zero formula_16 such that formula_17 for all formula_18. Given a metric tensor ""g"" on an ""n""-dimensional real manifold, the quadratic form associated with the metric tensor applied to each vector of any orthogonal basis produces ""n"" real values. By Sylvester's law of inertia, the number of each positive, negative and zero values produced in this manner are invariants of the metric tensor, independent of the choice of orthogonal basis. The signature of the metric tensor gives these numbers, shown in the same order. A non-degenerate metric tensor has and"
"three digits in balanced ternary. In this article, T (which resembles a ligature of the minus sign and 1) represents −1, while 0 and 1 represent themselves. Other conventions include using '−' and '+' to represent −1 and 1 respectively, or using Greek letter theta (Θ), which resembles a minus sign in a circle, to represent −1. In publications about the Setun computer, −1 is represented as overturned 1: """". Balanced ternary makes an early appearance in Michael Stifel's book ""Arithmetica Integra"" (1544). It also occurs in the works of Johannes Kepler and Léon Lalanne. Related signed-digit schemes in other"
"The number of trailing zeros in the decimal representation of ""n""!, the factorial of a non-negative integer ""n"", is simply the multiplicity of the prime factor 5 in ""n""<nowiki>!</nowiki>. This can be determined with this special case of de Polignac's formula: where ""k"" must be chosen such that more precisely and formula_5 denotes the floor function applied to ""a"". For ""n"" = 0, 1, 2, ... this is For example, 5 > 32, and therefore 32! = 263130836933693530167218012160000000 ends in zeros. If ""n"" < 5, the inequality is satisfied by ""k"" = 0; in that case the sum is empty,"
"by the pioneers of differential geometry. While some relativists consider the notation to be somewhat old-fashioned, many readily switch between this and the alternative notation: The metric tensor is commonly written as a 4 by 4 matrix. This matrix is symmetric and thus has 10 independent components. One of the central features of GR is the idea of invariance of physical laws. This invariance can be described in many ways, for example, in terms of local Lorentz covariance, the general principle of relativity, or diffeomorphism covariance. A more explicit description can be given using tensors. The crucial feature of tensors"
"Omega Omega (capital: Ω, lowercase: ω; Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the 24th and last letter of the Greek alphabet. In the Greek numeric system/Isopsephy (Gematria), it has a value of 800. The word literally means ""great O"" (""ō mega"", mega meaning ""great""), as opposed to omicron, which means ""little O"" (""o mikron"", micron meaning ""little""). In phonetic terms, the Ancient Greek Ω is a long open-mid ""o"" , comparable to the vowel of British English ""raw"". In Modern Greek, Ω represents the , the same sound as omicron. The letter omega is transcribed ""ō"" or"