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Additive Notation
A sign-value notation represents numbers using a sequence of numerals which each represent a distinct quantity, regardless of their position in the sequence. Sign-value notations are typically additive, subtractive, or multiplicative depending on their conventions for grouping signs together to collectively represent numbers. Although the absolute value of each sign is independent of its position, the value of the sequence as a whole may depend on the order of the signs, as with numeral systems which combine additive and subtractive notation, such as Roman numerals. There is no need for zero in sign-value notation. Additive notation Additive notation represents numbers by a series of numerals that added together equal the value of the number represented, much as tally marks are added together to represent a larger number. To represent multiples of the sign value, the same sign is simply repeated. In Roman numerals, for example, means ten and means fifty, so means eighty ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called ''numerals''; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any Integer, non-negative integer using a combination of ten fundamental numeric symbols, called numerical digit, digits. 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, a ''numeral'' is not clearly dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulla (seal)
A bulla (Medieval Latin for "a round seal", from Classical Latin ''bulla'', "bubble, blob"; plural bullae) is an inscribed clay, soft metal (lead or tin), bitumen, or wax token used in commercial and legal documentation as a form of authentication and for tamper-proofing whatever is attached to it (or, in the historical form, contained in it). In their oldest attested form, as used in the ancient Near East and the Middle East of the 8th millennium BC onwards, bullae were hollow clay balls that contained other smaller tokens that identified the quantity and types of goods being recorded. In this form, bullae represent one of the earliest forms of specialization in the ancient world, and likely required skill to create. From about the 4th millennium BC onwards, as communications on papyrus and parchment became widespread, bullae evolved into simpler tokens that were attached to the documents with cord, and impressed with a unique sign (i.e., a seal) to provide the same kind of author ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Location Arithmetic
Location arithmetic (Latin ''arithmetica localis'') is the additive (non-positional) binary numeral systems, which John Napier explored as a computation technique in his treatise ''Rabdology'' (1617), both symbolically and on a chessboard-like grid. Napier's terminology, derived from using the positions of counters on the board to represent numbers, is potentially misleading because the numbering system is, in facts, non- positional in current vocabulary. During Napier's time, most of the computations were made on boards with tally-marks or jetons. So, unlike how it may be seen by the modern reader, his goal was not to use moves of counters on a board to multiply, divide and find square roots, but rather to find a way to compute symbolically with pen and paper. However, when reproduced on the board, this new technique did not require mental trial-and-error computations nor complex carry memorization (unlike base 10 computations). He was so pleased by his discovery that he said i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Place-value Notation
Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the values may be modified when combined). In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian numeral system, base 60, was the first positional system to be developed, and its influence is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylonian Cuneiform Numerals
Babylonian cuneiform numerals, also used in Assyria and Chaldea, were written in cuneiform, using a wedge-tipped reed stylus to print a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. The Babylonians, who were famous for their astronomical observations, as well as their calculations (aided by their invention of the abacus), used a sexagesimal (base-60) positional numeral system inherited from either the Sumerian or the Akkadian civilizations. Neither of the predecessors was a positional system (having a convention for which 'end' of the numeral represented the units). Origin This system first appeared around 2000 BC; its structure reflects the decimal lexical numerals of Semitic languages rather than Sumerian lexical numbers. However, the use of a special Sumerian sign for 60 (beside two Semitic signs for the same number) attests to a relation with the Sumerian system. Symbols The Babylonian system is credited as b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Akkadians
The Akkadian Empire () was the first known empire, succeeding the long-lived city-states of Sumer. Centered on the city of Akkad ( or ) and its surrounding region, the empire united Akkadian and Sumerian speakers under one rule and exercised significant influence across Mesopotamia, the Levant, and Anatolia, sending military expeditions as far south as Dilmun and Magan (modern United Arab Emirates, Saudi Arabia, Bahrain, Qatar and Oman) in the Arabian Peninsula.Mish, Frederick C., Editor in Chief. "Akkad" '' Webster's Ninth New Collegiate Dictionary''. ninth ed. Springfield, MA: Merriam-Webster 1985. ). The Akkadian Empire reached its political peak between the 24th and 22nd centuries BC, following the conquests by its founder Sargon of Akkad. Under Sargon and his successors, the Akkadian language was briefly imposed on neighboring conquered states such as Elam and Gutium. Akkad is sometimes regarded as the first empire in history, though the meaning of this term is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sumerians
Sumer () is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during the Chalcolithic and early Bronze Ages between the sixth and fifth millennium BC. Like nearby Elam, it is one of the cradles of civilization, along with Egypt, the Indus Valley, the Erligang culture of the Yellow River valley, Caral-Supe, and Mesoamerica. Living along the valleys of the Tigris and Euphrates rivers, Sumerian farmers grew an abundance of grain and other crops, a surplus of which enabled them to form urban settlements. The world's earliest known texts come from the Sumerian cities of Uruk and Jemdet Nasr, and date to between , following a period of proto-writing . Name The term "Sumer" () comes from the Akkadian name for the "Sumerians", the ancient non- Semitic-speaking inhabitants of southern Mesopotamia.Piotr Michalowski, "Sumerian," ''The Cambridge Encyclopedia of the World's Ancient Languages." Ed. Roger D. Woo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuneiform
Cuneiform is a Logogram, logo-Syllabary, syllabic writing system that was used to write several languages of the Ancient Near East. The script was in active use from the early Bronze Age until the beginning of the Common Era. Cuneiform scripts are marked by and named for the characteristic wedge-shaped impressions (Latin: ) which form their Grapheme, signs. Cuneiform is the History of writing#Inventions of writing, earliest known writing system and was originally developed to write the Sumerian language of southern Mesopotamia (modern Iraq). Over the course of its history, cuneiform was adapted to write a number of languages in addition to Sumerian. Akkadian language, Akkadian texts are attested from the 24th century BC onward and make up the bulk of the cuneiform record. Akkadian cuneiform was itself adapted to write the Hittite language in the early second millennium BC. The other languages with significant cuneiform Text corpus, corpora are Eblaite language, Eblaite, Elamit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sexagesimal
Sexagesimal, also known as base 60, is a numeral system with 60 (number), sixty as its radix, base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinate system, geographic coordinates. The number 60, a superior highly composite number, has twelve divisors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6. ''In this article, all sexagesimal digits are represented as decimal numbers, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accounting Token
Number systems have progressed from the use of fingers and tally marks, perhaps more than 40,000 years ago, to the use of sets of glyphs able to represent any conceivable number efficiently. The earliest known unambiguous notations for numbers emerged in Mesopotamia about 5000 or 6000 years ago. Prehistory Counting initially involves the fingers, given that digit-tallying is common in number systems that are emerging today, as is the use of the hands to express the numbers five and ten. In addition, the majority of the world's number systems are organized by tens, fives, and twenties, suggesting the use of the hands and feet in counting, and cross-linguistically, terms for these amounts are etymologically based on the hands and feet. Finally, there are neurological connections between the parts of the brain that appreciate quantity and the part that "knows" the fingers (finger gnosia), and these suggest that humans are neurologically predisposed to use their hands in counti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. Terminology and notation In 1806, Jean-Robert Argand introduced the term ''module'', meaning ''unit of measure'' in French, specifically for the ''complex'' absolute value,Oxford English Dictionary, Draft Revision, Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
